Samuele Cornell
email: s.cornell@pm.univpm.it

Maurizio Omologo
email: omologo@fbk.eu

Stefano Squartini
email: s.squartini@univpm.it

Emmanuel Vincent
email: emmanuel.vincent@inria.fr

Detecting and Counting Overlapping Speakers in Distant Speech Scenarios

Keywords: overlapped speech detection, speaker counting, distant speech, forced alignment

We consider the problem of detecting the activity and counting overlapping speakers in distant-microphone recordings. We treat supervised Voice Activity Detection (VAD), Overlapped Speech Detection (OSD), joint VAD+OSD, and speaker counting as instances of a general Overlapped Speech Detection and Counting (OSDC) task, and we design a Temporal Convolutional Network (TCN) based method to address it. We show that TCNs significantly outperform state-of-the-art methods on two real-world distant speech datasets. In particular our best architecture obtains, for OSD, 29.1% and 25.5% absolute improvement in Average Precision over previous techniques on, respectively, the AMI and CHiME-6 datasets. Furthermore, we find that generalization for joint VAD+OSD improves by using a speaker counting objective rather than a VAD+OSD objective. We also study the effectiveness of forced alignment based labeling and data augmentation, and show that both can improve OSD performance.

Introduction

Reliable multi-party speech diarization [START_REF] Ryant | Enhancement and analysis of conversational speech: JSALT 2017[END_REF][START_REF] Sell | Diarization is hard: Some experiences and lessons learned for the JHU team in the inaugural DIHARD challenge[END_REF][START_REF] Diez | BUT system for DIHARD speech diarization challenge 2018[END_REF][START_REF] Ryant | The second DIHARD diarization challenge: Dataset, task, and baselines[END_REF] and recognition [START_REF] Li | Robust Automatic Speech Recognition -A Bridge to Practical Applications[END_REF][START_REF] Watanabe | New Era for Robust Speech Recognition -Exploiting Deep Learning[END_REF][START_REF]Audio Source Separation and Speech Enhancement[END_REF][START_REF] Haeb-Umbach | Speech processing for digital home assistants: Combining signal processing with deep-learning techniques[END_REF] is still one of biggest challenges in the field of speech processing. It is well known that one of the main obstacles is the presence of overlapped speech which arises naturally in spontaneous human conversations. In fact, when encountered, speech recognition and diarization performance can degrade significantly. For this reason, overlapped speech detection (OSD) [START_REF] Boakye | Overlapped speech detection for improved speaker diarization in multiparty meetings[END_REF][START_REF] Boakye | Two's a crowd: Improving speaker diarization by automatically identifying and excluding overlapped speech[END_REF][START_REF] Otterson | Efficient use of overlap information in speaker diarization[END_REF] is, along with voice activity detection (VAD) [START_REF] Ramırez | Efficient voice activity detection algorithms using long-term speech information[END_REF], one of the key components for any successful speech processing system [START_REF] García-Perera | Speaker detection in the wild: Lessons learned from JSALT 2019[END_REF][START_REF] Watanabe | CHiME-6 challenge: Tackling multispeaker speech recognition for unsegmented recordings[END_REF].

Supervised neural network based OSD systems have been shown to outperform more classical approaches [START_REF] Geiger | Detecting overlapping speech with long short-term memory recurrent neural networks[END_REF][START_REF] Andrei | Detecting overlapped speech on short timeframes using deep learning[END_REF][START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF]. Notably, Sajjan et al. [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF] have shown that a neural network based approach for joint VAD+OSD can outperform a Gaussian Mixture Model (GMM) based system on real-world distant speech data such as the AMI meeting dataset [START_REF] Mccowan | The AMI meeting corpus[END_REF]. Recent work focusing on OSD only [START_REF] Kunešová | Detection of overlapping speech for the purposes of speaker diarization[END_REF][START_REF] Bullock | Overlap-aware diarization: Resegmentation using neural end-to-end overlapped speech detection[END_REF] has shown even more impressive results in near-field conditions.

In parallel, Stöter et al. [START_REF] Stöter | Classification vs. regression in supervised learning for single channel speaker count estimation[END_REF] have shown that a neural network can be trained to estimate the number of concurrent speakers rather than simply performing joint VAD+OSD. This approach has been further expanded in [START_REF] Stöter | Countnet: Estimating the number of concurrent speakers using supervised learning[END_REF] where three different output distributions for this speaker counting problem are proposed, different neural architectures are explored, and the performance is compared with humans. Also, in [START_REF] Andrei | Overlapped speech detection and competing speaker counting -humans versus deep learning[END_REF], a deep learning based speaker counting algorithm was evaluated against

The work reported here was started at JSALT 2019, and supported by JHU with gifts from Amazon, Facebook, Google, and Microsoft. human ability and different single-channel features were compared. Crucially, these previous works on supervised speaker counting have relied only on close-talk, synthetic mixtures for training and testing.

Building on these previous works, we study supervised joint VAD+OSD and speaker counting in distant speech scenarios. We propose a Temporal Convolutional Network (TCN) architecture for these tasks, and evaluate it against previous works on joint VAD+OSD [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF] and speaker counting [START_REF] Stöter | Countnet: Estimating the number of concurrent speakers using supervised learning[END_REF] on AMI and CHiME-6 [START_REF] Watanabe | CHiME-6 challenge: Tackling multispeaker speech recognition for unsegmented recordings[END_REF]. Because, to the best of our knowledge, supervised speaker counting has never been studied on real-world data, we also explore how the class imbalance problem can be mitigated using data augmentation. Finally, we investigate the use of forced alignment (FA) as a labeling procedure for frontend speech segmentation applications, as used in [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF] on AMI and in CHiME-6 [START_REF] Watanabe | CHiME-6 challenge: Tackling multispeaker speech recognition for unsegmented recordings[END_REF]. This paper is structured as follows. In Section 2, we briefly explain the multi-class classification framework adopted for joint supervised VAD+OSD and speaker counting and introduce our proposed TCN network architecture. We describe the datasets used in our experiments in Section 3 and present our study on FA-based labeling in Section 4. Finally, in Section 5, we report and discuss our experimental results and, in Section 6, we draw conclusions.

Proposed Overlapped Speech Detection

and Counting Method

Overlapped Speech Detection and Counting Task

We treat supervised VAD, OSD, joint VAD+OSD, and speaker counting in a unified way, as instances of a general Overlapped Speech Detection and Counting (OSDC) task. This task can be formulated as a multi-class supervised learning problem, i.e., given a sequence of feature vectors X = {x1, x2, . . . , xn} and corresponding class labels y = {y1, y2, . . . , yn}, we wish to find the optimal parameters θopt of a model F(X; θ), which takes the feature vectors as inputs, and outputs the probability that the current frame belongs to a particular class.

In this framework, VAD and OSD can be treated either separately, as binary classification problems (speech vs. noise-only, overlap vs. non-overlap), or jointly, as a three-class (noise-only, single speaker, overlapped speech) problem. Speaker counting can be formulated as an (N + 1)-classes classification problem with N the maximum possible number of overlapping speakers [START_REF] Stöter | Classification vs. regression in supervised learning for single channel speaker count estimation[END_REF]. While this approach is not the only one for supervised speaker counting, it has been found to be the most effective [START_REF] Stöter | Countnet: Estimating the number of concurrent speakers using supervised learning[END_REF], provided the maximum possible number is known.

TCN Architecture

We explore the use of a Temporal Convolutional Network (TCN) for OSDC, as this type of architecture has been shown to achieve state-of-the-art performance in many sequence-related tasks [START_REF] Bai | An empirical evaluation of generic convolutional and recurrent networks for sequence modeling[END_REF] and for source separation [START_REF] Luo | Conv-tasnet: Surpassing ideal timefrequency magnitude masking for speech separation[END_REF]. By employing stacked dilated convolutional layers, it exploits a long context and, at the same time, being fully convolutional, it is significantly faster than recurrent models in both training and inference phases.

Our architecture, depicted in Fig. 1, borrows some key design choices from [START_REF] Luo | Conv-tasnet: Surpassing ideal timefrequency magnitude masking for speech separation[END_REF][START_REF] Howard | Mobilenets: Efficient convolutional neural networks for mobile vision applications[END_REF]. As input features, we use 80 logmel filterbank features extracted from 25 ms windows with 10 ms stride. These are fed to a normalization layer followed by a 80 × 64 convolutional (conv) layer and by R = 3 blocks of X = 5 residual blocks (res blocks) with 1-D dilated convolutions, where in each block dilation factor increases as 2 0 , 2 1 , . . . , 2 X-1 . Contrary to [START_REF] Luo | Conv-tasnet: Surpassing ideal timefrequency magnitude masking for speech separation[END_REF] we do not use skip connections as this degraded the performance for our task. Each residual block consists of a 64 × 128 point-wise convolution (conv 1×1), followed by normalization and activation, a dilated depth-wise separable 128 × 128 convolution (depth-conv), followed by normalization and activation, and another 128 × 64 point-wise convolution.

We use PReLU [START_REF] He | Delving deep into rectifiers: Surpassing human-level performance on imagenet classification[END_REF] as the activation function, layer normalization [START_REF] Ba | Layer normalization[END_REF] for all normalization layers, and a kernel size of 3 in depth-wise dilated convolutions. A final 64 × N pointwise convolution layer followed by softmax is used to output the probability of each frame belonging to one of the N classes (e.g., N = 3 for VAD+OSD). RAdam [START_REF] Liu | On the variance of the adaptive learning rate and beyond[END_REF] is used for optimization and we tune the learning rate and the batch size for each experiment on a development set. Inference is performed over blocks of 600 frames with a stride of 300 frames. The outputs on overlapping blocks are averaged to obtain the final estimate.

The total number of parameters is 269k, and the whole algorithm, including feature extraction, runs 192 times faster than real-time on an i7-4771 processor.

Datasets

We conduct experiments on two real datasets: AMI and CHi-ME-6. In order to assess the impact of labeling error, we also build a controlled synthetic dataset. We describe them below.

Synthetic Dataset

Our synthetic dataset simulates multi-speaker recordings. Each simulated recording consists of clean speech utterances from Librispeech [START_REF] Panayotov | Librispeech: an ASR corpus based on public domain audio books[END_REF] train-clean-100 convolved with artificial room impulse responses (RIRs) generated via gpuRIR [START_REF] Diaz-Guerra | gpuRIR: A Python library for room impulse response simulation with GPU acceleration[END_REF] and contamined with noise from the CHiME-6 training set [START_REF] Watanabe | CHiME-6 challenge: Tackling multispeaker speech recognition for unsegmented recordings[END_REF]. Each mixture involves 4 speakers, whose position and amount of overlap can change over time. For each mixture, we sampled randomly room size between 20 ÷ 50 m 2 and T60 reverberation time between 0.3 ÷ 0.7 s. We simulated a close-talk reference microphone for each speaker. Thus, each RIR relates each speaker with a close-talk cardioid microphone input for a particular relative position. Ground truth word-level speaker activity was obtained from the clean utterances via the Montreal Forced Aligner (MFA) [START_REF] Mcauliffe | Montreal Forced Aligner: Trainable text-speech alignment using Kaldi[END_REF] and shifted according to the delay introduced by each RIR. We generated 10 synthetic mixtures, each with 19-23 min duration and with 20% percentage of overlapped speech using a total of 1663 RIRs.

AMI

The AMI Corpus [START_REF] Mccowan | The AMI meeting corpus[END_REF] consists in over 100 h of meeting recordings. Each meeting has been recorded by a variety of devices including cameras, microphone arrays, and per-speaker headset and lapel microphones. Ground truth speaker activity was obtained by human annotators from close-talk worn microphones.

CHiME-6

The CHiME-6 corpus features more than 60 h of recordings organized in 20 sessions. Each session consists in a dinner party with 4 participants recorded with 6 microphone arrays. Due to the setting, it features highly conversational speech. Also, binaural microphones worn by each of the four participants were employed to provide close-talk references.

Labeling using Forced Alignment

We use our synthetic dataset to determine, in a controlled environment, whether FA can be considered as a reliable labeling procedure for the purpose of OSDC. In the past, FA-based labeling has been adopted in the CHiME-6 challenge for training and evaluation of diarization systems as well as in [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF], with mixed results according to [START_REF] Kunešová | Detection of overlapping speech for the purposes of speaker diarization[END_REF].

In Table 1 we report the statistics of word-level boundary errors resulting from FA, i.e., the difference in ms between the boundaries, estimated by a Kaldi [START_REF] Povey | The Kaldi speech recognition toolkit[END_REF] based Gaussian Mixture Model Hidden Markov Model (GMM-HMM) FA model applied on the simulated reference close-talk recordings, and the ground-truth boundaries, obtained with the MFA applied on the underlying clean utterances. We report the error percentiles achieved at the different training stages of the FA model from mono till tri3 for two different simulations: one where the distance between each speaker and its reference microphone is fixed at 5 cm and another where is placed farther, at 60 cm. Since we expect errors to increase in the presence of overlapped speech, the percentiles are computed separately for overlapped vs. non-overlapped speech.

Except for the monophone model, FA exhibits small errors Table 1: Absolute error in ms of word-level boundaries estimated by FA on the synthetic dataset. The columns correspond to 40%, 60% and 80% percentiles. For each entry, the first and the second values correspond to 5 cm and 60 cm distance between each speaker and its reference microphone. even when the reference microphone has been placed farther, most often below 30 ms and sometimes up to 50 ms, and the presence of overlapped speech does not significantly degrade the results. In the 60 cm case, greater errors up to 80 ms can be occasionally introduced in the presence of overlapped speech.

In the following, we will show experimentally on AMI, for which manual labels are available, that such errors do not impact the performance of a supervised speech segmentation algorithm. Conversely, using for training FA-based labels, obtained on per-speaker headset devices, improves the performance of the algorithm even when testing it on manually labeled data. This differs from the approach in [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF] where FA-based labels were used both for training and testing, a procedure which could possibly be subject to bias in evaluation if not double-checked with manual annotation.

Experimental Evaluation

Hereafter, we present the results obtained for the proposed method (TCN) as well as the method in [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF] (LSTM), originally proposed for joint VAD+OSD, and the best method in [START_REF] Stöter | Countnet: Estimating the number of concurrent speakers using supervised learning[END_REF] (CRNN), originally proposed for speaker counting. 1 We choose [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF] for comparison because, to the best of our knowledge, it is the only paper where supervised neural OSD has been applied to AMI far-field data. More recent works on supervised neural OSD such as [START_REF] Kunešová | Detection of overlapping speech for the purposes of speaker diarization[END_REF][START_REF] Bullock | Overlap-aware diarization: Resegmentation using neural end-to-end overlapped speech detection[END_REF] only report results on AMI headset data.

The LSTM architecture has 2M parameters and outputs a prediction for every frame given a context of 11 frames. The CRNN has a lower parameter count of 157k and outputs a prediction for every frame given a context of 500 frames. The proposed method is significantly more computationally efficient than both.

For each architecture, we evaluate two versions: one trained for joint VAD+OSD and another one trained for speaker counting (COUNT). We are interested in comparing these two approaches because, on the one hand, speaker counting discriminates a larger set of classes but, on the other hand, it is plagued by the class imbalance problem which arises from conversational speech. The class imbalance can be seen in Table 2, which reports the class statistics for AMI and CHiME-6. For both datasets, the number of 4-speakers and 3-speakers frames is a small fraction of the total number of frames. Joint VAD+OSD is less informative than counting but possibly more robust, because the class imbalance appears to be more manageable.

We decided to report the performance of our algorithms using Average Precision (AP) which summarizes the Precision-Recall curve and is widely used, for example, in object segmentation [START_REF] Lin | Microsoft coco: Common objects in context[END_REF] and other tasks where there is strong class imbalance. Scores are computed on 10 ms frame-level predictions. We also performed statistical significance testing for the values reported in Tables 3,4, 5, 6, 7, 8 between top-3 performing architectures. For each Table, in each column, we highlight in bold font the best result and ones which are statistically equivalent to the best (if any) with p = 0.001. We choose Wilcoxon-Signed Rank non-parametric test [START_REF] Demšar | Statistical comparisons of classifiers over multiple data sets[END_REF] as we found metrics distribution to be highly non normal.

AMI

In our experiments on AMI we use as training material all channels from all microphone arrays as well as headset and lapel mixes. For testing, the first microphone of array 1 is used as 1 Code for synthetic data and experiments is available at github.com/popcornell/OSDC. in [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF]. Unless stated otherwise, all scores in Tables 3,4, and 5 are computed with respect to manual labels. Training is performed on FA-based labels instead obtained with a tri3 Kaldi GMM-HMM model trained on speakers headset microphones.

To counteract the class imbalance problem, we use a data augmentation strategy similar to the one in [START_REF] Bullock | Overlap-aware diarization: Resegmentation using neural end-to-end overlapped speech detection[END_REF] which we extend here also to speaker counting. We dynamically create at training time new examples for 2, 3, and 4 concurrent speakers by overlapping respectively 2, 3, and 4 random single-speaker chunks from the original dataset. To further increase training material, we normalize each chunk using a random gain factor sampled from N (µ = -16.7, σ = 4) in dB scale. In this way, we augmented the original data by a factor of 70%. These hyperparameters were tuned on development-set. The impact of this augmentation scheme as well as the use of FA-based labels for training will be shown later in Section 5.3.

In Table 3, we report the AP scores achieved for VAD and OSD by the three architectures trained either for COUNT or for joint VAD+OSD. In the case of COUNT training, VAD and OSD are achieved at test time by summing the probabilities of the corresponding output classes. In Table 4, we report AP scores for each count (noise-only, 1 speaker, 2 speakers, etc.) for the architectures trained for COUNT. The proposed TCN-based architecture achieves the best figures for both joint VAD+OSD and COUNT variants. More generally, as we could expect, the AP score for VAD is remarkably higher than for OSD (Table 3). This suggests that OSD is a more challenging task, but also that the data augmentation scheme is not enough to counteract the class imbalance. This difference is even more extreme when looking at the counting performance (Table 4), where high AP values are obtained only for noise-only and 1-speaker classes and all architectures fail to give reliable predictions for 3 and 4 speakers. Table 5: Accuracy (%) on the AMI evaluation set compared with [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF]. The scores obtained in [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF] using their FA-based labels are reported in parentheses. [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF] 77 (71.0) 68 (87.9)

Method

An unexpected result is that the TCN architecture trained for COUNT outperforms the one trained for joint VAD+OSD when evaluated on the OSD task, while both training objectives result in similar performance on the VAD task.

In Table 5, we further compare the proposed approach as well as our re-implementation of [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF] with the results originally reported in terms of accuracy in [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF] on the AMI evaluation set. Both our re-implementation and our proposed method reach higher accuracy for both VAD and OSD. Having reimplemented the same architecture (LSTM-VAD+OSD), the improvement over the original [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF] is mainly due to the fact that we use a better data augmentation strategy while [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF] used out-of-domain synthetic data. FA-obtained labels, instead, are used both in [START_REF] Sajjan | Leveraging LSTM models for overlap detection in multi-party meetings[END_REF] and in this work. It must be noted, however, that accuracy does not fully reflect performance for OSD. In fact, by supposing no overlapped speech in all evaluation set, an accuracy of 83% is obtained.

CHiME-6

Hereafter we present the results obtained on the CHiME-6 corpus. Training was performed using all microphone channels from all array devices with FA-based labels obtained using the official challenge baseline Kaldi recipe 2 . For development and evaluation, we used the provided official FA-based labels as ground truth and we averaged predictions across all microphone channels. Regarding data-augmentation the same strategy adopted for AMI was used but with an augmentation factor of 40%.

Tables 6 and7 report the AP achieved by all architectures for VAD and OSD and for counting, respectively. Compared to AMI, we obtain lower AP values in general. In fact, due to its less constrained setting, CHiME-6 is arguably a much more challenging dataset.Nevertheless, the trends observed on AMI are preserved: the TCN architecture consistently performs better, and the AP for OSD remains much lower than the one for VAD. This is reflected in the lower AP values obtained for 2, 3, and 4 speakers.

Again, the TCN architecture trained for COUNT outperforms the one trained for joint VAD+OSD for the OSD task on the evaluation set, and performs similarly for VAD. This result is in accordance to what has been found on AMI. Teaching the network to count speakers, rather than merely identifying the presence of overlapped speech, leads the model to perform better. In this particular case, speaker counting helps generalization as the network is forced to learn a more difficult task.

Ablation Study

Table 8 compares the results obtained by our best performing method (TCN-COUNT) with those obtained by the same TCN architecture without data augmentation and without FA-based labeling (in the latter case, manual labels are used for training 2 FA-based labels were provided for the development and evaluation sets only. instead). We can see that performance drops significantly without FA labeling especially on AMI, possibly because, for this dataset, manual annotation is less reliable as explained in [START_REF] Kunešová | Detection of overlapping speech for the purposes of speaker diarization[END_REF]. Data-augmentation improves the performance on AMI but gives mixed results on CHiME-6. In fact while it slightly improves OSD AP the VAD AP degrades. We hypothesize this is due to the fact that CHiME-6 is considerably more noisy and by overlapping multiple speech segments also the noise adds up, resulting in less realistic synthetic mixtures especially in non-speech regions.

Conclusions

In this work we studied the problem of activity detection of multiple speakers with far-field microphones. Specifically, we focused and compared two different approaches: joint VAD+OSD and speaker counting which, to the best of our knowledge, has never been studied on real-world data. For both approaches we proposed a TCN-based neural network architecture which was shown to outperform previously proposed architectures on AMI and CHiME-6. As an additional contribution we also studied the use of forced-alignment as a labeling procedure for these tasks and we showed that it can improve performance even when manual annotation is used for evaluation.

In our experiments we found that the class imbalance problem which plagues speaker counting and, to a less extent, OSD can be partially mitigated by using data augmentation but both remain very challenging tasks in real-world distant speech scenarios. In particular, while we failed at training a reliable speaker counting system, we showed that it can be more convenient to use a speaker counting objective to perform joint VAD+OSD rather than training a network directly with a joint

Figure 1 :

 1 Figure 1: Proposed TCN architecture for the OSDC task.

Table 2 :

 2 Frame-level class frequency (%) for the AMI and CHiME-6 development and evaluation sets.

	Class frequency	noise	1-spk	2-spk	3-spk	4-spk
	AMI	dev eval	15.87 15.12	67.17 68.39	13.95 12.63	2.59 3.09	0.42 0.76
	CHiME-6	dev eval	24.05 33.47	54.25 51.52	17.74 12.03	3.49 2.46	0.47 0.51

Table 3 :

 3 AP (%) on the AMI development and evaluation sets for VAD and OSD.

	Method	VAD	OSD
		dev	eval	dev	eval
	TCN-COUNT	98.5	98.4	63.2	56.6
	TCN-VAD+OSD	98.5	98.5	60.1	54.2
	LSTM-COUNT	93.4	92.5	26.2	18.5
	LSTM-VAD+OSD	93.3	92.8	26.7	19.2
	CRNN-COUNT	94.1	93.2	33.4	27.5
	CRNN-VAD+OSD	94.1	93.1	33.5	25.9

Table 4 :

 4 AP (%) on the AMI evaluation set for counting.

	Method	noise	1-spk	2-spk	3-spk	4-spk
	TCN-COUNT	50.7	86.1	40.4	11.3	0.03
	LSTM-COUNT	44.6	77.8	14.9	2.4	0.02
	CRNN-COUNT	47.2	81.1	21.3	7.7	0.03

Table 6 :

 6 AP (%) on the CHiME-6 development and evaluation sets for VAD and OSD.

	Method	VAD	OSD
		dev	eval	dev	eval
	TCN-COUNT	93.5	94.2	55.8	51.1
	TCN-VAD+OSD	93.4	94.4	56.1	49.1
	LSTM-COUNT	91.8	89.4	20.1	17.4
	LSTM-VAD+OSD	92.5	91.2	20.4	17.1
	CRNN-COUNT	94.1	93.2	29.2	25.7
	CRNN-VAD+OSD	94.3	93.4	27.8	21.3

Table 7 :

 7 AP (%) on the CHiME-6 evaluation set for counting.

	Method	noise	1-spk	2-spk	3-spk	4-spk
	TCN-COUNT	89.8	77.6	31.1	12.1	0.003
	LSTM-COUNT	71.6	68.8	11.3	3.2	0.002
	CRNN-COUNT	79.3	72.5	13.4	6.2	0.003

Table 8 :

 8 AP (%) achieved by TCN-COUNT on the AMI and CHiME-6 evaluation sets for VAD and OSD without data augmentation and without FA-based labels.

	TCN-COUNT		VAD		OSD
		AMI	CHiME-6	AMI	CHiME-6
	Full	98.4	94.2	56.6	51.1
	w/o Augm	96.6	94.5	40.7	48.3
	w/o FA-labels	74.3	91.5	33.0	48.1


Laura Lintis

François-Xavier Ouf
email: francois-xavier.ouf@irsn.fr

Philippe Parent

Daniel Ferry

Carine Laffon

Cécile Vallières
email: cecile.vallieres@univ-lorraine.fr

Quantification and prediction of water uptake by soot deposited on ventilation filters during fire events

Keywords: fire soot, physical and chemical characterization, water adsorption, Dubinin-Serpinsky model

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Need for efficient filtration devices relevant for containment of hazardous materials as nuclear materials, nanoparticles or pathogens respectively in basic nuclear installations, nanomaterials Quantification and prediction of water uptake by soot deposited on ventilation filters during fire events manufacturing industry and, with regard to the SARS-CoV-2 pandemic of 2020, of biological/virological research institutes is of main importance. Beyond their initial efficiency, which is generally fixed to high level and characterized as High Efficiency Particulate Air for filters, their performance must be maintained despite hazardous situations which could eventually occur within an industrial or research confined and ventilated facilities. Furthermore, dramatic fires of the Notre-Dame Cathedral (15-16 April, 2019 in Paris, France), Lubrizol (26 September, 2019 in Rouen, France) and in contaminated surroundings of the Chernobyl site (04-05 April 2020, Chernobyl exclusion site, Ukrania) highlight the need for developing tools able to predict consequences of such fires in terms of dispersion of hazardous materials in the atmosphere [START_REF] Ouf | Airborne release of hazardous micron-sized metallic/metal oxide particles during thermal degradation of polycarbonate surfaces contaminated by particles: Towards a phenomenological description[END_REF][START_REF] Howes | Lead contamination risk near Notre-Dame cathedral[END_REF][START_REF] Evangeliou | Resuspension and atmospheric transport of radionuclides due to wildfires near the Chernobyl Nuclear Power Plant in 2015: An impact assessment[END_REF]. Exposition of firefighters but also of population to such hazardous airborne transported during wildland or industrial fires is also of societal importance and open the question of performance of protective personal equipment in such accidental situation and most particularly on filtration efficiency and clogging of filtering face piece.

Soot particles, defined by Petzold et al. [START_REF] Petzold | Recommendations for reporting black carbon measurements[END_REF] as agglomerates of monomers consisting solely of carbon with few amounts of hydrogen and oxygen, are inevitably produced during combustion processes encountered during wildland or industrial fires. For facilities manufacturing or handling hazardous materials, soot emitted during a fire can be confined in those installations using high efficiency particulate air (HEPA) filters, but massive emission can clog those filters by formation of "cakes" [START_REF] Mocho | Clogging of industrial pleated high efficiency particulate air (HEPA) filters in the event of fire[END_REF], increasing the aeraulic resistance of the air flow passing through the filters. This enhances the mechanical strains applied on the structure of the filters, leading in extreme case to their rupture. Similar phenomena could also occur for personal protective equipment worn by firefighters or population, which could leads to an increase of the pressure drop of the filtering part, enhancing leaks and, as a consequence, decreasing the protective factor of those devices. For each of those applications and especially for safety analysis of nuclear facilities, it is crucial to be able to describe this clogging phenomenon in order to predict consequences of fires on the containment of radioactive materials. A main parameter influencing the filters clogging is the cake porosity, formed by interstitial spaces between soot aggregates. Typical porosity of soot cake has been reported above 95% [START_REF] Thomas | Pressure drop model for nanostructured deposits[END_REF]. Aeraulic resistance of cakes depends also on humidity [START_REF] Gupta | Effect of Humidity and Particle Hygroscopicity on the Mass Loading Capacity of High Efficiency Particulate Air (HEPA) Filters[END_REF][START_REF] Joubert | Modelling the pressure drop across HEPA filters during cake filtration in the presence of humidity[END_REF], which can reach high values when water aspersion devices are used to extinguish the fire. The presence of organic vapors also influence the aeraulic resistance [START_REF] Mocho | Clogging of industrial pleated high efficiency particulate air (HEPA) filters in the event of fire[END_REF]. Thus, refined clogging models should take into account the dynamic regime of the clogging process, including high humidity variations and structural changes to which the filter and the cake are subjected to [START_REF] Lazghab | Wettability assessment of finely divided solids[END_REF][START_REF] Yu | On the relationship between porosity and interparticle forces[END_REF]. Furthermore, cake can be restructured in presence of liquid water due to capillary condensation [START_REF] Schnitzler | Coating surface tension dependence of soot aggregate restructuring[END_REF][START_REF] Adachi | Shapes of soot aerosol particles and implications for their effects on climate[END_REF], also changing the aeraulic resistance [START_REF] Ribeyre | Modelling of water adsorption-condensation isotherms on beds of nanoparticles[END_REF]. Yet, all these phenomena have not been specifically modelled for soot emitted during a realistic fire. Indeed, due to their morphology and their potential hydrophilic character, fire soot particles can strongly adsorb water molecules leading to such capillary condensation.

To develop a relevant clogging model, it is necessary to determine the water uptake of fire soot as a function of humidity and, in this context, it is particularly interesting to determine the transition between adsorption and capillary condensation. It is also relevant to understand the effect of the fire conditions (O2 concentration, air flux) on the water uptake, as these conditions can influence the physicochemical properties of soot [START_REF] Ouf | Physicochemical properties of aerosol released in the case of a fire involving materials used in the nuclear industry[END_REF]. Water uptake measurements have been performed for chemically or thermally treated synthetic carbons, such as activated carbon [START_REF] Pastor-Villegas | Adsorption-desorption of water vapour on chars prepared from commercial wood charcoals, in relation to their chemical composition, surface chemistry and pore structure[END_REF][START_REF] Choma | Monitoring Changes in Surface and Structural Properties of Porous Carbons Modified by Different Oxidizing Agents[END_REF], mesoporous carbon [START_REF] Horikawa | Scanning curves of water adsorption on graphitized thermal carbon black and ordered mesoporous carbon[END_REF] and commercial carbon blacks [START_REF] Kiselev | Effect of thermal treatment of various carbons on the adsorption of vapors[END_REF][START_REF] Carrott | Adsorption of Water Vapor By Non-Porous Carbons[END_REF], but have never been reported for fire soot. Carbon blacks could be considered, from a size and morphological point of view, as relevant surrogates of soot [START_REF] Ferraro | Multiscale Characterization of Some Commercial Carbon Blacks and Diesel Engine Soot[END_REF], but not from a chemical point of view since they are mostly composed of elemental (graphitic) carbon, while combustion soot usually denotes significant oxygen [START_REF] Ferraro | Multiscale Characterization of Some Commercial Carbon Blacks and Diesel Engine Soot[END_REF] and organic content [START_REF] Ouf | Physicochemical properties of aerosol released in the case of a fire involving materials used in the nuclear industry[END_REF]. Water uptake has been also measured on reference soot, emitted by laboratory burners or engines with various fuels, like diesel and kerosene [START_REF] Popovicheva | Quantification of water uptake by soot particles[END_REF][START_REF] Chughtai | Carbonaceous particle hydration[END_REF]. In all cases, the main parameters influencing the water uptake are the sample porosity and the particles' chemical composition, and the main adsorption mechanism is the formation of water clusters at hydrophilic adsorption sites [START_REF] Liu | Water adsorption on carbon -A review[END_REF]. Numerous models for water adsorption on carbon have been proposed, especially for very porous activated carbon [START_REF] Furmaniak | Water adsorption on carbons -Critical review of the most popular analytical approaches[END_REF].

Among them, the Dubinin-Serpinsky (DS) adsorption model [START_REF] Dubinin | The sorption of water vapour by active carbon[END_REF] is valid either for porous and non-porous carbonaceous materials. In the case of cakes of fire soot, the DS model seems relevant, as water adsorption can take place at the surface of the non-porous soot aggregates forming the cake.

Using small and pilot combustion test benches, we have produced fire soot under conditions representative of fire events [START_REF] Ouf | Physicochemical properties of aerosol released in the case of a fire involving materials used in the nuclear industry[END_REF][START_REF] Alibert | Effect of oxygen concentration on the combustion of horizontally-oriented slabs of PMMA[END_REF]. Different O2 concentrations of the oxidizing gas have been used to mimic the real case of a poorly ventilated and confined fire, representative of industrial facility handling hazardous materials (biological and radioactive nanoparticles).

For nuclear safety application, we have considered fuels commonly found in nuclear facilities or extensively studied in the past [START_REF] Ouf | Physicochemical properties of aerosol released in the case of a fire involving materials used in the nuclear industry[END_REF]. Significant amounts of soot have been collected in order to perform physicochemical analysis and sorption measurements. TEM image analysis [START_REF] Bourrous | A semi-automatic analysis tool for the determination of primary particle size, overlap coefficient and specific surface area of nanoparticles aggregates[END_REF], nitrogen sorption measurements [START_REF] Sing | Reporting physisorption data for gas/solid systems with special reference to the determination of surface area and porosity (Recommendations 1984)[END_REF], elementary and XPS analysis [START_REF] Parent | Nanoscale characterization of aircraft soot: a high-resolution transmission electron microscopy, Raman spectroscopy, X-ray photoelectron and nearedge X-ray absorption spectroscopy study[END_REF] have been used to determine respectively the soot primary particles diameters, the BET specific surface area and the global and surface oxygen contents. Water sorption measurements were carried out for soot compacted into pellet and let in powder form, using respectively a gravimetric microbalance and a manometric analyzer.

Experimental procedure a. Soot production

Soot samples were produced in two cones calorimeters, one at laboratory or "lab" scale and one at "pilot" scale, differing in their dimensions, their oxidizing gas flowrates and the residence times of the emitted particles inside their combustion chamber (Figure . 1). The calorimeter at laboratory scale consists of a combustion chamber of 0.03 m 3 topped with a column in which the combustion aerosol is transported to the sampling point. We used as fuel 40 mL of heptane (Sigma-Aldrich) or DTE Medium (Exxon Mobil), a hydraulic oil used in the French nuclear industry, placed in a cylindrical container of 5.7 cm of internal diameter. We have also tested polymethyl methacrylate (PMMA), the major compound of gloveboxes walls usually used for the containment of hazardous materials (along with polycarbonate). The total flowrate of the oxidizing air was fixed at 10.8 Nm 3 .h -1 , and the O2 concentration was varied by changing the air to nitrogen ratio with two mass flow controllers (model 5853S, Brooks). We chose three O2 concentrations of 15% (highly depleted air), 18% (depleted air) and 21% (ambient air) in the oxidizing gas for fires with heptane, DTE and PMMA. For each fuel, the soot samples are named accordingly to these oxidation conditions (e.g. heptane 15%, heptane 18% and heptane 21%). Soot was collected on a cellulose acetate membrane (type 11106, Sartorius Stedium Biotech) placed in a high-volume air sampler (TE-2000PX, TISCH Environmental Inc, Ohio) at a flowrate of 8 Nm 3 .h -1 . In order to carry out different ex situ analysis, soot has been kept in a dry hermetic desiccated container, and away from light. The calorimeter at pilot scale has a significantly larger size and residence times compared to the laboratory scale ones [START_REF] Alibert | Effect of oxygen concentration on the combustion of horizontally-oriented slabs of PMMA[END_REF]. PMMA sheets and heptane pools were used as fuels, and their respective dimensions are reported in Table 1. The true density of the primary particles of carbonaceous aggregates was determined using a measurement technique based on the displacement of a liquid induced by the immersion of a known mass of sample. This method, described in the ISO 787-23 standard and based on the Archimedes buoyancy principle (using ethanol as displacement liquid), has been recently demonstrated to be relevant despite type of soot samples [START_REF] Ouf | True density of combustion emitted particles: A comparison of results highlighting the influence of the organic contents[END_REF]. The diameters of the soot primary particles were determined by transmission electron microscopy (TEM). For TEM sampling, soot particles have been first diluted in ethanol and mixed in an ultrasonic bath during several minutes resulting to a homogeneous suspension. A microliter of this solution has been deposited

on TEM grids (holey carbon film 300 mesh Cu (X25), S-147-3H from Agar Scientific®) and let drying. Soot micrographs were recorded with a Jeol 100CXII microscope equipped with a CCD camera (Gatan® Erlangshein Dualvision 300W, 780 model). A hundred of TEM images were analyzed for each sample, both manually and automatically using respectively the ImageJ software and a semi-automatic software [START_REF] Bourrous | A semi-automatic analysis tool for the determination of primary particle size, overlap coefficient and specific surface area of nanoparticles aggregates[END_REF]. Measurements of nitrogen sorption at 77 K using a manometric analyzer (ASAP 2020, Micromeritics) provided the specific surface area of each sample from the conventional BET analysis [START_REF] Gregg | Adsorption, surface area and porosity[END_REF]. Prior to the measurements, the powdered samples were pumped into a primary vacuum during at least 12 hours at a temperature of 25°C.

The elemental compositions of soot were determined with an organic elemental analyzer (FlashEA 1112, Thermo Scientific). Carbon, hydrogen, nitrogen and sulfur (CHNS) contents are inferred from the gas analysis emitted during a flash combustion at 920°C under oxygen.

According to previous studies on carbon black samples [START_REF] Pastor-Villegas | Adsorption-desorption of water vapour on chars prepared from commercial wood charcoals, in relation to their chemical composition, surface chemistry and pore structure[END_REF][START_REF] Ferraro | Multiscale Characterization of Some Commercial Carbon Blacks and Diesel Engine Soot[END_REF][START_REF] Miura | Adsorption of Water Vapor from Ambient Atmosphere onto Coal Fines Leading to Spontaneous Heating of Coal Stockpile[END_REF], the soot oxygen content

[O]diff (in weight %) can be determined from this analysis. In the present study, soot particles were produced from fuels mostly composed of carbon and hydrogen, and we thus expect to detect no other elements than C and H, except nitrogen and oxygen resulting from the reactions with the oxidizing gas [START_REF] Ferraro | Multiscale Characterization of Some Commercial Carbon Blacks and Diesel Engine Soot[END_REF][START_REF] Boehm | Some aspects of the surface chemistry of carbon blacks and other carbons[END_REF]. The surface oxygen concentration [O]XPS of several soot produced at laboratory scale were determined by X-ray photoelectron spectroscopy (XPS).

Prior to the XPS analysis, the samples were compacted into 7 mm diameter pellets with a hand press (Pike Technologies®). The experiments were then performed under ultra-high vacuum using a Resolve 120 hemispherical electron analyzer (PSP Vacuum) and a TX400 (PSP vacuum) unmonochromatized X-ray source (Mg Kα at 1253.6 eV) operated at 100 W. The XPS lines were deconvoluted with the CasaXPS program, using Gaussian/Lorentzian profiles and after Shirley-type background subtraction. Elemental composition is obtained from the analysis of the survey spectra and after correction by the relative sensitivity factors provided in the program [START_REF] Parent | Nanoscale characterization of aircraft soot: a high-resolution transmission electron microscopy, Raman spectroscopy, X-ray photoelectron and nearedge X-ray absorption spectroscopy study[END_REF]. Those analytical methods have been preferred to thermo-desorption analysis of organic to elemental carbon ratio (OC/EC) since this method is not specific to surface composition and not only includes oxygen containing species but also alkyl or aliphatic groups [START_REF] Ess | In situ Raman microspectroscopic analysis of soot samples with different OC content : Structural changes during oxidation[END_REF] as examples.

c. Water uptake measurement

For water uptake measurements, soot samples were either in their natural powdered form, or compacted into a cylindrical pellet using a laboratory-made press functioning with a torque wrench (torque set at 0.5 N.m). Knowing the true density of soot, the global porosity (Table 2) of uncompacted εpowder or compacted samples εpellet can be respectively deduced either from the volume of the powder in the cylindrical glass container, or from the diameter and the height of the pellet. Water sorption measurements were performed using gravimetric and manometric methods [START_REF] Emmett | The Adsorption of Water Vapor on Carbon Black[END_REF][START_REF] Wolf | The watervapour sorption isotherms of microcrystalline cellulose (MCC) and of purified potato starch. Results of a collaborative study[END_REF]. They are in good agreement whether conducted under static or dynamic sorption conditions [START_REF] Arlabosse | Comparison between static and dynamic methods for sorption isotherm measurements[END_REF][START_REF] Belmabkhout | High-pressure adsorption measurements. A comparative study of the volumetric and gravimetric methods[END_REF]. Gravimetric measurements were performed only on pellets using a "dynamic vapor sorption" (DVS) Vacuum microbalance (Surface Measurements Systems, SMS). Pellets are first pumped into high vacuum during several hours at 25°C to remove water and adsorbed impurities at the sample surface. For water sorption measurements, this degassing is more recommended [START_REF] Snoeck | The influence of different drying techniques on the water sorption properties of cement-based materials[END_REF] than the conventional thermal pre-treatment that could alter surface properties, for instance by removing of hydrophilic adsorption sites. Then, the initial mass of the dried sample is determined. Subsequently, humidity steps are gradually applied at a constant water vapor flowrate. Water sweeps the sample with a limited residence time in the cell of the microbalance system, enabling to continuously renew the vapor phase in contact with the soot surface. The relative humidity RH (in %) in the microbalance is defined as the ratio between partial pressure of water PH2O,vap within the cell divided by the saturation pressure PH2O,sat (Eq. 1) at the measurements' temperature T:

𝑅𝐻 = 𝑃 𝐻 2 𝑂,𝑣𝑎𝑝 𝑃 𝐻 2 𝑂,𝑠𝑎𝑡 (𝑇) × 100 (Eq. 1)
The water uptake a(RH) (eq. 2) is then defined as the ratio of the mass of water adsorbed (mH2O, adsorbed), determined according to sample mass at each relativity humidity msample(RH), and the reference mass mreference, which is measured at RH= 0%.

𝑎(𝑅𝐻)

𝑚 sample (𝑅𝐻)-𝑚 𝑟e𝑓e𝑟𝑒𝑛𝑐𝑒

𝑚 𝑟e𝑓e𝑟𝑒𝑛𝑐𝑒 = 𝑚 𝐻 2 𝑂,𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑑 (𝑅𝐻) 𝑚 𝑟e𝑓e𝑟𝑒𝑛𝑐𝑒 (Eq. 2)
The transition between two humidity steps depends on the time needed to reach the thermodynamic equilibrium and the stabilization of the sample mass with an accuracy of 0.1 µg, according to SMS. Following this value and the uncertainty propagation principle, the water uptake uncertainty is lower than 10 -4 %. One obtains the time evolution of the mass and the maximal water uptake for a defined humidity (Figure 2) which, in fine, provides the sorption data needed to plot the sorption isotherms with a high accuracy. Manometric measurements were performed on uncompacted powered soot only, using a 3FLEX analyzer

d. Qualification of water uptake measurement protocol

Prior to the measurements on soot, the experimental protocols and apparatus were validated using microcrystalline cellulose (MCC) as a reference. For MCC, gravimetric, static and discontinuous sorption data are available for two kinds of samples, MCC Avicel Ph-101 provided by FMC [START_REF] Wolf | The watervapour sorption isotherms of microcrystalline cellulose (MCC) and of purified potato starch. Results of a collaborative study[END_REF] and MCC RM 302 [START_REF] Jowitt | The certification of the water content of microcrystalline cellulose at 10 water activities. Commission of the European Communities[END_REF], which are used as references for the COST90 standard European procedure. Figure 3 shows the water uptakes of these two MCCs following the COST90 procedure at different RH ensured by salt solutions [START_REF] Wolf | The watervapour sorption isotherms of microcrystalline cellulose (MCC) and of purified potato starch. Results of a collaborative study[END_REF], and those obtained with the DVS microbalance at the same RH steps [START_REF] Levoguer | Moisture sorption of EC standard reference material RM 302 on a DVS instrument[END_REF]. Our results are in good agreement with the COST90 data, except slight discrepancies at high water uptakes for the MCC Avicel Ph-101.

This can be explained by differences in the samples, such as size distribution or specific surface area [START_REF] Doelker | Comparative compaction properties of various microcrystalline cellulose types and generic products[END_REF]. Figure 4 compares water uptakes obtained on the MCC Avicel Ph101 at powdered form with the 3FLEX analyzer (circles symbols) and those obtained with the gravimetric (DVS) methods (squares symbols). One can see a good agreement between the methods, as reported by previous authors [START_REF] Emmett | The Adsorption of Water Vapor on Carbon Black[END_REF].

Results

a. Samples properties

The measured soot densities ρtrue range from 1492 kg.m -3 up to 1780 kg.m -3 (Table 2).

Upper values are in good agreement with the literature for soot having a low oxygen content [START_REF] Dobbins | Comparison of a fractal smoke optics model with light extinction measurements[END_REF][START_REF] Newman | Characterization of particulates from diffusion flames[END_REF]. Lower density values measured for some of our samples can be explained by the presence of an organic carbon phase, which is less dense than the elemental carbon phase, reducing the overall density [START_REF] Ouf | True density of combustion emitted particles: A comparison of results highlighting the influence of the organic contents[END_REF]. The diameter of the primary particles dpp ranges from 22.3 nm to 43.3 nm (Table 2), in agreement with values reported for soot emitted by gaseous flames [START_REF] Prado | A study of soot formation in premixed propane/oxygen flames by in-situ optical techniques and sampling probes[END_REF][START_REF] Megaridis | Morphological Description of Flame-Generated Materials[END_REF], and for more complex liquid and solid fuels [START_REF] Ouf | Physicochemical properties of aerosol released in the case of a fire involving materials used in the nuclear industry[END_REF]. For all samples, particles denote fractal morphology typical of soot particles and examples of TEM images are available in supplementary information in tables SI-1 and SI-2. Close agreement, in terms of size and morphology could then be reported between carbon black and soot samples. The specific surface area SBET ranges between 52 m².g -1 and 100 m².g -1 (Table 2). This is also typical of nonporous adsorbents and agrees with values determined for soot emitted in various combustion processes [START_REF] Ferraro | Multiscale Characterization of Some Commercial Carbon Blacks and Diesel Engine Soot[END_REF][START_REF] Popovicheva | Quantification of water uptake by soot particles[END_REF][START_REF] Chughtai | Carbonaceous particle hydration[END_REF][START_REF] Levitt | Heterogeneous Chemistry of Organic Acids on Soot Surfaces[END_REF]. This surface area is mostly due to the surface developed by the primary particles composing soot aggregates [START_REF] Bourrous | A semi-automatic analysis tool for the determination of primary particle size, overlap coefficient and specific surface area of nanoparticles aggregates[END_REF]. The smaller the primary particle diameter, the higher the specific area. This explains the high surface area of PRINTEX 90 (341 m².g -1 ), whose particles are small (25 nm) compared to FLAMMRUSS 101, whose surface area is 24.4 m².g -1 because of large particles of 136 nm. We note that the SBET of soot coming from hydraulic oil fire is slightly lower (53.3 to 54.2 m².g -1 ) than the other soot produced with PMMA and heptane (75.5 to 97.9 m².g -1 ), due to larger diameters of their primary particles. The elemental oxygen content [O]diff ranges between 6.4 wt. % and 11.8 wt. %, in agreement with values commonly reported in the literature [START_REF] Ferraro | Multiscale Characterization of Some Commercial Carbon Blacks and Diesel Engine Soot[END_REF][START_REF] Liang | Relationship between wettabilities and chemical compositions of candle soots[END_REF]. The oxygen content is higher (up to 10 wt. %) in soot than in carbon blacks, which are known to be mostly composed of elemental carbon with oxygen concentrations lower than 2 wt. %. The oxygen concentration at the surface of the particles

[O]XPS (Table 2) is in good agreement with the oxygen content found in the bulk [O]diff, indicating a homogeneous repartition of oxygen within the particles.

Global porosity ε (eq. 4) has been estimated using true density ρtrue composing the material of soot particles, the sample mass msample, the radius r and height H of the cylindrical soot pellet or of the glass container for the uncompacted samples. For soot pellets, the global porosity εpellet ranges between 29% and 66%. This wide range of values probably results from different adhesion properties of each sample during the compaction process. The global porosity of the powdered soot samples εpowder is around 96% for all samples, close to typical soot cake porosities reported on HEPA filter [START_REF] Thomas | Pressure drop model for nanostructured deposits[END_REF].

𝜀 = 1 - 𝑚 𝑠𝑎𝑚𝑝𝑙𝑒 𝜋𝑟 2 𝐻𝜌 𝑡𝑟𝑢𝑒 (Eq.4)
b. Water isotherms of soot particles produced under different fire conditions Fig. 6 presents the gravimetric water adsorption isotherms for soot compacted into pellets. The water uptakes are obtained considering a reference mass mreference as the mass of sample at RH=0%. Overall, all the samples present the same slopes and the water uptakes range from 2.4% and 3.6% (at RH=90%). This results from similar physicochemical properties of all soot in terms of structure and composition. From RH= 0% to 80%, the isotherms are of V th type according to the IUPAC classification [START_REF] Rouquerol | Adsorption by Powders and Porous Solids, 2nd Editio[END_REF]. They present a rather slight convex curvature at RH < 30%. On the isotherms, this convexity combined with a positive slope is characteristic of low interactions of water at the surface, with locally high interaction with some hydrophilic adsorption sites of the soot surface [START_REF] Velasco | Role of the surface chemistry of the adsorbent on the initialization step of the water sorption process[END_REF]. A slight inflexion point is observed at RH=80% for the heptane 15% soot obtained at pilot scale (Figure 6 left, red triangles), revealing the beginning of capillary condensation. The water uptakes measured on the DTE hydraulic oil soot samples are slightly higher than for the heptane and PMMA soot samples. Figure 7 compares the water uptakes obtained on fire soot samples produced at laboratory scale and at pilot scale. Except for the heptane soot produced at 21% of O2 concentration, water uptakes are globally similar whatever the scale, with a maximal difference of ±15%. For the considered fuels, fire scale has no major influence on the water adsorbing properties. (ambient air value) with those produced at depleted O2 concentrations (15%, 17% and 18 %), which adsorb up to 50% more water than soot produced at ambient concentration (see Figure

SI-1 in supplementary information

). This highlights the significant modification of size (decrease of primary particle size and increase of specific surface area) and composition (increase of oxygen content) of soot particles with decreasing oxygen concentration reported in Table 2 and in agreement with previous findings [START_REF] Ouf | Physicochemical properties of aerosol released in the case of a fire involving materials used in the nuclear industry[END_REF][START_REF] Léonard | Generation of CO and smoke during underventilated combustion[END_REF] indicates low carbon black-water interactions and a water uptake related to the specific surface area only. Additional data on carbon black samples available in the literature -whose compositions are globally similar to our samples -are also plotted in Fig. 10 (identified with an asterisk "*" [START_REF] Kiselev | Effect of thermal treatment of various carbons on the adsorption of vapors[END_REF][START_REF] Carrott | Adsorption of Water Vapor By Non-Porous Carbons[END_REF][START_REF] Popovicheva | Quantification of water uptake by soot particles[END_REF][START_REF] Charrière | Water sorption on coals[END_REF]). Over the whole specific surface area range, soot particles present higher water uptakes than carbon blacks and do not follow the linear correlation proposed on Fig. 10. Those discrepancies between soot and carbon blacks can be explained, beyond the geometric surface associated to the cake structure, by their specific chemical composition. To assess the influence of the sample composition on the water sorption capacity, water uptake can be expressed as the number of water statistical monolayers (ML) needed to cover entirely the sample surface (Eq. 5). This unravels the effect of the surface area from the chemical composition:

𝑀𝐿 = (𝑎(𝑚𝑚𝑜𝑙.𝑔 -1 )×10 -3 )×𝑁 𝐴 (𝑚𝑜𝑙 -1 ) 𝑆 𝐵𝐸𝑇 (𝑚 2 .𝑔 -1 ) 𝜎 𝐻 2 𝑂 (𝑚 2 ) (Eq. 5)
Where σH2O is the surface occupied by a water molecule (1.05.10 -19 m²), a the amount of adsorbed water per mass of sample, NA the Avogadro number (6.022.10 23 mol -1 ) and SBET the specific surface area (m².g -1 ).

Figure 10 shows the evolution of ML with the surface concentration of oxygen [O]surface, calculated as the mass of oxygen per surface area (Eq. 6).

[𝑂] 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 (𝑔. 𝑚 -2 ) =

[𝑂] 𝑑𝑖𝑓𝑓 (𝑤𝑡.%) 100.𝑆 𝐵𝐸𝑇 (𝑚 2 .𝑔 -1 )

(Eq. 6)

The oxygen content is known to significantly influence the water sorption [START_REF] Liu | Water adsorption on carbon -A review[END_REF]. The oxygenated chemical functions located at the surface strongly interact with water molecules, especially in the range of low humidity where they represent the energetically most favorable adsorption sites [START_REF] Velasco | Role of the surface chemistry of the adsorbent on the initialization step of the water sorption process[END_REF]. To highlight this effect, we have plotted ML at RH= 30% and RH= 90 % for the pellets with the DVS microbalance and for the powders with the 3FLEX analyzer (the corresponding water adsorption isotherms are available for 3FLEX as supplementary information, Fig. SI-3). This figure shows that water uptakes for powder and compacted samples are globally equivalent in a +/-15% interval. However, exceptions can be observed for heptane 15%, heptane 21% and PMMA 21% [pilot scale], where adsorption is higher for powder than for pellet, especially at high water uptake (related to higher relative humidity).

This could be explained by different mesostructures of these soot samples when they are characterized in pellet or in powder forms, changing the surface and volume available for water adsorption.

Discussion

Until now, the water sorption on carbon systems have been mostly modelled for activated carbon or carbon/zeolite [START_REF] Do | Adsorption analysis: equilibria and kinetics[END_REF] whose isotherms are systematically of V th type. Several common water sorption models have been established for such isotherms, considering a primary adsorption on specific hydrophilic surface sites followed by adsorption on already adsorbed water molecules. This second adsorption process is driven by water-water interactions, which are, overall, more favorable than those between water and a globally hydrophobic carbonaceous surface. Being an associating fluid, water can finally fill in the micro-and-mesoporous pore volume. Unlike activated carbon, soot particles are made of non-porous hydrophobic carbon, porosity being only due to interstitial spaces between the primary particles in the soot cakes, which also varies with the sample conformation (powder or pellet). The surface of soot is mostly hydrophobic, with some hydrophilic adsorption sites related to the presence of surface oxygen.

As previously mentioned, one of the most suitable sorption model for such porous solid is the Dubinin-Serpinsky (DS) one [START_REF] Dubinin | Water vapor adsorption and the microporous structures of carbonaceous adsorbents[END_REF][START_REF] Dubinin | Isotherm equation for water vapor adsorption by microporous carbonaceous adsorbents[END_REF]. This model describes a mechanism of water clusters formation on the adsorbent surface sites, which can be followed by a pore volume filling [START_REF] Barton | The Adsorption of Water Vapor by Porous Glass[END_REF][START_REF] Dubinin | Adsorption of water and the micropore structures of carbon adsorbents[END_REF]. In the DS model, the adsorption process is considered as an equilibrium state of a chemical reaction between water molecules in the gaseous phase H2Ogas and the adsorption sites located on the adsorbent surface Sadsorbent (Figure 12). Those sites can be primary or secondary, corresponding respectively to the initial number of hydrophilic sites a0 (%g.g -1 adsorbent) and the already adsorbed water molecules a per gram of sample (expressed here in terms of %g.g - 1 adsorbent). This equilibrium is formalized by the equilibrium constant c (defined as the ratio between kinetic constants associated to adsorption kads and desorption kdes), enabling to express a, the total amount of adsorbed water (Eq. 7), including the water vapor relative pressure h. Among all the DS model versions [START_REF] Furmaniak | Water adsorption on carbons -Critical review of the most popular analytical approaches[END_REF], the second version, commonly called DS2, has the simplest analytical form and takes into account the limitation of adsorption with the water uptake due to the steric hindrance. To this aim, a dimensionless and strictly positive factor (1ka), decreasing with the adsorbed water amount, has been added to the original DS equation (Eq. 8). The constant k has therefore a value that ranges from 0 to strictly inferior to 1/a. This constant corresponds to the proportion of water molecules which does not act anymore as a secondary adsorption site (steric hindrance). It leads to the analytical form of 2 nd version of DS model (eq. 8).

𝑎 = 𝑐(𝑎 0 + 𝑎)ℎ(1 -𝑘𝑎)

(Eq. 8)
Where k is the coefficient related to the steric hindrance due to the formation of water clusters (%gadsorbent.g -1 ).The adsorption isotherms obtained in the present study have all been successfully fitted with the DS2 model in the relative humidity range of 0%-90% (Fig. SI-4).

Fitted parameters k, a0 and c for all samples are also available in Table SI-3, with regression coefficients R² all above 0.99. This indicates a unique adsorption process consisting in the formation of water clusters on few hydrophilic sites, which we assume to occur on the oxidized surface sites.

The fitted values of k are 0.24 ± 0.02 and 0.14 ± 0.03 for pellets and powders, respectively. The higher k value for pellets is a consequence of a limited secondary adsorption process, indicating a higher steric hindrance to clusters formation compared to powders. This is likely due to the higher compaction of the pellets, which facilitates the blocking of interstitial spaces between the soot particles. Decrease of k values is consistent with the increase of mean concentrations of primary adsorption sites a0 (in %g.g -1 adsorbent), from 1.0% ± 0.4% for pellets to 2.6% ± 0.4% for powders. The lower value of a0 for pellets indicates a lower accessibility to the adsorption sites by the filling of the pores where the primary adsorption sites are located, while more sites are available in powders. The mean values of equilibrium constant c, corresponding to the ratio of the kinetic constants between adsorption and desorption processes, are 2.6 ± 0.4 and 1.6 ± 0.4 for the pellets and powders respectively. Taking into account their uncertainties, these values remain quite close and, at this stage, we cannot explain such a slight difference in the kinetic constant without any further investigations.

As previously reported in the literature [START_REF] Thomas | Pressure drop model for nanostructured deposits[END_REF], porosity of soot cake formed at HEPA filters surface are generally between those considered in the present study for pellets (mostly 50-60%) and powder (95%). To provide useable values of k, a0 and c that could be implemented in clogging models for similar kinds of hydrophobic soot [START_REF] Mocho | Clogging of industrial pleated high efficiency particulate air (HEPA) filters in the event of fire[END_REF][START_REF] Bourrous | Measurement and modeling of pressure drop of HEPA filters clogged with ultrafine particles[END_REF], we have averaged the fitting parameters k, a0 and c of the 22 studied samples, whether compacted into pellet or not. These values are reported in Table 3, along with their standard deviation. Figure 13 presents the computed water uptakes using these averaged values and deviations plotted against the experimental water uptakes for all soot samples. We observe that 95% of the water uptakes (limited in the present case to water uptake values higher than 1%) can be satisfactorily represented by the DS2 model using these averaged parameters, within a confidence interval of ± 47%.

Conclusion

This study aimed at measuring the water uptake in soot cakes representative of those formed on HEPA filters during fire occurring in a nuclear plant. For this purpose, soot was produced at laboratory and pilot scales with different fuels -heptane, PMMA and hydraulic oilrepresentative of fuels encountered in a real nuclear plant. The physicochemical properties of these samples have been determined ex situ with analytical techniques providing the specific surface area, the primary particle diameters and the oxygen contents, found respectively in the ranges of 52 m².g -1 -100 m².g -1 , 22.3 nm -43.3 nm and 6.7wt. % -9.9 wt. %. We have shown that these physicochemical properties are only slightly influenced by the fire scale, the fuel type, or the O2 concentration of the oxidizing gas. Using gravimetric and manometric techniques, we have measured the water uptake of these samples as well as two additional carbon black samples, let in powder form or compacted into pellets. Gravimetic and manometric approaches have been proven equivalent, with a variation coefficient lower than 10% for the whole relative humidity range (0%-100%). The adsorption isotherms of soot are of V th type and present maximal water uptakes between 2% and 4% at RH=90%. Under the investigated conditions, fire scale does not significantly impact the isotherms classification.

Two physicochemical properties of soot directly impact the sorption process: the specific

Figure 1 :

 1 Figure 1: Experimental setup of the controlled atmosphere cones calorimeters at lab scale (left) and at pilot scale (right)

(

  MICROMERITICS). Soot samples were first degassed in a cell at 0.1 mbar and 25°C using the low vacuum pump VacPrep 061. The cell is then introduced in the 3FLEX analyzer, and water is flowed in the cell. Pressure measurements are then performed only when a stabilization criterium of 0.01 mbar.min -1 is reached.

Figure 2 :

 2 Figure 2: Example of a gravimetric measurement with the DVS microbalance (in red the evolution of sample mass and in blue the evolution of relative humidity)

Figure 3 :Figure 4 :Figure 5 :

 345 Figure 3: Comparison of water sorption data on different microcrystalline celluloses (MCC Avicel Ph-101 and RM302) obtained with the COST90 procedure and DVS microbalance

Figure 6 :

 6 Figure 6: Water adsorption isotherms for soot produced with liquid fuels (left) and PMMA (right)

Figure 7 :Figure 8

 78 Figure 7: Comparison between water uptakes of soot samples produced at pilot and laboratory scale

Figure 8 :Figure 9

 89 Figure 8: Comparison between water uptakes obtained for soot samples produced at depleted oxygen concentrations (15-18%) and ambient oxygen concentration (21%)

Figure 9 :

 9 Figure 9: Effect of specific surface area on water uptake at 90% of relative humidity

(

  left and right sides on Fig.10respectively) as a function of[O]surface for all our samples and those available in the literature. ML linearly increases with[O]surface with a slope of 5.33 (RH=30%) and 13.57 (RH=90 %). This clearly shows that the oxygen concentration at the surface significantly enhances the adsorption process, with a similar physico-chemical mechanism within relative humidity range 30-90 % (as a same linear dependence is observed at RH= 30 % and 90 %).

Figure 10 :

 10 Figure 10: Evolution of the number of ML with the surface concentration of oxygen, at RH = 30% (left) and RH = 90% (right)

Figure 11 :

 11 Figure 11: Parity diagram comparing the water uptakes between pellets and powders at different humidity steps

Figure 12 :

 12 Figure 12: Scheme of the proposed mechanism of water adsorption and formula used to express the Dubinin-Serpinsky model

Figure 13 :

 13 Figure 13: Comparison between DS2 model, computed according to mean constants, and experimental water uptakes

  surface area and the oxygen concentration per surface area. The very good fit of the experimental isotherms with the second Dubinin-Serpinsky model (DS2) indicates that adsorption occurs by nucleation of water clusters on few oxidized and hydrophilic surface sites.The DS2 parameters have been obtained for the 22 studied samples, either compacted or as powders, and their average allows for a proper simulation of 95% of the experimental data. This model will contribute to the improvement of simulation codes and consequently to better predict the HEPA filter clogging phenomenon during a fire in nuclear facility. In addition, the use of the second Dubinin-Serpinsky model appears relevant to represent the water sorption isotherms of fire soot.

Table 1 :

 1 Summary of operational conditions for fire tests in the laboratory and pilot scale cone calorimeters

	Laboratory scale	Pilot scale

Table 2 :

 2 Summary of the physicochemical properties of soot and carbon black samples studied

	Samples	ρtrue (kg.m -3 )	dpp (nm)	SBET (m².g -1 )	[O]diff (wt.%)	[O]XPS (wt.%)	εpellet (%)	εpowder (%)
	Soot
	Heptane 21% (lab scale) Heptane 15% (lab scale)	1780±20 1	35.1±1.3 22.8±0.5	75.5±0.7 97.9±2.3	7.6±0.8 11.8±1.2	7.4 8.8	62±3 54±4
	PMMA 21% (lab scale) PMMA 18% (lab scale)	1492±12 1	39.9±0.8 32.2±0.8	79.3±1.1 84.4±1.2	6.7±4.8 9.2±0.6	9.9 8.1	54±4 29±7
	DTE Medium oil 21% (lab scale) DTE Medium oil 18% (lab scale)	1593±336	42.1±1.2 38.6±1.1	53.3±1.1 54.2±1.2	9.2 9.9±0.4	8.8 9	58±10 56±10	96±1
	Heptane 21% (pilot scale) Heptane 15% (pilot scale)	1780±20 1	34.1±1.3 29.9±0.9	69.5±0.7 86.9±1.2	6.8±0.8 9.1±0.6		66±3 58±4
	PMMA 21% (pilot scale) PMMA 18% (pilot scale)	1492±12 1	35.9±1.1 37.2±1.2	69.2±1.4 63.7±1.4	6.4±0.8 7.1±1.8	n.d.	59±4 52±4
	Carbon blacks
	PRINTEX 90	1783±45	25±1	340.0±1.6	1.1		62±5	88±2
	FLAMMRUS 101	1712±85	136±8	24.4±0.1	2.1		71±4	78±3
	COLOUR BLACK FW200	1800 2	21±2	506±2.0	18.6±0.2	n.d.	54±1	-

Table 3 :

 3 Calculated values from 22 water adsorption isotherms

	k (%)	a0 (%𝑔. 𝑔 𝑎𝑑𝑠𝑜𝑟𝑏𝑒𝑛𝑡 -1	)	c (-)

From[START_REF] Ouf | True density of combustion emitted particles: A comparison of results highlighting the influence of the organic contents[END_REF]

Acknowledgements

The authors would like to thank Guillaume Basso, Mickael Coutin, Vincent Cozar, Hugues Pretrel, Serge Pons and Pascal Zavaleta from the "Laboratoire d'Expérimentation des Feux" in Cadarache for providing soot samples emitted during large-scale fire experiments. This work was partially done within the framework of the LIMA joint research program (The Interactions Media-Aerosol Laboratory) between the Institut de Radioprotection et de Sûreté Nucléaire (IRSN) and the Reactions and Chemical Engineering Laboratory (LRGP) of the French National Centre for Scientific Research (CNRS).

Supplementary information I: Table

 SI-
COLOUR BLACK FW200

Supplementary information II: oxygen depletion effect on water uptake Fig. SII-1 presents the evolution, as a function of dioxygen concentration, of the dimensionless water uptake, defined as ratio between water uptake at considered oxygen concentration and water uptake at dioxygen concentration of 21%. One must notice that this ratio has been computed for the maximum water uptake, i.e. for a relative humidity of 90%.

𝐷𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠 𝑤𝑎𝑡𝑒𝑟 𝑢𝑝𝑡𝑎𝑘𝑒 (𝑅𝐻) =

Supplementary information III: water isotherms for carbon black samples

Supplementary information IV: water isotherms obtained for samples in powder forms

Supplementary information V: DS2 fitting of experimental water adsorption isotherms