Paden Tomasello

Akshat Shrivastava

Daniel Lazar

Po-Chun Hsu

Duc Le

Adithya Sagar

Ali Elkahky

Jade Copet

Wei-Ning Hsu

Yossi Adi

Robin Algayres

Tu Ahn Nguyen

Emmanuel Dupoux

Luke Zettlemoyer

Abdelrahman Mohamed

Meta Ai

STOP: A DATASET FOR SPOKEN TASK ORIENTED SEMANTIC PARSING

Keywords: spoken language understanding, assistant, domain adaptation

End-to-end spoken language understanding (SLU) predicts intent directly from audio using a single model. It promises to improve the performance of assistant systems by leveraging acoustic information lost in the intermediate textual representation and preventing cascading errors from Automatic Speech Recognition (ASR). Further, having one unified model has efficiency advantages when deploying assistant systems on-device. However, the limited number of public audio datasets with semantic parse labels hinders the research progress in this area. In this paper, we release the Spoken Task-Oriented semantic Parsing (STOP) dataset 1 , the largest and most complex SLU dataset publicly available. Additionally, we define low-resource splits to establish a benchmark for improving SLU when limited labeled data is available. Furthermore, in addition to the human-recorded audio, we are releasing a TTS-generated versions to benchmark the performance for low-resource and domain adaptation of end-to-end SLU systems.

INTRODUCTION

Assistant systems are becoming integrated into an increasing number of out daily devices, from cell phones and smart speakers to cars and televisions. Traditional assistant systems utilize a cascaded approach: an Automatic Speech Recognition (ASR) system transcribes the audio to text, followed by a separate Natural Language Understanding (NLU) system which predicts the user's intentions from the decoded text. Although cascade systems enable using audio-only and textonly training resources, they are prone to error propagation when the ASR systems fail to generate the correct transcript. Further, an NLU model fed with decoded text cannot leverage paralinguistic information in the input, e.g., pausing, intonation, and stress variations. Moreover, two separate models in a cascade system increase the computational requirements for End-to-end spoken language understanding (SLU) has recently shown great promise by directly predicting intent and slots values from audio using a single system [START_REF] Serdyuk | Towards end-to-end spoken language understanding[END_REF] [START_REF] Haghani | From audio to semantics: Approaches to end-toend spoken language understanding[END_REF]. It resolves the ambiguity of similarly sounding inputs that would be competing hypotheses of an ASR system. SLU has the advantage of leveraging acoustic information lost in the cascaded approach, like prosody and rhythm. One of the challenges for SLU research today is a lack of large and challenging audio datasets with semantic parse labels. In this paper, we release the Spoken Task-Oriented Semantic Parsing (STOP) dataset, which contains 1) three times as many audio samples as existing datasets 2) five times as many speakers as existing datasets 3) and compositional queries to support the ever-increasing demands of supporting real-world assis- We recognize that collecting audio and intent pairs is a challenging and resource intensive task. Speech audio could contain sensitive information and proper precaution needs to be taken during collection. These privacy considerations pose a challenge to large-scale dataset collection. Accordingly, we aim to establish the first-ever low-resource splits for an endto-end SLU dataset to support research on training with limited training data. Our baselines show the importance of audio and ASR pretraining for obtaining competitive performance versus cascaded systems.

We summarize our contributions as follows:

• Release of the STOP dataset, the largest and most semantically complex end-to-end spoken language understanding dataset publicly available,

• Defining low-resource splits as a benchmark for training with limited natural speech data samples,

• TTS-generated versions of the dataset for benchmarking low-resource training

• Experimental analysis on training end-to-end spoken language understanding models, with insights into speech pretraining, performance in the low-resource setting, domain adaptation, and how TTS audio can be incorporated into these settings.

• Open source release of our models and code for reproduction at https://github.com/facebookresearch/ fairseq/tree/main/examples/audio_nlp/ nlu

We conclude with promising future directions of research.

RELATED WORK

In the 1990s, the first audio dataset containing semantic labels was first released in the Air Travel Information System (ATIS) corpus [START_REF] Hemphill | The atis spoken language systems pilot corpus[END_REF], followed by the Switchboard-DAMSL Labeling Project [START_REF] Jurafsky | Switchboard-damsl labeling project coder"s manual[END_REF]. The successful application of sequenceto-sequence neural models to machine translation systems [START_REF] Sutskever | Sequence to sequence learning with neural networks[END_REF] and speech recognition [START_REF] Chan | Listen, attend and spell[END_REF] ignited the interest in end-to-end systems for SLU, which were introduced in [1] and [START_REF] Haghani | From audio to semantics: Approaches to end-toend spoken language understanding[END_REF]. Due to the scarcity of audio to intent data for the ever-increasing number of domains in practical assistant scenarios, transfer learning has been an area of active research explored in [START_REF] Schuster | Crosslingual transfer learning for multilingual task oriented dialog[END_REF], [START_REF] Tomashenko | Investigating Adaptation and Transfer Learning for End-to-End Spoken Language Understanding from Speech[END_REF] as well as ASR Pretraining in [START_REF] Lugosch | Speech Model Pre-Training for End-to-End Spoken Language Understanding[END_REF]. More recently, there have been several efforts around newer, larger datasets for SLU, namely, the Snips benchmark [START_REF] Coucke | Snips voice platform: an embedded spoken language understanding system for private-by-design voice interfaces[END_REF], Fluent Speech Command (FSC) corpus [START_REF] Lugosch | Speech Model Pre-Training for End-to-End Spoken Language Understanding[END_REF], and the SLURP dataset [START_REF] Bastianelli | SLURP: A spoken language understanding resource package[END_REF]. In this paper, we introduce the STOP dataset, which contains three times as many audio files and five times as many speakers compared to the largest of these datasets, SLURP. Further, our dataset includes compositional queries with nested intents, which no previous publicly available SLU dataset included. Compositional or nested queries for text-based systems were first introduced in [START_REF] Gupta | Semantic parsing for task oriented dialog using hierarchical representations[END_REF] with the first version of the TOP dataset with 2 domains. TOPv2 was release in [START_REF] Chen | Low-resource domain adaptation for compositional task-oriented semantic parsing[END_REF], which adds 6 additional domains for a total of 137k more samples across 8 domains.

DATASETS

STOP Data Collection and Verification

The STOP dataset builds upon the TOPv2 dataset [START_REF] Chen | Low-resource domain adaptation for compositional task-oriented semantic parsing[END_REF] which provides text-only inputs and target semantic parse trees. For every utterance-semantic parse pair, we collect an audio recording of the input utterance by requesting workers through Amazon's Mechanical Turk to record themselves. We ran the recordings through an ASR system to control the quality of the recorded audio. In our case, it is the fine-tuned wav2vec 2.0 [START_REF] Baevski | wav2vec 2.0: A framework for self-supervised learning of speech representations[END_REF] ASR model in the HuggingFace [START_REF] Wolf | Huggingface's transformers: Stateof-the-art natural language processing[END_REF] library. Recordings are automatically added to the dataset only if their character error rate is below 50% from the expected input text. Given that the wav2vec 2.0 model is trained on English audiobooks data, it performed poorly for non-native speakers, so any sample below the threshold was reviewed manually. In the event that the recording does not match the utterance it is discarded and recollected by another Mechanical Turk worker.

Normalizing text to spoken form

The TOPv2 dataset contains utterances in written text form, which may include digits or abbreviations like "4" and "CA." However, ASR systems are typically trained on spoken text forms like "four" and "California," respectively. To make our dataset more aligned with ASR system, we used an in-house spoken text normalization tool to enumerate possible pronunciations for each utterance and an in-house ASR model to predict the audio transcription. We then computed the edit distances across the possible normalizations and chose the normalization with the lowest distance. We include both the normalized and unnormalized form for each sample.

Low resource splits

Collecting audio recordings and annotating them with their semantic parses is laborious. We, therefore, believe a crucial research area for end-to-end NLU systems is low resource training, where the amount of training data is limited. Therefore, for our STOP dataset, in addition to the complete training set, we are also releasing low resource splits, which can be used as baselines for low-resource end-to-end NLU training and target datasets for domain adaptation. TOPv2 [START_REF] Chen | Low-resource domain adaptation for compositional task-oriented semantic parsing[END_REF] defined SPIS, or samples per intent and slot, which indicates the number of training samples available for each slot and in-tent and establishes a benchmark for training with only 25 SPIS.

TTS TOPv2

Going deeper in simulating real-world pre-release conditions in the STOP benchmark, we are releasing two different TTS versions of TOPv2. First, the utterances in TOPv2 are converted to spoken form as detailed in Section 3.2. We then run the VITS [START_REF] Kim | Conditional variational autoencoder with adversarial learning for end-to-end text-to-speech[END_REF] text-to-speech (TTS) system trained on Lib-riTTS [START_REF] Zen | Libritts: A corpus derived from librispeech for text-to-speech[END_REF] and the CSTR VCTK Corpus [START_REF] Yamagishi | CSTR VCTK Corpus: English multi-speaker corpus for CSTR voice cloning toolkit (version 0.92[END_REF]. In the lowresource and domain adaptation parts of Section 4, the performance of NLU models trained with these machine-generated datasets is compared to ones trained on natural human-spoken audio. Although it is a common practice in the industry to use TTS-generated speech for enabling pre-release NLU domains, STOP is the first publicly-available benchmark to offer the opportunity to academic institutions to conduct research in this area.

Dataset statistics and comparisons

We collected two audio recordings for every utterance in the validation and test sets of TOPv2 and one for each of the utterances in the train set. Speakers may only be in one split to ensure no data pollution exists between different partitions. Additionally, we limit the number of recordings any given speaker can submit to 3000. We ask speakers to self-identify their gender with options, Male, Female, or prefer not to say, or non-binary. Table 1 shows dataset statistics across different genders. Also, we ask speakers to self-identify whether they are English-native speakers, non-native speakers, or prefer not to say. The distribution can be seen in Overall, our STOP dataset is three times as large as previous datasets and contains five times as many speakers. A complete comparison with other Spoken NLU datasets is in Table 3.

EXPERIMENTS

Metrics

We use two metrics when evaluating our models. The first is the Exact Match (EM) accuracy, which reports the model's accuracy in perfectly reproducing the semantic parse tree with the correct intent and slot tags. The second is the Exact Match Tree (EM-Tree), which reports the accuracy of producing the parse trees' intent and slot labels but does not evaluate the tags' correctness. In End-to-End NLU, EM-Tree is a good proxy if the model understands the intent and the structure of the user interaction but cannot transcribe the audio perfectly, e.g., ASR errors in rare entity names. In contrast, EM represents understanding the intent and being able to transcribe the audio perfectly.

Models

Our experiments contain baseline results using cascaded and end-to-end NLU systems. The cascaded system first transcribes the audio using an ASR system, which is a pre-trained wav2vec2.0 model fine-tuned on either 960h of Librispeech [START_REF] Panayotov | Librispeech: An asr corpus based on public domain audio books[END_REF] or the full STOP training set. The text is then fed into an NLU model that is a pretrained BART-base model [START_REF] Lewis | BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension[END_REF] containing a 6 layer transformer encoder and 6 layer transformer decoder, augmented with a copy-generate mechanism [START_REF] Aghajanyan | Conversational Semantic Parsing[END_REF].

The end-to-end baseline system is an encoder-decoder Transformer architecture with an output vocabulary containing letters and all the intents and parses in STOP. For training, we use an Adam optimizer [START_REF] Kingma | Adam: A method for stochastic optimization[END_REF] with the betas set to 0.9 and 0.98. We use a tri-stage learning rate scheduler [START_REF] Park | SpecAugment: A simple data augmentation method for automatic speech recognition[END_REF], where the learning rate is warmed up for the first 10% of updates to a maximum of 1e-4, held constant for the next 40% and then linearly decayed for the remainder updates to 5e-6. We trained all our models with a maximum number of updates of 320,000 and chose the best checkpoint based on the validation set.

In-domain vs Out-of-domain ASR

Given the surge of publicly-available ASR models trained on public data, we sought to answer how well these models perform for the assistant domain. Including out-of-domain experiments in our benchmark opens the space for research work in transfer learning for end-to-end SLU models. We used publicly-available Wav2Vec2.0 [START_REF] Baevski | wav2vec 2.0: A framework for self-supervised learning of speech representations[END_REF] and HuBERT [START_REF] Hsu | Hubert: Self-supervised speech representation learning by masked prediction of hidden units[END_REF] pre-trained models, fine-tuned using a CTC loss [START_REF] Graves | Connectionist temporal classification: Labelling unsegmented sequence data with recurrent neural nets[END_REF] on Librispeech 960h and evaluated them on the STOP eval and test set in addition to the Libripeech test and dev sets. We then took the same models and fine-tuned them using the STOP training set to perform the same evaluation.

Speech pre-training for NLU

Similar to [START_REF] Lugosch | Speech Model Pre-Training for End-to-End Spoken Language Understanding[END_REF], we demonstrate that speech pre-training is a critical component for training end-to-end NLU systems. This work evaluates two speech pre-training methods, namely Wav2Vec 2.0 [START_REF] Baevski | wav2vec 2.0: A framework for self-supervised learning of speech representations[END_REF] and HuBERT [START_REF] Hsu | Hubert: Self-supervised speech representation learning by masked prediction of hidden units[END_REF].

ASR pre-training

In cascaded NLU systems, the semantic parse model can benefit significantly from employing a pre-training like BART [START_REF] Lewis | BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension[END_REF]. Currently audio pre-training is encoder only, leaving the decoder randomly initialized when starting the training for a downstream task in a seq2seq manner. This work also benchmarks the benefit of supervised pre-training of the decoder component. As a secondary pre-training task, we train a seq2seq ASR model that uses the pre-trained encoder. We present systems with ASR pre-training utilizing the STOP and the larger Librispeech datasets.

Low resource end-to-end NLU

Since collecting audio samples with the corresponding parse labels can be impractical due to a variety of concerns, we investigate how much audio intent pairs are needed to build an end-to-end system for a single domain. To this end, we train a HuBERT encoder on the Librispeech training set, then fine-tune it on the held-in domain (either Weather or Reminder). We leverage the low resource splits in 3.3, with SPIS in{10, 25, 50, 100, 250, 500, 1000}, and analyze the error rates with progressively more data.

Domain adaptation for end-to-end NLU models

One way of improving the performance of models trained in the low-resource setting is to perform source training on held in domains, then fine-tune on the low-resource target domain. Similar to the original TOPv2 paper, we study how end-to-end NLU models adapt to new domains.

We study this method by first taking the HuBERT encoder trained on Librispeech then source training on all data samples from "held-in" TOPv2 domains -all domains aside from Weather and Reminder as described in Section 3.3. We then fine-tune our model using the low-resource splits with varying amounts of data for both the Weather and the Reminder domain. We compare our results to the results of 4.6 to see how our models benefits from having previously been train on semantic parse data from different domains.

Leveraging TTS for zero resource and low resource end-to-end NLU

Another way to overcome the cost of collecting large natural datasets is to supplement or replace the training data with synthetic high resource data, which is much cheaper to generate than natural speech. Accordingly, we explore the feasiblity of building end-to-end NLU systems using only TTS data, or leveraging mostly TTS with a small amount of audio and intent pairs from our low-resource splits. To do so, we use the TTS versions of TOPv2 details in Section 3.4, optionally combined with the low-resource training split detailed in section 3.3. In this analysis, all data is from the held-out domain considered (Weather or Reminder).

A comparison of our these ablation studies can be seen in Table 4 Experiment Parse Data? TTS Data?

Low-resource Baseline No No Domain Adaptation Yes No TTS -Low-resource
No Yes Table 4. A comparison of low-resource and domain adaptation ablation studies for the Weather and Reminder domains.

RESULTS AND ANALYSIS

ASR Results for In-domain vs Out-of-domain data

Table 5 shows the results of training ASR models on Librispeech, STOP and a combined dataset. As can be seen, training purely on LibriSpeech performs quite poorly on the STOP eval and test sets, with WER above 25%. By finetuning on the STOP training set however, we are able to achieve the best WERs on the STOP eval and test sets of 4.29 and 4.26 respectively using a HuBERT encoder model. We hope this result demonstrates the significance of our dataset outside of end-to-end systems assistant systems, since it is the largest in-domain assistant ASR dataset as far as we know.

Speech pre-training for NLU

As can be seen in Table 6, speech pre-training is a critical component for end-to-end NLU. Compared to using a randomly initialized model, Wav2Vec2.0 and HuBERT have almost twice the EM accuracy for both valid and test sets. For Tree accuracy, Wav2Vec2.0 and HuBERT improve upon the randomly initialized model by roughly 25% points.

ASR pre-training

In Table 7, we compare the results of performing ASR pretraining across Librspeech and STOP for both HuBERT and Wav2Vec2.0 encoders. As can be seen, leveraging ASR

Low resource Baseline

As shown in Figure 2, we find that scaling up training data greatly improves training model accuracy. EM and EM-tree trend together, though in Reminder, EM benefits more from scaling up training data than EM-tree. This may be a result of the compositional nature of the Reminder domain, as opposed to Weather, which has a more flat semantic structures.

Domain Adaptation

We find that source training significantly increases downstream performance on the target task, especially for the very low resource regime (SPIS < 100), and especially when Weather is the target domain. Interestingly, in the higher resource setting for Reminder, sometimes not performing source training performs better than source training. We speculate that some domains transfer well, while others inter-

TTS-Augmented Low Resource NLU

We compare three models: (1) trained on low-resource natural speech only, (2) trained on a combination of low-resource natural speech and high-resource synthetic speech data, and

(3) trained only on high-resource synthetic speech. We find that even with no natural speech included, (3) performs better than [START_REF] Serdyuk | Towards end-to-end spoken language understanding[END_REF]. Adding natural speech further improves performance, and (2) always performs better than (1). We again observe a difference between the Weather and Reminder domains: the gap between (1) and ( 3) is larger in Weather than Reminder, whereas adding natural speech to TTS improves Reminder more than Weather.

We also compare the performance of the two different TTS methods described in Section 3.3 -for convenience abbreviated as Librispeech and VCTK. We compare models trained on low-resource natural speech supplemented with high-resource Librispeech, VCTK, and the union of the two TTS datasets. We find that including both Librispeech and VCTK generally improves model performance beyond models trained on either of the two individually. This suggests that adding diversity to TTS data transfers to improved per- formance on natural speech test samples.

CONCLUSION

In this work, we: release STOP, the largest SLU dataset for end-to-end semantic parsing, provide initial baselines using both an end-to-end as well as a cascaded system, and show the importance of in-domain ASR training for cascaded systems. Additionally, we find ASR pre-training on top of audio pretraining can lead to improvements in E2E systems, closing the gap to cascaded systems. We believe there are a three particularly promising directions to explore so we may one day reach parity and eventually out-perform cascaded systems. First, is pseudolabeling or model distillation, where we can use a cascaded model to train a end-to-end model on large amounts of unlabeled audio. Second, is building more semantically meaningful representations. We hypothesize cascaded systems surpass E2E systems due to large text pre-training datasets. Third, is building a larger TTS dataset on-top of synthetic utterance-parse pairs. Our current results show impressive performance using only TTS data, and our current TTS data is built only on-top of the TOPv2 utterances, but could be expanded further easily. Finally, while this work did not explore on-device models, we believe end-to-end NLU is especially promising in compute and memory limited environments.

Fig. 1 .

 1 Fig. 1. Semantic Parse from TOPv2 Utterance: Directions to the Eagles game Semantic Parse: [IN:GET DIRECTIONS Directions to [SL:DESTINATION [IN:GET EVENT the [SL:NAME EVENT Eagles ] [SL:CAT EVENT game ] ] ] ] Tree Representation:

Fig. 2 .

 2 Fig. 2. Low resource training in the Weather and Reminder domains, compared to low-resource training after source training on high resource held-in domains (domain adaptation). Source training generally improves downstream target performance.

Fig. 3 .

 3 Fig. 3. Comparison of low-resource training with only low-resource natural speech, low-resource natural speech and full-resource TTS, and full-resource TTS only. TTS generally greatly improves model accuracy, and adding natural speech improves it further in almost all cases.

Fig. 4 .

 4 Fig. 4. Comparison of TTS methods for aiding low-resource training.

Table 2 Table 1 .

 21 Gender Statistics

	Female	Male	Non-binary Unanswered
	44.55% 54.62%	0.79%	0.04%

Table 2 .

 2 Native English Statistics

	Native Non-native Prefer not to say
	95.18%	4.09%		0.73%
	Table 3. Spoken dataset comparison
		FSC	SNIPS SLURP STOP
	Speakers	97	67	177	885
	Audio Files	30043	5886	72277	236477
	Duration[hrs]	19	5.5	58	218

Table 5 .

 5 ASR ResultsEncoderTraining Set dev other dev clean test clean test other stop eval stop test

	HuBERT	Librispeech	8.47	2.99	3.25	8.06	25.68	26.19
	Wav2Vec2.0 Librispeech	9.02	3.31	3.42	8.81	26.53	26.93
	HuBERT	STOP	46.31	31.30	31.52	47.16	4.29	4.26
	Wav2Vec2.0	STOP	48.67	32.51	33.04	49.71	4.43	4.45

Table 6 .

 6 Speech Pre-training

	Encoder	Valid (EM/Tree) Test (EM/Tree)
	End-to-end
	Random	35.28 / 57.73	36.54 / 57.01
	Wav2Vec2.0	67.71 / 83.35	68.05 / 82.53
	HuBERT	67.86 / 83.43	68.40 / 82.85
	Cascaded
	STOP ASR	72.43 / 86.58	72.36 / 85.77
	Librispeech ASR	24.14 / 49.32	31.32 / 60.70
	Text GT	85.65 / 88.43	85.25 / 87.85
	pre-training improves in all scenarios by about 1%. Look-
	ing at HuBERT, the difference between Librispeech ASR
	pre-training and STOP ASR pretraining is small, with Lib-
	rispeech performing slightly better on Test EM accuracy
	and STOP performing slightly better on Test Tree Accuracy.
	Similarly for Wav2Vec2.0, we see STOP ASR pre-training
	perform only slightly better than Librispeech pre-training for
	both Test EM accuracy and Tree Accuracy. We conclude that
	for decoder initialization, having some intelligent initializa-
	tion obtained from ASR pre-training is adequate and does not
	require in-domain pre-training for decent performance gains.

Table 7 .

 7 ASR Pretraining

		Valid (EM/Tree) Test EM/Tree)
	HuBERT
	None	67.86 / 83.43	68.40 / 82.85
	Librispeech	68.83 / 83.45	69.36 / 82.84
	STOP	69.12 / 83.89	69.23 / 82.87
	wav2vec2.0
	None	67.71 / 83.35	68.05 / 82.53
	Librispeech	68.24/83.55	68.47/82.49
	STOP	68.52 / 83.83	68.70 / 82.78
	Cascaded
	STOP ASR	72.43 / 86.58	72.36 / 85.77
	LibriSpeech ASR	24.14 / 49.32	31.32 / 60.70
	GT Text	85.65 / 88.43	85.25 / 87.85
	fere with downstream performance. Further study is needed
	to understand and mitigate this effect.

The dataset can be downloaded at https://github.com/ facebookresearch/fairseq/tree/main/examples/audio_ nlp/nlu


Guillaume Picart

Matéo Pouhaër

Anne Dautel

Matthieu Perard

Justine Le Clerc
email: justine.leclerc@univ-rennes1.fr

Dental students' observations about teaching of endodontic access cavities in a French dental school

Keywords: Undergraduate teaching and learning, endodontics, dental pulp cavity, surveys and questionnaire

Introduction: Teaching in French universities has undergone deep changes for several years. Dental studies are no exception to the rule. Endodontics is one of the most difficult fields requiring good knowledge of anatomy before performing clinical procedures. The access cavity is the key step of endodontic therapy. The aim of this study was to collect and understand what students feel and expect from theoretical and practical training on endodontic access cavity.

Materials and methods:

A questionnaire survey on the teaching and learning of endodontic access cavities in a French dental school was sent by e-mail to the 4 th year students (n=66). The questionnaire consisted of 13 questions of different formats. Qualitative variables were analyzed using a word cloud according to the words of the participants. Students were also asked how to improve teaching with new educational tools.

Results: 60 students answered the questionnaire (response rate of 90.9%). When students were asked which stage of endodontic treatment they feared the most, performing access cavity came in 3 rd place. Upper molar (71%) and lower molar (58%) appeared to have the most difficult endodontic access cavities. Within the word cloud gathered after students' answers analysis, the words "fear","perforation", "cavity" and "axis" were highlighted. Among the 3 new educational tools proposed to students, most were in favour of realistic models of teeth with their ideal endodontic access cavity (79%).

Discussion: This study highlighted the feelings of students during their hands-on training on endodontic access cavities. Although they seemed satisfied with practical classes on endodontic access cavities, this step seemed to be stressful for students especially because of the great internal anatomical variabilities of teeth. To help them better understand the root canal anatomy and improve their training, students asked for new educational resources, especially macro-models of teeth with their optimal access cavities.

Introduction

Today, the field of education has to make a huge effort to offer new resources to improve students learning. Universities are permanently looking for new attractive innovative pedagogy. Medical studies are no exception to the rule. They have undergone deep changes in teaching and learning methods .

New digital simulation tools have been introduced for several years, for example, in nurse education or in the training of heart specialists [START_REF] Erlinger | High-Fidelity M annequin Simulation versus Virtual Simulation for Recognition of Critical Events by Student Registered Nurse Anesthetists[END_REF][START_REF] Oikonomou | Virtual reality and cardiac anatomy: Exploring immersive three-dimensional cardiac imaging, a pilot study in undergraduate medical anatomy education[END_REF].

In dentistry, practical skills development is a complex and challenging process [START_REF] Qualtrough | Undergraduate endodontic education: what are the challenges?[END_REF]. Endodontics is one of the most difficult and stressful dental fields for many students, especially because of the great internal anatomical variabilities of teeth which differ from one patient to another [START_REF] Grock | Experiences during the execution of emergency endodontic treatment and levels of anxiety in dental students[END_REF]. Root canal treatments are composed of several steps which range from access to root canal systems to root canal filling. Access cavity is the first step, which, if not carried out properly, may influence the final result. This generally causes anxiety for most students because bad achievement of this critical step may lead to permanent tooth loss.

To address this problem, the implementation of new educational resources is now considered to improve current teaching and learning. Indeed, Donnely et al. showed that introducing new pedagogical technologies significantly improves the endodontic treatments on multirooted teeth performed by undergraduates [START_REF] Donnelly | A re-audit of the technical quality of undergraduate root canal treatment after the introduction of new technology and teaching practices[END_REF].

Our dental school has already produced several digital resources available online (slideshows, digital sheets with photographs and videos, exercises with Multiple Choice Questions) since 2010, which aim to help 3 rd year students in the learning of theoretical and practical training on endodontic access cavity among other disciplines. However, our dental school has never asked students whether these tools are adequate for their learning and whether they should be interested in new educational devices. Therefore, it seems critical to collect and to consider students opinions in order to enhance key strategies in teaching of endodontics [START_REF] Seijo | Learning Experience in Endodontics: Brazilian Students' Perceptions[END_REF]. Many studies have stated that questionnaire surveys help to resolve lots of issues and to make students acquisition of knowledge and practical skills easier [START_REF] Tanalp | Evaluation of dental students' perception and self-confidence levels regarding endodontic treatment[END_REF][START_REF] Henzi | Appraisal of the Dental School Learning Environment: The Students' View[END_REF][START_REF] Oliver | Curriculum structure: principles and strategy[END_REF][START_REF] Kashbour | Students' perspectives of early and gradual transitioning between simulation and clinical training in dentistry and their suggestions for future course improvements[END_REF].

Accepted Article

The purpose of this study, carried out by a questionnaire, was to know the observations of the 4 th year students about the teaching of endodontic access cavities and about their needs to facilitate their learning and training and reduce stress.

Materials and Methods

Study population and questionnaire administration

The questionnaire survey (Fig. 1), which was drawn up on LimeSurvey (https://www.limesurvey.org/fr), was sent by email to the 4 th year dental students (n=66) of our French dental school during February 2019. As the questionnaire only concerned the learning outcomes, no ethics committee approval was required according to the French regulation. The population studied was composed of 57% of women and 43% of men. The mean age of students was 23 years (SD: 2). A single reminder was sent by email after two weeks to increase the number of respondents. This population was selected because the 4 th year students took part in all practical classes the year before (with 20 hours dedicated to endodontic access cavities during which students were asked to train on about 50 teeth of all types)

and because it shed lights on the students' skills after practical training and didactic teaching and learning. Information about the objectives of the questionnaire were given before completing the questionnaire. Participation was made on a voluntary basis and all answers were entirely anonymous.

The questionnaire consisted of 13 questions of different formats: yes/no questions, closed-ended questions with forced choice or multiple allowable answers and open-ended questions with open answers.

The survey included:

-3 questions related to the theoretical part of the teaching on endodontics and the contribution of the educational resources available online, -8 questions related to training on endodontic access cavities during practical courses (relevance of the program, number of hours devoted to endodontic access cavities, difficulties encountered, etc.), -2 questions related to new educational tools to be developed based on the students' opinions.

With the help of educational engineers of the education department of our university , the questionnaire was developed targeting the objectives of expected answers on the topic of the access cavity. Before the questionnaire was distributed, several readings were carried out by teachers and a few students from the upper years were selected to answer the questionnaire to ensure the relevance, the order of items and the understanding of the questions (pilot study). This questionnaire is a part of the project that was selected in 2018 after a call for proposals launched by the French National Research Agency (ANR), which aims to accelerate the digital transformation of higher educational institutions.

Data collection and analysis

Accepted Article

Data were instantly collected and processed by the LimeSurvey software. Data were recorded in a slideshow, whose statistics were modified after each new answer. Questions with forced choice or multiple allowable answers were presented in the form of graphs. Open-ended questions with qualitative variables were analyzed according to the participants words. The answers were analyzed by topics when possible ("Free comments" section) and with a word cloud generation (www.nuagesdemots.fr) in which the most cited words appeared in larger size and the least cited in smaller size.

Accepted Article

Results

Students' endodontic theoret resources and feelings about educational knowledge ical available online

The response rate for this questionnaire survey was 90.9%. Except for the question on repeating the year, no information on the age, gender or previous academic experience was requested among students who answered the questionnaire. Only one of the respondents repeated the 3 rd year. 39% of students thought their theoretical knowledge about root canal anatomy rather poor or even very poor before their 3 rd year practical classes. 87% of students considered that educational resources for the learning of access cavity preparation, available online, were complementary to lecture courses, tutorials and practical classes. These resources helped them to better understand the concepts seen in class (77%) and to practice dental access cavity preparation (59%). However, some students thought that these tools did not help them quite (29%) or not at all (12%). Furthermore, 60% of students used these resources all along the year while only 36% consult ed them after class and 4%

just before the exam.

Endodontic practical classes

Students were asked to classify the endodontic treatment process from the most difficult step to the easiest (Fig. 2A). Performing endodontic access cavity appeared in third position (55% of students)

after root canal filling (87%) and working length determination (76%). 40% of students considered the endodontic access cavity practical training really good and 54% good. When performing an access cavity, 32% said they had difficulty determining the axis of the tooth without causing perforation, 11% made perforation, 9% did not remove the whole roof of the pulp chamber and 4% achieved a destructive access cavity. Otherwise, 14% of students explained that they either had other difficulties -such as a reduced visibility or root canals that could not be found -sometimes several simultaneously or that they had none at all.

Difficulties differed according to the teeth. Students ranked them from the most difficult tooth to the easiest (Fig. 2B). Upper molar (71%) and lower molar (58%) were the teeth with the most difficult endodontic access cavities. In their clinical practices, students' feelings regarding the endodontic access cavity are quite similar. Half of them do not feel comfortable with this step of the endodontic treatment (Fig. 1).

In the word cloud collected after students' answers, the words "fear", "perforation", "cavity" and "axis"

were highlighted (Fig. 3). A better learning of dental anatomy, root canal system, instrumentation as well as a better preoperative visual and radiological analysis (axis of the tooth and depth of the pulp

Accepted Article

chamber) before gesture are some elements that students would improve if they had to redo their 3 rd year practical work (Fig. 1).

Proposition of new educational tools to students

When students were asked which educational tools and/or approaches should be developed, a lot of proposals were mentioned (Fig. 1). Among the 3 new educational tools proposed to students , realistic macro-models of teeth and their ideal access cavity came first (79%). Interactive 3-dimensional models in augmented reality to visualize root canal anatomy and the development of a virtual reality software allowing performing endodontic access cavity came in second (75%) and third position (56%), respectively (Fig. 1).

Discussion

Endodontics is one of the most technical fields for many students , which requires strong theoretical knowledge on dental anatomy and adequate practical training to better understand the importance of each step of the endodontic treatment. Most of the studies already published focused on students' confidence levels and feelings when undertaking root canal treatments in general and few about students' perceptions of the teaching of endodontics [START_REF] Tanalp | Evaluation of dental students' perception and self-confidence levels regarding endodontic treatment[END_REF][START_REF] Puryer | Undergraduate Confidence When Undertaking Root Canal Treatment and Their Perception of the Quality of Their Endodontic Education[END_REF][START_REF] Alrahabi | The confidence of undergraduate dental students in Saudi Arabia in performing endodontic treatment[END_REF][START_REF] Davey | The confidence of undergraduate dental students when performing root canal treatment and their perception of the quality of endodontic education[END_REF][START_REF] Baaij | Self-efficacy of undergraduate dental students in Endodontics within Aarhus and Amsterdam[END_REF]. The current study focused on students' feelings and expectations about the learning and teaching of the endodontic access cavity, which is one of the skills they should acquire during their curriculum [START_REF] De M Oor R, Hülsmann | Undergraduate Curriculum Guidelines for Endodontology[END_REF]. This study also aimed to evaluate from the students' point of view the relevance of the training program during the 3 rd year which is supposed to ensure an easier transition from preclinical to clinical practice. We obtained a satisfying response rate of 90.9%, which is representative of the opinions of the population studied.

During the dental course which lasts six years, the endodontic program starts in the 3 rd year and ends in the 4 th year in our dental school. The 3 rd year studies are devoted to the basics of endodontics with a year-round program while in the 4 th year, the learning approach is more in-depth and lasts only one published guidelines with a list of skills that students may acquire in endodontics during curriculum and after graduation [START_REF] De M Oor R, Hülsmann | Undergraduate Curriculum Guidelines for Endodontology[END_REF]. Similarly, the Association for Dental Education in Europe (ADEE) sought to develop a joint program, which could be applied in the overall European dental schools [START_REF] De M Oor R, Hülsmann | Undergraduate Curriculum Guidelines for Endodontology[END_REF][START_REF] Cowpe | Profile and competences for the graduating European dentist -update 2009[END_REF][START_REF] Field | The Graduating European Dentist: A New Undergraduate Curriculum Framework[END_REF].

Accepted Article

Our study raised the question of theoretical of our students on the anatomy of root canal systems. Although this topic is widely covered during tutorials, almost 40% of students considered that their knowledge is poor or even very poor. Some students underlined the lack of link between the importance of the access cavity and the quality of the following endodontic treatment. Unfortunately, this lack of knowledge is responsible for procedural errors (problem with teeth axis, perforation…) made when students performed an access cavity during practical classes in most cases [START_REF]Difficulties Encountered during Transition from Preclinical to Clinical Endodontics among Salman bin Abdul Aziz University Dental Students[END_REF]. It should be noted that, in our university, students who still have difficulties in correctly performing endodontic access cavities are invited to train more than the others before assessments. Only students who have acquired the required skills at the end of the evaluations, in particular in carrying out endodontic access cavities, are authorized to move on to the following year.

Students indicated that they felt stressed during the transition from preclinical to clinical endodontics especially when they start treating real patients. Indeed, students seemed to feel more confident with other clinical procedures such as local anesthesia and rubber dam isolation, than with endodontic (or root canal) access cavities [START_REF] Grock | Experiences during the execution of emergency endodontic treatment and levels of anxiety in dental students[END_REF][START_REF] Chandler | Undergraduate endodontic teaching in New Zealand: students' experience, perceptions and self-confidence levels[END_REF][START_REF] Luz | Self-reported confidence and anxiety over endodontic procedures in undergraduate students-Quantitative and qualitative study[END_REF]. Students mentioned upper and lower molars to have the most difficult root canal anatomy, which is consistent with other studies [START_REF] Tanalp | Evaluation of dental students' perception and self-confidence levels regarding endodontic treatment[END_REF][START_REF] Chandler | Undergraduate endodontic teaching in New Zealand: students' experience, perceptions and self-confidence levels[END_REF][START_REF] Luz | Self-reported confidence and anxiety over endodontic procedures in undergraduate students-Quantitative and qualitative study[END_REF]. Although the training in endodontic access cavity appeared to be satisfying or very satisfying for more than 90% of students, half of them stated they did not feel confident with this step of the endodontic treatment, especially in real clinical conditions, as was confirmed by Grock et al. [START_REF] Grock | Experiences during the execution of emergency endodontic treatment and levels of anxiety in dental students[END_REF]. Within the word cloud collected after students' answers analysis, the word "fear" is highlighted. Indeed, the words "perforation", "perforating" and "axis" underlined the main cause of students' anxiety because mistakes in performing endodontic access cavity could lead to permanent loss of teeth [START_REF] Luz | Self-reported confidence and anxiety over endodontic procedures in undergraduate students-Quantitative and qualitative study[END_REF]. Heimerl et al. raised that the use of word clouds in qualitative studies are significant because they summarize very important information lost in the large quantity of data [START_REF] Heimerl | Word Cloud Explorer: Text Analytics Based on Word Clouds[END_REF].

In our study, another point was identified by students. Educational resources, produced in our school on dental access cavities (photos, videos and explanatory texts) and available online, seem ed to be insufficient for some students. A quarter of them reported that they did not help them to unders tand this step of the endodontic treatment before training in practical classes. For others, they were unsuitable for training but were additional support to lecture courses. However, 59% of them thought that they helped them to train in performing access cavity in an effective way especially thanks to exercises with Multiple Choice Questions (MCQ) recently made available online. Furthermore, these resources were viewed all along the year by the majority of students, which confirms the seeking of available resources for reinforcing the knowledge base. Some disparities became apparent and it seemed that our students' needs differ. Indeed, while some students content themselves with face-toface lessons only, others fell the need to look for other information elsewhere such as in books, internet resources, demonstration videos… In order to target as many students as possible, it therefore seems necessary for teachers to diversify educational contents by offering a variety of activities and/or tools to give students the choice in the way to learn and facilitate their learning [START_REF] Pratt | Five perspectives on teaching in adult and higher education[END_REF].

Accepted Article

Some students complained about the absence of resources which could facilitate the learning dental access cavity preparation by allowing a better spatial visualization of the root canal spaces. Nevertheless, our students are already familiar with realistic model of teeth in restorative dentistry practical classes. In the questionnaire, they mainly asked for a three-dimensional endodontic model of teeth with their ideal access cavity pre-prepared to better visualize the location of root canal orifices, the root canal anatomy and the shape of dental access cavity. Luz et al. pointed up the importance of three-dimensional spatial visualization. Indeed, participants reported that they did not feel safe when performing endodontic treatments due to the difficulty in visualizing anatomical complexities [START_REF] Luz | Self-reported confidence and anxiety over endodontic procedures in undergraduate students-Quantitative and qualitative study[END_REF]. Clear instructions about the good axis of preparation and about the type of burs to use were also two important elements for students. They also requested videos showing the realization of endodontic access cavity in a real clinical situation. These videos could help them to view the techniques and the gesture to obtain an ideal access cavity. Training bas ed on drawing (that is already done in tutorials), additional photographs of access cavities and individual supervision during practical classes were also requested.

Surprisingly, among the 3 new educational tools proposed to students, realistic models of teeth and their ideal access cavity came first for almost 80% of them, ahead of digital technologies. It is very likely that our students find that handling physical models is more practical. It may also be easier for them to replicate the observed shape of the endodontic access cavity onto their training teeth.

Although explanations were given to students, it is also likely that students did not visualize perfectly what augmented or virtual reality is, especially since they have had very few opportunities so far to use these technologies in their curriculum. This is why the development of digital software to observe and/or to achieve endodontic access cavity has also been discussed. Some authors were interested in this type of new technologies but showed there was no difference in the reduction of procedural errors during endodontic access cavity preparation between students who trained on the haptic virtual reality simulator compared with those who trained on conventional phantom head [START_REF] Suebnukarn | Access cavity preparation training using haptic virtual reality and microcomputed tomography tooth models[END_REF]. Although they look promising in particular in learning endodontic access cavity preparation, these tools were not selected in our study because they need to be improved to facilitate the learning of endodontics. It is of course obvious that the use of physical macro-models can be easily combined with augmented and virtual reality software to perfect the knowledge and learning of the endodontic access cavity by our students.

However, this study has some limitations. First, as it aimed to obtain an overall opinion of the population studied and not an analysis of the data by age, gender or previous academic experience, no such information was requested to participants. The fact that they did not have to fill in this kind of descriptive element likely resulted in the high participation rate. Moreover, while students ranked the endodontic access cavity in third place after working length determination and root canal filling, this study focused more particularly on this particular step. With regard to the working length determination, it should be noted that our students do not have apex locators during practical work

Accepted Article

sessions. This may therefore explain why they found this difficult. Apex locators are available from the 4 th year during their clinical apprenticeship, which makes this step easier. In addition, the difficulties experienced by students in root canal filling undoubtedly come from the fact that they only carry out manual root canal shaping (and not with mechanized instruments) during their 3 rd year study. This final stage generally highlights all the steps previously carried out. Errors during endodontic access cavities or incorrect working length determination can be responsible for poor root canal fillings. Although aware that each stage of the endodontic treatment can present difficulties, it seemed important to take an interest in the particular stage of endodontic access cavities, which requires an in-depth knowledge of dental and root canal anatomy and for which teachers in our university reported the most procedural errors committed by students. Although a large majority of our 4 th year students answered the questionnaire, this only represents a little part of all of our students.

The choice to survey the 4 th year students and not the 3 rd year or final year students (5 th and 6 th year)

was made because the 4 th year students had participated in all endodontic hands -on training courses and had more perspectives on teaching than the 3 rd year students. Although they have not yet been confronted with emergency situations, they all had a little clinical experience. Indeed, in France, the care of patient by dental students starts at the beginning of the 4 th year and usually ends in 6 th year.

At the time of the questionnaire, the students interviewed had already treat ed patients, especially for endodontics. Without taking into account other disciplines, each 4 th year students are asked to perform 6 endodontic treatments on average over the year. Finally, this study only concerns one French dental school. A larger study including all French dental universities could be intended to confirm our results as it was done in other countries [START_REF] Qualtrough | Undergraduate endodontic teaching in the United Kingdom: an update[END_REF][START_REF] Raisi | How is Endodontics taught? A survey to evaluate undergraduate endodontic teaching in dental schools within the United Kingdom[END_REF].

Conclusion

Access cavity preparation is the first step in endodontic treatments, that should not be neglected because it may affect the rest of the treatment. Although students do not place the access cavity first in the most difficult stages, our study highlights that half of students are afraid to perform this step especially in real clinical situations because they are aware of any procedural errors. The aim of this study was also to collect information about the educational resources available online from students who carried out both practical and clinical work. These resources seem to be of interest but not enough for many students. The survey identified a need to improve teaching and learning in our university. The main difficulty in education lies in the fact that not all students learn and understand the lessons and given instructions the same way. To facilitate the learning of the greatest number of students, a few proposals of new innovative resources in addition to traditional resources have been made. The great majority of students expressed a real interest in realistic models of teeth and their ideal access cavity.

Accepted Article

Titles of figures

  semester. For the practical part, students benefit from several hands -on training sessions before being regularly assessed throughout the year. Without taking into account the students' personal working time, 3 rd year students have 27 hours of lecture courses and tutorials (including 6 hours on endodontic access cavity) and 60 hours of practical classes (including about a third of the time devoted to endodontic access cavities) throughout the year. The time allocated to endodontics in our university seems to be an appropriate time compared with some other dental schools in Europe and in the world[START_REF] Grock | Experiences during the execution of emergency endodontic treatment and levels of anxiety in dental students[END_REF][START_REF] Davey | The confidence of undergraduate dental students when performing root canal treatment and their perception of the quality of endodontic education[END_REF][START_REF] Qualtrough | Undergraduate endodontic teaching in the United Kingdom: an update[END_REF][START_REF] Hayes | An audit of root canal treatment performed by undergraduate students[END_REF][START_REF] Chandler | Undergraduate endodontic teaching in New Zealand: students' experience, perceptions and self-confidence levels[END_REF][START_REF] Qualtrough | Preclinical endodontology: an international comparison[END_REF]. Indeed, De Moor et al. showed that the time and resources dedicated to endodontics differed between dental schools. The European Society of Endodontology (ESE)

Fig. 1 2 3

 123 Fig. 1 Questionnaire and students' answers Fig. 2 Ranking in order of difficulty according to students (A) Stages of endodontic treatment (B) Endodontic access cavities for different groups of teeth Fig. 3 Frequency of words regarding the achievement of dental access cavities according to students

The authors would thank the DUNE DESIR committee (University of Rennes) for selecting and supporting this project, the educational engineers of SUPTICE especially Priscille Hébert and Clément Cariou for technical and logistical supports and the 4 th year students (year

Data Availability statement

The data that support the findings of this study are available on request from the corresponding author upon reasonable request.


C Dumouchel

J.-B Blaisot

V D Ngo

Representation of Laser Diffraction Diameter Distribution with a 3-Parameter Generalized-Gamma Function

The problem of the mathematical representation of liquid spray drop-size distribution has not been fully answered and is still debated in the literature. The present work participates to this debate by investigating the adequacy between the 3-parameter Generalized-Gamma function and the Laser Diffraction Technique (LDT) spray drop-size distribution. It is first pointed out that the 3-parameter Generalized-Gamma function and LDT distributions report similar properties. These similarities plead to the necessity of considering three parameters to reproduce LDT distribution. On this basis, a protocol to determine the three parameters is suggested and tested on experimental distributions measured for this purpose. In order to have the information concerning the actual small drop population, an Image Analyzing Technique (IAT) is used in complement to the LDT. The results show that the mathematical function reproduces very well the whole LDT drop-diameter distribution, its fractal characteristic and the mean-diameter series. Above this, these results were free of any parameter instability problem and the three parameters of the mathematical function display a clear relationship with the injection pressure. This work allows approaching a physical interpretation of the mathematical parameters in this situation. One of them characterizes the actual small drop population and the two others, the rest of the population as well as average information on the deviation from sphericity of the spray elements. These results reveal interesting aspects of the LDT diagnostic that are presented.

Introduction

The question of a universal mathematical function to represent spray drop-size distribution has been addressed for many years and the number of parameters such a function should include is still debated. The ability of a mathematical function to represent liquid spray drop-size distribution is quantified by exploring its capability of representing experimental data. Since experimental diagnostics are not sensible to the same spray characteristics, we have reasons to believe that the more appropriate mathematical function to represent experimental data depends on the diagnostic used. In the present paper, we investigate the adequacy between the 3-parameter Generalized-Gamma function and Laser Diffraction Technique (LDT) distribution. The objective is to investigate the appropriateness of the 3-parameter Generalized Gamma function to represent LDT distribution and to propose and test a protocol to determine the parameters.

The 3-parameter Generalized-Gamma function has been established by a Maximum Entropy Formalism model [1]. This distribution is mathematically identical to the empirical Nukiyama-Tanasawa distribution that has been identified as very competent to reproduce measurement data [START_REF] Paloposki | Drop-Size Distribution in Liquid Sprays[END_REF]. However, parameter instabilities that manifests by a drastic change of their values for reasonable changes in operating condition have been reported and question the relevance of the three parameters. This point is addressed here.

The LDT is a commonly used laser-based technique to measure spray drop-diameter distributions [3,4]. One of particularity of this technique is that it measures drops of any shape that goes through the instrument optical probe. Thus, the resulting drop-diameter distribution characterizes an equivalent system made of spherical elements [4]: it is the volume-based drop-diameter distribution of a set of spherical droplets that would produce the same diffraction pattern as the one recorded. Several investigations reported that this distribution is dependent on the shape of the droplets [5,6]. This aspect of the instrument is taken into account in the present work by conducting an experimental work that cumulates two diagnostics to characterize liquid spray: LDT and an Image Analyzing Technique (IAT).

The 3-Parameter Generalized-Gamma Function

The notations adopted throughout this paper are as follows. F(D) expresses a cumulative distribution of droplets with a diameter less than D and the distribution f(D) is the first derivative of this cumulative. Furthermore, the cumulative and distribution have a subscript n that indicates the description order: n = 0 designates the Corresponding author: Christophe.Dumouchel@coria.fr 2 number-based distribution; n = 1 the length-based distribution, n = 2 the surface-based distribution and n = 3 the volume-based distribution. The general n-order expression of the 3-parameter Generalized-Gamma function is:

q q n q n q n n n D D q exp D D q q n q D D F D f 0 0 1 d ) ( d ) ( (1)
where is the Gamma function and q, and D q0 are the three parameters. The two first parameters have no dimension and the last one is a mean-diameter of the series standardized by Mugele and Evans [1]. Despite the fact that q and can be either positive or negative provided they have the same sign [8], only positive parameters are considered in this work. One of the advantages of the 3-parameter Generalized-Gamma Distribution is that calculations can be performed [1]. In particular the mean-diameter series can be calculated:

b a q q b a b a ab D q b q a q D 0 (2)
where a and b can take any real values provided that they are different. In the literature a + b is sometimes called the mean-diameter order. Being based on an exponential function, the distribution attributes extremely low frequencies to extremely large drops and imposes infinitely great maximum diameter, which is non-physical. In consequence the calculation of high-order mean-diameters with Eq. ( 2) is prohibited since they monotonously increase with the order. In real sprays, the infinite order mean-diameter tends toward the diameter of the biggest drop.

The 3-parameter Generalized-Gamma function (Eq. ( 1)) is mathematically identical to the well-known Nukiyama-Tanasawa distribution and covers the Rosin-Rammler and the Weibull distributions [1]. These three empirical distributions have often been used in the literature to reproduce measurement data with sometimes a high degree of agreement. For instance, Paloposki [START_REF] Paloposki | Drop-Size Distribution in Liquid Sprays[END_REF] demonstrated that the Nukiyama-Tanasawa function is among the best to reproduce measurement data. Therefore, there is no doubt that the mathematical function given by Eq. ( 1) is competent in representing liquid spray drop diameter distribution in many different situations. (An illustration of this is available in [9].) A problem often reported when fitting measured data is the lack of stability of the parameters that manifests by a drastic variation of the parameters for reasonable changes in initial conditions. This can be illustrated by the fact that different parameter triplets can provide indiscernible distributions. This point is depicted in Fig. 1-top for a series of volume-based drop-diameter distributions f 3 (D). Such behaviour suggests that two parameters might be sufficient to provide an acceptable fit of the shape of the distribution. In other word, one may wonder whether we could take benefit of the presence of a third parameter to include another distribution characteristic in the fitting process.

The volume-based distributions shown in Fig. 1-top are reproduced in Fig. 1-bottom in a Log-Log plot. This representation reveals two important points: 1the distribution is proportional to a power of the diameter in the small diameter region; 2this dependency is a function of the parameters. The behaviour depicted in the small diameter region is observed for the cumulative as well as for the distribution whatever the order of description. It can be shown that in the small drop diameter region: From a physical point of view, the dependency expressed by Eq. ( 3) has often been related to the self-similarity nature of fragmentation processes and therefore to the concept of fractal scaling [10][11][12]. On the other hand the fractal nature of liquid atomization processes has been experimentally reported [13,14]. Therefore, the behaviour expressed by Eq. ( 3) in which is a fractal dimension is physically relevant.

By examining Eq. ( 1), we note that the new function D q0 f n (D/D q0 ) as a function of the new variable D/D q0 is independent of the mean diameter D q0 . Therefore, the fractal dimension is independent of this parameter. A parametric investigation where q was varied from 0.1 to 1.4, from 2 to 6 and was determined in the variable range D/D q0 [10 -5 ; 10 -4 ] reported the following relationships:

091 0 - exp 1 . q (4)
Equation ( 4) is illustrated in Fig. 2. We note that when q is greater than 1, the fractal characteristic is equal to the parameter . This agrees with Eq. ( 1). In this situation, the parameter q controls the large diameter drop population only [1]. However, we see that when q is less than 1, becomes a function of q, which therefore influences the small drop population also.

The results shown in Fig. 2 and in Eq. ( 4) reveal that different parameter triplets can report the same fractal characteristic. An example is presented in Fig. 3. However, this figure shows that despite the equality of the fractal dimension, the distributions are different. Therefore, the results in Figs. 1 and3 demonstrate that the three parameters ensure independence between the shape of the distribution and the fractal characteristic. Of course two-parameter drop-diameter function would not report such a performance. For instance, the Rosin-Rammler distribution which is mathematically identical to Eq.( 1) with = q -3 [1] has therefore a shape and a fractal dimension that both are imposed by the unique parameter q.

Equation ( 4) reproduced in Fig. 2 says that small q influence the fractal dimension. The influence of this parameter on the diameter distribution is shown in Fig. 4 (the two other parameters are kept constant, i.e., = 3; D q0 = 100 µm). The top graph shows the volume-based drop-diameter distribution when q ranges from 0.2 to 8. As expected, we see that when q is great the distribution is stiff and as q decreases, the distribution spreads towards the large diameter population. As far as f 0 (D) is concerned, we see that when q decreases, the maximum of the distribution first decreases and then increases whereas the peak diameter continuously decreases. We note that the distribution maximum is the smallest when the parameter q is of the order 0.4. This value is also the one under which the fractal dimension becomes dependent on q (see Fig. 2). Figure 4 illustrates to which extend small q influence Finally, it can be seen that the above behaviour has repercussion on the mean-diameter series by calculating the mean-diameter ratio D m2 /D 32 with the help of Eq. ( 2). This ratio that depends on the order m and on and q only, was calculated for a wide range of q and values, and for m maintained between 3 and 7, since, as explained above, high-order mean-diameters should not be calculated. For all calculations, the following relationship between the mean-diameter ratio and the order m was obtained:

0 1 2 2 32 2 ' a m ' a m ' a D D m (5)
The a' 2 coefficient introduced in Eq. ( 5) is presented in Fig. 5. We see that when q > 0.8, Eq. ( 5) is linear and that it is a second order polynomial relationship otherwise. Thus, small values of q also change the dependence between the mean-diameter series and the mean-diameter order.

Adequacy between LDT distribution and the 3-paramater Generalized-Gamma function and parameter determination

The question to be addressed here is whether the three parameters of mathematical function are necessary to reproduce LDT drop-diameter distribution. The answer can be approached by comparing LDT distribution and 3-parameter Generalized-Gamma function properties. A recent experimental work reported that LDT mean-drop diameter series followed a linear or a second order polynomial relationship with the mean diameter order [6]. As demonstrated in the previous section, the 3-parameter Generalized-Gamma allows reproducing such a characteristic thanks to the parameter q. Besides this, keeping the parameter ensures independence between the distribution shape and the fractal dimension, or, between the mean diameter series and the fractal dimension. Therefore, the three parameters should allow providing a better description than only two.

The question concerning the determination of the mathematical parameters is now addressed by considering the origin of the 3-parameter Generalized-Gamma function. This function has been established from a model based on the use of the Maximum Entropy Formalism (MEF) in which two constraints were written [1]. One of them ensures the existence of a maximum drop-diameter via the introduction of the parameters q and D q0 . The second constraint expresses the fact that diameter classes are not equally probable since the energy required to produce a given drop increases as its diameter decreases. Thus, a diameter-class probability distribution is imposed, limiting the production of small droplets. This second constraint introduced the parameter as the fractal dimension in the small drop-diameter range. In consequence, the analysis of this very population should return this parameter. The problem is that the LDT drop-diameter distribution depends on the shape of the droplets and characterizes an equivalent system of spherical drops that would produce the same diffraction pattern as the one recorded. As demonstrated by Mülhenweg and Hirleman [5], the variation of the shape of the elements modifies the whole equivalent LDT diameter distribution. Thus, the small drop population reported by LDT might not correspond to actual drops.

To overcome this problem, we suggest getting the information on actual small drops from a different diagnostic based on visualization and image analysis and to determine the value of the parameter on the actual small drop population. Once this parameter is determined, the two other parameters are determined as those ensuring the best fit of the LDT distribution. This protocol is tested in the second part of the paper.

Experimental setup and Diagnostics

Water sprays produced by a single injector at several injection pressures are characterized. The injector used is a triple-disk injector whose description can be found elsewhere (Inj. 2 in [6]). It has a single cylindrical orifice whose diameter is equal to 400 µm. The liquid flow issuing from this injector is a 2-dimension liquid sheet whose disintegration produces a rather 2-D spray. The injection pressure ranges from 0.2 MPa to 1 MPa and the injection is steady.

The Laser Diffraction Technique (LDT) equipment used in this work is the Spraytec 1997 from Malvern. It employs the Lorentz-Mie theory to calculate the drop-diameter distribution from the light diffraction pattern. The optical probe is a cylindrical laser beam with a wavelength equal to 670 nm and a diameter equal to 10 mm. The Spraytec is equipped with a 450 mm focal length collecting lens. This Fourier lens together with the 32 diodes of the receiver allows drop diameter ranging from 8.56 µm to 1040.72 µm to be measured. However, the parameters of the inversion code were determined in order to ensure a nice shape of the distribution in the small diame- ter range with no undesirable secondary peaks. This was obtained by fixing a minimum diameter equal to 5 µm to 12 µm when the injection pressure decreases from 1 to 0.2 MPa. The adjustable sampling frequency of the instrument was set to 10 Hz and measurements were performed during 5 s. The drop-diameter distributions measured during this time interval were averaged. The center of the laser beam was positioned at 12 mm from the nozzle exit, distance at which the atomization process is completed for each operating condition as shown by the images described later. The transmission of the measurements, which is defined by the ratio of the non-deviated light intensity to the incident light intensity, was never less than 75%. According to experimental results reported on similar sprays [15], this value indicates negligible multiple-scattering effects. The optional light multiple-scattering algorithm is therefore not selected. The LDT reports a volume-based drop-diameter distribution f 3 (D). Using the traditional relationship between the diameter distribution of different orders, the corresponding surface-based drop-diameter distribu-

tion f 2 (D) is calculated from ) ( ) ( 3 32 2 D f D D D f (6)
Snapshots of the sprays are performed using a shadowgraph optical arrangement. The light source is a Nanolite from HSPS with a flash duration equal to 20 ns. In the present configuration, this light source plays the role of the shutter. The high resolution CCD camera is a DALSA (4016x2672 pixels) equipped with an objective that allows covering a physical field equal to 10.5 mm x 7.0 mm. This arrangement corresponds to a spatial resolution equal to 2.6 µm/pixel. The centre of the image is located at 12 mm from the injector exit section. So LDT and Image Analysing Technique (IAT) cover almost the same portion of the spray.

The objective of the Image Analysing Technique is to provide supplementary information on the spray dropsize distribution in order to complete the LDT information. For this purpose, two points have to be addressed 1the drop characterisation; 2the drop selection. As far as the first point is concerned, we adopt here a classical approach that consists in characterizing each drop by the diameter of the circle that has the same area as the 2-D projection of the drop. Thus, being sensitive to the surface, the equivalent-diameters are used to build surfacebased drop-diameter distributions f 2 (D). The drop selection is a tricky problem that has been considered with care in this work. IAT and LDT do not have the same measurement volume. LDT integrates all information along the optical axis (x-axis) whereas IAT considers sufficiently in-focus drops only. Thus, the two diagnostics do not perform the same spray sampling. This problem has been solved by performing a tomographic spray sampling thanks to a sophisticated technique developed in previous investigations [16,17]. This technique allows the determination of the measurement volume, whatever the size of the drops, by the calibration of the Point Spread Function (PSF). For the present optical arrangement, the PSF calibration reported a measurement volume depth equal to 500 µm. Then, considering the size, contrast and grey level gradient of any drop in the image, it is possible to know whether this drop belongs to the measurement volume and therefore whether it should be taken into account. By moving the spray along the optical axis (x-axis) with a step equal to the measurement volume depth, this protocol allowed performing a tomographic sampling of the spray and reconstructing a whole spray information from each slice.

A preliminary test revealed that elements with an equivalent diameter less than 10 µm were incorrectly measured. Therefore, these elements were disregarded. At each position of the measurement volume along the optical axis and for each injection pressure, the number of images taken and analysed was equal to 40. It was checked that the information cumulated from these 40 images was statistically representative.

At 0.6 MPa, the number slices to cover the whole spray is equal to 15. This is shown in Fig. 6 which presents the percentage A s of local liquid surface fraction, namely, local liquid surface area divided by total liquid surface area, as a function of the position x of the measurement volume on the optical axis. As expected, the slice under the injector (x = 0) contains the greatest liquid proportion.

To lighten the experimental protocol and analysis, we evaluated the number of slices to be considered in order to ensure representative surface-based drop-diameter distributions. For the same situation as the one presented in Fig. 6, the results are shown in Fig. 7. This figure compares the surface-based drop-diameter distribution as a function of the considered spray slices. We see that when the four central slices are considered, the resulting surface-based drop-diameter distribution is identical to the one constructed with all slices. We note also that the distribution obtained with the central slice only is very close to the all-slice distribution. Therefore, we limited the measurement and analysis to the central slice only assuming that, for all injection pressures, it was sufficiently representative of the whole spray.

Results and Applications

Figure 8 presents the LDT volume-based drop-diameter distribution. The traditional bell shape are seen. When the injection pressure increases, the modal diameter (diameter for which the distribution is maximum) decreases, the distribution maximum increases and the distribution tail collapses. This behaviour illustrates the increase of small particle production as the injection pressure increases.

As said above, LDT reports the volume-based drop-diameter distribution of the set of spherical elements that would produce the same diffraction pattern as the one recorded. This information depends on the shape of the particles [5]. To estimate the presence of non-spherical droplets, one compares the surface-based dropdiameter distributions corresponding to the LDT distributions with those obtained by IAT. This comparison is shown in Fig. 9 (Top graph) where LDT surface-based distribution is calculated from Eq. ( 6). If all droplets were perfectly spherical, and considering that both diagnostics perform an identical spray sampling as demonstrated in the previous section, LDT and IAT surface-based distributions should be the same. We see in Fig. 9 that this is not the case. Generally speaking, the small drop population is always greater with LDT than with IAT. This result says that the present spray contain non-spherical drops.

Non-spherical drops are always among the biggest elements and are characterized by great equivalent diameters. These diameters might be meaningless if the deviation from sphericity is great. On the opposite side of the diameter space, the small droplets are rather spherical and the IAT equivalent diameter is very near the actual diameter. Thus, the small drop population reported by IAT can be seen as a good estimation of the actual small-drop population.

The small drop population difference between the two diagnostics is clearer in the bottom graph of Fig. 9 where the distributions are compared in a Log-Log scale. We see that the excess of small drops detected by LDT induces a decrease of the fractal dimension compared to the actual small drop population reported by IAT. Of course, we must keep in mind that the definition of the small drop population is dictated by the limitation of the experimental diagnostics. In the present work, the smallest detectable diameter for both diagnostics is of the order of 10 µm and the diameter of the small drop population ranges from 10 to 30-40 µm according to the injection pressure (see Fig. 9).

Following the MEF constraints from which the 3-parameter Generalized-Gamma function has been derived and that were men- tioned above, the parameter characterizes the actual small-drop population: is taken equal to the fractal dimension in the IAT small drop population and according to Eq. ( 3) is determined from the IAT surface-based drop-diameter distributions as indicated in Fig. 9-bottom. The parameters obtained this way are shown in Fig. 10 as a function of the injection pressure. The interesting aspect of these results is that the parameter shows a clear dependency with the injection pressure and no parameter instability is reported. Using these parameters, the two other parameters (q and D q0 ) ensuring the best fit with the LDT volume-based drop-diameter distributions have been determined. This was achieved via a 2 technique that consists in minimizing the "distance" between the measured and the mathematical distributions. This minimization was performed with the software Scilab. The resulting parameters q and D q0 are presented in Fig. 10 also. Note, as for the parameter , the clear evolution of these parameters with the injection pressure and the total absence of any parameter instability.

Figure 10 shows that the decrease of the parameters of the Generalized-Gamma function with the injection pressure follows a power law. Whereas the power for the parameter q appears constant over the injection pressure range, the powers for the two other parameters decrease when the injection pressure becomes greater than 0.6 MPa. Although this specific behaviour has not been physically interpreted, it reveals a certain coherence of the parameter evolution with the injection pressure. The arithmetic mean of the mathematical volume-based drop-diameter distribution, i.e., the mean-diameter D 43 , is plotted as a function of the injection pressure in Fig. 10. As often reported in the literature, we see that this mean-diameter decreases as the injection pressure increases following a power law. Note that, contrary to the parameters and D q0 , the power for D 43 is constant over the investigated range of injection pressures.

The comparisons between the measured and the mathematical volume-based drop-diameter distributions are presented in Fig. 11. The top graph of this figure is a plot with linear scales and shows the results for three injection pressures. We note the very good agreement between the mathematical and the measured distributions. Such agreements have been obtained for the other injection pressures. The bottom graph of the same figure presents the same result in a Log-Log scale. We see that, besides the whole distribution shape, the behaviour in the small drop-population is very well reproduced by the mathematical function. Remembering that the fractal properties of LDT and IAT distributions are different (Fig. 9) and that the mathematical function fractal dimension depends on and q only (Eq. ( 4)), we conclude that this agreement is due to an adjustment of the parameter q.

As far as the mean-diameter series is concerned, a good agreement between experimental and calculated results is obtained (Fig. 12). In complement, Fig. 13 shows that the experimental and mathematical evolutions of the mean-diameter ratio D m2 /D 32 as a function of the order m well agree also. The most interesting behaviour concerns the general evolution of the series. We see that both measured and calculated series report similar relationships with the order m: it is linear for low injection pressures and becomes a 2 nd order polynomial dependence as the injection pressure increases.

We have demonstrated that the 3-parameter Generalized-Gamma function is well adapted to represent LDT drop-diameter distribution and that, when correctly chosen, the adjustable parameters are not unstable. In this investigation, the LDT diameter distribution characterizes an equivalent system of spherical elements since the actual droplets are not spherical. The parameter characterizes the actual small drop population. These droplets are spherical. On the other hand, the parameters D q0 and q control the rest of the population that might contain non-spherical elements. We therefore wonder whether the parameter q is sensitive to the lack of sphericity of the droplets. This point is investigated by measuring two shape parameters from the spray images, namely, the sphericity and the uniformity, and to calculate their averages for each operating conditions. These parameters defined in [16] are equal to 0 for spherical elements and increase when the deviation from sphericity is more and more pronounced. The sphericity parameter varies from 0 to 2 whereas the uniformity parameter varies from 0 to infinity. Figure 14 shows that the parameter q strongly correlates with these two shape parameters. The correlations indicate that the two shape parameters become equal to 0 when q = 1. This result says that values of q less than 1 corresponds to a set of non-spherical drops. In agreement with previous results [6], Fig. 5 indicates that in these situations, the LDT mean-diameter series shows a second order dependence with the mean-diameter order. This result also says that LDT drop-diameter distribution contains average information on the deviation from sphericity of the spray droplets.

Discussion and Conclusions

As reported by other investigations ( [START_REF] Paloposki | Drop-Size Distribution in Liquid Sprays[END_REF]9] for instance), the results of this work confirm that the 3-parameter Generalized-Gamma function provides excellent reproduction of LDT volume-based drop-size distribution. Furthermore, this work proposes a protocol to determine the value of the adjustable parameters. Beside the LDT drop-diameter distribution, the results show that the 3-parameter Generalized-Gamma function provides a good representation of the fractal dimension of the distribution as well as of the mean-diameter series. Another interesting aspect of this result is that the adjustable parameters are not instable. Therefore, three parameters can provide a better representation of the measurement.

This work allows approaching a physical interpretation of the mathematical parameters when representing LDT drop-diameter distributions. The parameter qualifies the actual small-drop population, and is equal to the fractal characteristic of this population. The parameters D q0 and q qualify the rest of the population and q contains information on the lack of sphericity of the spray drops.

As far as the LDT technique is concerned we confirm that it is dependent on the shape of the droplets and learn that the presence of non-spherical droplets is interpreted as supplementary contribution in the small droplet range. Finally, thanks to the application of the mathematical function, we demonstrate that the LDT distributions contain average information on the lack of sphericity of the spray droplets. This conclusion agrees with those obtained in a previous investigation [6].

Figure 13

Comparison of the meandiameter ratio series (dots: measurements; lines: calculations) Figure 14 Correlation between the q parameter and men sphape parameters of the sprays

Figure 1

 1 Figure 1 Example of 3-parameter Generalized-Gamma function of different parameter triplets (q; ; D q0 ) (Top: linear plot; Bottom: Log-Log plot)

Figure 2 Figure 3 Figure 4

 234 Figure 2 The fractal dimension as a function of q

Figure 5

 5 Figure 5 Evolution of the parameter a' 2 as a function of q and

Figure 6 Figure 7

 67 Figure 6 Percentage of liquid surface in each spray slice

Figure 9 Figure 8 Figure 10

 9810 Figure 9 Comparison between LDT and IAT surface-based drop-diameter distribution (top: linear scale; bottom: Log-Log scale)

Figure 11 Figure 12

 1112 Figure 11 Comparison between the LDT (dots) and the 3-parameter Generalized-Gamma (lines) volume-based drop-diameter distributions