THE PEDAGOGICAL IMPLICATIONS OF VARIABILITY IN TRANSCRIPTION: THE CASE OF [i] AND [u]

Keywords: transcription, unstressed high vowels, syllabi cation, rhythm, variability

e problem of variability in transcription is raised in this paper through the analysis of the two sounds !"#$and !%#$in English, which appear in pronunciation dictionaries. e distribution for these sounds is not clear, the dictionaries often give di erent transcriptions and the literature does not help us with rules concerning the apparition of these sounds.

is paper shows that from the study of the distribution of !"#$ and !%#$ and of the variants that are given in the two reference pronunciation dictionaries (the Cambridge English Pronunciation Dictionary, 17th ed. and the Longman Pronunciation Dictionary, 3rd ed.) rules can be drawn. We show that as Wells mentions in LPD3 (2008, p. 892), there are "implications for syllabi cation […] and for rhythm". Morphology is also dealt with since the question of pre xes for example is a determining factor in the pronunciation of initial unstressed syllables. is study sheds light on many obscure details and contributes to the eld of teaching English pronunciation because rules are given that enable the teacher and the student to understand the distribution of !"#$and !%#$and the di erent variants associated with them.

Introduction

When teaching transcription or pronunciation to learners of English, teachers sometimes have to answer di cult questions and may look to pronunciation dictionaries for answers. e aim of this paper is to describe the distribution of !"#$ and !%#, both tense and short vowels as opposed to tense long /"&/ and /%&/ and to lax short /'/ and /(/. is is a di cult subject for students because they never know when these sounds should be pronounced and used in transcription. Our study was based on di erent transcriptions of these two sounds in two reference pronunciation dictionaries: Jones (2006), edited by Roach and colleagues, which will be referred to as CEPD17 (Cambridge English Pronunciation Dictionary, 17th edition) and [START_REF] Wells | Longman pronunciation dictionary[END_REF] which will be referred to as LPD3 (Longman Pronunciation Dictionary, 3rd edition).

is paper presents the theoretical background to the problem and analyses the di erent positions in which !"#$ and !%#$ appear in dictionary transcriptions. It then discusses the pedagogical issues raised and scope for future research.

In 1962, Gimson mentioned that "/'/ is increasingly replaced in the speech of younger generations by a short variety of /"&/" (p. 105). [START_REF] Wells | Accents of English[END_REF] was the rst to discuss the 'happY vowel'. He observes that "there is an increasing tendency throughout the English-speaking world to use a closer quality [i(:)], and for speakers to feel intuitively that happy belongs with FLEECE rather than with KIT." (p. 294). In an article entitled "Happy Land Reconnoitred", Windsor Lewis (1990) also mentions the tensing of nal /'/. 'HappY-tensing' is now a well-known phenomenon and several acoustic studies con rmed the tensing of nal /'/ in certain dialects of British English including the standard variety of English [START_REF] Fabricius | Weak vowels in modern RP: an acoustic study of happYtensing and KIT/schwa shift[END_REF][START_REF] Harrington | An acoustic analysis of 'happY-tensing' in the Queen's Christmas broadcasts[END_REF][START_REF] Lee | Dialectal variations in English happY-tensing[END_REF]. However, tensing applies not only in nal position. It also a ects /(/, as mentioned in the two pronunciation dictionaries and in [START_REF] Roach | English phonetics and phonology[END_REF].

What the authors agree about is that ["] and [%] are found in weak syllables only. Roach (2000, p. 84) explains that box entitled "Neutralization", Wells explains that !"#$ and !%#$ are used to represent the neutralization of the opposition between /"&/ and /'/ and /%&/ and /(/ respectively: "One type of neutralization is symbolized explicitly in LPD3 by the use of the symbols i and u" (LPD3, p. 539). Although these are phones and we are therefore in the eld of phonetics and not phonology, slashes and not brackets shall be used here for simplicity, in keeping with Roach (the editor of CEPD17) and Wells (in LPD3).

If )") and )%) neutralize these oppositions, the question arises of why there are two pronunciations for ecumenism (/'*+,%&-./'0-/ and /"&*+,%&-./'0-/). Wells provides a clue: "[…] some speakers use ', some "&, some use something intermediate or indeterminate, and some uctuate between the two possibilities. Modern pronunciation dictionaries use the symbol ", which re ects this" (LPD3, p. 539). erefore, when the two symbols /"&/ and /'/ are given, it probably means that there is no uctuation and we hear either /"&/ or /'/ and not something in between. However, this is not entirely clear.

is problem with the transcription of ecumenism is recurrent. Not only do entries for many words have the two variants /'/ and /"&/, there is also a noticeable di erence between the two dictionaries, where transcriptions vary a good deal for )") and )%). For this reason, I have decided to try and nd some order in this, hoping to be able to establish some rules or to at least identify constants which would help us to understand more precisely when )") and )%) should be used in transcription. Although Roach and Wells do mention these symbols in the introductions of the two dictionaries, they do not give rules enabling the student or the teacher of phonetics to know exactly when )") and )%) should be transcribed, and therefore when an intermediate or indeterminate vowel in between )') and )"&) and )() and ) %&) should be pronounced. e literature is rather poor on this subject and apart from the acoustic studies mentioned above, no study to our knowledge deals with the exact distribution of )") and )%).

Di erent environments

Using the CD ROMs from the two pronunciation dictionaries, I did a search according to the di erent environments in which )") and )%) are said to appear. ey are supposed to appear in the same environments and )%) in certain other contexts: "% is found not only in " environments, but also in certain others, for example, in one pronunciation of stimulate *12'-,%34'2" (Wells,LPD3,p. 539).

Final position

For )"), all the authors agree on the 'happY-tensing' as in valley )*563") or happy )*768")9 Roach (CEPD17 §2.9, p. xiv) also mentions that: word-nal )%&) and )"&) are possible both with stress (grandee, bamboo) and without stress (Hindi, argue) although in the unstressed case it is often not possible to draw a clear line between )"&) and )"), or between )%&) and )%).

Contrary to 'happY-tensing', this constitutes a shortening of the nal vowel.

A search through the database con rms that for )%), all the words ending with -ue, -ew, -u, or unstressed -oo are pronounced )%&):$Andrew, avenue, cuckoo, curfew, guru, Hebrew, issue, impromptu, jujitsu, Lulu, menu, nephew, rescue, residue, sinew, statue, tissue, venue, virtue, Zulu. Although Wells says that )%) appears in the same environments as )"), the nal position does not seem to conform to this. Final )%) seems to appear only in unstressed grammatical words where we nd the two variants )%) and ).): you, into, to…

As for )"), a consensus exists on 'happY-tensing' i.e. at the end of words. However, this does not always occur when word-nal)") is unstressed, eg. Hindi, for which CEPD17 and LPD3 give the two variants )") and )"&)9 is word seems to be the only one apart from words spelt with nal non stressed -ee (exceptions therefore) 1 . For these nal non stressed -ee words, the two dictionaries do not give the two variants; the endings are pronounced either )") or )"&). e choice seems to depend on rhythm, on the accentual pattern of the word:

-)"&) is found when the word is stressed on the antepenultimate syllable (stress pattern /100/ 2 ): 'pedigree, cor'roboree, ' jubilee, 'apogee. -)") is found when the stress is on the penultimate syllable of the word (stress pattern /10/): 'co ee, 'to ee, com'mittee, ' levee, 'yankee.

Windsor Lewis (blog) mentions rhythmic contrast as a possible in uence.

To conclude concerning nal unstressed position, for the region of i the neutralized vowel )") is assigned except in words ending with unstressed -ee showing a /100/ stress pattern. For u, tense long )%&) is heard in lexical words, the neutralized vowel )%) is only assigned to grammatical words.

Medial position

Whereas 'happY-tensing' is an acknowledged phenomenon in modern English, the tensing of non-nal unstressed vowels has not attracted the attention of theoretical practitioners. Following the same method as for nal vowels, I searched the two dictionaries for )") and )%) in medial position.

1

Exceptions because -ee is an accented ending so words ending with -ee are normally stressed on the nal syllable. 2 1 represents primary stress and 0 zero stress (2 represents secondary stress).

Compounds & prevocalic position

At the end of part of a compound word )")$is used, as in bodyguard )*;<=">?&=) for instance. is is logical since the rst part of the compound undergoes 'happY-tensing'. is is not the case for )%), as it does not appear in nal position in lexical words. In an unstressed prevocalic position, )") and )%) are also always assigned, for example: piano )8"*6/.(),$ geography$ $ $ $ $ $ )=@"*<>A.B),$in uenza$)C'/D%*4/0.),$graduation$)C>A6=,%*4'E . /). is leads to the problem of -ion type endings, since in these endings, the rst vowel is in an unstressed prevocalic position.

-ion type endings Roach (2000, p. 85) explains that "the su xes spelt 'iate', 'ious' when they have two syllables, eg. appreciate, hilarious" will be pronounced with )"4'2) and )".1). [START_REF] Wells | Longman pronunciation dictionary[END_REF] also gives the examples of graduation )C>A6=,%*4'E/) and glorious )*>3F&A".1) . ese are words with -ion type endings 3 . Roach refers to the number of syllables, which seems to be a very important aspect; -ion type endings are considered as monosyllabic endings in most pedagogical books. When students are taught that -ion type endings are stress-imposing endings, they learn that the stress in such words bears on the syllable preceding the ending, and the stress pattern is /10/. is means that the ending counts as only one syllable. However, Roach attributes two syllables to -ious, to take one example. erefore, a useful analysis could be made of the transcriptions of -ion type endings in the two dictionaries. If the sounds )") or )%)$ occur, it means they are disyllabic endings and the rules thus have to be revised. In CEPD17, )") and )%) are found, for example, in scorpion )*1+F&8"./) or beauteous )*;,%&2".1), acrimonious )C6+A'*-.(/".1), cardiac )*+?&="6+), cordial )*+F&=".3), habitual )7.*;'2E%.3), etc… (CEPD17). ese examples show that -ion type endings are disyllabic endings, )") and )%) counting as one syllable. e stress pattern should be /100/ and the rst vowel of the ending is transcribed )") or )%) since it is placed before another vowel (prevocalic position). However, we need to distinguish between the phonological and the phonetic level. Although -ion type endings are disyllabic on a phonological level, they are not always disyllabic phonetically.

e words above are transcribed in LPD3 with the symbol [ G ], indicating a possible compression: acrimonious )C6+A'*-.(/"$G .1), habitual )7.*;'2E%$G .3) for example. is means that acrimonious is pronounced !C6+A'*-.(/,.1# and is transcribed )C6+A'*-.(/"$ G .1), habitual is pronounced !7.*;'2EH.3# 3 ese words include endings in {i,e,u}V(C) (where V represents a vowel and C a consonant), such as -ia, -iac, -ial, -ian, -iate, -iel, -ient, -io, -iod, -ion, -ious, -ium, -ius, -eal, -ean, -eon, -eous, -ual, -uar, -uate, -uence, -uous, etc… . and transcribed )7.*;'2E%$ G .3).

e phenomenon of synaeresis takes place: two adjacent unstressed vowels are pronounced as one (cf. Fournier, 2010, p. 186). In the case of -ion type endings, the rst vowel of the ending ()") or )%)) is transformed into the corresponding semi-vowel (),) or )H)).

In some words like action )*6+E/), courageous )+.*A4'=@.1), precious )*8A4E.1), crucial )*+A%&E.3), Belgium )*;43=@.-), and words with two variants like acacia ).*+4'E.)I).*+4'1".), amnesia ).-*/"&0".)I).-*/"&@.), consortium )+./*1F&2".-)I)+./*1F&E.-), a second step takes place. is step is exempli ed in the rst variant above for the words which have two variants.

e second step consists in an assimilation and more precisely a palatalisation. For example, )1) + ),) becomes )E) as in acacia ).*+4'E.), action )*6+E/), precious )*8A4E.1) or )0) + ),) becomes )@), as in amnesia ).-*/"&@.), courageous )+.*A4'=@.1) or Belgium )*;43=@.-). In such cases, the -ion type ending is pronounced as one syllable, and is therefore monosyllabic. However, this is due to the assimilation which is a consequence of syllable compression, i.e. phonetic phenomena. A syllable compression is the total reduction of a syllable. It occurs alongside palatalisations, as in the cases mentioned here, but also in words like history or evening which are pronounced with two syllables

)*7'12A")$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ )*"&5/'J)9
is is why the phonetic and the phonological levels have to be distinguished. It is interesting to note that some words only have one variant, the compressed pronunciation. ey may be very common words and it may be a question of frequency, but these are only hypotheses.

Adding a su x

Adding a su x to a word ending with )") or )%&) is another problematical issue, especially in the region of u. When a su x beginning with a vowel is added to )"), then )") is in medial prevocalic position, so there is no change: happier )*768".), easiest )*"&1".12), carrying )*+6A"'J). However, when u is in nal position, we nd tense long )%&) and not tense short )%). Logically, with the adding of a vowel-initial su x, )%&) is in a prevocalic position, and should therefore be transformed into neutralized )%) (shortening of the tense long vowel). is is not always the case:

-when a short ending is added, )%&) remains: mildewy )*-'3=,%&"), sinewy )*1'/,%&"), interviewer )*'/2.5,%&.), issuer )*'E%&.). -and when a longer ending is added, such as -ary, -ance or -able, then neutralized )%) appears: statuary )*1262,%.A"), issuance )*'E,%./1), issuable )*'E,%.;3).

is does not seem to be linked to the number of syllables, because -able is considered monosyllabic, as is -ance. However, they are longer than -y or -er, which are phonetically composed of one vowel only, and this may be the reason why they trigger a shortening of )%&) into )%)9

If a su x beginning with a consonant is added, Windsor Lewis explains that "unlike the su xes -less, -ness, etc., the ending -ly when added to happy-type words in GB only permits their nal -y to be schwa ).) or the SIT vowel )')" (blog). Consequently, if a consonant-initial su x is added, lax )() should occur as it is no longer nal or prevocalic. As far as u is concerned, in the two dictionaries only one word exhibits this: argument. Logically, CEPD17 gives )() or ).), but LPD3 gives )%) or ).). is is one of the "certain other contexts" like stimulate mentioned by Wells (LPD 3, p. 539) which will be discussed in the next section of this paper. For examples with nal tense )"), the results are very confusing. Di erent transcriptions are found with the di erent endings: LPD:

)") + -hood 4 , -ment 5 , -ness 6 , -wise 7

)')I).) + -ful 8 , -less 9 , -ly 10 EPD:

)") + -hood, -less, -wise

)') + -ful, -ness, -ment

)')I).) + -ly, -ful (beautiful and bountiful) erefore, the two dictionaries only agree on the transcriptions with -ly ()')) and -hood ()")). is con rms Windsor Lewis's statement about -ly, but not about the other endings.

Before a consonant

Medial position before a consonant in the middle of a word with no particular ending added was also analysed: )") never appears before a consonant, and )%) never appears in CEPD17 but it does appear in LPD3.

ese are the "certain other contexts like stimulate" indicated by Wells (2008, p. 539). erefore, I tried to de ne the contexts in which )%) appears in LPD3, because at rst sight it is very complex. Many di erent variants were found: , bountiful, dutiful, fanciful, merciful, pitiful, plentiful, unmerciful. 9 Merciless, penniless, pitiless. 10 Up to 451 words such as arbitrarily, momentarily, necessarily, etc…

-)%)I).) LPD3 (CEPD17: )()I).)): stimulate )*12'-,%34'2)$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
)*12'-,.34'2), tuberculosis )2,%C;K&+,%*3.(1'1)$ )2,%C;K&+,.*3.(1'1), accumulation ).C+,%&-,%*34'E/)$).C+,%&-,.*34'E/)$ -)()I).) LPD3 & CEPD17: contributive )+./*2A';,(2'5)$)+./*2A';,.2'5), accuracy )*6+,(A.1")$)*6+,.A.1"), ridiculous )A'*='+,(3.1)$)A'*='+,.3.1) -)() LPD3 (CEPD17: )()I).)): acidulous ).*1'=,(3.1), tributary

)*2A';,(2$G .A"/ 11 -)%&) LPD3 & CEPD17: prosecutor$ )*8A<1'+,%&2.), absolutism )*6;1.3%&2'0-), executable )*4+1'+,%&2.;3) -)%)I)() LPD3 (CEPD17: )()I).)): 'postulate (vb) )*8<12,%34'2)$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ )*8<12E(34'2)
For CEPD17, things are quite clear. )%) is never found in medial position, it is either )()I).) or )%&) and this also holds for the same words in LPD. Nonetheless, LPD3 seems to follow a much more precise logic. Series of words deriving from the same base were examined: words like ac'cumulable )()I).), ac'cumulate )%)I).), ac'cumulative )()I).), ac,cumu' lation )%)I ).), ac'cumulator )%)I).)$ or a'cidula )()I).), a'cidulate )%)I).), a'cidulous )()I).). Words in -ate help us understand this logic : verbs in -ate are pronounced with the diphthong )4'), whereas in nouns, -ate is reduced and pronounced$).2) or )'2). LPD3 proposes 'conjugate (adj, noun) )()I).), 'conjugate (vb) )%)I).), ar'ticulate (adj) )()I).) and ar'ticulate (vb) )%)I).). In verbs, u is pronounced with tense short )%)L but with lax )() in nouns.

is means that rhythm plays an important role: the pronunciation of u depends on the reduction of the following vowel. Other examples follow the same pattern: tu'bercular, tu'berculin, tu'berculous )()I).)$(u is followed by a reduced vowel), tu,bercu' losis )%)I).) (the vowel o afterwards is not reduced); 'tumulus )()I)./ (the vowel following unstressed u is reduced to schwa), 'tumuli )%)I).) (the vowel following unstressed u is a diphthong).

erefore, when u is in medial position and followed by a stressed syllable or a diphthong, it is pronounced )%) or ).) as in 'adulate (vb) ) *6=,%34'2), ,acu'punture )C6+,%*8MJ+2E.), and when it is followed by a weak syllable, it is reduced to )() or ).), as in e'masculate (adj) )'*-61+,(3.2), 'accuracy )*6+,(A.1"), a'cidulous ).*1'=,(3.1/12 .

)%&$) in medial position? e problem of )%&) in medial position is still an enigma, for example )%&) in words like prosecutor )*8A<1'+,%&2.) , prosecutorial )C8A<1'+,%&*2F&A".3), absolutism )*6;1.3%&2'0-), executable )*4+1'+,%&2.;3), acoustician )C6+%&*12'E/). Our initial hypothesis was that this was due to derivation, because all these words derive from words with )%&): prosecute )*8A<1'+,%&2), absolute )*6;1.3%&2), execute )*4+1'+,%&2), acoustics ).*+%&12'+1/. However, a few similar words are pronounced with )()I).): executive )'*>04+,(2'5)$ $ $ $ $ $ $ $ $ $ $ )'*>04+,.2'5) , distributor )='*12A';,(2.)$)='*12A';,.2.). e word constitutive sheds light on the issue, as it has two variants where rhythm is a determining factor: )+./*12'2,(2'5) with stress pattern /100/ and )*+</12'2,%&2'5) when stress pattern /1000/. If )%&) is preceded by an unstressed syllable, )%&) seems to occur, as in )*+</12'2,%&2'5) with a /1000/ stress pattern or prosecutorial )C8A<1'+,%&*2F&A".3). If a stressed syllable precedes, )() or ).)$are found, as in )+./*12'2,(2'5) with a /100/ stress pattern. e tense long pronunciation )%&) seems to play a rhythmic role, easing the pronunciation if there are several unstressed syllables in a row.

Initial Syllables

Initial position is the most complex and this part of our study is still in progress. Even though no clear-cut systemic pattern can be distinguished at this stage of the investigation, a few conclusions can be drawn.

)"$) in initial syllables

As far as )") is concerned, Roach (2000, p. 85) talks about the pre xes re-, pre-, de-, when followed by a vowel, claiming that we can nd )") "in a pre x such as those spelt 're', 'pre', 'de' if it precedes a vowel and is unstressed, eg react, preoccupied, deactivate." is is the medial prevocalic position. In CEPD17, when these pre xes are followed by a consonant, /'/ is assigned. CEPD17 only gives the neutralized vowel )") in initial position in one word: Ebonics. However, we were unable to identify any shared features across the many variants given in CEPD17: most words can be pronounced with either )') or ).).

In LPD, the pre xes be-, de-, pre-and re-are transcribed with )"), as explained in the introduction of the dictionary: "Entries for words containing be-, de-, e-, pre-, re-, and se-(also rede-, unre-etc.) have been simpli ed. When unstressed, these pre xes are now shown with i. is re ects the fact that, like words ending in ", such as happy, they may be pronounced indi erently with ' or "&9 ( ese pre xes also have variants with ., shown explicitly)." (LPD3, p. xiii). erefore, )") is used in decipher, begin, prefer, repair for example, but also in words beginning with be-or de-where beand de-do not seem to be pre xes, as in December, begonia or benevolence for instance. As for the pre x se-, it is not transcribed )") in LPD3 but )') or ).), nor are other pre xes such as em-, en-or di-(also pronounced )=N')). When there is no pre x, )") is only found in LPD3 in "begonia type" words (those words beginning with be-or de-but which are not pre xed). In these, there are many variants and derivation may be a key factor:

-)') or ).) occur when there is no obvious derivation: civility, velocity, vivacity, -)'), )4) or ).) occur in melodious, probably because it is derived from melody with )4), -)') or )"&) occur in velaric or venality because they are derived from words with )"&), respectively velar and venal. -only )') with no variant is given for viscosity for example, probably because closed syllables are typical laxing contexts.

To conclude, there are no shared features for words beginning with e-, neither in CEPD17 nor in LPD3. All the combinations of variants were found for these words: EPD:

)'L"&)$)'L"&L4)$)')$)"&)$)'L"&L.)$)"&L4)$)'L.L4)$)'L4)$)'L.L4L"&)$ LPD: )"L.)$)'L.)$)")$)'L"&)$)'L"&L.)$)"L.L"&)$)"L.L4)$)'L.L4L"&)
Words in e -seem to be transcribed )"L.L4) in LPD3, except e ect and derived words and e cient, e ciency. Words in er-seem to be pronounced )'L.) (erupt, eradicate, erase, erotic, erode). ese conclusions are far from satisfactory. e roles of morphology and of rhythm merit further investigation.

Initial )%$)

It is di cult to draw conclusions for initial )%). In CEPD17, )%) is only found in one word: cupidity. In all other words )%&) is used, except for a few words where the two variants )%&)I)() are given: words in tu-(12 words tubercular and derived forms, tumescent, tumidity, tumultuous, Tunisia, tutorial), in su-(8 words: Sudan, sudanic, super ous, superior, superlative, supremacy, supreme) 13 , words in ru-(3 words: rubato, rubeola, rubidium) 14 and bulimia, dubiety, museum, pubescence. In LPD, there are more variants: most words are pronounced with )%), although 5 words are pronounced with )%) or ).) : bulimia and tubercular and derived forms and 6 words are pronounced with )%&) or )%) (humane, municipality, museum, supreme, unite and unique). e words in lu-(except proper nouns) and 5 other words are pronounced )%&) with no variant: lubricious, lubricity, lucidity, lunation, nutation, numismatic, putrescence, putridity, ufology.

Conclusion

e distribution of the three pronunciation variants is very complicated. Full understanding of the behaviour of English high vowels is not possible without taking into account an impressive range of parameters: syllabi cation, rhythm, derivation, morphology. Much research remains to be done. Nevertheless, this study contributes to the description of presentday English pronunciation for pedagogical purposes. First, this study shows that -ion type endings are phonologically 2-syllable endings. Secondly, )") and )%) are very di erent. ey are both found in unstressed positions but they do not appear in the same environments at all, except for the prevocalic position. erefore, if a phonetics teacher has to explain the environments in which these two neutralized vowels appear, they can explain that: $ -)") appears word-nally ('happY-tensing') except in words in -ee with a stress pattern /100/; -nal tense )") followed by -hood remains the same vowel. In other cases, )') is the best transcription; -in the pre xes be-, re-, pre-and de-, )") also appears. In all other cases, students should transcribe )') or ).).

$ -)%) is found in nal position only in grammatical words. Otherwise, )%&) is pronounced.

$ -)%) is also found word-medially when it replaces nal )%&) followed by a long ending.

$ -)%) is also the right transcription when u is followed by a stressed syllable or a diphthong and not derived from a word in )%&).

$ -)%) is found in the initial syllable in most words.

Many questions remain unanswered. Initial position should be investigated further, as should pre xes. Cases where )%) should be pronounced or transcribed in initial position still remain unclear. Nonetheless, pronunciation dictionaries are precious tools. e inclusion of these pronunciation variants in dictionaries has pedagogical interest because, instead of neutralizing the opposition between )"&) and )') and )%&) and )(), they seem to introduce a new type of contrast. is issue deserves further scrutiny, and perception and acoustic studies might be useful to this end.

vowels are commonly found in weak syllables, one close front (in the general region of /"&/ and /'/) and the other close back rounded (in the general region of /%&/ and /(/. In strong syllables it is comparatively easy to distinguish /"&/ from /'/ and /%&/ from /(/, but in weak syllables the di erence is not so clear.

symbol $G indicates possible syllable compression.

It is to be noted that argument is an exception to this rule since u in this word is transcribed in LPD3 with /u/ and is followed by a weak syllable. is may be due to the morphology (adding of a su x).

sudarium is pronounced with )%&) only.


Pauline Welby
email: pauline.welby@lpl-aix.fr

Robert Espesser
email: robert.espesser@lpl-aix.fr

Christine Meunier
email: christine.meunier@lpl-aix.fr

In search of intonational cues to content word beginnings in conversational speech

Keywords: intonational cues, word segmentation, lexical access, conversational speech

We used an annotated conversational French speech corpus to 1. investigate whether the intonational rises that occur at the beginning of French content words in read speech (APRs) are also present in spontaneous speech and therefore available as cues to word segmentation and lexical access, and 2. test two measures of characterizing intonation patterns using automatically extracted F0 and time values. The two measures tested both proved problematic: they were sensitive to the segmental composition of the critical region. We found no evidence that APRs are reliably present in the corpus as a whole, although we suggest that they may be present in particular types of conversational speech.

Introduction

There is growing evidence from a number of languages that listeners use intonational patterns as cues to word segmentation, the process of locating word boundaries in the speech stream, and to lexical access, the retrieval of words from the mental lexicon. In the present study, we examine whether the intonational cues shown to be present in earlier studies of French read speech are also present in spontaneous, conversational speech.

French accentual phrases (APs) that are not utterance-final are typically realized with fundamental frequency (F0) rise whose peak is aligned to the last syllable of the AP (the late rise, final rise or primary accent). If an AP is long enough, another rise is often, but not always, realized toward the beginning of the AP. (see [START_REF] Jun | Realizations of Accentual Phrase in French[END_REF][START_REF] Welby | The slaying of Lady Mondegreen, being a study of French tonal association and alignment and their role in speech segmentation[END_REF][START_REF] Welby | French intonational structure: Evidence from tonal alignment[END_REF] and references therein). This early rise (initial rise or secondary accent) does not typically contribute to the meaning (but see [START_REF] Astésano | Functions of the French initial accent: A preliminary study[END_REF]). In short APs, a single rise combining the characteristics of the late rise and the early rise may be realized. [START_REF] Welby | The slaying of Lady Mondegreen, being a study of French tonal association and alignment and their role in speech segmentation[END_REF][START_REF] Welby | The role of early fundamental frequency rises and elbows in French word segmentation[END_REF] [START_REF] Welby | The slaying of Lady Mondegreen, being a study of French tonal association and alignment and their role in speech segmentation[END_REF][START_REF] Welby | The role of early fundamental frequency rises and elbows in French word segmentation[END_REF] showed that French listeners use the early rise to locate content-word beginnings in an offline identification task, as suggested by [START_REF] Vaissière | Langues, prosodies et syntaxe[END_REF][START_REF] Di Cristo | Vers une modélisation de l'accentuation du français : seconde partie[END_REF]. Listeners interpreted sequences like [me.la.mo~.din] as a single 4syllable content (non)word mélamondine when the early rise began at the first syllable [me] and as a proclitic function word followed by a 3-syllable content (non)word mes lamondines 'my lamondines' when the rise began at the second syllable [la].

These results were recently extended [START_REF] Spinelli | Fine-grained access to targets and competitors in phonemically identical spoken sequences: The case of French elision[END_REF][START_REF] Spinelli | An intonational cue to word segmentation in phonemically identical sequences[END_REF], using an online task (cross-modal priming with lexical decision) and resynthesis of the F0 of real word stimuli to show that these AP-initial boundary rises (APRs), which include both early rises and the single rises found in short APs, speed lexical access (see also [START_REF] Michelas | Accentual Phrase boundaries and lexical access in French[END_REF]).

Researchers working on other languages have also found evidence for the use of intonational cues to word boundaries (e.g., [START_REF] Kim | The use of phrase-level prosodic information in lexical segmentation: Evidence from wordspotting experiments in Korean[END_REF] for Korean, and [START_REF] Warner | Intonational structure as a word-boundary cue in Tokyo Japanese[END_REF] for Japanese), and these studies include analyses of speech corpora.

The earlier studies of French are all based on read speech, and the perception studies examine pairs of phonemically identical sequences. For example, Spinelli et al. [START_REF] Spinelli | Fine-grained access to targets and competitors in phonemically identical spoken sequences: The case of French elision[END_REF][START_REF] Spinelli | An intonational cue to word segmentation in phonemically identical sequences[END_REF] compared 30 pairs of items like l'affiche 'the poster'/ la fiche 'the sheet' and l'allocution 'the (short) speech'/la locution 'the phrase, idiom', which differ systematically in the alignment of the AP-initial boundary rise (APR). In read speech, the APR consistently begins at the beginning of a content word; it therefore begins later in la locution, since the noun locution is preceded by a clitic function word (the definite article la) (See Figure 1). This pattern is quite robust; we have found it for all of the speakers in our various production studies, without exception. 1Figure 1: Illustration of tonal alignment contrast in the pair la location/ l'allocation (from [START_REF] Spinelli | An intonational cue to word segmentation in phonemically identical sequences[END_REF])

This F0 rise, however, is more common in certain speaking styles (see, for example, [START_REF] Di Cristo | Vers une modélisation de l'accentuation du français : première partie[END_REF]), including a "didactic" style and the style of newsreaders, and the extent to which it is available to listeners as a cue to word segmentation and lexical access in spontaneous speech is unclear.

The goals of this study were twofold: 1. to investigate whether the intonational patterns observed in read speech are also present in spontaneous speech and therefore available to listeners as cues to word segmentation and lexical access 2. to test two measures of characterizing intonation patterns using automatically extracted F0 and time values. Developing such automatic methods is important, since hand annotation is labor-intensive and often prohibitively expensive in time and money, particularly for large corpora of many hours of speech.

Methods

We analyzed the Corpus of Interactional Data (the CID), a corpus of conversational French speech. The corpus contains eight hours of audio/video recordings of conversations between eight pairs of speakers, yielding a total of 16 hours of speech [START_REF] Bertrand | Le CID -corpus of interactional data[END_REF]. The CID is fully or partially annotated on a number of levels, including: lexical, segmental, syntactic (part of speech), discourse, and gestural. The segmental annotation was performed using forced alignment and the lexical and syntactic annotation using a morpho-syntactic analyzer (for details, see [START_REF] Bertrand | Le CID -corpus of interactional data[END_REF]). Only a very small portion of the corpus is prosodically annotated, and this partial analysis was performed by hand.

Using information from the syllabic and syntactic annotation tiers, we searched the CID to find sequences comparable to the materials in our studies of read speech. We defined two types consisting of two-syllable sequences (s1, s2):

Type 1: s1: determiner 1 s2: first syllable of a noun or adjective 2 e.g., la locution, la chaussure, un moment Type 2: s1, s2: first two syllables of a noun preceded by a determiner e.g., l'allocution, (la) chaussure, (un) moment

For Type 2, we included only nouns and adjectives of at least two syllables.

The search returned a total of 7443 pairs. Syllables shorter than 72 ms or longer than 400 ms were excluded from the analyses, since these values are often due to alignment errors. Syllables whose median F0 appeared to be an outlier (men: < 60 Hz and > 230 Hz, women: < 150 Hz and > 300 Hz) were also excluded. This left 4724 pairs (3045 Type 1, 1679 Type 2) for the analyses.

For each pair, we extracted time points for the boundaries of s1 and s2, as well as F0 values, and calculated two types of measures of the F0 differences associated with the presence or absence of an intonational rise. As in our earlier studies, we attempted to quantify the F0 differences between conditions while avoiding the problems posed by segmental perturbations (e.g., due to the presence of voiceless obstruents). For the twosyllable target region, we calculated 1. median F0 for each target syllable (s1, s2), which takes into account only the voiced portion of the target region, and 2. normalized Tonal Center of Gravity (TCoG). The TCoG is a measure of the ''the overall distribution of the 'mass' or bulk of raised F0 in both time and frequency space'' [START_REF] Barnes | The effect of global F0 contour shape on the perception of tonal timing contrasts in American English intonation[END_REF].

Results

Automatic extraction of intonation patterns

Median F0

If AP boundary rises (APRs) are present, we would expect the difference in median F0 from s1 to s2 to be greater in Type 1 sequences (determiner+noun) than in Type 2 sequences (first two content-word syllables). As we have noted earlier, the [START_REF] Spinelli | Fine-grained access to targets and competitors in phonemically identical spoken sequences: The case of French elision[END_REF][START_REF] Spinelli | An intonational cue to word segmentation in phonemically identical sequences[END_REF] [START_REF] Spinelli | Fine-grained access to targets and competitors in phonemically identical spoken sequences: The case of French elision[END_REF][START_REF] Spinelli | An intonational cue to word segmentation in phonemically identical sequences[END_REF] stimuli are characterized by clear and consistent AP boundary rises (APRs) beginning at content word-initial syllables. These stimuli were based on the 1 The determiners were all monosyllables (le, la, les, un, une, des, ma, mes, ta, tes, sa, ses, nos, vos…). A closer examination, however, revealed that the effect was sensitive to segmental composition. When a French accentual phrase begins with a clitic function word (such as a determiner), there is often a clear inflection point in the F0 curve at the function-word/content-word boundary (e.g., between la and locution and between c'est and l'allocution in Figure 1). This inflection point is clear when there are voiced consonants at the critical region (for example, the liquid [l]), but is not present (at least physically) when vocal fold vibration is interrupted by voiceless segments. In the

Hz). Note that there is a significant difference between sequence type when the vowel alone contributes to the median F0 (when there are voiceless s2 onsets). 3A similar model was fitted on the CID with random intercepts to account for the variability of the 16 speakers and the 2089 phonetic sequences represented in the s1s2 sequences across the 4724 observations. The results show a similar pattern, although the differences are much smaller and must be interpreted with caution. For items with voiceless s2 onsets, the F0 median is significantly different, in the expected direction (the Type 2 ratio of the medians is significantly smaller than the Type2, ß = -0.043, SE = 0.0077, t = -5.66, p < 0.0001, Type 1: 178 Hz vs. 185 Hz, Δ 7, Type 2: 181 Hz vs. 185 Hz, Δ 4). For items with voiced s2 onsets, there was a significant difference between types, but in the opposite direction (ß = 0.035, SE = 0.0097, t = 3.7, p < 0.0001).

Tonal Center of Gravity

We expected that the Tonal Center of Gravity measure would be able to capture the intonational differences present in the Spinelli et al. (2007, 2010) [START_REF] Spinelli | Fine-grained access to targets and competitors in phonemically identical spoken sequences: The case of French elision[END_REF][START_REF] Spinelli | An intonational cue to word segmentation in phonemically identical sequences[END_REF] materials and in particular that the measure would be robust in the face of segmental perturbations from voiceless segments. The TCoG was developed to address a range of difficulties for models of intonation based on tonal targets or turning points (TPs), including the interruption of the F0 by segmental perturbation: "Among the problems confronting a purely TP-based approach to intonational phonetics and phonology are the following: (1) Crucial TPs are frequently missing from the F0 curve owing to, e.g., intervals of voicelessness or irregular phonation" [START_REF] Barnes | The effect of global F0 contour shape on the perception of tonal timing contrasts in American English intonation[END_REF]. The TCoG "focus[es] not on the onsets and offsets of pitch movements, but rather on the overall distribution of the "mass" or bulk of raised F0 in both time and frequency space" [START_REF] Barnes | The effect of global F0 contour shape on the perception of tonal timing contrasts in American English intonation[END_REF].

We calculated the TCoG according to the formula in (1) (from [START_REF] Barnes | The effect of global F0 contour shape on the perception of tonal timing contrasts in American English intonation[END_REF]).

(

) 1
The time values obtained were normalized to 1, i.e., they were expressed as a proportion of the duration of the target twosyllable sequence. We predicted that the normalized TCoG (NTCoG) would be greater in Type 1 (determiner+noun) than in Type 2 (first two content-word syllables), corresponding to an F0 rise starting at the boundary between these two syllables (e.g., farther to the right).

We expected that the NTCoG measure would allow us to abstract away from perturbations of the F0 curve caused by voiceless segments (for which F0 is set to 0, in order to respect the definition of center of gravity). Our analysis of the Spinelli et al. 2007 materials, however, revealed no differences in NTCoG across sequence types (Type 1 vs. Type 2), even considering items with voiceless s2 onsets and voiced s2 onsets separately (for voiceless onsets, ß = -0.0018, SE = 0.007, t = -0.26, p = 0.79; for voiced onsets, ß = 0.0039, SE = 0.006, t = 0.49, p = 0.78).

In addition, the results show that the TCoG is sensitive to segmental composition. Within a sequence type, the presence of a voiceless s2 onset shifts the NTCoG to the left (ß = -0.035, SE = 0.014, t = 2.47, p < 0.05). We can illustrate why this should be the case with the simple example of a C 1 V 1 .C 2 V 2 sequence, where C 1 is voiced and C 2 is either voiced or voiceless. All other things being equal, the first syllable (s1) C 1 V 1 , which is voiced throughout, will necessarily have a greater "mass" of F0 than C 2 V 2 when C 2 is voiceless, since the F0 mass of the voiceless C 2 is zero. This shifts the TCoG to the left.

The CID corpus offered us the opportunity to examine the sensitivity of TCoG to segmental composition, specifically the influence of voiced versus voiceless segments, using a large corpus with a much greater variety in segmental composition (e.g., first syllables other than [la]). The results indicate that the measure is sensitive to the presence or absence of voiceless segments. Given the predominance of open syllables (e.g., CV, CCV) in French, we expect the presence of voiceless consonants in syllable onsets to shift the NTCoG to the right.

A linear mixed model was fitted, with group (Type 1, Type 2) and voicing as predictors and the NTCoG as the dependent variable. A random intercept was added to account for the variability across the 2089 phonetic sequences in the 4724 observations. The results show a very small but significant difference (ß = -0.011, SE = 0.0044, t = -2.48, p < 0.05) in the expected direction. The NTCoG for Type 2 is slightly smaller than for Type 1 (0.502 vs. 0.513), corresponding to a shift of only about 3 ms in two-syllable target sequences with a mean duration of about 300 ms. As expected, for items with voiceless syllable onsets, there was a strong shift to the right for Type 2 (ß = 0.07, SE = 0.003, t = 20, p < 0.0001). The comparison between Type 1 and Type 2 sequences with voiceless s2 onsets is complicated, however, by the fact that the many of most frequent determiners of French (s1 in Type 1 sequences) contain voiced segments (e.g., all the forms of the definite and indefinite articles: le, la, les, un, une, des).

Discussion and Conclusions

The study had two main goals: 1. to investigate whether the intonational patterns observed in read speech are also present in spontaneous, conversational speech, 2. to test two measures of characterizing intonation patterns using automatically extracted F0 values.

Each of the two measures tested proved problematic. The F0 median successfully quantified the intonational differences between the two sequence types in the [START_REF] Spinelli | Fine-grained access to targets and competitors in phonemically identical spoken sequences: The case of French elision[END_REF][START_REF] Spinelli | An intonational cue to word segmentation in phonemically identical sequences[END_REF] [START_REF] Spinelli | Fine-grained access to targets and competitors in phonemically identical spoken sequences: The case of French elision[END_REF][START_REF] Spinelli | An intonational cue to word segmentation in phonemically identical sequences[END_REF] read speech materials, but only for items with a particular segmental composition. The normalized Tonal Center of Gravity (NTCoG) also failed to fully capture the intonational differences between sequence types and was sensitive to segmental composition in ways unpredicted by the hypothesis. Recent work on German and Italian also calls into question certain predictions of the TCoG hypothesis and offers another perception-based explanation of intonational contrast [START_REF] D'imperio | Alignment perception of high intonational plateaux in Italian and German[END_REF].

Turning to the comparison between speaking styles, the results provide no conclusive evidence that the accentual phrase boundary rises (APRs) found in careful, read speech are reliably present in the spontaneous speech of the CID corpus, although durational differences are present. There were significant differences across sequence types only for certain limited cases.

Whether or not further study shows that AP-initial boundary rises are present in spontaneous speech of this type, however, this intonational pattern may still be reliably present in other styles of spontaneous speech and therefore available to listeners as a cue to word segmentation and lexical access. Beckman (1997) [START_REF] Beckman | A typology of spontaneous speech[END_REF] identifies ten types of "spontaneous speech" (see also discussion in [START_REF] Xu | In defense of lab speech[END_REF]). So, for example, early rises may be present in spontaneous, but careful speech or in speech directed at young children.

Our analyses of the CID were conducted on the totality of the corpus. However, speaking style in conversational speech is not homogeneous, and different styles may be present even within a single dialog or conversation. For example, factors such as the organization of the discourse and interactions between interlocuters may create alternating stretches of clear, even hyper-articulated speech and stretches of extremely reduced, hypo-articulated speech. We plan to conduct further analyses to automatically search for stretches of clear, careful speech in the corpus. This will allow us to examine the hypothesis that prosodic cues for lexical segmentation may be more reliably present in spontaneous, conversational speech, when the speech is careful, clear and slower, than when the speech is faster and more subject to segmental and prosodic reduction.

Segmental durations are quite short for most of the segments of the CID [START_REF] Meunier | Vowel reduction in conversational speech in French: The role of lexical factors[END_REF]. To evaluate our hypothesis, we plan to identify stretches of speech with longer segmental durations (e.g., greater than 150 ms). If prosodic cues for word segmentation are used in conversational speech, we expect that they will appear in these stretches.

We note that other types of cues to word segmentation, such as those based on segmental transitional probabilities, may be less reliable in casual than in careful speech. For example, the massive segmental reduction found in casual speech (see [START_REF] Meunier | Vowel reduction in conversational speech in French: The role of lexical factors[END_REF] on reduction in the CID) may give rise to word-initial segment sequences unattested in citation forms (e.g., [pti] for petit 'small'). These style-dependent differences are not unexpected, and the context-dependent weighting of cues to word segmentation and lexical access is included in a recent model [START_REF] Mattys | Sentential, lexical, and acoustic effects on the perception of word boundaries[END_REF].

  of a single speaker reading targets (e.g, la locution (Type 1), l'allocution (Type 2)) embedded in a carrier phrase. A comparison between F0 median values of the first two syllables revealed the expected difference by sequence type (Type 1: 182 Hz vs. 216 Hz, Δ 34 Hz, Type 2: 200 Hz vs. 222 Hz, Δ 22 Hz).

2

This was usually a noun, since French noun phrases are typically left-headed. speech

  [START_REF] Spinelli | Fine-grained access to targets and competitors in phonemically identical spoken sequences: The case of French elision[END_REF][START_REF] Spinelli | An intonational cue to word segmentation in phonemically identical sequences[END_REF] [START_REF] Spinelli | Fine-grained access to targets and competitors in phonemically identical spoken sequences: The case of French elision[END_REF][START_REF] Spinelli | An intonational cue to word segmentation in phonemically identical sequences[END_REF] materials, the first syllable was always [la], either the feminine singular of the definite article la (la locution, la fiche) or an elided form of the definite article and the vowel of a vowel-initial noun (l'allocution, l'affiche). The segmental composition of the second syllable (s2) therefore varied, and it sometimes contained a voiced onset ([l] for s2 of of la locution/l'allocution), sometimes a voiceless onset ([f] for the s2 of la fiche, l'affiche). Our analyses revealed that the difference in F0 median was significant only for items with a voiceless s2 onset

A linear mixed model was fitted, with the ratio s2/s1 of the medians as dependent variable, group (Type1, Type2) and voicing (voiced, voiceless) as predictors. A random intercept was added to account for the variability of the 29 pairs (e.g., l'allocution/la locution) across the 58 observations. The difference between the Type 1 ratio (1.22) and the Type 2 (1.144) ratio was significant (SE = 0.016, t = -4.7, p < 0.0001, Type 1: 182 Hz vs. 222 Hz, Δ 40 Hz, Type 2: 200 Hz vs. 224 Hz, Δ 24 Hz). However, this difference was not significant for those with a voiced s2 onset (Type 1 ratio (1.146) and Type 2 ratio (1.116) (SE = 0.018, t = -1.29, p = 0.2, Type 1: 182 Hz vs. 205 Hz, Δ 23 Hz, Type 2: 195 Hz vs. 222 Hz, Δ

[START_REF] Spinelli | Fine-grained access to targets and competitors in phonemically identical spoken sequences: The case of French elision[END_REF] [START_REF] Spinelli | Fine-grained access to targets and competitors in phonemically identical spoken sequences: The case of French elision[END_REF] used stimuli based on the read speech of a single speaker. Of the 30 critical pairs in that study,

were produced with the expected tonal alignment pattern. These 29 pairs were used in[START_REF] Spinelli | An intonational cue to word segmentation in phonemically identical sequences[END_REF] [START_REF] Spinelli | An intonational cue to word segmentation in phonemically identical sequences[END_REF].

Spinelli et al. 2007 [13] quantified F0 differences by measuring F0 at vowel midpoints. We performed additional analyses on the stimuli from that study.


D A Tobon-Mejia

K Medjaher
email: kamal.medjaher@ens2m.fr

N Zerhouni

G Tripot

Estimation of the Remaining Useful Life by using Wavelet Packet Decomposition and HMMs

This paper deals with an estimation of the Remaining Useful Life of bearings based on the utilization of the Wavelet Packet Decomposition (WPD) and the Mixture of Gaussians Hidden Markov Models (MoG-HMM). The raw data provided by the sensors are first processed to extract features by using the wavelet packet decomposition. This latter provides a more flexible way of time-frequency representation and filtering of a signal, by allowing the use of variable sized windows and different detail levels. The extracted features are then fed as inputs of dedicated learning algorithms in order to estimate the parameters of a mixture of Gaussian Hidden Markov Model. Once this learning phase is achieved, the generated model is exploited during a second phase to continuously assess the current health state of the physical component and to estimate its remaining useful life with the associated confidence value. The proposed method is tested on a benchmark data taken from the "NASA prognostic data repository" related to several bearings'. Bearings are chosen because they are the most used and also the most faulty mechanical element in some industrial systems and process. Furthermore, the method is compared to a traditional timefeature prognostic and some simulation results are given at the end of the paper.

INTRODUCTION

The competitiveness requirement in industry involves the improvement of the availability, the reliability, the security while reducing the life cycle cost of the production means. One of the possible solutions that can contribute to fulfill 1 978-1-4244-7351-9/11/$26.00 ©2011 IEEE. 2 IEEEAC Paper #1141, Final Version, Updated December 8, 2010.

these objectives consists in acting on the maintenance by implementing new maintenance strategies like the Condition Based Maintenance (CBM) [START_REF] Jardine | A review on machinery diagnostics and prognostics implementing condition-based maintenance[END_REF][START_REF] Vachtsevanos | Intelligent fault diagnosis and prognosis for engineering systems[END_REF] and reducing the traditional corrective and preventive maintenances. The CBM is based on the exploitation of the data provided by the monitoring system which continuously tracks the health state of the system. The data gathered are processed and transformed to relevant knowledge in order to estimate the current state of the system and to predict its future one, and thus helping the maintainers to take adequate decisions at appropriate time. The input data in the prognostic process are signals, where the degradation information is usually masked by noise. To solve this problem and provide the correct information to perform failure prognostic, several methods have been proposed, based in the time domain behavior of the signal, or on traditional spectral analysis. Time domain uses statistical properties from the raw signal as RMS, Kurtosis or crest factor to track failures with some limited success in localized defects [START_REF] Tandon | A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings[END_REF]. Frequency analysis are widely used in vibration signals for bearing fault detection [START_REF] Kurfess | Advanced diagnostic and prognostic techniques for rolling element bearings[END_REF]. The Fast Fourier Transform (FFT) is the simplest frequency domain analysis method. This method is the examination of high-frequency resonances caused by a fault in the spectrum of the signal. However the impact vibration generated by a bearing fault has relatively low energy, it is often overwhelmed by noise with higher energy and noise from the environment. In order to overcome FFT problems, recent advanced signal processing methods such as Short-Time-Fourier-Transform, Wigner-Ville and wavelet analysis have been used. Wavelets have been established as the most widespread tool in many areas of signal processing, due to their flexibility and their efficient computational implementation [START_REF] Strang | Wavelets and Filter Banks[END_REF]. Failure prognostic activity aims at anticipating the failure date by predicting the future health state of a given system and its Remaining Useful Life (RUL). According to the International Standard Organization [START_REF] Afnor | Condition monitoring and diagnostics of machines -prognostics -part 1: General guidelines[END_REF], failure prognostic corresponds to the "estimation of the time to failure and the risk for one or more existing and future failure modes". Several other definitions have been proposed in the literature [START_REF] Jardine | A review on machinery diagnostics and prognostics implementing condition-based maintenance[END_REF][START_REF] Provan | Prognosis and condition-based monitoring: an open systems architecture[END_REF][START_REF] Wang | Prognosis of machine health condition using neuro-fuzzy systems[END_REF][START_REF] Muller | Formalisation of a new prognosis model for supporting proactive maintenance implementation on industrial system[END_REF][START_REF] Heng | Rotating machinery prognostics: State of the art, challenges and opportunities[END_REF] during this last decade. All the reported definitions agree on prediction step and the estimation of the time before the failure. This time is called RUL in some of them, Estimated Time To Fail-1 ure (ETTF) in the ISO's one [START_REF] Tobon-Mejia | The iso 13381-1 standard's failure prognostics process through an example[END_REF] and in a small number of publications [START_REF] Farrar | A coupled approach to developing damage prognosis solutions[END_REF][START_REF]Recursive filters for a partially observable system subject to random failure[END_REF] it is defined as a probability that a machine operates without a fault up to some future time. Contrary to fault diagnostic which is a mature activity, well developed and spread within the research and the industrial communities, failure prognostic is a new research domain [START_REF] Jardine | A review on machinery diagnostics and prognostics implementing condition-based maintenance[END_REF][START_REF] Isermann | Model-based fault-detection and diagnosis -status and applications[END_REF][START_REF] Venkatasubramanian | Prognostic and diagnostic monitoring of complex systems for product lifecycle management: Challenges and opportunities[END_REF]. However, the increasing interest accorded to failure prognostic has led to numerous methods, tools and applications during the last decade. According to what is reported in the literature [START_REF] Jardine | A review on machinery diagnostics and prognostics implementing condition-based maintenance[END_REF][START_REF] Heng | Rotating machinery prognostics: State of the art, challenges and opportunities[END_REF][START_REF] Lebold | Open standards for condition-based maintenance and prognostic systems[END_REF] and taking in account the latest contributions in the field, failure prognostic methods can be classified into three main approaches: model-based, experiencebased and data-driven prognostic, see Fig. 1. In addition to these three categories, other sub-categories resulting from the intersection between the main ones has been developed.

The methods of the model-based prognostic approach are

Model-based prognostic

-+ based on the use of an analytical model to characterize the behavior of the system including the degradation phenomenon.

Applicability

Assessment criteria

Reliability-based prognostic

Data-driven prognostic

The model can be a set of equations obtained by using traditional laws of physics (crack by fatigue, wearing and corrosion phenomena, etc.) [START_REF] Luo | Modelbased prognostic techniques applied to a suspension system[END_REF][START_REF] Kacprzynski | Predicting remaining life by fusing the physics of failure modeling with diagnostics[END_REF]. The advantage of the methods used in this approach is that they provide more precise results. However, their disadvantage dwells in the fact that real systems are often nonlinear and the degradation mechanisms are generally stochastic and difficult to obtain in the form of analytical models. Consequently, the applicability of this approach may be limited by the modeling hypothesis. Reliability-based prognostic methods use mainly the data of the experience feedback gathered during a significant period of time (maintenance and operating data, failure times, etc.) in order to adjust the parameters of some reliability models (Weibull law, exponential law, etc.). These latter are then used to estimate the RUL [START_REF] Goode | Plant machinery working life prediction method utilizing reliability and condition-monitoring data[END_REF]. The reliability prognostic methods are the simplest to implement when a significant amount of experience feedback data is available. The main advantage of these methods is that they do not use on-line sensors' data, neither complex mathematical models. Instead, they are rather based on the use of simple reliability functions. However, the prognostic results they offer are less precise than those provided by model-based and data-driven approaches, especially when the operating conditions are variable or in the case of new systems because of a lack of experience data. Data-driven methods attempt to transform the raw monitoring data into relevant information and behavior models of the system including the degradation instead of building mod-els based on comprehensive system physics and human expertise. They use artificial intelligence (AI) tools (neuronal networks, Bayesian networks, hidden Markov models, etc.) [START_REF] Chinnam | A neuro-fuzzy approach for estimating mean residual life in condition-based maintenance systems[END_REF][START_REF] Swanson | Prognostic modelling of crack growth in a tensioned steel band[END_REF] or statistical models to learn the degradation model [START_REF] Wang | A similaritybased prognostics approach for remaining useful life estimation of engineered systems[END_REF][START_REF] Li | Gas turbine performance prognostic for condition-based maintenance[END_REF] to predict the future health state and the associated RUL of the system. The principle of these methods consists in two stages: a first phase during which a behavior model is learned from the monitoring data and a second phase where the learned model is used to estimate the current health condition of the system and to predict its future state. These methods can be considered as a trade-off between the model-based and the experience-based methods. This is because, on one hand, in real industrial applications getting reliable data is easier than constructing physical or analytical behavior models. On the other hand, the generated behavioral models from real monitoring data lead to more precise prognostic results than those obtained from experience feedback data.

In addition to the aforementioned prognostic approaches, three fusion ones, resulting from the intersection of the main approaches, have been reported in the recent literature. They are named "model-based/data-driven fusion", "model-based/reliability fusion" and "data-driven/reliability fusion". Model-based/data-driven methods use mathematical and physical models of a degradation and parametric models obtained from artificial intelligence and advanced statistics to build accurate models. Unfortunately, the implementation of these methods are cost and time consuming. In this category, one can cite [START_REF] Cadini | Monte carlo-based filtering for fatigue crack growth estimation[END_REF] where the authors proposed a fatigue degradation model using the well-known Paris-Erdogan law coupled with a particle filtering model to estimate the failure probability, and built a cost per unit time variable to choose the best replacement time.

The model-based/reliability fusion approach offers a good accuracy, due to the use of mathematical models, and a long forecasting time horizon by the integration of the experience feedback data. In this field the works of Kacprzynski et al. [START_REF] Kacprzynski | Predicting remaining life by fusing the physics of failure modeling with diagnostics[END_REF][START_REF] Kacprzynski | Enhancement of physics-offailure prognostic models with system level features[END_REF] deserve to be mentioned. The authors used the Paris law to determine the crack length in a helicopter's gearbox pinion, combined with reliability equations to confirm the degradation phase and to refine the fatigue propagation parameters.

Finally, data-driven/reliability fusion approach combines the ability of data-driven models to capture the non linearity and the transient phenomena associated to the real world process by using machine learning techniques. These artificial intelligence models merged with the reliability data allows to make a good forecasting for a long time horizon. In this category, one can cite the works of Heng et al. [START_REF] Heng | Intelligent conditionbased prediction of machinery reliability[END_REF] where the Kaplan-Meier estimator is used to model complete and incomplete monitoring data histories. The probabilities given by the estimator and the data taken from the monitoring system are used in a Feed Forward Neuronal Network (FFNN) to estimate the probability of asset survival for a long future time horizon.

In this paper a data-driven prognostic method based upon the use of Mixture of Gaussians Hidden Markov Model (MoG-HMM) and the wavelet packet decomposition for feature extraction is proposed. The use of this AI tool is motivated by the fact that it permits to handle complex emission probability density functions (pdfs) generated by a set of continuous features extracted from raw monitoring signals using the WPD that generalize the wavelet transform. The method, presented in section 3, is performed in two steps: an off-line step where the raw data are used to learn a behavioral model of the physical component's condition, and an on-line step in which the learned model is used to identify the current condition of the component and to estimate its RUL. In section 4 the method is tested on real operating data related to bearings, and simulation results are given.

BACKGROUND

A brief introduction to the fundamentals required to deploy the method are presented in this section. First the WPD for feature extraction is presented and then the MoG-HMM used to build the models is exposed.

Wavelet Packet Decomposition

Wavelet packet decomposition is now becoming a competent tool for signal analysis. Compared with the normal wavelet analysis, it has special abilities to attain higher discrimination by analyzing the higher frequency domains of a signal. The frequency domains separated by the wavelet packet can be easily selected and classified according to the characteristics of the analyzed signal. So the wavelet packet is more appropriate than wavelet in signal analysis and has much wider applications such as signal and image compression, de-noising and speech coding [START_REF] Akansu | Emerging applications of wavelets: A review[END_REF].

Wavelet packet decomposition uses a pair of low pass and high pass filters to divide a space; this corresponds to splitting the frequency content of a signal into approximately a low-frequency and a high-frequency component. Wavelet decomposition leaves the high-frequency part alone and keeps splitting the low-frequency part. In wavelet packet decomposition, we can choose to split the high-frequency part also into a low-frequency part and a high-frequency part. Thus, in general, wavelet packet decomposition divides the frequency space into various parts and allows better frequency localization of signals [START_REF] Zarei | Bearing fault detection using wavelet packet transform of induction motor stator current[END_REF].

As shown in Fig. 2, the wavelet packet decomposition can be viewed as a tree. The root of the tree is the original data set. The next level of the tree is the result of one step of the wavelet transform. Subsequent levels in the tree are constructed by recursively applying the wavelet transform step to the low and high pass filter results from the previous wavelet transform step. Then when the decomposition process is achieved the energy in the different spectrum bands can be calculated.

Mixture of Gaussians Hidden Markov Models

A MoG-HMM is primarily an Hidden Markov Model (HMM). In [START_REF] Rabiner | A tutorial on hidden markov models and selected applications in speech recognition[END_REF] an HMM is defined as a statistical model used to represent stochastic processes where the states are not directly observed, see Fig. 3. An HMM is completely defined by the following parameters:

• N: number of states in the model. The individual states are 1, 2, ..., N , and the state at time t is defined as s t .

• M: the number of distinct observations for each state. The observation symbols correspond to the physical output of the modeled system. The individual observation symbols are denoted as V = v 1 , v 2 , ..., v M .

• A: the state transition probability distribution, A = a ij , where

a ij = P [s t+1 = j |s t = i ] , 1 ≤ i, j ≤ N. • B: the observation probability distribution of a state i, B = b i (k), where b i (k) = P [v k |s t = i ] , 1 ≤ i ≤ N, 1 ≤ k ≤ M.
• π: the initial state distribution π = π i , where

π i = P [s l = i] , 1 ≤ i ≤ N.
For simplicity and clarity of presentation, a compact notation (λ = π, A, B) is used for each HMM. In practice, HMMs are used to solve the following problems [START_REF] Rabiner | A tutorial on hidden markov models and selected applications in speech recognition[END_REF]:

• Problem 1 (detection): given a model λ and an observation sequence O = (O 1 , O 2 , ..., O T ), compute the probability P (O|λ) of the sequence given the model. The solution of this problem is obtained by using the forward-backward algorithm [START_REF] Baum | An inequality with applications to statistical estimation for probabilistic functions of a markov process and to a model for ecology[END_REF].

• Problem 2 (decoding): given an observation sequence O = (O 1 , O 2 , ..., O T ), find the hidden state sequence S = (S 1 , S 2 , ..., S T ) that have most likely produced the observation sequence. This problem is solved by using the Viterbi algorithm [START_REF] Viterbi | Error bounds for convolutional codes and an asymptotically optimal decoding algorithm[END_REF].

• Problem 3 (learning): find the model parameters (π, A, B) that better fit the observation sequence O, i.e., that maximize the probability P (O|λ). To solve this problem a solution is proposed by using the Baum-Welch algorithm [START_REF] Dempster | Maximum likelihood from incomplete data via the EM algorithm[END_REF].

Usually, HMMs consider the observations as discrete symbols and use discrete probability densities to model the transition and the observation probabilities. The problem with this approach is that in condition monitoring the observations are typically continuous signals. In order to use a continuous observation density, some restrictions are placed to insure that the parameters of the probability density function are reestimated. The most general representation of the pdf, for which a re-estimation procedure has been formulated [START_REF] Rabiner | A tutorial on hidden markov models and selected applications in speech recognition[END_REF], is a finite mixture of pdfs in the form:

b i (O) = M m=1 C jm ξ(O, µ jm , U jm ), 1 ≤ j ≤ N ( 1
)
Where O is the observation vector, C jm is the mixture coefficient for the m th mixture in state i and ξ is any log concave or elliptically symmetric density (e.g. Gaussian) with mean vector µ jm and covariance matrix U jm for the m th mixture component in state j. Usually a Gaussian density is used for ξ and the corresponding model is called a MoG-HMM, that is completely defined by the parameters: the A matrix, the B matrix and the initial probability π. For a MoG-HMM the observation matrix B is modeled by a Gaussian density with a mean µ, a standard deviation σ and a mixture matrix M .

WPD/MOG-HMM BASED PROGNOSTIC METHOD

An unified diagnostic and prognostic method to evaluate the current health state of a physical component and its remaining useful life is proposed in this section. The method is based on a nondestructive control and uses the data provided by sensors installed to monitor the component's condition. The originality of the proposed method dwells in the fact that raw signals are processed using the WPD to extract the relevant information to learn the behavior models. Also in the generated MoG-HMM the states' stay durations are not assumed to be a geometrically decaying functions [START_REF] Dong | A segmental hidden semimarkov model (hsmm)-based diagnostics and prognostics framework and methodology[END_REF] (which is the case in traditional HMM based prognostic methods), but are learned from the monitoring data (note that multiple observations are considered for both learning and simulation phases, instead of the traditional mono observation approach). Moreover, in the proposed method there is no limitation for the type of the generated MoG-HMM (the model can be an ergodic, a left-right or a parallel left-right). The principle of the proposed method relies on two main stages, as shown in Fig. 4: a learning phase and an exploitation phase.

In the first phase, which is executed off-line, the raw data recorded by the sensors are processed in order to extract the energy of each node at the last decomposition level [START_REF] Zarei | Bearing fault detection using wavelet packet transform of induction motor stator current[END_REF] using the WPD. These features are then used to learn several behavior models (in the form of MoG-HMMs) corresponding to different initial states and operating conditions of the component. Indeed, each raw data history corresponding to a given component's condition is transformed to a feature matrix F , by using the WPD. In the matrix F , each column vector (of C features at time t) corresponds to a snapshot on the raw signal, and each cell f ct represents the node c of the last WPD level at time t.

Raw signal

W P D ----→ F = (f 1t f 2t • • • f ct ) ′ with 1 ≤ t ≤ T and 1 ≤ c ≤ C (2)
The nodal energy (features) are then used to estimate the parameters (π, A and B) and the temporal parameters (stay duration in each state) of the MoG-HMMs. The advantage of using several features instead of only one dwells in the fact that it can happen that a single feature may not capture all the information related to the behavior of the component. The parameters (π, A and B) of each MoG-HMM are learned by using the well known Baum-Welch algorithm [START_REF] Baum | An inequality with applications to statistical estimation for probabilistic functions of a markov process and to a model for ecology[END_REF], whereas the temporal ones are estimated by using the Viterbi algorithm [START_REF] Viterbi | Error bounds for convolutional codes and an asymptotically optimal decoding algorithm[END_REF]. In addition, this latter permits to obtain the state sequence and to compute the time duration for which the component has been in each state of the corresponding MoG-HMM (Fig. 5). Thus, by assuming that the state duration in each state follows a normal law, it is possible to estimate the mean duration (3) and the corresponding standard deviation (4) by computing the duration and the number of visits in each state. Moreover, the Viterbi algorithm permits to identify the final state which represents the physical component's failure state.

µ (D (S i )) = 1 Ω Ω w=1 D (S iw ) (3)
σ (D (S i )) = 1 Ω Ω w=1 [D (S iw ) -µ (D (S i ))] 2 (4)
In ( 3) and ( 4) D(•) stands for the visit duration, i is the state index, w is the visit index and Ω corresponds to the total of visits. A compact representation of each learned MoG-HMM used to perform diagnostic and prognostic is given by the following expression:

λ = (π, A, B, µ (D (S i )) , σ (D (S i )) , S f inal ) (5)
where S f inal is the final state (corresponding to the end of the considered condition monitoring history), µ(D(S i )) is the mean state duration for the state i and σ(D(S i )) is the standard deviation over the state duration for the state i.

The second phase, which is performed on-line, consists in exploiting the learned models to detect the component's current condition (using the Viterbi algorithm) and to compute the corresponding RUL. The processed data and the extracted nodal energy using the Wavelet toolbox from Matlab ® are thus continuously fed to the learned models in order to select the one that best represents the observed data and therefore the corresponding component's condition, see Fig. 4. The selection process is based on the calculation of a likelihood P (O|λ) of the model over the observations HMMs problem 1). Finally, by knowing the current condition and by using the stay durations learned in the off-line phase, the component's RUL and its associated confidence value can be estimated.

The generated MoG-HMMs are used during the on-line phase to estimate the RUL and the associated confidence value of the physical component by using a dedicated procedure whose steps are the following:

• The first step consists in detecting the appropriate MoG-HMM that best fits and represents the on-line observed sequence of nodal energy. Indeed, the features are continuously fed to the set of learned models (completely defined) and a likelihood is calculated in order to select the appropriate model (Fig. 6). The selected model is then used to compute the RUL.

• The second step of this procedure concerns the identification of the current state of the component. The Viterbi algorithm is thus applied on the selected model in order to find the state sequence, which corresponds to the observed sequence of nodal energy, and to identify the current state of the component by choosing the most persistent state in the last observations [START_REF] Afnor | Condition monitoring and diagnostics of machines -prognostics -part 1: General guidelines[END_REF].

state sequence = (S 1 , S 2 , . . . , S t ) , Last states = (S t-l , . . . , S t-2 , S t-1 , S t ) , with l = past observations factor and t = current time.

• The third step consists in using the current identified state, the final state (the failure state) and the probability transition matrix A of the selected MoG-HMM to find the critical path, which goes from the current state to the end state. The idea is to identify all the non-zero probabilities in the transition matrix as potential transitions, and then to choose the minimal path among all the possible ones (Fig. 7) with only one visit per state. In the same way, it is possible to find the longest path by considering a maximum number of states in the path with only one visit per state. The shortest path is assimilated to the pessimistic path (rapid evolution to the failure), whereas the longest path is taken as the optimistic scenario. • Finally, in the fourth step the paths identified previously are used to estimate the RUL. This latter is obtained using the temporal parameters of the stay duration in each state. In addition, a confidence value over the RUL is calculated based on the standard deviation values of the stay durations. Thus, three values [START_REF] Provan | Prognosis and condition-based monitoring: an open systems architecture[END_REF] are calculated for each path: the upper RUL (µ + n • σ), the mean RUL, and the lower RUL (µn • σ).

APPLICATION AND SIMULATION RESULTS

The failure prognostic method presented previously is tested on a rich condition monitoring data base taken from [START_REF]NSF I/UCRC Center for Intelligent Maintenance Systems[END_REF] and containing several bearings tested until the failure. The choice of bearings can be explained by the fact that these components are considered as the most common mechanical elements in industry and are present in almost all industrial processes, especially in those using rotating elements and machines. Moreover, bearings are the main components which most frequently fail in rotating machines [START_REF] Donnell | Report of large motor reliability survey of industrial and commercial installations, part I, II & III[END_REF] (Fig. 8). Thus, the prediction of the ETTF or RUL of these components may help improving the reliability, the availability and the safety of the rotating machines while reducing their maintenance costs, and the operational impact and environmental impact. The test data extracted from [START_REF]NSF I/UCRC Center for Intelligent Maintenance Systems[END_REF] correspond to several tests under constant conditions. Four bearings were installed on one shaft. The angular velocity was kept constant at 2000 rpm and a 6000 lb radial load was applied onto the shaft and bearings (Fig. 9). On each bearing two Accelerometer were installed for a total of 8 accelerometers (one vertical Y and one horizontal X) to register the accelerations generated by the vibrations, the sampling rate was fixed at 20 kHz. For simulation purposes (learning and on-line failure prognostic) twelve condition monitoring data histories are used (eleven for learning and one for test), each bearing was considered failed at the end of its associated history. For both learning Figure 9: The bearing test bed [START_REF]NSF I/UCRC Center for Intelligent Maintenance Systems[END_REF].

and prognostic phases, the nodal energy in third level of the WPD (using the "Daubechies" wavelet family) at each instant t have been extracted from the raw signals (vibration signals). The level chose using (8) that defines the maximum decomposition level where at lest 3 harmonics of the characteristic defect frequency are caught. In this expression J f is the decomposition level, F s the sampling frequency and F d the defect frequency. For this case the fault frequency is the band pass frequency of the outer race (BPFO) this suggest a decomposition level of 3.8. Being conservative the decomposition level is fixed to three. This choice permits to obtain wide frequency bands of 2.5 kHz. The principle of the procedure for feature extraction is shown in Fig. 10. In order to simulate an on-line failure the "test" data history is used. The selection process shown in Fig. 6 is then applied on the data history corresponding to the bearing 2 in the test N • 2 in order to identify the "best MoG-HMM" and to estimate the RUL. A simulation result of the predicted RUL and his error is shown in Fig. 11, where the data history used to perform the test correspond to a faulty bearing that ends at 9840 min.

J f log 2 F s 3F d -1 (
From Fig. 11-(a) and Fig. 11-(b) one can see that the precision of the estimated RUL increases as the prediction time is approaching the real failure time. Similarly, after 7440 min the mean estimation error drops below 16.5 % whereas when considering the upper RUL limit the error drops to 7 % and continues to decrease as the real failure time approaches. After 9610 min the mean error stabilizes arround the value of 1.08 %. The 68 % confidence interval keeps the RUL estimation limits near acceptable values, a wide confidence intervals (95 % and 99.5 %) will give more sparse limits and will increase the prediction error. These results are better that those obtained in our previous work [START_REF] Tobon-Mejia | A mixture of gaussians hidden markov model for failure diagnostic and prognostic[END_REF] where the temporal features used where: RMS, mean, skewness and kurtosis. The RUL and the associated prediction error of the same test history using temporal features are shown in nent by learning the parameters of the corresponding MoG-HMMs models. The derived models are finally exploited to asses the current condition and to estimate the RUL and the confidence value. The time-frequency features allowed getting more precise result than using only time features as shown in the comparison done in this paper.

Figure 1 :

 1 Figure 1: Classification of prognostic approaches.

Figure 2 :

 2 Figure 2: Wavelet packet decomposition tree.

Figure 3 :Figure 4 :

 34 Figure 3: A three state left-to-right HMM.

Figure 5 :

 5 Figure 5: Example of Viterbi decoding state.

Figure 7 :Figure 6 :

 76 Figure 7: Path estimation.

  RU L upper = N i=current state [µ (D (S i )) + n • σ (D (S i ))], RU L mean = N i=current state µ (D (S i )), RU L lower = N i=current state [µ (D (S i ))n • σ (D (S i ))],∀i ∈ state in the active path, n = confidence coef.[START_REF] Provan | Prognosis and condition-based monitoring: an open systems architecture[END_REF]

Figure 8 :

 8 Figure 8: Failure distribution of motors of power greater than 200 hp.

8 )Figure 10 :

 810 Figure 10: Feature extraction principle.

Fig. 11 -

 11 (c) and Fig.11-(d). One can appreciate the strong inertia on the behavior of the prognostic results whereas the model that uses WPD for feature extraction evolves progressively converging to the real RUL.

  An estimation of the current health condition of physical components, particularly bearings, and an estimation of their remaining useful life before their complete failure has been proposed in this paper. The method is based on the transformation of the data provided by the sensors installed to monitor the component into relevant models. These latter are represented by MoG-HMMs, which take as input continuous observations and permit to model the state of the component at each time. A WPD has been used to extract appropriate features from the monitoring signals. This type of decomposition allowed getting deeper into the signal features by adjusting both the time and the frequency scales. These features are then used to model the degradation behaviour of the compo-

Figure 11 :

 11 Figure 11: Simulation results: (a) RUL estimation for the bearing 2 in test N • 2 using WPD; (b) prediction error for the bearing 2 in test N • 2 using WPD; (c) RUL estimation for the bearing 2 in test N • 2 using temporal features; and, (d) prediction error for the bearing 2 in test N • 2 using temporal features.