Jasmina Wallace

Wendi Shang

Christophe Gitton

Laurent Hugueville

Lydia Yahia-Cherif

Brahim Selmaoui
email: brahim.selmaoui@ineris.fr

Theta band brainwaves in human resting EEG modulated by mobile phone radiofrequency

Keywords: electromagnetic fields, radiofrequency, mobile phone, human EEG, resting-state individual alpha frequency. Int

Wireless communication has become an integral part of our lives. The growing number of antennas in our environment and the expanding use of mobile phones (MPs) are increasing the population's exposure to electromagnetic fields. The present study aimed to examine the potential impact of MPs radiofrequency electromagnetic fields (RF-EMF) exposure on the brainwaves of the resting electroencephalogram (EEG) in humans. Twenty-one healthy volunteers were exposed to Global System for Mobile communications (GSM) signal at 900 MHz MP RF-EMF. The maximum specific absorption rate (SAR) of the MP averaged on 10 g tissue and 1 g tissue were measured at 0.49 W/kg, 0.70 W/kg, respectively. Results showed that while delta and beta rhythms of resting EEG were not affected, theta brainwaves were significantly modulated during exposure to RF-EMF related to MPs. For the first time, it was shown that this modulation is dependent on the eye condition, i.e., closed or open. This study strongly suggests that acute exposure to RF-EMF alters the EEG theta rhythm at rest. Long-term exposure studies are required to explore the effect of this disruption in highrisk or sensitive populations.

Introduction

The intensive use of mobile phones (MPs) and the growing electromagnetic fields in the environment have dramatically increased people's exposure to radiofrequency electromagnetic fields (RF-EMF). This exposure has raised questions about the potential effects of RF-EMF on human health. In this context, the electroencephalogram (EEG) has been an interesting neuroimaging technique to study potential effects of MPs RF-EMF emission on brain activity. Indeed, the EEG is an important non-invasive approach largely used in clinical and basic research to measure the brain electrical activity by recording the electrical signals generated by the addition of synchronized postsynaptic potentials from a large number of neurons in the cerebral cortex with millisecond resolution [START_REF] Cacioppo | Handbook of psychophysiology[END_REF]. To do that, the EEG uses electrodes placed on the scalp, as well as reference electrodes.

Although the electrical activity of the brain can vary between individuals, age, or health state, five main periodic rhythms of electrical potential oscillation of neurons in the cortex can be recognized in adult EEGs according to their frequency and voltages: gamma (>30 Hz), beta (13-30 Hz), alpha (8-13 Hz), theta (4-8 Hz), and delta (0.5-4 Hz) bands.

Several studies investigated MPs effects on EEG resting-state of healthy volunteersadolescents, adults, and elderly-as well as epileptic patients [START_REF] Wallace | Effect of mobile phone radiofrequency signal on the alpha rhythm of human waking EEG: A review[END_REF]. In particular, all of these studies focused on different MPs technologies, covering the whole range of RF-EMF signals from the 1 st generation of MPs (1G) to at least the 4G [START_REF] Wallace | Effect of mobile phone radiofrequency signal on the alpha rhythm of human waking EEG: A review[END_REF]. Even though some investigations did not find any significant effect of the exposure on the EEG, the bulk of the studies on this topic reported that exposure to RF-EMF seems to affect the EEG power spectral density at rest. The main effect has been seen on the spectral power of the alpha band (for review, see [START_REF] Danker-Hopfe | Effects of RF-EMF on the Human Resting-State EEG-the Inconsistencies in the Consistency. Part 1: Non-Exposure-Related Limitations of Comparability Between Studies[END_REF][START_REF] Hinrikus | Threshold of radiofrequency electromagnetic field effect on human brain[END_REF][START_REF] Wallace | Effect of mobile phone radiofrequency signal on the alpha rhythm of human waking EEG: A review[END_REF]. More precisely, the alpha band has been one of the most studied parameters in relation to the effect of RF-EMF. It should be noted that few other studies have examined the effects of RF-EMF exposure on other frequency bands (delta, theta, beta, and gamma) with conflicting results [START_REF] Croft | Acute mobile phone operation affects neural function in humans[END_REF][START_REF] D'costa | Human brain wave activity during exposure to radiofrequency field emissions from mobile phones[END_REF][START_REF] Hinrikus | Parametric mechanism of excitation of the electroencephalographic rhythms by modulated microwave radiation[END_REF][START_REF] Hinrikus | Effect of low frequency modulated microwave exposure on human EEG: individual sensitivity[END_REF][START_REF] Hinrikus | Effect of 7, 14 and 21 Hz modulated 450 MHz microwave radiation on human electroencephalographic rhythms[END_REF][START_REF] Roggeveen | EEG Changes Due to Experimentally Induced 3G Mobile Phone Radiation[END_REF][START_REF] Suhhova | Effect of microwave radiation on human EEG at two different levels of exposure[END_REF].

The aim of the present study was to examine the potential impact of Global System for Mobile communications (GSM) RF-EMF signal exposure on the delta, theta, and beta bands of the resting EEG. Moreover, we aimed to provide additional information to fill certain gaps in our current knowledge of the effects of GSM RF-EMF exposure on control parameters, such as eye condition (closed or open).

Materials and methods

a. Participants

Twenty-one right-handed healthy volunteers with normal or corrected to normal vision (10 females and 11 males; mean age ± SD: 25.1 ± 3.6 years; mean body-mass index ± SD: 21.5 ± 1.9) entered the study. We assessed inclusion criteria with a routine clinical examination and a clinical interview to exclude subjects with any history of head injury, neurological or psychiatric disease, any chronic disease, disability, or recent acute illness during last month. Inclusion criteria also included regular sleep habits with a regular sleep-wake cycle (8 am-11 pm ± 1 h), no medication, no smoking, and no drug use. Participants were not allowed to consume alcohol and caffeine for at least 24 hours before each experimental session. They have to maintain the regular sleep-wake cycle, not to use their personal MP on the days of the experiment, and to fast for at least two and half hours before experimental sessions. All women participated in the experimental sessions only during the follicular phase of the menstrual cycle. All participants provided a written informed consent before the investigation and were compensated for their participation. All procedures were approved by the French Ethics Committee and were in accordance with the Declaration of Helsinki.

b. RF-EMF exposure and dosimetry

In order to follow a double-blind design, we used two identical commercial dual-band GSM MPs (Nokia 6650), which differ only in the type of RF-EMF emission. Indeed, the sham or real exposure was carried out using a 'load' or a 'dummy load' of the MP, respectively. The real MP was set to transmit a modulated 900 MHz GSM signal (peak 2 W, average 250 mW, pulse modulated with a duty cycle of 1/8) at its maximum power using a service software (Phoenix, Nokia Corp., Finland). Further details about the RF-EMF exposure setup are available elsewhere [START_REF] Wallace | Human resting-state EEG and radiofrequency GSM mobile phone exposure: The impact of the[END_REF].

A dosimetry analysis revealed that the maximum specific absorption rate (SAR) of the real MP averaged on 10 g tissue and 1 g tissue were measured at 0.49 W/kg, 0.70 W/kg, respectively. On the contrary, the SAR of the sham MP was below the detection level of the system (0.001 W/kg). Moreover, a polystyrene phantom head test was used to avoid any interferences between RF-EMF and EEG recordings during the exposure phase. Results showed that MPs did not affect EEG signals during the exposure. Further details about dosimetry and phantom assessment are described elsewhere [START_REF] Ghosn | Radiofrequency signal affects alpha band in resting electroencephalogram[END_REF][START_REF] Wallace | Human resting-state EEG and radiofrequency GSM mobile phone exposure: The impact of the[END_REF].

c. Experimental protocol

This study is part of the broad study published previously [START_REF] Wallace | Human resting-state EEG and radiofrequency GSM mobile phone exposure: The impact of the[END_REF]. A double-blind, randomized, counterbalanced, crossover design was employed where each volunteer underwent two experimental sessions one week apart at the same time of day to avoid circadian rhythm bias. According to the protocol described previously [START_REF] Wallace | Modulation of magnetoencephalography alpha band activity by radiofrequency electromagnetic field depicted in sensor and source space[END_REF][START_REF] Wallace | Human resting-state EEG and radiofrequency GSM mobile phone exposure: The impact of the[END_REF] and shown in Figure 1, each experimental session started with 12 minutes of baseline EEG recordings combined with magnetoencephalography (MEG) in a specific MEG room (from run 1 to run 2), followed by 12 minutes of baseline EEG recording in another room (from run 3 to run 4). During both baseline phases, there was no RF-EMF exposure. During the sham or real RF-EMF exposure phase, EEG was recorded for 25 minutes and 30 seconds (from run 5 to run 8). During EEG recordings from run 3 to run 8, subjects were comfortably seated in a sound-attenuating shielded room, while remaining still and staring at a central black fixation mark (black dot surrounded by a black circle) presented on a gray background at a viewing distance of 1 m from the eye. Finally, during the post-exposure phase with no RF-EMF exposure (from run 9 to run 12) EEG combined with MEG was recorded for 25 minutes and 30 seconds. Each run included a 3-minutes recording interval with eyes-open (EO) and 3-minutes interval with eyesclosed (EC) in alternation with a 30-second pause at the end.

d. Data acquisition

Depending on whether the EEG was combined with the MEG recordings or not, different acquisition systems were used. For this reason, we included the analyses of EEG recorded only during the baseline (runs 3 and 4) and the exposure phase (runs 5-8). The EEG signal from run 3 to run 8 was acquired using the BrainVision BrainAmp MR plus Amplifiers (Brain Products GmbH, Germany; Figure 1), from 74 EEG-channel system with Ag/AgCl sensors placed on the participant's scalp according to the standard 10/10 system (Figure 2), referenced to mastoids, and grounded on the left scapula. EEG data were recorded with a sampling frequency of 1 kHz and a bandwidth of 0.016-250 Hz. Ocular movements were recorded with horizontal electro-oculogram (EOG) applying two electrodes near the outer canthi of the left and right eyes, as well as two electrodes placed above and below the right eye to measure vertical EOG.

EEG electrical impedances were maintained lower than 20 kΩ, while impedances of reference signal, ground signal, and EOG were maintained lower than 5 kΩ.

e. EEG data preprocessing and frequency analysis

EEG data from run 3 to run 8 were analyzed using MNE-Python, version 0.19.2 [START_REF] Gramfort | MEG and EEG data analysis with MNE-Python[END_REF]. First, we removed from all data analysis the electrodes too close to the EEG cap ear-slits (i.e., T9, TP9, T10, TP10) for all subjects, and bandpass filtered the EEG signal between 1-20 Hz using the finite impulse response filter

f. Statistical analysis

Statistical analysis was performed using a custom-written MATLAB (R2019) toolbox [START_REF] Wallace | Human resting-state EEG and radiofrequency GSM mobile phone exposure: The impact of the[END_REF]. First, we used a three-way repeated measures analysis of variance (ANOVA) on power values computed for each frequency band to determine a period effect (factor 1 with two levels: baseline and exposure), eyes condition effect (factor 2 with two levels: EO and EC), and exposure condition effect (factor 3 with two levels: sham exposure and real exposure), as well as their interactions. Second, we applied the one-way repeated measures ANOVA on baseline-corrected exposure power values of each frequency band comparing the two exposure conditions, and considering EO and EC data separately. F and p-values of both ANOVA analyses were computed for each electrode on the scalp. Statistical significance was set as p < 0.05.

We further applied a post-hoc cluster-based permutation test to ANOVA analyses of theta band power values to correct for multiple comparisons [START_REF] Maris | Nonparametric statistical testing of EEG-and MEG-data[END_REF]. For each main effect or interaction of theta band, samples whose F-value exceeded a threshold (here, F-values corresponding to a one-tail p-value of 0.05) were clustered based on space adjacency given by an electrodes neighboring matrix.

We estimated the distribution of the maximum cluster level F-statistics under the null hypothesis through 1000 randomizations for each main effect and each possible interaction, while we rejected the null hypothesis with a Monte-Carlo p-value < 0.05 if the observed statistic was greater than 95% of the statistic values obtained from randomized data. Finally, statistical analysis results were plotted as topographic maps showing the p-values calculated for each electrode on the scalp.

Results

a. Three-way repeated measures ANOVA results

As shown in Figure 3A, results of beta band three-way repeated measures ANOVA reported that only the FT9 electrode showed a statistically significant difference (p = 0.0132) for time factor (two levels: baseline and exposure), and only one frontal electrode (F7) showed a statistically significant difference (p = 0.0358) for the exposure condition factor (two levels: real and sham). On the other hand, the eye condition factor (two levels: EO and EC) showed statistically significant differences widespread over the central and occipital scalp regions. Considering the interactions between factors, results revealed a significant interaction between all factors at electrodes C6 (p = 0.0359) and CP6 (p = 0.0469).

Results of the theta band three-way repeated measures ANOVA are reported in Figure 3B. The time factor showed statistically significant differences at centroparietal and occipital electrodes (FT9, FC5, CP5, CP3, P9, P7, P5, P3, P1, Poz, PO4, PO8, and O1), while the exposure condition factor showed a statistically significant difference depicted only by the FT9 electrode (p = 0.0248). The eye condition factor showed significant differences widespread over the whole scalp. The interaction between all factors showed a statistically significant difference involving the central, parietal, and occipital electrodes (C1, Cz, C2, C4, C6, T8, CP5, CP3, CP1, Cpz, CP2, CP4, CP6, TP8, P9, P7, P5, P3, P1, Pz, P2, P4, P6, PO9, PO7, PO3, Poz, PO4, O1, and Oz).

Results of the delta band three-way repeated measures ANOVA are reported in Figure 3C. The time factor showed a statistically significant difference between power values measured at baseline and exposure recording phases depicted by electrodes FT9 (p = 0.0031) and P9 (p = 0.0045). Similarly, only two electrodes, FT9 (p = 0.0456) and TP7 (p = 0.0155), showed a statistically significant difference between real and sham exposure phases for the exposure condition factor. On the contrary, the eye condition factor showed significant differences widespread over the scalp. As before, the interaction between all factors showed a slight statistically significant difference involving centro-parietal and posterior electrodes (CP5, CP3, P5, and O10).

In Figure 4 are shown the results of the cluster-based permutation of the three-way repeated measures ANOVA. Only time factor, eyes condition factor, and interaction between all factors reported significant clusters. Considering the time factor, results showed one significant cluster involving left centro-parietal electrodes (Monte Carlo p < 0.001), one significant cluster involving left parietal electrodes (Monte Carlo p < 0.001), two significant clusters involving fronto-temporal electrodes (Monte Carlo p < 0.001), and one significant cluster involving right parieto-occipital electrodes (Monte Carlo p < 0.001). Considering the eyes condition, we found one significant cluster involving all electrodes over the scalp (Monte Carlo p < 0.001). The interaction between all factors showed one significant cluster involving central, temporal and parietal areas (Monte Carlo p < 0.001) and two more significant clusters at the parieto-occipital region ( Monte Carlo p = 0.001 and Monte Carlo p < 0.05, respectively).

b. One-way repeated measures ANOVA results

As shown in Figure 5A, the one-way repeated measures ANOVA showed that power values of the beta band significantly decreased at the C6 (p = 0.0489) and CP6 (p = 0.0448) electrodes during the real RF-EMF exposure phase relative to the sham exposure with EO. However, no statistically significant differences were found between beta band power values measured during the real and sham exposure phases with EC.

Results of the one-way repeated measures ANOVA showed a statistically significant decrease of the theta band powers computed at centro-parietal and occipital electrodes (C4, C6, CP1, CPz, CP2, CP4, P3, P1, Pz, P2, P4, P6, PO3, Poz, PO4, and O2) with EO during the real RF-EMF exposure compared to sham exposure. On the other hand, with the EC condition, the power values computed for the theta band revealed a slight statistically significant increase during the real exposure phase relative to sham exposure at parietal electrodes (P9, P7, P3, and PO7) (Figure 5B).

Concerning the delta band one-way repeated measures ANOVA, results reported a slight decrease of power values depicted at the P4 electrode (p = 0.0418) during the real RF-EMF exposure, relative to sham with EO, while showing an increase of power values depicted by P10 (p = 0.0370) during the real exposure relative to sham exposure with EC (Figure 5C).

In Figure 6 are shown the results of the cluster-based permutation of the one-way repeated measures ANOVA. Considering the EO condition, we found one significant cluster involving centro-parietal electrodes (Monte Carlo p < 0.001) and one significant cluster at parieto-occipital region (Monte Carlo p < 0.05), while we found one significant cluster involving left parietal electrodes (Monte Carlo p < 0.05) for the EC condition.

Discussion

In this study, we investigated the potential effects of the exposure to RF-EMF related to GMS 900 MHz MPs on the electrical brain activity of healthy volunteers at rest in a double-blind, randomized, counterbalanced, and crossover EEG protocol. We analyzed the EEG power spectral density of the beta (13-20 Hz), theta (4-8 Hz), and delta (1-4 Hz) bands before and during RF-EMF exposure, considering EEG recordings with EO and EC. The analysis of baseline-corrected data showed that, among the three investigated frequency bands, the theta band seemed to be significantly affected by RF-EMF exposure. Indeed, the beta and delta oscillations reported slight effects of RF-EMF exposure, as shown by both three-way and oneway ANOVA statistical analysis. We could assume that the weak effect observed on these bands is likely to represent a random occurrence rather than a real effect. On the contrary, the theta band reported a greater effect of the exposure (which survived to multiple comparison correction) with a significant decrease of the power during the real exposure compared to the sham exposure with the EO and a significant increase with the EC. This power modulation related to RF-EMF exposure was depicted by the centro-parietal and occipital electrodes. It is noteworthy that, even though the theta oscillation is generally widely distributed across the scalp [START_REF] Segalowitz | Electrophysiological changes during adolescence: a review[END_REF], it has shown a high degree of MEG resting-state reliability in the parietal cortex over three years [START_REF] Lew | Three-year reliability of MEG resting-state oscillatory power[END_REF], which could explain our findings. Moreover, we can exclude any influences on brain electrophysiology related to physiological factors known to modulate EEG activity. As previously shown elsewhere [START_REF] Wallace | Modulation of magnetoencephalography alpha band activity by radiofrequency electromagnetic field depicted in sensor and source space[END_REF], we assessed some confounding factors (salivary biomarkers of stress, heart rate, heart rate variability, and salivary caffeine concentration), which did not report any statistically significant differences related to the exposure condition.

Our EEG results are in line with previous results by [START_REF] Hinrikus | Parametric mechanism of excitation of the electroencephalographic rhythms by modulated microwave radiation[END_REF], which reported a power increase of the theta band related to 450 MHz RF-EMF exposure during EEG resting-state recording of healthy volunteers with EC; in particular, our theta band results confirm these previous results with the eyes-closed condition. On the other hand, the data obtained with EO went in the opposite direction. The theta band spectral power decreased when the eyes were open in our experiment. This suggests that the eyes-open or eyes-closed condition could affect the results of the theta band response to RF-EMF exposure. This is in agreement with our previous results [START_REF] Wallace | Modulation of magnetoencephalography alpha band activity by radiofrequency electromagnetic field depicted in sensor and source space[END_REF], which highlighted that RF-EMF exposure affected the alpha band activity differently depending on the condition of the eyes (open or closed).

Furthermore, previous studies investigating RF-EMF effects on EEG reported somewhat different results for the delta and beta bands. Indeed, findings showed either a decrease in the delta [START_REF] Croft | Acute mobile phone operation affects neural function in humans[END_REF] and beta bands powers [START_REF] D'costa | Human brain wave activity during exposure to radiofrequency field emissions from mobile phones[END_REF]Yang et al., 2017), or an increase in the delta [START_REF] Hinrikus | Parametric mechanism of excitation of the electroencephalographic rhythms by modulated microwave radiation[END_REF] and beta bands powers [START_REF] Hinrikus | Parametric mechanism of excitation of the electroencephalographic rhythms by modulated microwave radiation[END_REF][START_REF] Hinrikus | Effect of low frequency modulated microwave exposure on human EEG: individual sensitivity[END_REF][START_REF] Hinrikus | Effect of 7, 14 and 21 Hz modulated 450 MHz microwave radiation on human electroencephalographic rhythms[END_REF][START_REF] Roggeveen | EEG Changes Due to Experimentally Induced 3G Mobile Phone Radiation[END_REF][START_REF] Suhhova | Effect of microwave radiation on human EEG at two different levels of exposure[END_REF]. Other studies reported a modulation of the gamma band activity with an increase in the power spectral density related to the RF-EMF exposure [START_REF] Curcio | Electromagnetic fields and EEG spiking rate in patients with focal epilepsy[END_REF][START_REF] Hinrikus | Parametric mechanism of excitation of the electroencephalographic rhythms by modulated microwave radiation[END_REF][START_REF] Roggeveen | EEG Changes Due to Experimentally Induced 3G Mobile Phone Radiation[END_REF]. This divergence in results may be the result of differences between studies in protocol designs as reported above (e.g., eyes condition), participant inclusion criteria, RF-EMF frequencies and intensities, EEG data acquisition, or data analysis, and statistics, as reviewed elsewhere [START_REF] Danker-Hopfe | Effects of RF-EMF on the Human Resting-State EEG-the Inconsistencies in the Consistency. Part 1: Non-Exposure-Related Limitations of Comparability Between Studies[END_REF][START_REF] Wallace | Effect of mobile phone radiofrequency signal on the alpha rhythm of human waking EEG: A review[END_REF].

Since the theta band is considered a marker of memory functions, processing information and attention, and its synchronization reflects working memory performance [START_REF] Grover | Long-lasting, dissociable improvements in working memory and long-term memory in older adults with repetitive neuromodulation[END_REF][START_REF] Jensen | Frontal theta activity in humans increases with memory load in a working memory task[END_REF][START_REF] Klimesch | Memory processes, brain oscillations and EEG synchronization[END_REF][START_REF] Klimesch | EEG alpha and theta oscillations reflect cognitive and memory performance: a review and analysis[END_REF][START_REF] Klimesch | Brain oscillations and human memory: EEG correlates in the upper alpha and theta band[END_REF][START_REF] Klimesch | The functional significance of theta and upper alpha oscillations[END_REF], a question arises spontaneously: what is the clinical implication of its modulation related to RF-EMF exposure? Based on the results of the current study, it is too early to answer this question; however, it has been shown that the MP RF-EMF exposure modulated the event-related desynchronization of the alpha band, enhancing human cortical neural efficiency and cognitive-motor processes [START_REF] Vecchio | Mobile phone emission modulates event-related desynchronization of alpha rhythms and cognitive-motor performance in healthy humans[END_REF]. Generally, previous results suggested that RF-EMF related to GSM MPs may have a slight effect on human attention and working memory [START_REF] Barth | A meta-analysis for neurobehavioral effects due to electromagnetic field exposure emitted by GSM mobile phones[END_REF]. Moreover, it is noteworthy that some noninvasive brain stimulation techniques, such as transcranial magnetic stimulation, transcranial direct current stimulation (tDCS), oscillatory tDCS, or transcranial alternating current stimulation (tACS), employ either magnetic or electric fields in order to stimulate the cortical neuron assemblies and modulate behavioral responses. In particular, it has been shown that theta-tACS administration had a positive effect on working memory functions [START_REF] Albouy | Driving working memory with frequency-tuned noninvasive brain stimulation[END_REF], allowing to enhance long-lasting working memory capacities in the elderly through repetitive applications [START_REF] Grover | Long-lasting, dissociable improvements in working memory and long-term memory in older adults with repetitive neuromodulation[END_REF].

Conclusions

In conclusion, this work contributes to the growing literature that suggests the potential modulation of human spontaneous EEG by exposure to RF-EMF. Indeed, it showed that acute exposure to MP RF-EMF at 900 MHz modulates the spectral power of the theta band in healthy volunteers at rest. To our knowledge, it also emphasized the role of the eye condition in the effect of RF-EMF on EEG for the first time.

Clinical implications of this modulation need further investigation. In particular, chronic exposure effects should be assessed, especially in high-risk and sensitive populations.

Figure 1 .

 1 Figure 1. Experimental protocol. EEG/MEG: electroencephalography combined with magnetoencephalography; EEG: electroencephalography; EO: eyes-open; EC: eyes-closed.

Figure 2 .

 2 Figure 2. Electroencephalogram layout according to the standard 10/10 system

Figure 3 .

 3 Figure 3. Results of the three-way repeated measures ANOVA for the EEG (A) beta, (B) theta, and (C) delta bands. Results are shown as p-value topography maps, where p-values were computed and plotted for each electrode. Statistical significance was set as p < 0.05. Factor 1: baseline vs. RF-EMF exposure; Factor 2: eyes-open vs. eyesclosed; Factor 3: sham RF-EMF exposure vs. real RF-EMF exposure; *: interaction between factors.

Figure 4 .

 4 Figure 4. Results of the cluster-based permutation of three-way repeated measures ANOVA for the EEG theta band. Results are shown as p-value topography maps, where p-values were computed and plotted for each electrode. Statistical significance was set as p < 0.05. Factor 1: baseline vs. RF-EMF exposure; Factor 2: eyes-open vs. eyesclosed; Factor 3: sham RF-EMF exposure vs. real RF-EMF exposure; *: interaction between factors.

Figure 5 .

 5 Figure 5. Topography maps for (A) beta, (B) theta, and (C) delta bands. Power topography maps show EEG baselinecorrected power values computed for each electrode during the real and sham RF-EMF exposures with eyes-open and eyes-closed. p-value topography maps show the results of one-way repeated measures ANOVA on the EEG baseline-corrected powers (real exposure vs. sham exposure). P-values were computed and plotted for each electrode. Statistical significance was set as p < 0.05.

Figure 6 .

 6 Figure 6. Results of the cluster-based permutation of one-way repeated measures ANOVA (real exposure vs. sham exposure) for the EEG baseline-corrected powers of the theta band. Results are shown as p-value topography maps, where p-values were computed and plotted for each electrode for eyes-closed and eyes-open conditions. Statistical significance was set as p < 0.05.

Acknowledgments

This work was fully funded by Program 190 of INERIS, supported by the French Ministry for the Ecological and Inclusive Transition. We thank René de Seze (Department of Experimental Toxicology and Modeling, INERIS) for the clinical support.

Disclosure statement

The authors declare no competing interests.


Marwan Al Heib
email: marwan.alheib@ineris.fr

Nathalie Conil

Philippe Gombert

Influence of geology and topography on the occurrence of mine massive collapse -Back-analysis of a historical collapse of chalk mine (France)

Keywords: collapse, massive, chalk mine, back-analysis, cliff, fault, stiff bed

Pillars of an underground mine are designed to ensure long-term stability and preserve the surface assets from the consequences of mining. However, long-term stability is never guaranteed. Over time, subsidence and collapses can occur, and the consequences are sometimes dramatic. Such collapses depend on the exploitation characteristics, the mechanical properties of the terrain, and the potential presence of water, but additional factors can play a major role. This study aims to identify the predisposing and triggering factors of the collapse, including stiff beds, cliffs, and faults. Back-analysis was carried out on a historic dramatic massive collapse of a chalk mine (Beaulieu, France, 1910). Numerical modeling (finite and distinct elements) was carried out to highlight the influence of mining geometry, the stiff bed, and the cliff. Then, the mechanism of the collapse of the Beaulieu mine was investigated. The results demonstrate the importance of the geometric configurations of the site for the development of such a phenomenon, particularly the cumulative effects of the excavation (extraction ratio), the cliff, and the stiff bed. These cumulative factors increase the risk of a massive collapse. This study has shown that the stability of abandoned room and pillar underground mines should cover three concepts: estimation of the stress state of the pillars, the strength of the pillars, and the presence of a cliff as well as a significant discontinuity crossing the rock mass which could be a fault.

Introduction

Shallow underground mines are mainly excavated by the room-and-pillar extraction method. The pillars are designed to ensure the long-term stability of the excavations and to preserve the surface assets from the consequences of mining. However, long-term stability is never guaranteed. In fact, these underground mines are likely to deteriorate over time and cause collapses or subsidence of the ground, the consequences of which are sometimes dramatic (Figure 1). These collapses can occur during or after the cessation of exploitation (Kaufmann and Quinif, 2002;Gilbride et al., 2005;Edmonds, 2008;Al Heib et al., 2014). They induce short-and long-term technical and socio-economic risks for the environment, the surface structures, and the population [START_REF] Bell | Mining Subsidence and Its Effect on the Environment: Some Differing Examples[END_REF]Gutiérrez et al., 2009). A distinction can be made between a localized collapse which generally involves only one part of the cavity, and a massive collapse (mass collapse) which involves a large part of the underground mine with a surface that can concern several hectares [START_REF] Franck | Évaluation des aléas miniers[END_REF]. The massive collapse can sometimes generate a low magnitude earthquake (Wang et al., 2008). Predicting localized or massive collapses is often difficult because of the numerous natural and anthropic factors that intervene.

Table 1 presents examples of massive collapses that have occurred in different countries. In France, several significant events can be mentionned: such as the collapse at Clamart (Hauts-de-Seine) in 1961 which caused 21 deaths and 50 injuries, the collapse at Roquevaire (Bouches du Rhône) in 2005, which led to a subsidence measuring 50 m in diameter, the collapse at Bapaume under a supermarket carpark (Pas-de-Calais) in 2010. Several massive collapses have also affected the iron mines of Lorraine leading to the destruction of part of the villages concerned (Kouniali et al., 2000). In Belgium, the collapse of the Malogne underground chalk mine in 2015 damaged a high-speed train line. Salt and potassium mines are also prone to this type of "catastrophic" collapse (Whyatt and Varley, 2008;Bérest et al., 2010), as in the case of the Varangéville (France) salt mine collapse in 1873.

Causes of massive collapse

A massive collapse involves a sudden movement of the surface that results in discontinuous subsidence. These collapses usually affect large areas and shallow mines (less than 100 m in depth). They are specific to extensive underground excavations consisting of rooms and pillars and presuppose a general instability (cascade failure) of the underground excavation (Figure 2). In some cases, collapses are linked to the landslide of undermined cliffs. In this specific case, the collapse corresponds to a sudden movement during which a significant and voluminous mass breaks away from a generally very steep slope to spread or propagate at the foot of the slope.

Various studies have been conducted to identify the causes of massive collapses. The primary cause is often a high excavation ratio. However, regardless of their nature, the deterioration processes of underground mines result from a combination of one or more unfavourable configurations likely to upset the equilibrium of the environment and accelerate the rupturing mechanisms. These configurations generally result from geological, hydrogeological, and geometric factors, as well as site and human factors. For example, the properties of the overburden (depth, stiff bed, etc.) may contribute to the deterioration of some structures. A discriminant analysis of the sudden collapses in the iron basin in France (Kouniali et al, 2000) showed that the main causes are an extraction ratio exceeding 60% and the presence of a stiff bed in the overburden, close to the surface. The laboratory test [START_REF] Liakas | Influence of heterogeneity on rock strength and stiffness using discrete element method and parallel bond model[END_REF] showed that the mode and intensity of the sudden rupture of the overburden depends on the alternation of stiff and deformable (less resistant) beds, and that an increased ratio of stiff beds promotes brittle rupture. [START_REF] Fairhurst | Examen de la méthode GEODERIS d'évaluation des risques et des conséquences potentielles relatifs aux affaissements de surface dans le bassin ferrifère lorrain[END_REF] proposed a mechanism of massive collapse in the presence of a sufficiently thick stiff bed. In fact, the pillars and the immediate roof continuously deform over time (creep phenomenon, Figure 2). These deformations are transmitted to the high roof which is resistant and therefore not very deformable. At a certain level of deformation, the stiff bed reaches its maximum permissible bending deflection, with very significant shear effects at its supports. A collapse can then occur suddenly by shearing at the supports or by sliding along vertical cracks. Homand ( 2004) defined the stiffness of the mine roof based on the properties of the underground excavation, the topography, the Young's modulus of the intact layers, and the density of the fractures or discontinuities.

Figure 2. Vertical section presenting the main elements of an underground room and pillar mine

The topography, especially when excavating a mine near a slope or cliff, can negatively impact stability. [START_REF] Savage | Gravitational stress in long symmetric ridges and valleys[END_REF][START_REF] Savage | Tectonic and gravitational stress in long symmetric ridges and valleys[END_REF] and [START_REF] Savage | Gravity induced stresses in finite slopes[END_REF] demonstrated that gravitational stresses are affected by the topography of the site (cliff) and the Poisson's ratio of the rock, even in the absence of underground excavation. They also identified the presence of tensile stresses. They can affect the stability conditions of the cavities and the likelihood of ground movements in the area. However, this influence of the slope on the cavity and/or of the cavity on the slope decreases as the distance from the voids increases. [START_REF] Moiriat | Observations sur la fracturation liée à l'incision d'une vallée-Carrière souterraine des Brillants (Hauts-de-Seine)[END_REF] studied the configuration of a chalk cavity excavated near a slope consisting of alternating layers of marl, limestone, and clay. They demonstrated the presence of tensile stresses in the limestone bed in this case. Fougeron (2007) studied the effect of a valley on the occurrence of massive and sudden collapses. The results of his numerical computations show that this situation can lead to over-stressed areas, particularly in the presence of a limestone bed (stiff bed). [START_REF] Cherkaoui | Critères de détermination de l'aléa versant rocheux sous-cavés[END_REF] studied the case of under-excavated cliffs and found that the tensile and shear stresses that develop within adjacent buried structures, at the level of the pillars, spacer boards, and gallery vaults, can become preponderant. The collapse of the Clamart mine chalk in 1961 [START_REF] Heib | Analysis of the historical collapse of an abandoned underground chalk mine in 1961 in Clamart (Paris, France)[END_REF] corresponds to the configuration of an undermined cliff. [START_REF] Trigueros | Stability of an abandoned siderite mine: A case study in northern Spain[END_REF] also observed an increase in instability of an underground iron mine linked to the presence of a nearby open pit mine and a roof marked by a stiff limestone bed.

In conclusion, these studies show that massive collapses are dependent on several parameters including predisposing factors and triggering factors. Predisposing factors include mining geometry, geology, and the initial and modified mechanical properties of the terrain, while triggering factors concern dynamic actions, water presence and climatic and environmental factors. Table 2 presents the main predisposing and triggering factors in the occurrence of a massive collapse of an underground mine by room and pillar underground excavation, which includes 9 predisposing factors and 7 triggering factors. These triggering factors can be natural or man-made. The assessment of massive collapse hazards should consider both the predisposing and triggering factors. To explain the causes of the collapse, strength tests were done on samples taken from the neighbouring mine by the French Mining Authorities immediately after the mine collapse. The compressive strength values obtained at different degrees of water saturation reveal that this chalk loses all coherence when immersed for a few hours. In fact, the massive collapse of the Beaulieu underground chalk mine occurred following a 10-days rain event with heavy rainfall the day before the collapse (Figure 5). According to observations described in the archive documents [START_REF] Liénard | Procès-verbal d'enquête. Effondrement d'une carrière[END_REF], this exceptional rainy event caused a centennial flood of the Loing: the river and its tributaries overflowed and flooded the alluvial plain, without however reaching the mine. As a result, the origin of the initial collapse of the mine has been attributed to the flooding of the lower sections by the sudden rise of the chalk water table, which would have caused the rupture of the "small pillars" zone further to north, followed by the massive collapse of the remainder of the mine, which would in turn have triggered the sliding of the cliff [START_REF] Ph | Analyse climatologique, hydrologique et hydrogéologique des effondrements survenus à Château-Landon (77) aux XIXe et XXe siècles[END_REF].

However, several points remain open for consideration. While the collapse of the most heavily mined sector seems logical, the spread of the disorder towards the larger pillars is difficult to explain. It is also legitimate to investigate Nord the chain of events in order to try to understand the magnitude of the subsidence and to verify whether these sitespecific conditions could have been aggravating factors. [START_REF] Watelet | Analyse and questioning on 1910 collapse of Lorroy chalk underground quarry[END_REF] also noted that the collapse of the lower sector of the mine does not, on its own, explain the rupture mechanism. Other phenomena would probably have to be included to explain the observed movements.

Geological and hydrological context

The geology of the exploited zone is relatively simple: starting from the top of the plateau, the terrains encountered are indicated on the map and on the simplified cross-section (Figure 6). Above the chalk mass, one can see the alternating layers of conglomerate (puddingstone), limestone, and silt near the slope. The chalk is fractured due to various tectonic movements and to the decompression caused by excavation of the Loing valley. Within the mine environment, excavated at the base of the slope, there is a river (Loing) and a canal. From a hydrogeological perspective, the two main aquifers are the Loing alluvial aquifer and the regional chalk aquifer which join together at the edge of the valley, perpendicular to the old Beaulieu mine. Near the site, the chalk water table currently fluctuates between 67 and 73 m asl [START_REF] Conil | An underground research laboratory at Château-Landon (France) to study the impact of climate change on the stability of abandoned mines[END_REF], while the alluvial water table, close to the level of the Loing, is around 65-67 m asl. Wells which were present inside the Beaulieu mine, attest that the water table was located at a depth of around 2 m during exploitation of the mine.

History of the extraction

At the outset, the chalk exploitation appears to have started as an open pit quarry. The underground extraction activity began in this sector in the middle of the 19 th century, via entrances dug at the base of the hillside (Figure 7). Along the Loing river, over one kilometre away, five other abandoned underground mines can be found, of which four have already collapsed. A single mine, the Royer mine, remains today, and is instrumented as an underground observation site [START_REF] Conil | An underground research laboratory at Château-Landon (France) to study the impact of climate change on the stability of abandoned mines[END_REF]. The exploitation was carried out in long vaulted galleries that were 3 to 5 m high, without any specific organization (Figure 7-a). The overburden varied from a few meters to about thirty meters in the deepest sectors (Figure 7-c).

Chalk behaviour

Immediately after the collapse, simple compression tests were conducted on chalk samples taken from the collapsed mine. They were performed at different degrees of saturation (Sr). The resistance values obtained in saturated conditions were very low (ranging from 0.4 to 0.8 MPa). This chalk was shown to have a complex behaviour, and a sudden drop in resistance values was observed when the samples were "saturated by immersion". New tests were conducted more recently [START_REF] Delage | Comportement de la craie du site de Lorroy[END_REF], Lafrance et al., 2014) on samples taken from the neighbouring Royer mine. The authors showed that this chalk has a mean porosity (n) of 44% and a dry density of 1.5. The gradual decrease in compressive strength as the saturation level increases (Figure 8) was again demonstrated. [START_REF] Delage | Comportement de la craie du site de Lorroy[END_REF] showed a decrease from 1.3 MPa (for an Sr of 60%) to less than 0.5 MPa (about the values measured in 1910) when approaching full saturation. According to [START_REF] Lafrance | Study of the effects of water on the phenomena of rupture and deformation affecting underground chalk quarries[END_REF], the chalk from Château-Landon differs from other chalks mined in France by its higher sensitivity to water. In these tests, the saturation of a sample caused its strength to drop sharply from 3.5 MPa to 0.8 MPa. However, Figure 8, when the material is saturated, the rupture is not as clean, the chalk is crushed, and the material quickly enters plasticity and exhibits dilatancy before the rupture as indicated in Figure 8. In addition to laboratory tests in situ measurements of the volumetric water content of the chalk mass in the Royer mine were conducted [START_REF] Delage | Comportement de la craie du site de Lorroy[END_REF]. They show that the chalk is slightly unsaturated in the gallery wall (Sr=81%) and almost fully saturated at depth (Sr=96% at 3 m from the wall). The authors concluded that the outer surface of the pillars may have better mechanical properties due to the suction caused by desaturation in contact with the atmosphere, while the more saturated part at the heart of the pillar has a lower resistance. This results in a containment that allows the pillar to be maintained but conditioned by the hydric state of the structure, itself dependent on the inflow of water by capillarity from the water table (or from the surface by percolation) and the air humidity cycles in galleries (evaporation, wetting, etc.). The loss of resistance of the pillars during the 1910 collapse could thus be linked to the reduction of suction at their outer surfaces, caused by the hydric changes that occurred in the galleries when they were suddenly flooded by the rise of the water table.

and observations made in the Royer mine (stable at present) show that the following factors may play a main role and characterize the collapsed zone: areas with high excavation ratios, small-sized pillars with a relatively high slenderness ratio, exploitation of a material very sensitive to water, presence of a water table at shallow depth, presence of an cliff with an average dip of around 25°, presence of a north-south fracture parallel to the cliff with a dip of the order of 70°, and presence of a stiff bed in the overburden (limestone layer) of quite significant thickness (about 10 m).

The objectives of this back-analysis are to identify the predisposing factors and the triggering factors of the collapse, and to establish the most probable mechanism. Thus, it considers the mechanical properties of the chalk, the stability conditions of the underground mine and slope, as well as the effect of the presence of the fault. First, we study the influence of the chalk behaviour on the pillars: the mine geometry. Then, two groups of numerical modelling were carried out. The first group highlights the influence of the stiff bed, and the cliff presences. The second group studies the case of the Beaulieu mine collapse: the influence of cliff and fault presences. The result will be discussed to suggest a mechanism of the collapse.

Influence of the chalk -pillar strength

To study the influence of the strength chalk, the average vertical stresses in the Beaulieu mine pillars were calculated analytically by the tributary area method (Figure 9). The principle of the method is that a pillar takes the weight of overlying rock up to half distance of the rooms width surrounding it. The vertical stress (v) is given by the equation:

𝜎 𝑣 = 𝜎 𝑣0 1 -𝜏
Where v0 the initial vertical stress and  is the local extraction ratio of the mine. The initial vertical stress depends on the depth of the mine and the density of the overburden. The depth depends on the location of each pillar. The density is taken constant and equal to 20 kN.m -3 . The extraction ratio is:

𝜏 = 𝑆 𝑡-𝑆 𝑝 𝑆 𝑡
Where St the total surface and Sp the pillar surface. We locally calculated, for each pillar, the extraction ratio.

Examining the mine's archived plans and visiting the Royer mine provided information on the probable geometry and state of deterioration of the Beaulieu mine (Figure 6, state of the roof and pillars and orientation of fracturing in particular). Based on this information, the vertical stresses of the computed pillars correspond to the values following the excavation of the mine, taking their geometry and the thickness of the overburden into account. To calculate a safety factor (F= v/UCS), the vertical stresses were compared to the compressive strength (UCS) of chalk. Two configurations were analysed: firstly, the compressive strength is equal to 1.4 MPa, and secondly the strength is equal to 0.8 MPa corresponding to the saturated chalk. The comparison between the two configurations clearly shows that total saturation increases the number of unstable pillars. This phenomenon results in a decrease value of the calculated safety factor (Figure 9). However, this approach helps to better explain the failure of the southern part of the Beaulieu mine, but it does not explain the sliding of the cliff and the massive collapse that followed.

Figure 9. Evolution of the safety factor (F) of the pillars (using analytical approach: tributary area method) in the case of a drop in the compressive strength (UCS) of the chalk (1.4 MPa on the right and 0.8 MPa on the left).

Influence of Influence of stiff bed

The analytical calculation presented previously did not consider the effect of the overburden into account.

However, research suggests it likely plays a role in massive collapses. The analysis of the Beaulieu mine collapse zone's geology revealed the presence of a limestone stiff bed about 10 m thick above the chalk layer (see Figure 6). Figure 10 schematically shows the behaviour (subsidence) as a function of time, for a deformable and a stiff bed. The stiff bed initially undergoes weak deformations until failure, which is marked by a significant increase in deformation and brittle behaviour. This behaviour is also observed in massive collapses.

Figure 10. Difference in behaviour (subsidence) in the presence of a soft overburden and a stiff layer [START_REF] Whyatt | Mining Publication: Catastrophic Failures of Underground Evaporite Mines[END_REF].

To quantify the effect of the stiffness of limestone bed, a 2D numerical model was made with a thick bed in the roof, and a single rectangular cavity 10 m long, 5 m high, and located 30 m deep. The cavity is in the less rigid layer, the chalk layer. The model also considers the presence of a cliff measuring 35 m in height from the base of the mine (Figure 11). The configuration with a vertical cliff was compared with the configuration without a cliff. The simulation of the cliff was done by considering free horizontal displacements.

The cavity was taken to be sufficiently long to be able to use the plan strain hypotheses and to produce a 2D model.

The dimensions of the model were large enough compared to the dimensions of the cavity to avoid the effect of boundary conditions on the numerical results. The roof of the cavity was made up of three identical beds of 10 m thickness. The stiff bed was characterized by a Young's modulus (Er) "n" times higher than the underlying and overlying beds (Em). The weight of the terrain was considered as the only load. The Young's modulus of the bed located in the middle (Em) was equal to 1 GPa (corresponding to well-consolidated marly rocks) and that of the chalk layer was 0.1 GPa. The Poisson's ratio of the three beds was identical and equal to 0.25. The bulk density of each of the rocks was equal to 20 kN.m -3 .

Figure 11. Modelling of a cavity (model 1) in the case of a configuration with a cliff (on the left) or without a cliff (on the right) and a bed (Er) which is n times stiffer than the underlying and overlying terrain (Em).

For each configuration, three sub-configurations are -without a cavity and with stiff bed (SC-SB), -with a cavity and with stiff bed (AC-SB), -with a cavity and with homogenous terrain (AC-HM),

In total 6 configurations were analysed. In term of numerical results, Table 3 shows the maximum and minimum computed vertical and horizontal stresses for a stiff bed (SB) with a 100 times higher modulus than underlying and overlying beds. The great differences observed between these six configurations concern the horizontal stresses (of compression and traction). Even in the absence of a cavity, the presence of a vertical cliff generates tensile stresses (SC-TR: 0.63 MPa) which are in the stiff bed of the overburden. However, the presence of the cavity accentuates the tensile stresses in this stiff bed. The tensile stresses at the roof of the cavity increase from 0.35 MPa (AC-HM) to 1.13 MPa with a stiff bed (AC-SB), i.e. by 223%, and from 1.13 to 1.94 MPa with a cliff, i.e. by 71%, compared to a cavity dug in homogeneous ground without cliff. These tensile stresses favour the predisposition to collapse, particularly when they exceed the tensile strength of the stiff bed rock. The computed stress values are to be compared with the tensile strength of the rock, which is generally quite low [START_REF] Lafrance | Study of the effects of water on the phenomena of rupture and deformation affecting underground chalk quarries[END_REF].

Table 3. Comparison of the modelling results with and without a cliff (without cavity SC and with cavity AC)maximum and minimum stresses (horizontal and vertical) for a homogeneous medium (HM) and in the presence of a stiff bed (SB) with a 100-times higher modulus than underlying and overlying beds. To better understand the role of the stiff bed, its rigidity was varied from 1 to 100 GPa. Figure 12 therefore represents the evolution of the minimum horizontal stresses (traction) and maximum horizontal stresses (compression). It clearly shows that the magnitude of these stresses increases as the rigidity of the stiff bed increases. The stiff bed as well as the overburden behave and deform like a bending bed, with the semi-rigid supports (the pillars), following excavation of the cavity. The deformation of the stiff bed depends on the supports (chalk layer) and the size of the cavity. The horizontal stresses in the stiff bed, due to the bending, depend on its thickness and Young's modulus. The relationship between the Young's modulus and the stresses is parabolic, as shown in Figure 12.

Figure 12. Evolution of the minimum (traction, sxx (min)) and maximum (compression, sxx (max)) horizontal stresses in the stiff bed (for n varying from 1 to 100). The correlation between the stresses and the ratio n a second-degree parabolic function (poly).

Influence of the slope of the cliff

The goal of this section is to quantify the influence of the cliff which can induce a high concentration of stresses and an inclination of the main stress which is accompanied by shearing at the pillars level closer to the slope. The cliff is given as vertical in the first model (Figure 11). To study the effect of the cliff and especially of its slope in the presence of a stiff bed, a second conceptual numerical model has been produced in which a slope of the cliff is considered () varying between 15° and 90°. The stiff bed was kept at its maximum rigidity, i.e n=100 (Figure 13).

Figure 13. Model 2: influence of the slope () with an isolated cavity and a stiff bed (n=100)

Figure 14 represents the evolution of the stresses (horizontal and vertical) in the stiff bed as function of the cliff slope. The green line separates both configurations: the cavity is under the slope, or the cavity is under the plateau.

The stresses before the excavation of the cavity, i.e. the initial stresses, were compared to those induced by the excavation. These results allow to formulate two important observations: before the excavation, the compression and tensile stresses increase as a function of the angle of the cliff slope up to 35°, then they remain constant from 35° to 55°, and decrease beyond 55°. The excavation of the cavity induces compression and tensile stresses that are slightly dependent on the presence of the cliff. The combined effects of the cavity and the cliff are maximal for a slope between 30 and 50°.

Global model and mechanism of the collapsed mine (1910)

The preceding results demonstrated how the saturation of the chalk and the presence of the cliff and stiff bed affect the stress field. In this section, a 2D model of the Beaulieu mine collapse in 1910 was created which integrates a fault that crosses the overburden and various beds within, as well as the cliff (Figure 7). This model was developed based on observations and new data from the Royer mine, which highlighted a North-South fault, inclined at 70° with respect to the horizontal. Table 4 shows the mechanical properties of the chalk, and of the overburden, derived from laboratory characterization tests and the literature [START_REF] Renaud | Understanding the instability mechanisms of chalk mines in presence of water (France). 14 Inter. National Congress on rock Mechanicks and Rock engineering[END_REF] Figure 15 shows the results obtained for the four calculation phases. It is noted that horizontal tensile stresses develop in the stiffer beds (limestone and puddingstone) and are slightly greater when the chalk is saturated. The presence of the fault also changes the distribution of stresses, with the area behind the fault exhibiting significantly lower tensile and compression stresses. The horizontal compression stresses of the pillars are lower than in the case without cliff or fault. On the other hand, the vertical stresses increase in the pillars located just after the fault. Furthermore, the vertical stresses at the level of the fault plane are normal tensile or compression stresses of low amplitude. The relaxation of the fault, or the decrease of the vertical stress, is maximal after phase 3, for which the angle of friction of the fault is reduced to 10°. This configuration, corresponding to a fault that crosses the mine and which is located inside the rock mass, seems to be the most critical.

Figure 15. Distribution of the horizontal and vertical stresses for the four calculation phases.

This analysis, done using numerical modelling, shows that the presence of a cliff and a fault modifies the state of the stresses in the rock mass before the mine excavation. This excavation, followed by the degradation of the fault's properties and the saturation of the pillars, induces an increase of the tensile stresses in the stiffer limestone and puddingstone beds of the roof (with the beds acting as beams). The deformation of the pillars by water saturation induces a bending behaviour in them. This deformation will increase and lead to the appearance of tensile stresses until failure. Since the friction angle of the fault is small (reduced by the action of water), it is equivalent to a low shear strength of the fault plane. The normal stresses in the fault zone are tensile because of the presence of the cliff and the mine (excavation). In this situation, the fault is no longer contained and can easily favour the sliding of the mass located above the mine. This sliding, which is both horizontal and vertical, results in the crushing of the mine pillars that are located between the cliff and the fault. This mechanism, demonstrated by numerical computations, was observed in the collapse of the Beaulieu mine in 1910 -the sliding (free rupture) of the cliff is clearly visible in the photos of the collapse taken at the time. Water played a major role in this analysis and its effect was introduced via two mechanisms: reduction in the chalk strength and degradation of the friction properties of the fault. In these computations, water is the triggering factor. The other predisposing factors, such as the presence of the cliff, the fault, and the stiff beds, are aggravating predisposing factors. The failure mechanisms are schematically displayed in Figure 16: the cliff modifies the distribution of stresses in the chalk mass and within the pillars, the stiff beds promote the concentration of tensile and compression stresses, while the fault breaks the continuity of the mass and accentuates the effect of the cliff and the stiff beds. This study clarifies the effect of the fault observed by [START_REF] Renaud | Understanding the instability mechanisms of chalk mines in presence of water (France). 14 Inter. National Congress on rock Mechanicks and Rock engineering[END_REF].

Thus, the action of water (by percolation from the surface or flooding of the pillars from the water table) weakens the existing equilibrium. The very rapid and sudden reduction in the properties of the chalk mass and the fault can thus lead to a massive collapse of the mine. Given the results presented, two hypotheses can be put forward concerning the kinetics of this collapse: (1) the sliding of the cliff caused the collapse of the pillars weakened by their saturation and consequently the collapse the mine, and (2) failure of the pillars promoted the sliding of the cliff at the level of the fault plane, the shear strength of which had been weakened by the percolation of rainwater.

Conclusions

This article presents a study on the massive collapse of underground mines extracted by the room and pillar method and the role of the presence of a cliff and a stiff bed as predisposing factors. In 1910, the centennial flood of the Loing River induced the collapse of the Beaulieu underground chalk mine at Château-Landon, followed by a largescale landslide that destroyed the Loroy hamlet. In the initial analysis, the collapse was attributed to the behaviour of the chalk as well as the climatic conditions, which induced a sudden rise in the chalk water table. Nevertheless, this analysis did not explain the landslide of the entire cliff concomitant with the collapse. In fact, the modification of the stress field at the edge of the slope and the geology were not investigated. A new retro-analysis (analytical, finite, and distinct elements) was carried out to identify the influence of the extraction ratio, the presence of a stiff bed in the overburden and a cliff and a fault crossing the mine, on the stability of the pillars and more generally on the mine.

The results obtained demonstrate the importance of the geometric configurations of the site for the development of such phenomenon, in particular the cumulative effects of the excavation (extraction ratio), the cliff, and the stiff bed presences. Consideration of these factors makes it possible to demonstrate the development of specific stresses and especially tensile stresses in the overburden. Water also plays a significant role on the behaviour of the chalk and the fault promotes shear stresses. These cumulative factors therefore increase the risk of a large-scale collapse. Thanks to the results obtained, a scenario for the sliding and collapse of the Beaulieu mine at Château-Landon has been put forward. The fault plays a part in the sliding of the mass which is weakened by weak pillars. When it has a high dip (70°) and an angle of friction reduced by the action of rainwater, the fault constitutes a privileged sliding plane, and the foot of the embankment is weakened both by the voids in the mine and by the reduction of the strength of the pillars. This collapse/sliding is the result of a combination of predisposing factors (geometry of the mine, extraction ratio, nature of the chalk), aggravating factors (cliff and fault), and triggering factors (water). Thus, it has been shown that water could have played two main roles: reduction of chalk strength by saturation and reduction of the shear strength fault by percolation from the surface.

From a methodological perspective, this study has shown that the evaluation of the stability of abandoned underground mines rests on three concepts: the estimation of the stress state of the pillars, the strength of the pillars, and the feedback from the analysis of similar configurations. In this paper we have worked with these three concepts, integrating the geometry of the pillars (and particularly their slenderness), the presence of a cliff as well as a significant discontinuity crossing the massif which could be a fault.

Figure 1 .

 1 Figure 1. In-situ observation (on the left) and theoretical model (on the right) of a massive collapse by crushing of the pillars with the creation of a discontinuous subsidence on the surface (PPRN, 2008).

3

  Historical massive collapse (1910) of the Beaulieu chalk mineIn 1910, the sliding of a cliff undercut by the underground Beaulieu chalk mine in Château-Landon (Seine-et-Marne, France) caused the death of 7 people and considerable material damage (Figure3). The catastrophe was characterized by the massive collapse of the hillside and by a landslide near the base of the slope (Figure4). The volume of material suddenly set in motion was of the order of 100 000 m 3. The collapse of the chalk mass extended linearly over about 100 m and the tearing surface, about 20 m high, was set back about 40 m from the original edge of the hillside.

Figure 3 .

 3 Figure 3. Location of the collapsed Beaulieu mine in Château-Landon in the south of Paris (France)

Figure 5 .

 5 Figure 5. Relationship between rainfall (Precipitations) and water level of the Loing during the 1910 flood (in Gombert and Cherkaoui, 2011). The date of the Château-Landon massive collapse is represented by a yellow diamond.

Figure 6 .

 6 Figure 6. Left-Extract from the geological map of Château-Landon (BRGM) (the land shown in pink is Oligocene limestone and sand which does not appear perpendicular to the Beaulieu mine), right-Section of the geological layers.

Figure 7 .

 7 Figure 7. (a) Plan view of the Beaulieu mine and position on the current land registry, (b) recent location of the mine area and (c) schematic cross-section specifying the mine, the geology, and the location of the fault.

  Figure 8. Chalk behaviour, (a) Ruptures of the Château Landon chalk and (b) results of the simple compression tests done at different saturation levels, Sr (Delage et al., 2011).

Stress

Figure 14 .

 14 Figure 14. Model 2: variation of maximum stresses (horizontal (sx) and vertical (sy)) in the stiff chalk bed (n=100, where n is the stiffness ratio) as a function of the cliff slope for two configurations; cliff without cavity (F) and cliff with cavity (C+F).

  . The properties of the discontinuities, mainly stiffness and strength for both faults and layers, are practically unknown, and thus, common values were considered. The Mohr-Coulomb elastic-perfectly plastic constitutive model was used for all materials. The selected parameters of the fault are based on the experience of the authors and the literature (Al[START_REF] Heib | Analysis of Faults' Effect on the Stability of Surface Lignite Mining Areas Using the Distinct Element Method[END_REF]. The model includes four calculation phases: the initial state (a cliff cut by a fault, without mine), the excavation of the mine in one go, the reduction of the friction angle of the fault -initially at 30° -to the value of 10° (simulating deterioration due to heavy rainfall causing percolation water to enter the fault), and finally the reduction of the properties of the chalk, but only in the pillars reaching saturation to simulate an inflow of water into the mine. The reduction of the friction angle of the fault is arbitrary. Note that phases 3 and 4 can be interchanged or executed in a single phase (deterioration of the friction angle and saturation of the pillars -in other words, reduction in the chalk resistance).

Figure 16 .

 16 Figure 16. Mechanism of mine rupture (collapse)combination of predisposing and triggering factors.

Table 1 .

 1 Examples of massive collapses in various countries over more than a century

	Year	Country	Material	Collapse	Maximal	Damage	and	Refernces
				surface	depth	consequences
				(ha)	(m)
	1885	France	Limestone 5	70	14 victims and 10 houses
	1910	France	Chalk		30	7 victimes and several houses
	1923	France	Limestone 0,3	20	2 victims, 2 enjuried, 1 house, 1 road	PPRN
	1958	Italie	Marle	1	45	Road completley destriod		Longoni et al., 2016
	1960	Chine	Coal	2.4	38-55	4 victims, 11 enjuried Cui et al., 2014
	1960	Afrique de Sud	Coal	300	150			Szwedzicki, 2001
	1994	Chine	Coal	2.8	30-40	23 victims, 23 enjuried, 20 houses.	Cui et al., 2014
	1961	France	Chalk	3		21 victims et 50 enjuried, severla houses		Al Heib et al., 2015
	1986-1999	Espagne iron	0.3 and 0,1	100	1 road and mining installations	Trigueros et al., 2021
	1988	Pay-Bas	Chalk	0.4	17-24	1 restaurant		Bekendam, 2020
	2011	Italie	Chalk	1.17	10-25	Several buildings		Fazio et al., 2017
	2011	Iran	Chromite 0.4	< 100			Dehghan et al., 2013
	2015	Belgique Chalk	1.2	20-30	Train line		Georgieva et al., 2020
	2015	Etats-Unis	Limestone 3 ha	120 m	3 injured minors		Esterhuizen et al., 2018

Table 2 .

 2 List of the main predisposing and triggering factors of massive mine collapses

	Predisposing factors		Triggering factors
	Mining geometry	High extraction level High slenderness pillar Irregular pillars	Dynamic actions	Natural seismicity (Italie et Japan), De Lucia et al., 2022 Traffic Induced seismicity
	Geology	Stiff beds Complex tectonic environment and faults	Water	Flooding Heavy raining Leakage of surface networks (water, sewage, etc.)
	Material characterisations	Brutal and creep behaviour High water sensitivity	Climatic (heavy rainfall, drought, etc.) and environmental factors (aging and erosion), (Castellanza et al. 2018)

Table 4 .

 4 Mechanical characteristics of the chalk and overburden (equivalent parameters calculated from the Mohr-Coulomb theory).

	Rock	Density Young	Poisson	Cohesion	Friction	Compression	Tensile
			Modulus	ratio			angle	strength*	strength
	Unit	kN.m -3	MPa		MPa	(°)	MPa	MPa
	Chalk	20	500	0.22	1		30	3.5	0.2
	Saturated	20	100	0.23	0.35		30	0.9	0.2
	chalk
	Poudingue 22	2000	0.30			Elastic
	Limestone 25	4000	0.30
	Table 5. Mechanical characteristics of the fault.
	Joints/fault	Normal	Tangential	Cohesion	Friction	Tensile
			stiffness	stiffness				angle	strength
		Unit	MPa.m -1	MPa.m -1			MPa	(°)	MPa
	Fault		298	205				30
	Degrade fault	298	205				10
	Horizontal Joints 2500	1150		5		45	5

Back-analysis of the collapse(1910) While several analyses have been done to try to explain this collapse, they do not make it possible to formulate a definitive conclusion regarding the scenario at the origin of the collapse. The analysis of the Beaulieu mine collapse

Acknowledgement

The authors thank the department of Seine et Marne, owner of the "Royer" mine within the framework of the project for the protection of bats, for the authorisation to access and instrument this site and the Ministry of Ecological Transition for the financial support. They also thanks Meteo France to allow us to use the weather data from its station


I Wardhana

A Gouiaa-Mtibaa
email: amal.gouiaa-mtibaa@univ-orleans.fr

P Vrignat
email: pascal.vrignat@univ-orleans.fr

F Kratz

DATA PREPROCESSING IN THE CONTEXT OF PHM -CHALLENGES AND SOLUTIONS

Keywords: prognosis and health management (PHM), predictive maintenance, preprocessing data, feature extraction

This study presents a comprehensive framework for addressing data preprocessing challenges in diverse scenarios. The framework covers various aspects, including feature extraction in the time domain, frequency domain, and wavelet domain, as well as feature selection techniques, noise reduction strategies, and data normalization approaches for time series data. Through experimental analysis, we demonstrate the effectiveness of our proposed strategy in enhancing the Signal-to-Noise Ratio value. In particular, the application of the Savitzky-Golay Filter proves successful in reducing signal noise and achieving normalization across all bearings. These findings highlight the potential of our framework in improving data quality and preprocessing procedures for bearing data set which can be generalized for a wide range of applications.

INTRODUCTION

SCADA environments are connected to various database management systems. These databases are becoming more and more essential for the efficient management of the company. Industry 4.0 and its technological panel offer today, a very large collection of this information. In fact, this evolution is taking place at all levels, including the maintenance level. This is a crucial activity, like a part of PHM, as it determines the availability and performance of production systems. However, various perturbations (e.g. power cuts, digital communication network interruptions, wrong choice of technology...) have a significant impact on the quality of the collected data. Data must be checked to see if it incorrect, incomplete, inaccurate, irrelevant, inconsistent, different, repeated, poorly described, or missing. Big data problems are no secret, as it is difficult to compile a large and accurate database.

The main data quality target is accuracy [START_REF] Li | HVAC Room temperature prediction control based on neural network model[END_REF]. Previous studies often use three types of data errors: inaccuracy, incompleteness, and mismatch [START_REF] Parssian | Assessing data quality for information products: Impact of selection, projection, and cartesian product[END_REF]. The method proposed by [START_REF] Ben Amor | Data accuracy aware mobile healthcare applications[END_REF] combines dimensionality reduction with the identification and separation of erroneous data. Due to the measurement data used as input for data acquisition, the presence of uncertainties and unknown measurement inaccuracies would be a concern. Sources of uncertainty in Machine Learning are divided into two groups. Group I is related with data acquisition error, data annotation, imbalance and skewness, incompleteness, and input data sampling. Group II includes feature selection, model selection, and model hyperparameter estimation [START_REF] Yang | HVAC Equipment, Unitary: Fault Detection and Diagnosis[END_REF].

Several steps have been carried out to improve for reducing the error. Data preprocessing is an inevitable step before applying Machine Learning methods for energy or load prediction. According to previous experiences, data preprocessing typically accounts for a large portion of the total data mining task, about 80% [START_REF] Davidson | Data preparation using data quality matrices for classification mining[END_REF]. As shown in Figure 1, the "observe" step in PHM includes two steps data acquisition and data preprocessing. The common steps of data preprocessing include data imputation, data resolution processing, data normalization, outlier detection, and data smoothing [START_REF] Amasyali | A review of data-driven building energy consumption prediction studies[END_REF]. This latter could reduce the influence of noisy data and improve data quality, which contributes to the improvement of model performance [START_REF] Zhao | Feature Extraction for Data-Driven Remaining Useful Life Prediction of Rolling Bearings[END_REF].

Signal preprocessing plays a critical role in understanding and analyzing various types of data. In this study, we are interested in bearing data and especially vibration signals obtained from accelerometers. To gain a deeper understanding of these signals, researchers often explore four primary domains: time domain, frequency domain, time-frequency domain, and wavelets [START_REF] Vrignat | Sustainable manufacturing, maintenance policies, prognostics and health management: A literature review[END_REF]. By converting the signal from the amplitude domain to the time domain [START_REF] Benkedjouh | Fault prognostic of bearings by using support vector data description[END_REF], researchers can examine its behavior over time and identify any patterns or variations. In addition, exploring the frequency domain allows researchers to analyze the signal in terms of its component frequencies and their respective amplitudes. Through extensive research and experimentation, scientists have made significant strides in understanding and interpreting accelerometer signals, enabling advances in fields as diverse as structural health monitoring, vibration analysis, and predictive maintenance. In Figure 1, we present a summary of the data chain with a focus on the step data preprocessing which will be the objective of our study. Zone (adopted from [START_REF] Eren | Bearing fault detection by one-dimensional convolutional neural networks[END_REF])

The organization of this paper is as follows: Section 2 provides a comprehensive review of preprocessing steps in signal bearing, highlighting their relevance to the state of the art. In Section 3, a case study involving the Bearing FEMTO dataset is presented, along with the framework, method algorithm, or equation employed. Section 4 presents and discusses the results derived from the analysis. Finally, the paper concludes by summarizing the findings and suggesting potential future research directions.

STATE OF THE ART

The quality of input data has a significant impact on the quality of the model and the accuracy of prediction results. Many problems have been detected in the bearing data and a preprocessing step is compulsory. One common issue encountered is the presence of excessive unwanted frequencies in the data. A high Signal-to-Noise Ratio (SNR) indicates a clear and easily detectable or interpretable signal, whereas a low SNR suggests that the signal is corrupted or obscured by noise, making it challenging to distinguish or recover meaningful information. To achieve a high SNR [START_REF] Liu | Fault Diagnosis of Rolling Element Bearings Based on Adaptive Mode Extraction[END_REF], the separation of low-frequency signals containing information related to bearing rotation and bearing faults from the middle and high-frequency components has been the focus of exploration. The operational status of rotating machines (embedded bearing) and the presence of four specific faults are restricted to zones 1 and 2 [START_REF] Eren | Bearing fault detection by one-dimensional convolutional neural networks[END_REF], as shown in Figure 1 (b). This means that the occurrence of these faults is associated with low frequencies, while medium and high frequencies are ignored, potentially leading to degradation of signal quality due to the presence of noise. Several techniques have been investigated for this purpose, including Variational Mode Decomposition (VMD), Empirical Wavelet Transform (EWT), Empirical Mode Decomposition (EMD), Vold-Kalman Filter Order Tracking (VKF_OT) [START_REF] Liu | A comparative study of four kinds of adaptive decomposition algorithms and their applications[END_REF], Maximal Overlap Discrete Wavelet Transform (MODWT) [START_REF] Shrifan | Maximal overlap discrete wavelet-packet transform aided microwave nondestructive testing[END_REF], and others. These methods aim to effectively extract the desired low frequency signals while filtering out the unwanted medium and high frequency components. By using such techniques, researchers aim to improve the SNR and increase the accuracy of fault detection and prediction in bearing analysis. These approaches have been investigated under different SNR ranges, and the research results have demonstrated prediction accuracy levels of up to 99 percent [START_REF] Zhang | Fault diagnosis of marine electric thruster bearing based on fusing multi-sensor deep learning models[END_REF]. Researchers often use denoised signals for fault prediction to improve the noise immunity of diagnostic models and minimize the influence of noise on the overall performance.

Before determining the appropriate feature extraction method, stationarity tests such as Augmented Dickey-Fuller (ADF) are commonly used to assess the stationarity of the signal.

Once the time domain features have been generated, it is essential to perform an effective feature selection process in order to identify the most optimal feature for the data input.

The RMS time domain feature has been widely used by many researchers as a health indicator [START_REF] Nie | Remaining useful life prediction for rolling bearings based on similarity feature fusion and convolutional neural network[END_REF], [START_REF] Liu | Fault prediction of bearings based on LSTM and statistical process analysis[END_REF], [START_REF] Yan | An effective method for remaining useful life estimation of bearings with elbow point detection and adaptive regression models[END_REF]. The RMS has been found to have a positive correlation with changes in vibration intensity, providing valuable insights into the progressive degradation path of bearings.

It deals with high-dimensional data, where the number of features greatly exceeds the number of samples. One popular method for feature selection is the Laplacian Score, which effectively measures the relevance of features based on the underlying manifold structure of the data. The advantage of using the Laplacian Score is its ability to efficiently handle high-dimensional data in unsupervised learning [START_REF] Ferreira | Efficient feature selection filters for highdimensional data[END_REF], resulting in a reduced feature set without sacrificing predictive performance. This leads to improved computational efficiency and enhanced interpretability of the selected features, making it a valuable tool in various domains. Noise reduction and normalization are also two important steps before moving on to training and testing. Several methods are used depending on the type of signal [START_REF] Liu | Remaining useful life prediction of rolling element bearings based on health state assessment[END_REF], [START_REF] Sun | Bearing fault diagnosis based on EMD and improved Chebyshev distance in SDP image[END_REF]. The Savitzky-Golay Filter (SGF) is a powerful tool for denoising and smoothing faultgenerated signals [START_REF] Biswal | Savitzky-Golay Filter integrated matrix pencil method to identify high impedance fault in a renewable penetrated distribution system[END_REF].

METHOD AND CASE STUDY

Rolling bearings are critical to the operation of rotating machinery, ensuring efficient performance and minimizing friction. Consisting of components such as the outer ring, inner ring, cage, and rollers. They play a key role in various industrial equipment. The condition of rolling bearings has a direct impact on the overall safety and reliability of the system. Research shows that rolling element bearings are responsible for a significant portion, approximatively 45-55% [START_REF] Loutas | Remaining useful life estimation in rolling bearings utilizing data-driven probabilistic e-support vectors regression[END_REF], of equipment failures.

Dataset

The challenge data was obtained from a well-designed experimental platform called PRONOSTIA [START_REF]IEEE PHM 2012 Prognostic challenge outline, experiments, scoring of results, winners[END_REF]. The dataset consists of vibration and temperature data collected during run-to-failure tests. The sampling frequency used in the experiment is 25.6 kHz, with a recording interval of 10 seconds and a data length of 0.1 seconds per recording. In other words, each data recording consists of 2560 data points. For example, the total duration of the bearing degradation data in Bearing 1-1 is 28030 seconds. There are a total of 17 run-tofailure bearing records representing three different operating conditions. These different operating conditions are summarized in Table 1. Of these, six training datasets contain complete run-to-failure data, while the remaining dataset provides only censored bearing life data.

Table 1: Operation Conditions of FEMTO Bearings

Framework

We present a novel approach, illustrated in Figure 2, for the initial processing of rolling bearing components. The scheme is derived from a previous study [START_REF] Rathore | An Attention-based Stacked BiLSTM Framework for Predicting Remaining Useful Life of Rolling Bearings[END_REF], which employed various techniques such as time-frequency, and time-domain feature extraction, wavelet transform with different decomposition levels depending on SNR values, and feature selection for optimal feature identification. In addition, this technique was further enhanced with noise reduction and normalization.

Figure 2: Framework for Bearing Preprocessing (adopted from [START_REF] Rathore | An Attention-based Stacked BiLSTM Framework for Predicting Remaining Useful Life of Rolling Bearings[END_REF])

In the first step, data is collected from sensors using only the vibration accelerometer signal and excluding the temperature signal. In the second step, the raw signals are examined using the stationarity method to define the signal. The SNR is used to evaluate the signal quality. Signals with low SNR are extracted using Fast Fourier Transform (FFT) to identify the frequency distribution. The high frequencies based on the bearing zone are not used and can be removed. To eliminate the high frequencies, a signal decomposition method is also applied for all bearings. This step generates new high SNR signals that can be further processed for time-domain features. The time-domain features contain 21 different features, including Mean, Crest Factor, Standard Deviation, and Margin Factor. In the third step, the 21 time-domain features must be evaluated to determine which one has the highest correlation with the health indicator. Unsupervised learning techniques are devoted in bearing analysis to evaluate the correlation between features and variations. To account for the presence of noise in the signal, noise reduction methods are implemented. In addition, to facilitate accurate comparison and analysis, the signals are normalized to bring them into a consistent range. All of the methods used in this framework are described in [START_REF] Biswal | Savitzky-Golay Filter integrated matrix pencil method to identify high impedance fault in a renewable penetrated distribution system[END_REF], [START_REF] Lotfi | Predicting wastewater treatment plant quality parameters using a novel hybrid linear-nonlinear methodology[END_REF], [START_REF] Liu | Bearing feature extraction using multi-structure locally linear embedding[END_REF], and [START_REF] Barile | Laplacian score and K-means data clustering for damage characterization of adhesively bonded CFRP composites by means of acoustic emission technique[END_REF]. These methods are shown in Figure 2 in bold red text.

RESULTS AND DISCUSSIONS

In order to investigate data preprocessing in FEMTO Bearing with different SNR, we conducted experiments using the new proposed framework. The main focus on this step consists to extract the decomposed signal based on the SNR value.

The ADF test is employed to analyze the signal under three different operating conditions. Table 1 shows that almost all bearings have a stationary signal. The SNR is in the range of -12 to -9 dB for normal bearings and -13 to -11 dB for faulty bearings. Given the high level of noise present, it is necessary to process the signal by removing the high frequencies using a decomposition method. Contrary to the expectation, the normal bearing contains predominantly low frequencies. Figure 3 (1)(b) shows the raw signal in blue and the decomposed signal in orange. The low frequency signal has only low amplitudes. Figure 3 (2)(a) shows the presence of low, medium, and high frequencies in the normal condition. However, in this particular case, only the rotational frequency (30 Hz for operating condition 1) and the harmonics, should be present in the normal bearing signal. The remaining frequencies, especially the medium and high frequencies, are likely to be considered as noise. Then, in Figure 3 (2)(b), the elimination of the medium and high frequencies is observed. In addition, the power spectral density decreases from a maximum of 150 to 60. Consequently, the SNR increases from -12.71 dB to a new value of -0.21 dB. These results were obtained by using the MODWT with the sym4 wavelet and performing the transform down to level 4.

In Figure 3 (3) (a), observed as Bearing 1-2, it is evident that the highest power spectrum occurs toward the end of the bearing rotation. This power spectrum contains frequencies exceeding 1000 Hz, which are associated with bearing degradation and potential faults. To reduce noise, it is essential to reduce the frequencies above 1000 Hz in Bearing 1-2. On the other hand, Figure 3 (3) (b) shows samples obtained using a moving window of 20, where only the lower frequencies are present.

The analysis involves the use of 21 time-domain features, including mean, standard deviation (Std), variance, Kurtosis, skewness, RMS, maximum, minimum, margin factor, form factor, peak to peak, square RMS, coefficient variation, shape factor, impulse factor, crest factor, clearance factor, absolute mean, energy, mean, and peak index (Figure 2). These features are used in both the training of six bearings and the testing of eleven bearings. In Figure 3 (5 -a), (1, 2, 3)), the standard deviation of the raw signal is depicted for Bearing 1-2, 2-1, and 3-1. Figure 3 (5-a), ( 1)) illustrates that Bearing 1-2 exhibits noise values between time 100 to 700. However, the use of the decomposed signal as an input permit to obtain the standard deviation feature values. The noise reduction is evident in Figure 3 (5-b), ( 4), where the noise has been effectively eliminated. In Figures 3 (5-a), [START_REF] Eren | Bearing fault detection by one-dimensional convolutional neural networks[END_REF][START_REF] Li | HVAC Room temperature prediction control based on neural network model[END_REF], fluctuations in the signal are observed. However, after signal decomposition, Figures 3 (5-b), [START_REF] Ben Amor | Data accuracy aware mobile healthcare applications[END_REF][START_REF] Yang | HVAC Equipment, Unitary: Fault Detection and Diagnosis[END_REF] show a relatively stable and consistent signal without pronounced peaks. This indicates a consistent behavior of the signal over time.

Table 2 displays the SNR values for Bearing 1_1 in normal condition, which is -12.84 dB. However, after applying the decomposed signal using the MODWT method, the SNR increases to 1.83 dB. In the fault condition, Bearing 1_3 initially has an SNR of 2.08 dB, which then spectacularly increases to 293.38 dB. The SNR values of this particular raw signal differ from those of other signals, indicating a higher signal level compared to the noise. This can be observed in Figure 3 (4), (a), where the signal predominantly exists in low frequencies. The signal decomposition shown in Figure 3 (4), (b). The medium and high frequencies are eliminated, resulting in a high impact on the SNR values. These results suggest that the MODWT method is highly effective in significantly reducing noise.

To order the 21 features time domain, unsupervised feature selection Laplacian-score is used. Figure 4 (1) show that the Standard Deviation, Root Mean Square get the same value for high scores. In this context, several authors propose results with RMS ( [START_REF] Hong | Condition assessment for the performance degradation of bearing based on a combinatorial feature extraction method[END_REF], [START_REF] Guo | A recurrent neural network based health indicator for remaining useful life prediction of bearings[END_REF]). The use of the standard deviation (Std) shows that signal processing is more efficient compared with RMS (Figure 3 (6-a), (1, 2, 3)). Nevertheless, upon decomposition as depicted in Figure 3 (6-b), [START_REF] Parssian | Assessing data quality for information products: Impact of selection, projection, and cartesian product[END_REF][START_REF] Ben Amor | Data accuracy aware mobile healthcare applications[END_REF][START_REF] Yang | HVAC Equipment, Unitary: Fault Detection and Diagnosis[END_REF], the noise reduction in the RMS values is not as prominent as observed in the Std. This contrasts with the findings reported in various articles, which could be attributed to the effective elimination of noise in the Std. In Figure 4 (2), (a), it is apparent that the standard deviation of the feature domain in Bearing 2-2 still contains noise. To solve this issue, the SGF is employed with a frame length of 51 samples and a specified Polynomial Order (PolyOd, Polynomial Order=5). Upon closer inspection in the zoomed window of Figure 4 (2), (b), it shows clearly that the noise is still present. After applying a polynomial order of 7, as shown in the zoomed window of Figure 4 (2), (d), a smoother signal is achieved. This suggests that the use of a higher polynomial order enhances the noise reduction capabilities of the SGF in Bearing 2-2. Figure 4 (2), (a, b, c and d) depicts values ranging from 0 to 0.015. These values subsequently undergo a normalization process, resulting in a transformation to the range of 0 to 1. The rescaling of the values to the interval [0, 1] can be observed in Figure 4 (3).

CONCLUSION

In this study, we introduced a framework that addresses the challenges of data preprocessing in rolling scenarios. Our framework encompasses time-domain and frequencydomain feature extraction techniques, feature selection methods, noise reduction strategies and data normalization approaches for time-series data. Experimental results indicate that the proposed strategy effectively reduces the influence of noise on the signal. This reduction in noise will enable better detection of bearing faults. The next stage of our work will enable us to address the challenges associated with fault diagnosis (Figure 1).

Figure 1 :

 1 Figure 1: (a) PHM cycle (adopted from [1]) and (b) Bearing Damage Stage III and MultipleZone (adopted from[START_REF] Eren | Bearing fault detection by one-dimensional convolutional neural networks[END_REF])

Figure 3 :

 3 Figure 3: 1 (a) Raw Signal Bearing ,1 (b) Signal After Decompose, 2 (a) FFT Raw, 2 (b) FFT Decompose, 3 (a) FFT-Power-Time Raw Bearing 1-2, 3 (b) FFT-Power-Time Decompose, 4 (a) FFT-Power-Time Bearing 1-3, 4 (b) FFT-Power-Time Decompose 5 (a) (1, 2, 3), 5 (b) (4, 5 ,6) Decompose Std, 6 (a) (1, 2, 3), 6 (b) (4, 5 ,6) Decompose RMS

Figure 4 : ( 1 )

 41 Figure 4: (1) Laplacian Score from 21 Feature Time-Domain, (2) Noise Reduction, (3) Normalization

Table 1 : Stationary check and SNR of Three Operation Condition

 1

	Name	of	Stationary Check	SNR (dB)
	Bearing
			Normal	Fault	Normal	Fault
	Bearing 1_1		Stationary	Stationary	-12.84	-13.25
	Bearing 2_1		Stationary	Stationary	-9.93	-11.78
	Bearing 3_1		Stationary	Stationary	-12.37	-11.13

Table 2 : Comparison of Bearing SNR in Normal and Fault Condition

 2

	Name of	SNR (dB) Original	SNR (dB) Decompose
	Bearing	Normal	Fault	Normal	Fault
	Bearing 1_1	-12.84	-13.25	1.83	-1.62
	Bearing 1_2	-12.72	-13.22	-0.22	-9.1
	Bearing 1_3	-12.59	2.08	1.82	293.38