P Godard

G Adda

Martine Adda-Decker

J Benjumea

Laurent Besacier
email: laurent.besacier@univ-grenoble-alpes.fr

J Cooper-Leavitt, G-N Kouarata

L Lamel

H Maynard

M Müller

Conference chair Nicoletta Calzolari

Khalid Choukri

Christopher Cieri

Thierry Declerck

Sara Goggi

Koiti Hasida

Hitoshi Isahara

Bente Maegaard

Joseph Mariani

Hã©lã¨ne Mazo

Asuncion Moreno

Jan Odijk

Stelios Pi

J Cooper-Leavitt

G-N Kouarata

M M Üller

A Rialland

S St Üker

F Yvon

M Zanon-Boito

A Very Low Resource Language Speech Corpus for Computational Language Documentation Experiments

Keywords: language documentation, field linguistics, spoken term discovery, word segmentation, zero resource technologies, unwritten languages

published or not. The documents may come

Introduction

Many languages will face extinction in the coming decades. Half of the 7,000 languages spoken worldwide are expected to disappear by the end of this century (Austin and Sallabank, 2011), and there are too few field linguists to document all of these endangered languages. Innovative speech data collection methodologies [START_REF] Bird | Aikuma: A mobile app for collaborative language documentation[END_REF]Blachon et al., 2016) as well as computational assistance [START_REF] Adda | Breaking the unwritten language barrier: The Bulb project[END_REF][START_REF] Stüker | Innovative technologies for under-resourced language documentation: The Bulb project[END_REF] were recently proposed to help them in their documentation and description work. As more and more researches are related to computational language documentation [START_REF] Duong | An attentional model for speech translation without transcription[END_REF]Franke et al., 2016a;[START_REF] Godard | Preliminary Experiments on Unsupervised Word Discovery in Mboshi[END_REF][START_REF] Anastasopoulos | A case study on using speech-to-translation alignments for language documentation[END_REF], there is a need of realistic corpora to fuel reproducible and replicable language studies at the phonetic, lexical and syntactic levels. To our knowledge, very few corpora are available for computational analysis of endangered languages. 1 Our work follows this objective and presents a speech dataset collected following a real language documentation scenario. It is multilingual (Mboshi speech aligned to French text) and contains linguists' transcriptions in Mboshi (in the form of a non-standard graphemic form close to the language phonology). The corpus is also enriched with automatic forced-alignment between speech and transcriptions. The dataset is made available to the research community 2 . This dataset is part of a larger data 1 We are only aware of a Griko-Italian corpus [START_REF] Lekakou | Documentation and analysis of an endangered language: aspects of the grammar of Griko[END_REF], and of a Basaa-French corpus [START_REF] Hamlaoui | BULBasaa: A bilingual Bàsàá-French speech corpus for the evaluation of language documentation tools[END_REF].

2 It will be made available for free from ELRA, but its current collection conducted on Mboshi language and presented in a companion paper [START_REF] Rialland | Parallel Corpora in Mboshi (Bantu C25, Congo-Brazzaville)[END_REF]. Expected impact of this work is the evaluation of efficient and reproducible computational language documentation approaches in order to face fast and inflexible extinction of languages. This paper is organized as follows: after presenting the language of interest (Mboshi) in section 2., we describe the data collection and processing in sections 3. and 4. respectively. Section 5. illustrates its first use for an unsupervised word discovery task. Our spoken term detection pipeline is also presented and evaluated in this section. Finally, section 6. concludes this work and gives some perspectives

Language Description

Mboshi (Bantu C25) is a typical Bantu language spoken in Congo-Brazzaville. It is one of the languages documented by the BULB (Breaking the Unwritten Language Barrier) project [START_REF] Adda | Breaking the unwritten language barrier: The Bulb project[END_REF][START_REF] Stüker | Innovative technologies for under-resourced language documentation: The Bulb project[END_REF].

Phonetics, phonology and transcription Mboshi has a seven vowel system (i, e, E, a, O, o, u) with an opposition between long and short vowels. While the language can be considered as rarely written, linguists have nonetheless defined a non-standard graphemic form for it, considered to be close to the language phonology. Affricates and prenasalized plosives were coded using multiple symbols (e.g. two symbols for dz, three for mbv).

Long and short vowels were coded respectively as V and as VV.

Mboshi displays a complex set of phonological rules. The deletion of a vowel before another vowel in particular, common in Bantu languages, occurs at 40% of word junctions [START_REF] Rialland | Dropping of the class-prefix consonant, vowel elision and automatic phonological mining in Embosi[END_REF]. This tends to obscure word segmentation and introduces an additional challenge for automatic processing.

Morphology Mboshi words are typically composed of roots and affixes, and almost always include at least one prefix, while the presence of several prefixes and one suffix is also very common. The suffix structure tends to consist of a single vowel V (e.g. -a or -i) whereas the prefix structure may be both CV and V. Most common syllable structures are V and CV, although CCV may arise due to the presence of affricates and prenasalized plosives mentioned above.

The noun class prefix system, another typical feature of Bantu languages, has an unusual rule of deletion targeting the consonant of prefixes3 . The structure of the verbs, also characteristic of Bantu languages, follows: Subject Marker -Tense/Mood Marker -Root-derivative Extensions -Final Vowel. A verb can be very short or quite long, depending of the markers involved.

Prosody Mboshi prosodic system involves two tones and an intonational organization without downdrift [START_REF] Rialland | How intonations interact with tones in Embosi (Bantu C25), a two-tone language without downdrift[END_REF]. The high tone is coded using an acute accent on the vowel while low tone vowel has no special marker. Word root, prefix and suffix all bear specific tones which tend to be realized as such in their surface forms. 4 Tonal modifications may also arise from vowel deletion at word boundaries.

A productive combination of tonal contours in words can also take place due to the preceding and appended affixes. These tone combinations play an important grammatical role particularly in the differentiation of tenses. However, in Mboshi, the tones of the roots are not modified due to conjugations, unlike in many other Bantu languages.

Data Collection

We have recently introduced Lig Aikuma5 , a mobile app specifically dedicated to fieldwork language documentation, which works both on android powered smartphones and tablets [START_REF] Blachon | Parallel speech collection for under-resourced language studies using the LIG-Aikuma mobile device app[END_REF]. It relies on an initial smartphone application developed by [START_REF] Bird | Aikuma: A mobile app for collaborative language documentation[END_REF] for the purpose of language documentation with an aim of long-term interpretability. We extended the initial app with the concept of retranslation (to produce oral translations of the initial recorded material) and speech elicitation Focusing on Mboshi data, our corpus was built both from translated reference sentences for oral language documentation (Bouquiaux and Thomas, 1976) and from a Mboshi dictionary [START_REF] Beapami | Dictionnaire Mbochi-Franc ¸ais[END_REF]. Speech elicitation from text was performed by three speakers in Congo-Brazzaville and led to more than 5k spoken utterances. The corpus is split in two parts (train and dev) for which we give basic statistics in Table 1. We shuffled the corpus prior to splitting in order to have comparable distributions in terms of speakers and origin. 6 There is no text overlap for Mboshi transcriptions between the two parts.

Data Processing

4.1. Cleaning, Pre-/Post-Processing

All the characters of the Mboshi transcription have been checked, in order to avoid multiple encodings of the same character. Some characters have also been transcoded so that a character with a diacritic effectively corresponds to the UTF-8 composition of the individual character with the diacritic. Incorrect sequences of tones (for instance tone on a consonant) have been corrected. It was also decided to remove the elision symbol in Mboshi.

On the French side, the translations were double-checked semi-automatically (using linux aspell command followed by a manual process -3.3% of initial sentences were corrected this way). The French translations were finally tokenized (using tokenizer.perl from the Moses toolkit7 ) and lowercased. We propose an example of a sentence pair from our corpus in Figure 1.

Forced Alignment

As the linguists' transcriptions did not contain any timing information, the creation of timed alignments was necessary. The word and phoneme level alignments were Mboshi wáá ngá iwé léekundá ngá sá oyoá lendúma saa m ótéma French si je meurs enterrez-moi dans la forêt oyoa avec une guitare sur la poitrine ). The alignment tool is an ASR system that is used in a forcedalignment mode. That is, it is used to associate words in the provided orthographic level transcription with the corresponding audio segments making use of a pronunciation lexicon which represents each word with one or more pronunciations (phonemic forms). The word-positionindependent GMM-HMM monophone models are trained using the STK tools at LIMSI [START_REF] Lamel | The Oxford Handbook of Computational Linguistics, chapter Speech Recognition[END_REF].

A set of 68 phonemes are used to represent the pronunciation dictionary, with multiple symbols for each vowel representing different tones [START_REF] Cooper-Leavitt | Developing an Embosi (Bantu C25) speech variant dictionary to model vowel elision and morpheme deletion[END_REF][START_REF] Bedrosian | The Mboshi noun class system[END_REF] and a symbol for silence. The acoustic model is estimated iteratively, with 5 rounds of segmentation and parameter estimation, and the model resulting from the last iteration was used to resegment the data. Since vowel elision and morpheme deletion are known to be characteristic of the Mboshi language, variants explicitly allowing their presence or absence are included in the pronunciation lexicon. Details of how this was implemented can be found in (Cooper-Leavitt et al., 2017a).

Illustration: Unsupervised Word Discovery from Speech

In this section, we illustrate how our corpus can be used to evaluate unsupervised discovery of word units from raw speech. This task corresponds to Track 2 in the Zero Resource Speech Challenge 2017. 8 We present below the evaluation metrics used as well as a monolingual baseline system which does not take advantage yet of the French translations aligned to the speech utterances (bilingual approaches may be also evaluated with this dataset but we leave that for future work).

Evaluation Metrics

Word discovery is evaluated using the Boundary, Token and Type metrics from the Zero Resource Challenge 2017, extensively described in [START_REF] Ludusan | Bridging the gap between speech technology and natural language processing: an evaluation toolbox for term discovery systems[END_REF] and [START_REF] Dunbar | The zero resource speech challenge 2017[END_REF]. They measure the quality of a word segmentation and the discovered boundaries with respect to the gold corpus. For these metrics, the precision, recall and F-score are computed; the Token recall is defined as the probability for a gold word token to belong to a cluster of discovered tokens (averaging over all the gold tokens), while the Token precision represents the probability that a discovered token will match a gold token. The F-score is the harmonic mean between these two scores. Similar definitions are applied to the Type and Boundary metrics.

Unsupervised Word Discovery Pipeline

Our baseline for word discovery from speech involves the cascading of the following two modules:

8 http://zerospeech.com

• unsupervised phone discovery (UPD) from speech: find pseudo-phone units from the spoken input,

• unsupervised word discovery (UWD): find lexical units from the sequence of pseudo-phone units found in the previous step.

Unsupervised phone discovery from speech (UPD)

In order to discover a set of phone-like units, we use the KIT system which is a three step process. First, phoneme boundaries are found using BLSTM as described in [START_REF] Franke | Phoneme boundary detection using deep bidirectional lstms[END_REF]. For each speech segment, articulatory features are extracted (see (Müller et al., 2017a) for more details). Finally, segments are clustered based on these articulatory features [START_REF] Müller | Towards phoneme inventory discovery for documentation of unwritten languages[END_REF]. So, the number of clusters (pseudo phones) can be controlled during this process.

Unsupervised word discovery (UWD)

To perform unsupervised word discovery, we use dpseg [START_REF] Goldwater | Contextual dependencies in unsupervised word segmentation[END_REF][START_REF] Goldwater | A Bayesian framework for word segmentation: Exploring the effects of context[END_REF]. 9 It implements a Bayesian non-parametric approach, where (pseudo)-morphs are generated by a bigram model over a non-finite inventory, through the use of a Dirichlet-Process.

Estimation is performed through Gibbs sampling. [START_REF] Godard | Preliminary Experiments on Unsupervised Word Discovery in Mboshi[END_REF] compare this method to more complex models on a smaller Mboshi corpus, and demonstrate that it produces stable and competitive results, although it tends to oversegment the input, achieving very high recall and a lower precision.

Results

Word discovery results are given in Tables 2, 3 and 4 for Boundary, Token and Type metrics respectively. We compare our results to a pure speech based baseline which does pair-matching using locally sensitive hashing applied to PLP features and then groups pairs using graph clustering [START_REF] Jansen | Efficient spoken term discovery using randomized algorithms[END_REF]. The parameters of this baseline spoken term discovery system are the same 10 as the ones used for the Zero Resource Challenge 2017 [START_REF] Dunbar | The zero resource speech challenge 2017[END_REF].

A topline where dpseg is applied to the gold forced alignments (phone boundaries are considered to be perfect) is also evaluated.

For the pipeline, we experience with different granularities of the UPD system (5, 30 and 60 units obtained after the clustering step). For each granularity, we perform 3 runs and report the averaged results. We note that the baseline provided by the system of [START_REF] Jansen | Efficient spoken term discovery using randomized algorithms[END_REF] has a low coverage (few matches). Given that our proposed pipeline provides an exhaustive Pipeline compared with an unsupervised system based on [START_REF] Jansen | Efficient spoken term discovery using randomized algorithms[END_REF].

parse of the speech signals, it is guaranteed to have full coverage and, thus, shows better performance according to the Boundary metric. The quality of segmentation, in terms of tokens and types is, however, still low for all systems. Increasing the number of pseudo phone units improves Boundary recall but reduces precision. For Token and Type metrics, a coarser granularity provides slightly better results.

Conclusion

We have presented a speech corpus in Mboshi made available to the research community for reproducible computational language documentation experiments. As an illustration, we presented the first unsupervised word discovery (UWD) experiments applied to a truly unwritten language (Mboshi).

The results obtained with our pipeline on pseudo-phones are still far behind those obtained with gold labels, which indicates that there is room for improvement for the UPD module of our pipeline. The UWD module should, in future work, make use of the bilingual data available to improve the quality of the segmentation. Future work also includes enriching our dataset with some alignments at the word level, in order to evaluate a bilingual lexicon discovery task. This is possible with encoderdecoder approaches, as shown in [START_REF] Boito | Unwritten languages demand attention too! word discovery with encoder-decoder models[END_REF].

As we distribute this corpus, we hope that this will help the community to strengthen its effort to improve the technologies currently available to support linguists in documenting endangered languages.

Acknowledgements

This work was partly funded by the French ANR and the German DFG under grant ANR-14-CE35-0002. Pipeline compared with an unsupervised system based on [START_REF] Jansen | Efficient spoken term discovery using randomized algorithms[END_REF].

which was supported by JHU and CMU (via grants from Google, Microsoft, Amazon, Facebook, and Apple).

Figure 1 :

 1 Figure 1: A tokenized and lowercased sentence pair example in our Mboshi-French corpus.

Table 1 :

 1 Corpus statistics for the Mboshi corpus from text or images (to collect speech utterances aligned to text or images). In that way, human annotation labels can be replaced by weaker signals in the form of parallel multimodal information (images or text in another language). Lig Aikuma also implements the concept of respeaking initially introduced in[START_REF] Woodbury | Defining documentary linguistics[END_REF]. It involves listening to an original recording and repeating what was heard carefully and slowly. This results in a secondary recording that is much easier to analyze later on (analysis by a linguist or by a machine). So far, Lig Aikuma was used to collect data in three unwritten African Bantu languages in close collaboration with three major European language documentation groups (LPP, LLACAN in France; ZAS in Germany).

	language split	#sent #tokens #types
	Mboshi	train 4,616	27,563	6,196
		dev	514	2,993	1,146
	French	train 4,616	38,843	4,927
		dev	514	4,283	1,175

Table 3 :

 3 Precision, Recall and F-measure on word tokens.

	9 http://homepages.inf.ed.ac.uk/sgwater/
	resources.html
	10 Notably the DTW threshold -which controls the number of
	spoken clusters found -is set to 0.90 in our experiment

Table 4 :

 4 Some experiments reported of this paper were performed during the Jelinek Summer Workshop on Speech and Language Technology (JSALT) 2017 in CMU, Pittsburgh, Precision, Recall and F-measure on word types.

	method	P	R	F
	gold FA phones + dpseg	7.5 13.9 9.7
	(Jansen and Van Durme, 2011)	4.6	4.8	4.7
	UPD+dpseg pipeline (5 units)	2.5	6.7	3.6
	UPD+dpseg pipeline (30 units)	2.0	4.5	2.8
	UPD+dpseg pipeline (60 units)	2.0	4.4	2.7

A prefix consonant drops if the root begins with a consonant[START_REF] Rialland | Dropping of the class-prefix consonant, vowel elision and automatic phonological mining in Embosi[END_REF].

The distinction between high and low tones is phonological (see[START_REF] Rialland | How intonations interact with tones in Embosi (Bantu C25), a two-tone language without downdrift[END_REF]).

http://lig-aikuma.imag.fr

Either (Bouquiaux and Thomas, 1976) or[START_REF] Beapami | Dictionnaire Mbochi-Franc ¸ais[END_REF].

http://www.statmt.org/moses/


Lama Iulian Rosu
email: rosu@lma.cnrs-mrs.fr

Frederic Lebon
email: lebon@lma.cnrs-mrs.fr

Thermo-viscoelastic modeling of the aircraft tire cornering

Keywords: Tire, finite element, modeling, viscoelastic, heat generation

Some numerical models are proposed for simulate the aircraft tire behaviour on the ground in critical situations. Fully coupled thermo-mechanical analysis procedures taking into account finite deformation, dynamics and frictional contact are studied; the visco-elasticity properties of the rubber were identified. A good agreement is observed at moderate speed, thus the model is extrapolated to high speeds and seems able to predict results in cases for which it is not possible to obtain realistic experimental data. In order to understand the thermal evolution of tire tread rubber materials during rolling and skidding steps, new experimental and numerical studies were also realized on tire tread rubber. The aim of this approach is to simulate and understand the effect of frictional heating on the tire behaviour.

Introduction

Landing and take-off operations are the most critical phases of an aircraft flight. Indeed, the high speed, the violent impact when the aircraft touches the ground, the need of braking efficiently, the ground irregularities, the climatic conditions (crosswind, contaminations, etc.) as well as other parameters can make these ground maneuvers very complex. Knowing at each time the forces in the contact patch allows controlling the behaviour at the tire/ground interface. For aeronautical applications, the experiments realized on real tire, at moderated speeds (less than70 km/h), help to analyze the tire/ground behaviour in this reduced field. However, numerical models based of Finite Element Method, FEM are still fundamental ways to predict the tire behaviour at higher speed, taking into account the high non-linearities related to materials especially for rubber material, and coupled phenomena (contact with friction, thermal-mechanical couplings, and internal dissipation).

In this study, FEM models are proposed to simulate the aircraft tire behaviour in contact with the runway in critical situations. Fully coupled thermo-mechanical analysis procedures taking into account finite deformation, dynamics and frictional contact are studied. In the present models, the complete frictional work is converted to heat. The contact-friction state is governed by a variable friction coefficient depending on sliding velocity, contact pressure and temperature. The proposed models are compared with experimental data such as contact area, lateral and longitudinal stiffnesses, surface temperature evolution due to friction, self-alignment torque, and lateral friction coefficient. A good agreement is observed at moderate speed (less than 70 km/h). The present model is then extrapolated to high speeds and seems to be able to predict results in cases for which it is not possible to obtain realistic experimental data. The thermal evolution of tire tread rubber materials during rolling and skidding steps was also investigated; new experimental and numerical studies were realized on tire tread rubber specimens. The aim of the thermal approach is to simulate the frictional heating of the tire tread developed during real situations by applying an equivalent external heat flux. In the same time, the thermal diffusion through the tire tread was analyzed.

Mechanical and a fully coupled thermo-mechanical Finite element model

In this study, mechanical and fully coupled thermo-mechanical analyses are developed to predict the friction ratio µ y (the ratio between the normal and the tangential force) and the self-aligning torque M z (the torque in the vertical direction). A classical rolling (CR) method based on a Lagrangian formulation was studied, thus from an observer point of view, the tire mesh (51circumferential elements) is rotating and moving forward. A variable friction coefficient µ (P,T) depending on pressure and temperature was used in the thermo-mechanical model, real viscosity parameters were also introduced in this model. Concerning the mechanical model, a fixed friction coefficient µ 0 was adopted. These simulations (for both models) require two numerical steps, an acceleration step from zero to a given velocity and a rolling cornering step at a constant given velocity and a given slip angle.

Self aligning torque/ lateral friction coefficient

Concerning the mechanical and thermo-mechanical analyses, our analysis is focused on grooved aircraft tires. Fig. 1 shows the evolution of the self aligning torque M z versus the slip angle. In order to show the influence of the temperature on the lateral friction coefficient µ y and on the self-aligning torque M z , purely mechanical, and thermo-mechanical models were performed under the same loading conditions and for the same slip angles. Results were compared with experimental data. In the case of the pure mechanical simulation without any temperature dependence, we can observe that the lateral coefficient µ y (Fig. 2) reaches a plateau equal to µ 0 with respect to the Coulomb's friction low. β max , the angle for which the self-aligning torque is maximum, seems to be in good agreement with experimental data. The self-aligning torque M z increases up to β max at which the full grip potential is reached. The self-aligning torque M z decreases when β > β max , and tends to negative values. In the case of a thermo-mechanical approach, the dependence of the lateral friction coefficient on the temperature (Fig. 2) leads to a decrease in µ y beyond the β max value. The selfaligning torque M z (Fig. 1) falls quickly toward null values. Fig. 1: Self aligning torque M z , comparison between experimental data and mechanical and thermo-mechanical FE models, under given loading conditions (F z , p 0 , v 0 ). Fig. 2: Lateral friction coefficient µ y , comparison between experimental data, mechanical and thermo-mechanical FE models, under given loading conditions (F z , p 0 , v 0 ).

Thermo-mechanical model, temperature evolution of an aircraft tire

Thermo-mechanical simulation of skidding tire (tire is subjected to an inflation P 0 , a concentrated vertical loading Fz, rolling velocity v 0 and small slip angle β 0 ) was investigated; the rolling is obtained by imposing longitudinal and lateral velocities related to a slip angle. Figure 4 presents the temperature distribution in this case.

After a few seconds of rolling in cornering, an increase of the temperature occurs on tire tread and especially on groove sides; a warming zone is observed on the entire contact zone. However a slight diffusion of temperature is observed after a short period of rolling. Figure 5 presents a comparison between thermo-mechanical FEM and experimental data of a cornering simulation of an aircraft loaded tire for a given velocity v 0 and for small slip angle β 0 . In this case a good agreement is observed between the simulation and experimental data for a small angle of skidding.

In order to understand the role of a thermal barrier presented by the reinforced zones, different experimental and numerical tests were performed in laboratory tests; their purpose was to verify the evolution of the rubber behaviour during cornering rolling. These studies confirmed the necessity of taking into account the frictional heating of rubber and also internal heating produced by energy dissipation (visco-elasticity properties). Recently we have developed a new thermo-mechanical model, able to predict the temperature evolution of skidding tire at high vertical loading and for different velocity values. Our current model was developed assuming that heat generation is governed by inelastic energy. Several experimental runs have been done on the tire for different speeds and skidding angles, temperature evolutions have been recorded by an infrared camera. Figure 6 shows temperature evolution of tread tire from experimental measurement for a given velocity v 1 and slip angle β 1 . Figure 7 presents the first results of this new approach, comparison between experimental data and FEM model. A significant rising of temperature was observed after a short skidding time (about 0,8 second). As we mention, the thermo-mechanical FE model was developed assuming heat generation, this energy is highly depending on the stress and strain evolution during the deformation process, these in turn depend on the material viscoelastic properties of the tire. In the case of our model (fig. 7) we can reasonably consider that the initial part of the temperature evolution comes from the inelastic dissipation effects while the "plateau" results of the frictional work transformed into heat flux. That is why we consider that an improved analysis of the viscoelastic rubber tread properties is necessary for the development of FEM model, whoever, the current model is able to predict the tire evolution at a high velocities (more than 250 km/h) for which it is not possible to obtain realistic experimental data (fig. 7, FEM model for rolling velocity v 2 ).

Simulated frictional heat

The main goal of this section is to evaluate the temperature evolution of the tire tread, by mean of a simple heat-up experiment. This study aims to simulate the frictional heating of the tire tread by applying an external heat flux and also to study the thermal diffusion through the tire tread.

Experimental study

The experimental test consists in warming-up the tire tread (fig. 8) by heating flux at different temperatures 60°C and 100°C and measuring simultaneously the temperature evolution on the outer surface using two external sensors facing the tread and the groove, and inside the tire structure by means of two other infrared sensors. The heating flux was normal to the tread surface. Fig. 8: Heat-up setting Figure 9 presents the experimental analysis, as we can see, the surface temperature of tire tread rises from ambient to almost the prescribed limit within the heated area (green triangles). The surface groove temperature is almost not evolving (blue cross). For the inner evolutions corresponding to the heated zone, we find time shifted raises, smaller amplitudes and different slopes (blue solid). For the inner grooves the evolution profiles look very similar to the tread ones (red solid). But we can easily remark that after turning off the heating flux, while the outer tread rubber temperature starts decreasing, the groove temperature keeps rising for a while, then reaches a plateau. This proofs that the heat is "stocked" and "diffused" throughout the tire rubber and in the same time that rubber has a very small conductivity coefficient.

Numerical simulation 3D numerical model was developed to predict the thermal evolution of tread tire under heating flux. A numerical specimen identical to the physical one was created. Figure 9 presents a numerical simulation of the tire tread rubber heated up by a given heating flux during 300 seconds. As we can observe, a good agreement is occurred between the simulated temperature of tire tread and the measured one, our present model is able to predict the temperature evolution of tread tire, and the thermal diffusion through the tire tread in a simple case of heat-up.

Conclusion

In this paper, we have proposed some numerical models to simulate the aircraft tire behaviour in cornering. Fully coupled thermo-mechanical analysis procedures taking into account finite deformation were studied. The proposed models have been compared with experimental data such as a surface temperature evolution due to friction, self-alignment torque, and lateral friction coefficients. A good agreement was observed at moderate speeds (less than 70 km/h), the model seems to be able to predict results at high speeds, in which case it is not possible to obtain realistic experimental data.

New experimental and numerical studies were also realized on tire tread rubber. The aim of this thermal approach was to simulate and understand the effect of frictional heating on the tire rubber behaviour, a good accord was observed between experimental and numerical data. In the future, we intend to improve the models introducing more complex constitutive equations coupling thermomechanical effects, particularly taking into account viscosity and internal dissipation. Other kind of experimental devices will be also proposed in order to confirm the validity's domain of our models in various critical situations.

Fig. 3 :

 3 Fig. 3: Experimental measurement. Fig. 4: FE model.

Fig. 5 :

 5 Fig. 5: Temperature evolution of tire tread, comparison between FEM and experimental data for a cornering simulation for given velocity v 0 and small slip angle.

Fig. 6 :

 6 Fig. 6: Temperature evolution of tire tread, vertical loading F z1 , rolling velocity v 1 and slip angle β 1 .

Fig. 7 :

 7 Fig. 7: Temperature evolution of tire tread, comparison between two skidding tires rolling for two different velocity v 1 and v 2 , for a given slip angle β 1.

Fig. 9 :

 9 Fig. 9: Temperature evolution of external and internal layers of tread tire under heating flux, experimental and numerical results


Damien Chablat
email: damien.chablat@cnrs.fr

Swaminath Venkateswaran

Frédéric Boyer

Dynamic Model of a Bio-Inspired Robot for Piping Inspection

Keywords: Piping inspection robot, Bio-inspired mechanism Dynamic analysis, Newton-Euler algorithm

Piping inspection robots are of great importance in industries such as nuclear, sewage and chemical where the internal diameters of the pipeline are significantly smaller. Mechanisms having closed loops can be used in such areas as they generate contact forces and deployable structures. With the help of a bio-inspired mechanism, a piping inspection robot is presented which mimics the motion of a caterpillar. The robot is composed of three modules: a central module for elongation and two other modules on the front and rear for clamping. A slot-slider mechanism is chosen for the legs of the robot. Using industrial components such as DC motors, servo-controllers, ball screws and fasteners, the entire robotic system was realized in CATIA software and a prototype was made at the Laboratoire des Sciences du Numérique de Nantes (LS2N). In this article, we present the forces induced on the motors under locomotion using a dynamic analysis. With the help of the recursive Newton-Euler algorithm, the torques generated on the motor under locomotion have been identified which ensures the stability of the system while moving inside pipes.

Introduction

Pipeline installations are of great importance in industries such as sewer, chemical and nuclear. Maintenance of these facilities requires regular inspections and repairs. The context of the installations varies in terms of topology (diameters, complexity), environment with chemical risks (gas, deposits, corrosion) and radiations (gamma, beta). The inspection of such pipelines is thus restricted for human beings thereby necessitating the need for an industrial robot. A robot inside a pipeline is subject to various problems such as: (i) locomotion of the system, (ii) positioning of the robot, (iii) inspection of the pipeline and (iv) perform mechanical tasks (welding, cleaning etc.). In order to simplify the robot design, there are methods to facilitate the choice of the robot's different elements, such as the paw mechanism for managing the contact forces between the robot and the environment. We can distinguish two types of robot family according to their locomotion namely mechanical and bio-inspired systems. A distinction between the two categories was proposed by Kassim et al. [START_REF] Kassim | Locomotion techniques for robotic colonoscopy[END_REF]. A bio-inspired mechanical system that mimics the motion of a caterpillar has been presented by Henry1 et al. [START_REF] Henry | MultiObjective design optimization of the leg mechanism for a piping inspection robot[END_REF]. The robot has two leg mechanisms for contact points with the walls of a pipe and a central system for elongation. The study of forces and torques on the motor were not done in detail which is very essential to understand the robustness of the system under various inclinations and obstacles within the pipeline. Thus, in this article the force analysis on the robot during locomotion using a dynamic model has been presented. The outline of the article is as follows. The locomotion principle as well as the architecture of the bio-inspired robot is presented. Followed by that, the Newton-Euler algorithm for the dynamic analysis and the results of dynamic forces under locomotion are presented. The article then ends with closing conclusions.

Locomotion and Architecture of the Robot

The locomotion of the robot is inspired from the motion of a caterpillar. It comprises of three steps: one for elongation and two others for clamping. A classic way to accomplish this would be with the help of pneumatic bellows and electric motors [START_REF] Anthierens | Design of an electro pneumatic micro robot for in-pipe inspection[END_REF][START_REF] Anthierens | Micro robots dedicated to small diameter canalization exploration[END_REF]. However, electrical motors are used in all three modules for actuation as they serve better inside pipelines having dust particles. Using the actuators and leg mechanisms, the motion of a caterpillar is mimicked in the robot. The architecture of the robot used in the system as well as the rendered model of the robot inside a pipeline are depicted in Figs. 1 and2. Three identical actuators, one for elongation in the center and two others for clamping in the front and rear are used in the system. At least one pair of legs remains in contact with the walls of the pipe at all instances of the locomotion cycle. A hyper-static posture exists when both the pair of legs are in contact with the walls of the robot. In our case study [START_REF] Henry | MultiObjective design optimization of the leg mechanism for a piping inspection robot[END_REF], the pipe diameters ranges from 74 mm to 54 mm. Owing to an offset of 11 mm caused by the actuators used in the system, the target radius to be swept now ranges from 26 mm to 16 mm. With the help of multi-objective optimization and genetic algorithm [START_REF] Ur-Rehman | Multiobjective path placement optimization of parallel kinematics machines based on energy consumption, shaking forces and maximum actuators torques: application to the orthoglide[END_REF] in MATLAB, a slotslider mechanism was chosen for the leg mechanisms of the robot among a set of three architectural candidates. The direct and inverse kinematic models (DKP &IKP) (1 and 2) as well as the inverse of the Jacobian (3) serves as the objective functions for the optimization technique. The equations are as follows:

P y = l 2 2 e + ρ 2 e + l 2 1 l 4 2 + l 2 1 l 2 2 ρ 2 l 2 2 + ρ 2 (1)
η f = (ρ 2 + l 2 2 ) 3/2 l 2 l 1 ρ = F p F a ( 3
)
In Eqs. 1 and 2, P y signifies the position of the leg that establishes a contact with the walls of the pipeline. In Eq. 3, F a represents the actuation force of the motor and F p signifies the contact forces between the legs of the robot and the walls of the pipeline. The dimensions for the leg mechanism used in the robot are: l 1 = 57 mm, l 2 = 7 mm and ρ = 8.5-45.5 mm. The six locomotion steps of the robot inside the pipe are depicted in Fig. 3. The three legs of the rear and forward mechanisms have the same dimensions and they ensure non-hyper-static contacts at almost all phases of the locomotion. A Maxon motor GP 16 S (φ 16) [START_REF] Maxon Motor's | Program 2017/18. precision Drives and Systems[END_REF] is used for actuation. Each module has its own motor system. The gear ratio offered by this motor is 1:455. The entire mass of the robotic system is 657 g not taking into account the electronic boards and the power supply. An ESCON 36/3 DC servo-controller (Torque and speed control) [START_REF] Maxon Motor's | Program 2017/18. precision Drives and Systems[END_REF] is used within the robotic system for an efficient control of the DC motors used for actuation.

The torque on the motor can be calculated in two phases: a dynamic algorithm during locomotion and a static algorithm during clamping.

Dynamic Modeling

The robot is a multi-body mobile-based system with closed loops. It moves relative to a fixed Galilean frame. A closed loop is a structure composed of two kinematic chains, a passive (not actuated) and an active (actuated) joined together at their ends [START_REF] Boyer | Recursive inverse dynamics of mobile multibody systems with joints and wheels[END_REF]. We also distinguish the direct dynamic model which is used for estimating the accelerations in the links of the robot with the help of the wrench equations and the inverse dynamic model which is used for estimating the torques and wrench using the accelerations and velocities of the links. In this context, we employ the inverse dynamic model in order to estimate the torques generated on the motor under locomotion. In order to calculate the efforts on the motor under locomotion, two different dynamic models are used and they are represented in Fig. 4.

Fig. 4. Change of models in dynamic mode

In Model-A, the reference body is placed on the left clamping module whereas in the Model-B the reference body is placed on the right clamping module. Each model is composed of 29 bodies as represented in Fig. 5 with 9 non-zero masses, 3 active links (red arrows), 18 passive links (blue arrows) and 8 clamping's (E i ).

The entire system appears complex and thus the Denavit-Hartenberg (DH) [START_REF] Khalil | A new geometric notation for open and closed-loop robots[END_REF] table is constructed which makes it easier to describe each model. The details of the key body components of Fig. 5 and the material used is provided in Table 1.

Inverse Dynamics Using the Recursive Newton-Euler Algorithm

Generally, dynamic models are solved by either the Lagrange equations or the Newton-Euler equations. The Lagrange equation is based on the difference between the kinetic and potential energy of the system and the system torque [START_REF] Khalil | Dynamic modeling of robots using recursive Newton-Euler techniques[END_REF] which is given by the equation:

Γ = A(q)q + H(q, q) ( 4
)
where A is the inertia matrix of the robot and H represents the Coriolis, centrifuge and gravity torques. As this method is time consuming, Khalil proposed the recursive Newton-Euler (NE) [START_REF] Khalil | Dynamic modeling of robots using recursive Newton-Euler techniques[END_REF], which has proven to be an excellent tool for modeling rigid robots. It involves two recursive algorithms namely: Forward and backward recursions. In the former, the link velocities, accelerations and ultimately the wrench on each links are calculated from link 1 to n. In the backward recursion, the reaction wrenches are calculated from link n to the base of the robot. Also this method provides the joint torques in terms of the joint positions, velocities and accelerations without computing the A and H matrices and the equation is given by:

Γ = f (q, q, q) (5)
In order to use the Newton-Euler algorithm, we move from a mobile-based multibody system with closed loops to a tree-based multi-body system. The homogenous transformation matrix which defines a frame R j relative to frame R i as a function of six geometric parameters (γ j , b j , α j , d j , θ j , r j ) is given by the relation:

i T j = i R j i P j 0 1×3 1 ( 6
)
where i R j defines the (3 × 3) rotation matrix and i P j defines the (3 × 1) vector that specifying the position of frame j with respect to frame i. The forward NE recursive equations [START_REF] Khalil | Dynamic modeling of robots using recursive Newton-Euler techniques[END_REF] are given by:

j Vj = j T i i Vi + j γ j + qj j A j (7)
where j A j is a (6 × 1) columns matrix called as the transposition vector for velocities and accelerations and is given by:

j A j = 0 0 σ j 0 0 σj T (8)
Here σ j is a coefficient of the joint type. If the joint is revolute σ j = 0 and for prismatic joint σ j = 1. Also σj = 1σ j . j V j is a kinematic screw vector of frame j with a size of (6 × 1) and it contains the linear and angular velocity components. The equation is given by:

j V j = V j T ω j T T (9)
where j T i is the screw transformation matrix and it is given by the equation:

j T i = j R i -j R i i Pj 0 3×3 j R i ( 10
)
The wrench equation comprises of the external forces and torques and is provided in (11). These forces and torques in the forward recursion is given by ( 12) and (13).

j F j = j F j j M j (11) j F j = M j j Vj + j U j j MS j (12) j M j = j J j j ωj + j ω j × ( j J j j ω j ) + j MS j × j Vj (13)
Here MS j and J j refers to the standard inertial parameters of the link j. The backward recursive equations are calculated with the help of the reaction forces and torques generated on the joints j. The torque induced on the motor is calculated with the help of the reaction forces based on (14) which is given below [START_REF] Khalil | Dynamic modeling of robots using recursive Newton-Euler techniques[END_REF]:

Γ j = (σ j j f j + σj j m j ) T j a j + Ia j qj + F sj sign( qj ) + F vj qj (14)
Here f j and m j are the reaction forces and torques from the links. Ia j is the inertia of the motor. F sj and F vj are the coulomb and viscous friction parameters. The forward and the backward recursive equations using NE algorithm are implemented in MATLAB with the help of which the locomotion sequence of the robot and the forces on the actuators are estimated.

Results of Simulation During a Locomotion Cycle

With the help of the geometric parameters, links and joints of the robot, using MATLAB the NE recursive algorithm is executed in order to calculate the forces generated on the actuators used in the leg mechanisms as well as the central actuator. The displacement, velocity and acceleration of these actuators are also estimated during the entire locomotion cycle inside a horizontal and vertical pipeline. The diameter of the pipeline used in the prototype as well as the simulation is 74 mm with a diametrical reduction to 54 mm in the middle of the trajectory. The total length of the trajectory (pipeline) taken into account for the simulation is approximately 2.5 m. A fifth-order polynomial interpolation is employed for the motion planning [START_REF] Khalil | Modeling, Identification and Control of Robots[END_REF]. This interpolation ensures the continuity of the movement in position, velocity and acceleration. The maximum the umbilicus and the effect of gravity (static masses). The constant lines in the curves represents the effects of gravity. It could be observed that the forces on the leg actuators remain the same during horizontal and vertical orientation of the pipelines. On the other hand, the forces on the central actuator is affected by the orientation of the pipeline as they have no legs attached to them. During horizontal orientation of the pipeline, the forces on the central actuator ranges between 0-0.04 N whereas in the vertical orientation of pipeline the forces ranges between 10.66-10.7 N which indicates the effect of gravity. For the Model-A (not presented here), the forces induced on the central actuator were estimated to be between 8.04-8.1 N. The dynamic effects are caused only by the movement of masses and gravity but there exists no effect from the umbilicus. The forces on the leg actuators in Model-A was exactly the inverse of Model-B and the values remains the same during horizontal and vertical orientation of the pipeline.

The clamping forces on the legs can be estimated with the help of static model using the Coulomb's law of friction. This model has not been presented and it helps in estimating the tangential radial and longitudinal forces as well as the normal forces between the legs of the robot and the walls of the pipeline. These forces are essential to estimate the torques induced on the leg actuators during clamping.

Conclusions

Thus, a dynamic model using the recursive Newton-Euler algorithm has been presented for a bio-inspired piping inspection robot. It could be observed that during vertical travels, a higher amount of force is induced on the central actuator of the robot when compared to horizontal travel where the force induced on the central motor is closer to zero. The static model for estimating the clamping forces have not been presented. With the velocity of the robot being small (0.00043 m/s), a static analysis using Coulomb's law of friction will be done in the future in order to determine the clamping forces as well as the stability of the system. The impact on the forces induced on the motors caused due to the orientation of the robot inside the pipeline will also be taken into account for further studies. An increase in the speed of the robot will also be proposed by using optimization techniques as well as by changing the motors with smaller gear ratios in order to produce higher velocities.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Cross section of the robot inside a pipeline of radius r

Fig. 3 .

 3 Fig. 3. Six locomotion steps of the robot inside the pipeline

Fig. 5 .

 5 Fig. 5. Dynamic model of the robot for Model-A

Fig. 6 .Fig. 7 .Fig. 8 .

 678 Fig. 6. (From left) Position, Velocity and Acceleration of the right leg actuator, central actuator and the left leg actuator

Table 1 .

 1 Description of key body parts represented in Fig.5

	Body No. Description	Material
	Body 1	Left leg actuator	Steel
	Body 4	Left leg-1	Bronze
	Body 8	Left leg-2	Bronze
	Body 12 Left leg-3	Bronze
	Body 15 Central & right leg actuator Steel
	Body 18 Right leg-1	Bronze
	Body 22 Right leg-2	Bronze
	Body 26 Right leg-3	Bronze
	Body 29 Umbilicus(Cables)	Copper

We would like to thank Renaud Henry, Daniel Kanaan and Mathieu Porez for their participation in the study of this robot.