Pierre-Alain Boucard
email: pierre-alain.boucard@lmt.ens-cachan.fr

-Pierre Ladeveze

A multiple-solution method for non-linear structural mechanics

Keywords: structural mechanics, non-linear computations, multiple solution

The numerical solution process for complex, time-dependent non-linear problems (material stamping, cyclic viscoplasticity, crashes, etc.) requires, even with the most powerful computers, a computation time which turns out to be prohibitive. Moreover, with respect to those structural analyses involving multiple solution sequences (parametric studies, probabilistic analyses, flawed structures, etc.), each series of data necessitates performing a full calculation, even if the problems to be solved do resemble one another.

The goal of the work presented herein is to develop a strategy that is well-suited to multiple-solution problems. Such a strategy is to be based on the LATIN method and, more specifically, on its capacity to reuse the solution to a given problem in order to solve similar problems. The goal then is both to assess the major obstacles encountered during this computational procedure and to define and apply a strategy that enables minimizing total computing costs with respect to multiple-solution problems.

INTRODUCTION

Whenever the analysis of a structure involves multiple solutions (parametric studies, probabilistic analyses, flawed structures, etc.), each set of data utilized necessitates a separate, full-scale calculation. As such, a good number of similar types of problems wind up getting solved. The choice of an efficient and welladapted computational method is thus of vital importance. The LATIN method [5],

[6] is non-incremental in nature and, consequently, would appear to represent a more promising approach, inasmuch as the set of principles inherent in this method tend to be more applicable than are the majority of conventional incremental algorithms (stochastic finite element approaches, perturbation-related methods

[1], [7], and Monte Carlo simulations [8]).

The objective of the work presented herein is to demonstrate the potential of the LATIN method with respect to multiple-solution problems. For the special case of buckling, a strategy adapted to multiple solutions has been developed which relies on the LATIN method and, more specifically, on its capacity to reuse the solution to a given problem in order to solve similar problems.

A full presentation of the LATIN method can be found in [5], [6]. The solution process for buckling problems, along with a set of pertinent examples, is provided in [2], [3].

REVIEW OF THE LATIN METHOD

Notation

The structure being studied occupies a domain Ω of the ordinary three-dimensional Euclidean space, whose corresponding vectorial space is denoted by E 3 . The vectors of E 3 , displacement for instance, are denoted by U _ . The current point of Ω is noted M _ . The linear operators of E 3 , strain and stress, are denoted by ε ε and σ σ , respectively. These quantities, in a given base, are represented by a matrix (3,3); this notation is also used for the internal variables. For more complex operators, such as Hooke's elasticity tensor, they are written as: K. To define the work, one uses the trace operator denoted by "Tr", thus:

Tr[σ σ ε ε] = ∑ i =1,2,3 j =1,2,3 [σ σ] ij [ε ε] ij
where [σ σ ] i j and [ε ε ] i j are the components of the operators σ σ and ε ε, respectively.

Reference problem

For the whole time interval, denoted by [0, T], the structure being studied is subjected to surface loading F _d on a part ∂ 2 Ω of the boundary, ∂Ω, of Ω, and to volume loading f _d . On the complementary part, ∂ 1 Ω, to ∂Ω, the displacement U _ d is assigned. The method is carried out by means of small perturbations in order to simplify the presentation of the concept. This method has been conducted in [5] for large transformations and has been developed in [2], [3] for the analysis of both buckling and post-buckling.

Let us consider small displacement problems and quasi-static loading. U [0,T] ,

S
U 0 = { U _ (M _ ) ; U _ (M _ ) ∂ 1 Ω = 0} U [0,T] 0 = { U _ (M _ ,t) ∈ U [0,T] ; ∀ t ∈[0,T] U _ (M _ ,t) ∈ U 0 }
The material state is completely determined by the values of strain, the inelastic strain ε ε p and additional internal variables X X _ . In general, X X _ is a column of R m . The conjugate quantity of X X _ is denoted by Y Y _ ; it is also a column of R m .

Then, the structure's evolution is described by the following problem: Find U _ (M _ ,t)) and σ σ(M _ ,t) M _ ∈Ω, t ∈[0,T] such that:

• kinematic constraints: U _ (M _ ,t) ∈ U [0,T] , U _ ∂ 1 Ω = U _ d • equilibrium equation: σ σ ∈ S [0,T] , ∀ U _ * ∈ U [0,T] 0 ∫Ω dΩ Tr[ σ σ ε ε( U _ * ) ] = ∫Ω dΩ f _d . . . . U _ * + ∫∂ 2Ω d S F _d . . . . U _ * • state laws ε ε • = ε ε • p + ε ε • e , σ σ = Kε ε e Y Y _ = G(X X _ ) • evolution laws d dt       ε ε p -X X _ = B       σ σ Y Y _ ε ε p (t=0) = 0 Y Y _ (t=0) = 0
K, G are given material characteristics. B is a given positive operator which depends on the material.

Principles of the method

Let us introduce S = ( ε ε . p , X X To derive a formulation of the normal material (linear state laws, Y Y _ = Λ Λ Λ Λ X X _ ), the only non-linear relations are the evolution laws; moreover, these laws are local in space variable.

In the case of normal material models, the splitting used is the following:

(i)     kinematic constraints equilibrium equations (∀t ∈ [0, T]) σ σ = K (ε ε -ε ε p ), Y Y _ = Λ Λ Λ Λ X X _ (ii)     d dt       ε ε p -X X _ = B       σ σ Y Y _ ε ε p (t=0) = 0 and X X _ (t=0) = 0
The first group is associated with the free energy and the second one with the

• local stage: find S ^n+1/2 ∈ Γ Γ Γ Γ such that S ^n+1/2 = (Γ Γ Γ Γ) ∩ ( S n + E + )
• linear global stage: find S n+1 ∈ A d such that

S n+1 = (A d ) ∩ ( S ^n+1/2 + E -)
Where E + and Eare parameters.

Practically, the search directions E + and Eare defined by two linear operators H + and Hsuch that: techniques are necessary in order to limit this particular stage's cost.

E + = {∆S / d dt       ∆ε ε p -∆X X _ + H +       ∆ σ σ ∆Y Y _ = 0 ; ∆S ∈ S [0,T] } E -= {∆S / d dt       ∆ε ε p -∆X X _ -H +       ∆ σ σ ∆Y Y _ = 0 ; ∆S ∈ S [0,T] } H +

Processing of the global stage -Representation of the unknowns

The global stage consists of searching for a new element S n+1 that's better than S n ;

similarly, the difference between these two elements of A d could be chosen as an unknown during this stage. Through working on the corrections of the unknowns, two new quantities naturally get introduced:

∆ S ^ = S ^-S n = (∆ ε ε . ^p, ∆X X . _ ; ∆σ σ ^, ∆Y Y _ )
and

∆S n = S n+1 -S n = (∆ε ε . p n , ∆X X . _ n , ∆σ σ n , ∆Y Y _ n )
It should be pointed out at this juncture that the element The representation for each variable is as follows:

ε ε . p n+1 (M _ , t) -ε ε . p n (M _ , t) = ∑ i = ı m a i (t) A A i (M _ ) X X • _ n+1 (M _ , t) -X X • _ n (M _ , t) = ∑ i = ı m c i (t) C C _ i (M _ ) σ σ n+1 (M _ , t) -σ σ n (M _ , t) = ∑ i = ı m b i (t) B B i (M _ ) Y Y _ n+1 (M _ , t) -Y Y _ n (M _ , t) = ∑ i = ı m d i (t) D D _ i (M _ )
In practice, m is limited to either 1 or

MULTIPLE-SOLUTION METHOD

The LATIN method makes it possible to obtain a representation of the problem's solution in the form of a product sum of both time and space functions. As such, it could be considered that the method serves to automatically build an optimal basis for representing the solution. The notion herein then is to use this representative basis for determining the solution to a problem that's similar to the one for which this basis was built in the first place. In this context, a similar problem would be one whereby an initial consideration would suggest that both the geometry and the limit conditions are identical (this requirement ensures respecting the "zero-admissibility" condition of the space functions), yet whereby the material characteristics can vary throughout the structure.

This procedure allows utilizing the fact that the algorithm can be initialized by any solution belonging to the set A d (though usually an elastic solution). The notion herein therefore is to initialize the process associated with the similar problem (the "flawed" structure) by the results of the computation carried out on the "flawless" structure. In this manner, a basis of space functions with a strong mechanical content is available immediately as of the first iteration, thereby making it possible to represent the solution.

In this instance, the preliminary stage plays a vital role: it enables both verifying that the basis of the space functions is welladapted to the target problem and searching for new time functions which allow deriving the solution to the "flawed" problem. In the best-case scenario, when the basis is sufficient, no new space function will be generated and the problem's solution will thus be obtained at low cost. The alternative would be the automatic computation of new space functions in order to enhance the initial basis: the number of such functions however must remain less than the number in the initial basis in order to ensure the method's efficiency. Should the solutions to both the "flawed" and "flawless" problems be close enough, the solution to the latter problem can then be derived at a significantly lower cost than that of a fullscale computation.

EXAMPLES

The selected scope of application for testing this method is the buckling of both

[ 1 ] BENAROYA H., REHAK M., "Finite element methods in probabilistic structural analysis:

A selective review", Applied Mechanics Reviews, Vol. 41, No. 5, pp. 201-213, 1988.

[ 2 ] BOUCARD P.A., LADEVÈZE P., POSS M., ROUGÉE P., "A non-incremental approach for large displacement problems", Computers and Structures Vol. 64, 1-4, pp. 449-508, 1997.

[ 3 ] BOUCARD P.A., LADEVÈZE P., "A Non-Incremental Approach for Post-Critical Analysis", Numerical Methods in Engineering 96, J.-A. Désidéri et al. Eds., J. Wiley, pp. 164-170, 1996.

[ 4 ] COCHELIN B., AZRAR L., DAMIL N., POTIER-FERRY M., "An asymptotic-numerical method to compute the post-buckling beahviour of elastic plates and shells", International Journal for Numerical Methods in Engineering, Vol. 36, 1251-1277, (1993).

[ 5 ] LADEVÈZE P., "Non Linear Mechanics of Structures -New approaches and nonincremental methods of calculation", Springer, 1998, also available in French (Hermès, 1996) AIAA Journal, Vol. 10, No. 4, pp. 456-462, 1972.

  [ 0 , T ] denote the spaces where displacement U _ and stress σ σ respectively, defined on Ωx[0, T], are searched. The subspaces of displacement kinematically admissible for homogeneous equations are such that:

•_;

  σ σ , Y Y _ ) for which each component is defined on Ω x[0, T]. The corresponding space is denoted by S [0,T] . S is what we are looking for; it is defined by a set of equations. The principle of the method consists of constructing a sequence of elements S n , defined over Ωx[0,T]. The entire loading is then handled in a single time interval. The method is based on the following three principles: P1: the problem's equations are divided into two groups which serve to define two sets: Γ Γ Γ Γ and A d, where: • A d : linear and ultimately global equations, • Γ Γ Γ Γ : : : : local in space variable and ultimately non-linear equations P2: The method then proceeds by means of a two-stage iterative sequence: One iteration is composed of both a local stage, during which a solution belonging to Γ Γ Γ Γ is built, and a global stage during which a solution belonging to A d is sought. Thus, the solution to the problem being posed lies at the intersection of these two solution sets. In order to resolve these two stages, two search directions E + and E -, parameters of the method, are to be used. P3: The problem's unknowns are represented by a product sum of both time and space functions.

Figure 1 :

 1 Figure 1: Iteration scheme

  and Hdepend on the time and space variables. The local stage then leads to a local non-linear, evolution problem in space variables. The resolution of this stage turns out to be rather straightforward. In contrast, the global stage requires the solution to a global linear problem in space variable that's been parametered by the time interval over which specific solution

  S n+1 must belong to A d in order to remain within the framework of the LATIN method. The direct solution to global linear problems which have been parametered by time within the procedure of the global stage can lead to sizable computing times. As a means of lowering these computing times, representations of both time and space unknowns are introduced in order to solve the global stage at a low computing cost. The separation of the functional dependencies in both time and space has yielded satisfactory results for quasi-static loadings [3], [5], [6]. The corrections are then sought by means of superimposing solutions of the simple-loading type. Such solutions are recognized as being good approximations of non-linear, quasi-static problem solutions.

2.Figure 2 :

 2 Figure 2: Insertion of the preliminary stage

Figure 5 :Figure 6 :

 56 Figure 3 and 4. A similar computation was carried out on a half-embedded bar; the results are presented in Figure 5 and 6. For both of the cases analyzed, figures 4 and 6 display the number of space functions added during the computations at the level of the initial basis (6 time-space function couples). This number provides an indicator of the total computing cost inasmuch as this phase constitutes the algorithm's most costly stage. It can be observed that for the majority of cases processed, at most one space function gets added. The basis of initial functions therefore enables conducting many computations "with flaws" at a much lower cost than that of a full-scale computation: within the cases presented herein, the computing time necessary for obtaining the solution on the "flawed" bar is between 10% and 20% of that associated with a fullscale computation. 5. CONCLUSION These initial numerical examples have exhibited the algorithm's very satisfactory behavior when applied to the case of multiple solutions in the analysis of buckling. The basis of space functions generated by an initial solution on the

  . [ 6 ] LADEVÈZE P., New advances in the LArge Time INcrement method, New Advances in Computational Structural Mechanics, Ladevèze P., Zienkiewicz O.C. Eds., pp. 3-21, 1991. [ 7 ] MACIAS O.F. -LEMAIRE M., "Eléments Finis stochastiques et Fiabilité Application en mécanique de la rupture", Revue française de génie civil, Vol. 1 -No. 2,1997. [ 8 ] SHINOZUKA M., ASTILL J., "Random eigenvalue problems in structural mechanics",

scheme (see Figure1).The iterative procedure starts with an initial S 0 belonging to A d , for example the elastic response of the structure over [0, T].Then, successively, elements belonging to Γ Γ Γ Γ and to A d are built up until the practical convergence.


George Christodoulides
email: george@mycontent.gr

Anne Catherine Simon

Exploring Acoustic and Syntactic Cues to Prosodic Boundaries in French A Multi-Genre Corpus Study

Keywords: prosodic boundaries, pauses, prosodysyntax interface

This paper investigates the way prosody and syntactic structure combine in the perception of prosodic boundaries in French. Based on a 3.5-hour balanced corpus, we first analyse the distribution of boundary types across genres, and then examine the acoustic correlates of prosodic boundaries their relationship to linguistic features (part-of-speech categories and syntactic clauses).

INTRODUCTION

Prosodic segmentation is known to be fundamental for discourse comprehension ( [START_REF] Cutler | Prosody in the comprehension of spontaneous spoken discourse[END_REF], [START_REF] Watson | Intonational phrasing and constituency in language production and comprehension[END_REF]). However, there is no consensus on how prosodic boundaries (PB) should be defined and identified.

In order to model the prosodic segmentation of speech, several dimensions have to be taken into account. First, we need to decide on the degrees of PB strength (assuming that PBs are perceived as categorical and not gradual phenomena). Although most models on French prosody admit at least three degrees of PBs ( [START_REF] Rossi | L'intonation, le système du français: description et modélisation[END_REF], [START_REF] Mertens | Intonational grouping, boundaries and syntactic structure in French[END_REF], [START_REF] Di Cristo | Vers une modélisation de l'accentuation du français: première partie[END_REF]), most large-scale corpus annotations are limited to 1 or 2 degrees ( [START_REF]C-ORAL-ROM. Integrated Reference Corpora for Spoken Romance Languages[END_REF]). Second, we have to decide on which acoustic features to base the modelling of prosodic segmentation. Wagner & Watson [START_REF] Wagner | Experimental and theoretical advances in prosody: A review[END_REF] reported that silent pauses, duration, f 0 movement and phonation type are the most salient cues to PB, and those cues are known to be somewhat language-specific. In French, since the primary (final) accent is located on the last syllable of the unit, it co-occurs with the PB (see [START_REF] Cristo | Une approche intégrative des relations de l'accentuation au phrasé prosodique du français[END_REF]). However, this does not mean that French listeners cannot distinguish between prominence and PB (as evidenced experimentally by [START_REF] Astésano | Perception des frontières et des proéminences en français[END_REF]).

Third, we know that prosodic and linguistic (lexical-grammatical, syntactic) structures interact with each other. There is no consensus on how these structures are related: phonological approaches posit that grammar strongly constrains the size and structure of prosodic units (see for French [START_REF] Jun | A Phonological Model of French Intonation[END_REF], [START_REF] Kentner | A new approach to prosodic grouping[END_REF], [START_REF] Post | Tonal and phrasal structures in French intonation[END_REF]), while acoustic or interactionist approaches consider that speakers make strategic use of PB to avoid ambiguity and guide listeners' interpretation (e.g. [START_REF] Swerts | The Prosody of Information Units in Spontaneous Monologue[END_REF], [START_REF] Barth-Weingarten | The fuzziness of intonation units: Some theoretical considerations and a practical solution[END_REF]).

More recent studies tried to investigate to what extent signal-related properties and expectationbased (linguistic) information are responsible for the perception of PB by listeners, under natural conditions of speech production. In English, [START_REF] Cole | Signal-based and expectation-based factors in the perception of prosodic prominence[END_REF] demonstrated that the contribution of syntax to the perceived PB slightly overcomes the contribution of (prosodic) duration, both factors being partially dependent. Modelling the contribution of acoustic features and linguistic information to the prediction of PB in Swedish, [START_REF] Heldner | Exploring the Prosody-Syntax Interface in Conversations[END_REF] found that the combination of silent pause duration and word-final syllable rhyme duration yielded 86.2% correctly classified PBs, while the combination of content/function word distinction and POS gave 66.3% correct results.

Our contribution seeks to investigate strong and intermediate perceived PB, as well as their acoustic and linguistic correlates in a multi-genre corpus of French. The acoustic features studied include silent pauses (position and length), word-final syllable lengthening, pitch movement and relative pitch of the last syllables before a PB, while the linguistic features include syntactic units and POS categories.

METHOD

Material

This study is based on the LOCAS-F Corpus [START_REF] Degand | Unités discursives de base et leur périphérie gauche dans LOCAS-F, un corpus oral multigenres annoté[END_REF], which is a balanced corpus of spoken French with samples of 14 different speaking styles (discourse genres). Its duration is 3.5 hours and it contains 43.000 tokens. The discourse genres covered are the following: official speech in an academic setting [

Corpus processing

The corpus was orthographically transcribed within Praat [START_REF] Boersma | Praat: doing phonetics by computer[END_REF], and automatically phonetised and segmented into phones, syllables and words using the EasyAlign software [START_REF] Goldman | EasyAlign: an automatic phonetic alignment tool under Praat Proc. InterSpeech[END_REF]. All aligned transcriptions were manually corrected and several annotation layers were added to the corpus. In order to process this multi-level annotation, we used Praaline [START_REF] Christodoulides | Praaline: Integrating tools for speech corpus research[END_REF], a toolkit for corpus management, annotation, querying and visualization. Using its interface, we applied Prosogram [START_REF] Mertens | The ProsoGram: Semi-automatic transcription of prosody based on a tonal perception model[END_REF] for pitch stylisation on the entire corpus. Prosogram operates in two phases; for each syllable, vocalic nuclei are detected based on intensity and voicing. The f 0 curve on the nucleus is then stylised into a static or dynamic tone, using an algorithm that takes into account the perception of tones. The features extracted (duration, pitch, pitch movement etc.) were added to the database, and used to calculate the acoustic correlates (see section 3). The morphosyntactic annotation (see section 2.4) was also added to the database.

Prosodic boundaries annotation

The speech material was manually annotated for perceived prosodic boundaries by two experienced transcribers. Each word was marked as being followed by a strong PB (///), an intermediate PB (//), or as not followed by any boundary (0). The annotators used the code "hesi" to indicate that they perceive the speaker was hesitating: this includes filled pauses (e.g. "euh") and drawls.

A function was also attributed to each PB, based on the shape of the corresponding intonation contour. Four types of contours were used: C (continuation), T (final prosody), S (suspense) and F (focus). This annotation was primarily based on the annotators' perception; however they did have visual access to the pitch contour as displayed in Praat. In cases of disagreement, the annotators listened to the relevant section once again and agreed on the final PB and contour label.

POS and syntactic annotation

The corpus was annotated using the DisMo [START_REF] Christodoulides | DisMo: A morphosyntactic, disfluency and multi-word unit annotator. An evaluation on a corpus of French spontaneous and read speech[END_REF] morphosyntactic and disfluency tagger. DisMo attributes detailed part-of-speech tags on minimal tokens and multi-word expressions (on separate annotation levels), and performs an automatic detection of common types of disfluencies, using a combination of language resources and statistical models based on Conditional Random Fields. For this study we used the output of the automatic annotation without manual correction (DisMo typically attains 95-97% precision in POS-tagging spoken French corpora). We have based our analyses on the level of annotation that takes into account multi-word expressions.

Regarding syntactic structures, a manual annotation has been carried out by two expert linguists, based on the principles of dependency syntax for spoken French (outlined in [START_REF] Bilger | Propositions pour un étiquetage en 'séquences fonctionnelles[END_REF], [START_REF] Blanche-Benveniste | Trois remarques sur l'ordre des mots dans la langue parlée[END_REF], [START_REF] Degand | Mapping prosody and syntax as discourse strategies: How Basic Discourse Units vary across genres[END_REF]). The annotation results in two tiers: the encompassing level delimits dependency clauses, the maximal syntactic unit that is any governing element (most often a verb) and its governed elements; dependency clauses are analysed into functional sequences: Verb Sequence (SV), Subjet Sequence (SS), Dependent Sequence (SR), Incomplete Sequences (I), Adjuncts (A), Other (mostly non-verbal sequences), Discourse Markers (DM).

RESULTS AND DISCUSSION

Genres and prosodic boundaries

On average, there is a prosodic boundary at the end of 27.7% of the tokens in the corpus; 14.5% are of intermediate strength (//) and 13.1% are strong (///), while 2.9% are marked as hesitations (hesi). The distribution of prosodic boundary types presents significant variation across genres, as can be seen in Figure 1. This variation corresponds mainly to the extent the speaker has had the opportunity to prepare. We observe that there is a positive correlation between the degree of preparation and the number of strong PBs (///), with the sole exception of radio news bulletins (this can be explained, as the pressure to transmit a lot of information in a limited amount of time leads to a particular speaking style, with a high speech rate and few pauses; see [START_REF] Simon | Tendances prosodiques de la parole radiophonique[END_REF]). On the other hand, the number of perceived hesitations is greater in more spontaneous, non-prepared speaking genres. In only

Linguistic and syntactic cues to prosodic boundaries

Figure 2 shows the relationship between the types of PBs and the part-of-speech tag of the associated token. We observe that PBs occur mostly on lexical words (LEX: adjectives ADJ, nouns NOM, adverbs ADV, verbs VER and clitic pronouns), while less than 3% of PBs would occur on a clitic word (CLI).

An intermediate category (INT, including interrogative or relative pronouns PRO, negation particles ADV, conjunctions CON, determiners DET and auxiliary verbs VER) co-occurs with a PB in < 10% of potential positions. These findings seem to confirm the analysis in [START_REF] Goldman | Prominence perception and accent detection in French. A corpus-based account[END_REF]. Sequences may be rather long and complex syntactic units. As can be seen in Figure 3, in approximately 50% of the cases, verb sequences (SV) and subject sequences (SS) do not bear a PB, because they are followed by another sequence that is prosodically grouped with them (cf. word order in French, [START_REF] Blanche-Benveniste | Trois remarques sur l'ordre des mots dans la langue parlée[END_REF]). Conversely, the majority of dependent sequences (SR), Adjuncts and Others (sequences without verb) are followed by strong (///) prosodic boundary. Incomplete sequences are found inbetween these two tendencies.

Acoustic correlates to prosodic boundaries

For each potential PB position (last syllable of each token), several acoustic features were extracted:

 the duration of a subsequent silent pause, excluding the pauses at turn-taking;  relative duration: the duration of the last syllable divided by the average duration of 2…5 previous syllables;  relative pitch: the difference between the pitch (in semitones) of the last syllable and the average pitch of 2…5 previous syllables;  intra-syllabic pitch movement (in semitones) We observed that a local analysis (window of 2 syllables) is sufficient: the results presented here remain valid for windows of 3…5 syllables. A first analysis indicates that the presence or absence of a silent pause is the main feature that distinguishes between strong (///) and intermediate (//) PBs (see Figure 4). Strong PBs (///) are almost always followed by a silent pause, while this is rare for intermediate PBs (//); hesitations are occasionally followed by a pause. Syllable lengthening occurs on PBs regardless of their associated contour, and it is more pronounced in cases of Focus (Figure 5). Taking non-PB syllables as the baseline, PBs associated with the C (continuation) and F (focus) show a rising intonation, while T (final) PBs exhibit a falling intonation, followed by S (suspense) PBs, while hesitations are more similar to T (final) PBs (Figure 6). Focus (F) PBs have the most dynamic (pronounced) intrasyllabic pitch movement, followed by C (continuation). Strong continuation (///C) PBs are clearly marked with both inter-and intra-syllabic pitch movement, whereas intermediate continuation (//C) PBs are only marked with relative pitch differences. The interaction of the 3 most important parameters in marking different types and contours of prosodic boundaries can be readily seen in Figure 8.

CONCLUSION AND PERSPECTIVES

Our main findings confirm that silent pauses are a decisive cue to strong PBs in French, and that the use of other acoustic cues differs according to the strength (intermediate or strong) and function (continuation, finality, focus or suspense) of the PB. To some extent, hesitation markers behave like "suspense" PBs (lengthening and relative pitch). Linguistic cues are also decisive, as PBs co-occur with certain grammatical categories. Types of PB differ significantly across speech genres; this incites us to extend our modelling to macro-genres (e.g. interaction vs. monologue).

3

  cases does the number of strong PBs (///) exceed the number of intermediate PBs (//): ACA, HOM and POL, leading to what can be perceived as an over-segmented speech flow.

Figure 1 :

 1 Figure 1: Distribution of PBs per discourse genre.

Figure 2 :

 2 Figure 2: Relationship between PBs and POS tag of the token on which it occurs.

Figure 3 :

 3 Figure 3: Relationship between PBs and syntactic structures.

Figure 4 :

 4 Figure 4: Subsequent silent pause duration per PB type and contour.

Figure 5 :Figure 6 :

 56 Figure 5: Syllable lengthening (relative syllable duration) by PB type and contour.

Figure 7 :Figure 8 :

 78 Figure 7: Intra-syllabic pitch movement by PB type and contour.

Table 1 :

 1 Corpus description: number of samples, duration (min:sec), tokens, prosodic boundaries (strength 2 and 3), and syntactic units.

	aca], scientific conference presentation [conf], face-
	to-face dialogue in a formal [conv-f] or informal
	[conv-i] setting, political debate [deb], sermon /
	homily [hom], radio interview [int-rad], socio-
	linguistic interview [int-soc], informal TV interview
	[int-tv], monologue narration of life event [mono-n],
	semi-prepared radio monologue [mono-r], radio
	news bulletin [

news], political public address [pol], and neutral reading of a newspaper text

[read]

. The corpus composition is detailed in Table

1

.


George Christodoulides
email: george@mycontent.gr

Praaline: Integrating Tools for Speech Corpus Research

Keywords: corpus management, corpus annotation, data analysis and visualisation

This paper presents Praaline, an open-source software system for managing, annotating, analysing and visualising speech corpora. Researchers working with speech corpora are often faced with multiple tools and formats, and they need to work with ever-increasing amounts of data in a collaborative way. Praaline integrates and extends existing time-proven tools for spoken corpora analysis (Praat, Sonic Visualiser and a bridge to the R statistical package) in a modular system, facilitating automation and reuse. Users are exposed to an integrated, user-friendly interface from which to access multiple tools. Corpus metadata and annotations may be stored in a database, locally or remotely, and users can define the metadata and annotation structure. Users may run a customisable cascade of analysis steps, based on plug-ins and scripts, and update the database with the results. The corpus database may be queried, to produce aggregated data-sets. Praaline is extensible using Python or C++ plug-ins, while Praat and R scripts may be executed against the corpus data. A series of visualisations, editors and plug-ins are provided. Praaline is free software, released under the GPL license.

Introduction

This paper presents Praaline, an open-source software system for managing, annotating, analysing and visualising speech corpora. It attempts to address the needs of researchers working with speech corpora, who are often faced with multiple tools and formats and need to work with ever-increasing amounts of data in a collaborative way.

Praaline is based on and extends Praat (Boersma & Weenink 2014) and Sonic Visualiser [START_REF] Cannam | Sonic Visualiser: An open source application for viewing, analysing, and annotating music audio files[END_REF], and interfaces with the R statistical language (R Core Team 2013). Instead of creating a system from scratch, we have chosen to focus on the integration of open-source tools that are already widely-used in the community. As a result, researchers using Praaline can benefit from the features, extensions and contributions to these tools. This design allows for the reuse of many existing tools and scripts providing automated annotation and analyses.

Praaline is written in C++ using the Qt framework (Nokia) for both its core functions and user interface. It is cross-platform software that runs under Windows, Linux and Mac.

Recordings and corpus annotations may reside in a file system (cf. infra) and are managed through a relational database. It is possible to use SQLite for local installations or MySQL for client-server access. Praaline can import and export annotations in different formats, including Praat TextGrids, TranscriberAG [START_REF] Barras | Transcriber: a Free Tool for Segmenting, Labeling and Transcribing Speech[END_REF], ELAN [START_REF] Brugman | Annotating Multimedia/ Multi-modal resources with ELAN[END_REF] and EXMARaLDA Partitur (Schmidt, 2012) files. An integrated user interface permits the management of corpus data and metadata, annotation using editors or automated procedures, visualisation for the purposes of data exploration or demonstration, and querying the data for analysis. Praaline can be extended with plug-ins written in C++ or Python, and also supports executing scripts written in the Praat scripting language or for the R system against the corpus data and annotations.

Corpus Management

Users may construct their corpora from scratch or by importing a set of existing files (e.g. recordings and annotations). The user interface for defining and managing a corpus is shown in Figure 1. A corpus is organised in Communications (communicative situations) and Speakers. Each Communication may consist of several Recordings and Annotations. Speakers participate in Communications with specific Roles; and Annotations contain Annotation Levels (see section 3).

Using these basic concepts, users define the Annotation Structure and the Metadata Structure of their corpora. These definitions specify the information stored for each type of object. Corpus definitions are stored in a relational database and/or in XML files. It is possible to import and export the XML formats of EXMARaLDA's Coma editor. Users may also create projects and collaborate with colleagues using version control (i.e. compare and merge changes made to the corpus metadata and annotation).

Corpus metadata can be used to define sub-corpora, and selectively apply automated annotation procedures or queries to them, in other parts of the system. Aggregate data (e.g. number of samples, total recording time, counts of specific units like tokens or syllables) may be exported.

Annotation

While following the classical timeline model for annotating speech data, Praaline offers a key improvement: the option to define structural links between the annotation tiers, such as hierarchy, containment, attachment, controlled vocabularies etc. The annotation includes knowledge about the relationships between the different layers. An Annotation Level may contain any number of attributes, and relationships between Annotation Levels are encoded as part of the corpus structure. Praaline does not impose any specific set of Annotation Levels or attributes (sample sets are included to help users). Annotation attributes have associated data types, and may be marked as optional.

Annotations may be imported, entered manually using an editor, or obtained automatically by applying annotation plug-ins. Praaline allows the user to apply a cascade of annotation plug-ins on the entire corpus, or on subsets of it. Heterogeneous annotation utilities can be applied sequentially on the corpus. For example, a compiled plug-in for feature extraction, may be followed by a Praat script for prosodic annotation, and then by a POS tagger and an NLP parser in Python, while finally an R script is used to perform a statistical analysis. Praaline handles the data conversions needed to allow such combinations.

The Annotation Level and Annotation Attribute can represent timeline annotations, and also ensure integrity of the data. It is often the case that congruent annotation tiers are used (e.g. in Praat) to represent multiple features of the same object (e.g. a syllable, and an indication of whether it was perceived as prominent or not, or whether it is disfluent). While practical for small amounts of data, this system quickly leads to problems when corpora get larger: e.g. discrepancies in tier boundaries that should had been aligned according to the model; or data incoherence between tiers that are supposedly linked (e.g. phones-syllables). Since these relationships are explicitly captured explicitly in Praaline, it is possible to check the data integrity of a set of corpus annotations, possibly correcting them automatically.

A spreadsheet-like editor allows the user to simultaneously edit attributes belonging to several different Annotation Levels. For example, in a corpus for prosodic studies, we may discern at least three levels: phones, syllables and tokens (words). Each level may have a number of associated Attributes (e.g. syllables may be described by several automatically extracted prosodic features). The editor (Figure 2) allows the user to view and update a selection of attributes from each level; it is The Annotation Level -Annotation Attribute data model translates directly into a relational SQL database. Each Annotation Level is a table, and Annotation Attributes are columns. Praaline uses this system to provide querying functionality (see section 5, infra). In addition to the possibilities offered by the user interface and through scripting, an advanced user can directly query Praaline's SQL database. It is important to note that the schema is dynamic and adapted to each corpus definition (with the exception of system tables that are always present). Finally, it is envisaged that this corpus metadata and annotation database can be linked to web interface to provide outside users with limited access to the corpus.

Visualisation

The visualisation module of Praaline is based on Sonic Visualiser [START_REF] Cannam | Sonic Visualiser: An open source application for viewing, analysing, and annotating music audio files[END_REF]. Visualisations can display waveforms, spectrograms, melodic spectrograms, any combination of annotation levels and tiers, numerical data (points, curves, histograms, colour-coded regions etc.). Plug-ins may add visualisations: for example, we have adapted Prosogram [START_REF] Mertens | The Prosogram: Semi-Automatic Transcription of Prosody based on a Tonal Perception Model[END_REF]) do display prosodic analysis information.

These elements can be combined to present annotations in a format appropriate for each type of investigation. For example, a dialogue involving multiple speakers can be visualised in speaker turns. In Figure 3, we show a colour-coded annotation of prominent syllables (along with a waveform, spectrogram, intensity, f0, and transcription). As can be seen in Figure 4, in order Figure 3: A visualization of prominent syllables with colour coding Figure 4: A visualisation for comparing the prosody of a speaker and an interpreter using a multi-channel recording and Prosogram [START_REF] Mertens | The Prosogram: Semi-Automatic Transcription of Prosody based on a Tonal Perception Model[END_REF] to study the prosody of simultaneous interpreting, we used a Praaline visualisation comparing the prosodic characteristic of the speaker's and the interpreter's speech, based on [START_REF] Mertens | The Prosogram: Semi-Automatic Transcription of Prosody based on a Tonal Perception Model[END_REF], and calculating similarity measures (cf. DeLooze & Rauzy 2011; Christodoulides 2013).

Querying

Corpus annotations are stored in a relational database, the schema of which is dynamically constructed based on the annotation structure definition. Annotation levels correspond to database tables and annotation tiers to columns. The relationships between the different levels are also encoded. Praaline simplifies the conversion of structured annotation into two-dimensional tables suitable for statistical analysis. SQL queries can be used to select and summarise a subset of the corpus.

It is possible to construct a Dataset by an interactive query editor. For each attribute, functions can be applied to calculate aggregate measures (e.g. sum, mean, standard deviation, etc.); a filter can be used to limit the returned values; and a normalisation transformation (e.g. z-score over all samples of the same sub-corpus) may be applied. In this way, researchers may more easily explore and analyse the information in the corpus, in an interactive way and without necessarily resorting to scripts.

Furthermore, concordances can be extracted using Praaline, based on simple value filters or regular expressions (search term, left and right context). The results of such queries are objects that can be further processed, using the statistical analysis module, or exported for use with other software.

Statistical Analysis

Praaline interfaces with the R statistical environment, through the Rcpp package [START_REF] Eddelbuettel | Rcpp: Seamless R and C++ Integration[END_REF]. Corpus annotations (as well as the results of corpus queries) are exposed to R as data frames, allowing for the use of R commands, scripts and extensions to analyse the data. Praaline provides a two-way link between the corpus and R: the results of analyses performed using R can be posted back into the corpus database, by adding to or updating an existing annotation level, or by creating a new annotation level.

Programmability

Praaline can be extended with plug-ins, written in C++ using a simple API and compiled. This method is suitable for plug-ins adding substantial functionality to the system. Praaline is also scriptable with Python, by providing bindings to its core functionality. Praat scripts can be executed, in which case the corpus data are available as (virtual) Praat objects. Finally it is possible to evaluate R scripts accessing corpus data in the form of data frames. A programmer may mix the following techniques in order to use the tool that is best suited to each task. Currently available plug-ins include the following:  An adapted version of [START_REF] Mertens | The Prosogram: Semi-Automatic Transcription of Prosody based on a Tonal Perception Model[END_REF] Prosogram.  An automatic rule-based syllabifier, based on the increasing sonority principle (a list of allowed syllable onsets for each language is required).

 A plug-in version of the DisMo morphosyntactic annotator, for English and French [START_REF] Christodoulides | DisMo DisMo: A Morphosyntactic, Disfluency and Multi-Word Unit Annotator. An Evaluation on a Corpus of French Spontaneous and Read Speech[END_REF].  A plug-in for calculating similarity and convergence measures in dialogue, based on the methodology of De Looze & Rauzy (2011).

Conclusion and Future Work

Praaline is currently under active development, and is made available to the research community under the GPL licence. It can be downloaded from www.praaline.org. We welcome feedback on the functionality and future directions of the project. We are exploring the development of a bridge between Praaline databases and open-source content management systems, in order to facilitate the publishing of corpus data to the web.

Figure 1 :

 1 Figure 1: Corpus management mode (left pane: corpus structure; middle: metadata; right: annotation structure)