César Leroy
email: cesar.leroy@umontpellier.fr

Sébastien Mittelette

Gautier Félix

Nicolas Fabregue

Jessica Špačková

Philippe Gaveau

Thomas-Xavier Métro

Danielle Laurencin
email: danielle.laurencin@umontpellier.fr

Operando acoustic analysis: a valuable method for investigating reaction mechanisms in mechanochemistry

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

Main text

The growing attention to mechanochemistry has led to an impressive range of research areas to which this "green" synthetic method can be applied to, ranging from pharmacy to catalysis as well as crystal engineering or materials science. 1,2 Although widely used for synthesizing elaborate compounds, the details of grinding and more specifically of the physical and chemical mechanisms taking place are still mainly seen as unfathomable. In the case of ball-milling, this is mainly due to the opaque and closed environment of the milling reactors in which most reactions take place.

In light of the great interest in mechanochemistry, several research groups have thus strongly focused their attention on developing in situ as well as operando analytical methods in order to monitor reactions and observe evolutions in the structure, crystallinity and/or texture of compounds involved during the milling processes. [3][4][5][6] Except for temperature, these methods usually require the use of transparent reactor materials (for Raman or X-ray diffraction monitoring, for example), 4,7 or the adaptation of the geometry and size of the reactor itself (in particular in the case of NMR analyses). [8][9][10][11][12][13][14] However, several studies have shown that the kinetics and/or reaction mechanisms in ball milling can be greatly affected by the size and materials composing the reactor and beads, meaning that the latter methods cannot be readily applied to different reactions without re-investigating the synthetic conditions. 15,16 Hence, developing new operando approaches allowing the evolution of reaction media to be followed, but without requiring any modification of the initial set of experimental parameters, would be greatly beneficial for the mechanochemistry community.

Several mechanical behaviours involving the beads and reactors have been shown to come into play during a ball-mill synthesis. [17][18][19][20] The reacting particles undergo direct impacts from the beads, as well as shearing forces, which both can lead to particle size reduction and the creation of "fresh reactive surfaces", and thereby enable the chemical reactions to take place. Moreover, under some milling conditions, specific trajectories of the beads have also been identified, such as their direct back and forth movements from one wall of the reactor to another, or their rolling along the sides of the milling reactor.

Such processes are generally difficult to predict, and depend on numerous experimental parameters such as the type of beads (size, number and material), the type of reactors (volume, geometry, and material), the milling parameters (frequency, time), not to mention the type of movements imposed to the reactors by the mill (e.g., planetary, oscillating vertically or horizontally), but also the physical and chemical properties of the milled reagents. Various sounds can sometimes be noticed during the milling of compounds, which attest of changes in the beads' motions in the reactor. Yet, although a few previous attempts to follow the sound during ball milling experiments had been reported, notably in 2004 by Cuadrado-Laborde et al, 21 to the best of our knowledge, only sounds resulting from the impact of a bead on the reactor were identified and analysed. No systematic investigation was made at the time on how the sound recorded could inform on other movements of the bead (aside from the simple impact), nor, more importantly, on how it could be used to directly follow different physico-chemical changes occurring in the milling reactors. 21 In this context, we decided to record the sound produced by a vertical mixer mill upon milling, in order to try to decipher the acoustic variations arising from different movements of the beads, and how they can be related to changes in the composition or physical-chemical properties of the medium. Moreover, as detailed below, we investigated how this method compares to other known operando techniques, i.e. Raman spectroscopy and temperature measurements, for following reaction mechanisms taking place during ball milling (see Fig. 1).

As a first system of study, we decided to follow the mechanochemical formation of a 1:1 cocrystal of terephthalic acid (H2BDC) and 1,4-diazabicyclo[2.2.2]octane (DABCO) (see Fig. 2a). The sound was recorded through the use of a microphone situated close to the milling reactor. This recording was then used to generate an audio-frequency spectrogram (AF spectrogram), which allows the Fourier transform of the signal to be monitored as a function of time, and different sound harmonics to be observed. In parallel to the sound recording, Raman analyses and temperature measurements were also carried out to follow the evolution of the reaction medium (Fig. 1). These three operando methods were adapted to a vertical mixer mill (Pulverisette 23, Fritsch) using a Perspex reactor with two ZrO2 beads (Ø 10 mm).

Here, the experiments were conducted at a frequency of 50 Hz with a reaction time of 60 min, for a total mass of reactants ~500 mg (see ESI for more details). During the mechanochemical formation of the H2BDC-DABCO cocrystal (Fig. 2a), 22 various sounds were noticed. Careful analysis of the AF spectrogram revealed contrasts in signal intensity in the 105-145 Hz and 145-155 Hz regions (see Figure S3b), i.e. close to the 3 rd harmonic of the milling frequency (50 Hz in this case). Notably, the acoustic intensity between 145 and 155 Hz was found to significantly increase between ~1000 and 1500 s of milling (Fig. 2b, red shaded zone). This experimental observation could be reproduced in the same time-frame by repeating the experiment (see Figure S4). Interestingly, when looking at the measurements recorded using the other operando methods, an increase of the reactor's temperature by about 10-12 °C was simultaneously observed using the thermal imaging camera (Fig. 2b). Moreover, the Raman spectra recorded over the same period of time also revealed shifts in the DABCO and H2BDC vibration bands (Fig. 2b). Hence, these first results suggest that changes in sound can be directly correlated to chemical reactions occurring in the reactor.

Further analysis of the Raman spectra was performed (Figure S5), focussing notably on the zone between 950 and 1050 cm -1 , in which the DABCO νCC/ωCH 2 vibration bands appear. The latter vibration mode was first found to shift from 970.8 cm -1 to 984.3 cm -1 after ~1000 s of milling, 23 and then to further shift to 1013.5 cm -1 (after ca 500 s), which corresponds to the vibration frequency expected for the final cocrystal (Fig. 2b). Although the exact nature of the intermediate has not yet been unambiguously identified, it can tentatively be assigned to an {H2BDC-DABCO} species, in which only one of the nitrogen atoms of DABCO becomes protonated, leading to a single N-H•••O hydrogenbonding motif (in contrast with the final cocrystal which contains two). Remarkably, the previously noticed variation of sound around 150 Hz (3 rd harmonic) happens precisely during the short lifespan of this intermediate, i.e. between ~1000 and 1500 s. To the best of our knowledge, it is the first time that evidence of the presence of reaction intermediates in mechanochemistry is accounted for by analysing the sound occurring during the milling.

Fig. 2: a) Dry milling reaction between H2BDC (1.0 eq) and DABCO (1.0 eq) during 60 min at 50 Hz, inducing the formation of a cocrystal (see Figures S1 and S2 for ex-situ pXRD and Raman analyses of the cocrystal). b). Left: intensity of the 3 rd harmonic of the AF spectrogram as a function of time, obtained by integration between 145 and 155 Hz. Centre: Temperature profile of the reactor during the milling reaction presented in a). Right: Time-resolved operando Raman spectra for a selected area (between 950 and 1050 cm -1 ); the intensity scale goes from low (blue) to high (red and then white). The red shaded rectangle emphasizes the presence of the intermediate species, while purple ones highlight the erratic rolling motions.

In order to help rationalize the origin of the changes in sound during the formation of the intermediate, the movements of the beads across the transparent Perspex milling reactors were visualized using a digital camera. In doing so, it was found that when the intermediate appears (thus when the intensity of the sound is maximum in the 145-155 Hz frequency range, i.e. in the red-shaded area on Fig. 2b), the beads undergo a rolling type of movement on the wall of the reactor. Such motion can be opposed to the erratic impact of the beads which occurs during most of the remaining time, and can be identified here on the AF spectrogram by the more intense inharmonic signals between 105 and 145 Hz (see ESI Figure S3). It is possible that the predominance of rolling between 1000 and 1500 s may be caused by the significant changes in texture of the medium upon formation of the intermediate. More generally speaking, to the best of our knowledge, it is the first time that an acoustic signature characteristic of rolling events in mechanochemistry is identified through sound measurements.

Beyond the possibility of directly observing the formation and/or disappearance of a reaction intermediate, we also found that the analysis of the AF spectrogram actually helps understand deeper some of the details of the data recorded using Raman spectroscopy and the thermal imaging camera. For this reaction system, the "rolling" vs. "impact" sound signatures were found to largely appear in specific regions, as illustrated in Figure S6. Indeed, the impact is appearing in the 105-145 Hz region, while rolling is visible in the 145-155 Hz one. Yet, interestingly, the signature characteristic of rolling motions was observed not only during the life-span of the intermediate, but also intermittently before and after its appearance (see for example the purple-shaded rectangles in Fig. 2b), with a simultaneous decrease in the Raman signals intensities and increase in temperature. Concerning the Raman data, this can be explained by the fact that when rolling occurs, the beads are more likely to remove the powder from the point of focus of the Raman laser, implying that less compound is then analysed during the Raman acquisition time, hence the decrease in signal intensity. Regarding temperature, the small increase may be caused by a more significant frictional heating of the beads against the reactor's walls during the rolling events. 24 Overall, throughout this first example, we have been able to show how sound modifications can attest of a chemical evolution of the medium inside the milling reactor in a complementary way to two other operando techniques (Raman analyses and thermal imaging measurements), and how they can also explain some of the smaller features observed during the acquisition of the operando data (notably when rolling motions occur). In light of these first results, we decided to study on one hand whether other changes in the physical aspect of a reaction medium could be correlated to variations in sound, and on the other hand how sound measurements may actually inform on chemical events taking place in the milling reactors, in situations when temperature measurements or Raman operando analyses can be ambiguous, poorly informative, or not even applicable.

In order to investigate how changes in physical aspect of a reaction medium can be followed through the recording of AF spectrograms, we decided to study the hydrolysis of SiO2 (initially introduced in the reactor as "fumed silica"), upon progressive addition of small amounts of water during ball-milling. Indeed, as shown in Fig. 3, this system appeared to us as ideal for such investigations, because it goes through many of the physical states commonly encountered in ball milling reactions.

First, the medium is under the form of a light fluffy powder, which upon addition of water forms more agglomerated particles (leading to a "heavy powder"), which then further agglomerate and stick to the beads (leading to a so-called "snow-ball" effect). The subsequent addition of water enables the medium to re-spread onto the walls of the reactor (the phase then having the aspect of a "sticky gel" or "gel"), and finally evolves towards a slurry type of texture. These changes were thus followed using a similar set-up as for the study of the H2BDC-DABCO cocrystal (P23 vertical mixer mill operated at 50 Hz, using a Perspex reactor with two zirconia beads), and after each addition of water, the milling was performed for 5 minutes. Here, in addition to recording the AF spectrogram, the changes in temperature of the reactor were monitored using a thermal-imaging camera, and the movements of the beads inside the reactor were also filmed at specific time-points using a digital camera. It is worth noting that the observations described below were found to be essentially reproducible (see Figure S7 for comparison of AF spectrograms).

When looking at the full AF spectrogram, it is clear that it is around the third harmonic (~150 Hz) that the contrast is the most significant and the intensity the highest (see Figure S8 in ESI for changes in sound intensity in other spectral regions). As for the H2BDC-DABCO system, it was found that high intensity signals around this frequency can attest of rolling-types of motions, as shown for example by analysing the results in the zone corresponding to the addition of 180-300 μL of water, in which the presence of rolling is clearly visible when visualising the movement of the beads and looking at the aspect of the medium after opening of the reactor. Concomitantly, the events with the lowest intensity signals at ~150 Hz (i.e. after addition of 140 and 170 μL) could be corroborated with more "impact-like" movements (see blue arrows in Fig. 3b, zone corresponding to the "sticky gel" aspect of the mixture). These events were also found to correspond to a simultaneous increase in signal intensity in the 105-145 Hz region, in line with previous observations made for the H2BDC-DABCO system (see Figure S9). However, it is important to highlight that in the case of the hydrolysis of silica, a lower intensity signal at ~150 Hz did not systematically correlate with a higher intensity sound in the 105-145 Hz region (see ESI, Figure S8), in contrast with what had been seen previously for the cocrystal (see below for further discussion). This shows that in order to help interpret the subtleties of the movements of the beads within the reactor and of the physico-chemical processes taking place, the investigation of several zones of the AF spectrograms is actually needed.

When analysing in more detail the overall plot of the changes in sound intensity around the 3 rd harmonic as a function of the amount of water added (Fig. 3), it is clear that the most significant increase occurs in the zone corresponding to the formation of the "snow-ball" (i.e. after addition of 90-130 μL of waterred-shaded zone), when the beads start rolling against the reactor's walls and accumulating powder at their surface. Most interestingly, when looking at the movement of the beads in this regime using a digital camera, a rolling of both beads in separate zones of the reactor could be observed, as tentatively illustrated in Fig. 3d. A possible explanation to the related increase in sound would be that upon the formation of the snow-balls, the walls of the reactor then become mostly free of powder, inducing such sound intensification. A contrario, when the powder is homogeneously spread over the walls of the reactor, as is the case upon formation of the "heavy powder" (zones highlighted in light blue in Fig. 3, which correspond essentially to rolling motions), the sound intensity is much more dampened (see Fig. 3 and Figure S7 andS9).

The importance of being able to follow the sound during the milling further appears when comparing the results of the AF spectrogram analyses to those of the temperature measurements. In several situations, just like for the H2BDC-DABCO system, the rolling events were found to be associated to temperature increases inside the milling reactor, as shown in particular after addition of 150 µL and of 180 to 250 µL of water. However, changes in sound intensity around 150 Hz did not systematically correlate in the same way to changes in temperature. For example, while the temperature profiles after addition of 70 and 110 μL of water were essentially the same (see green arrows on Fig. 3c), the sound intensity at ~150 Hz over that same period of time was very different, in one case corresponding to the milling of a "heavy powder", while in the other to a snowball. Such results clearly demonstrate the complementarity of acoustic and temperature measurements in trying to decipher the evolution in the physico-chemical properties of the medium during the milling. Considering the increasing number of studies in which temperature measurements are reported, [24][25][26] and related to endoor exothermal chemical reactions occurring in the milling reactors, being able to take into consideration that changes in beads motions can also be correlated to changes in temperature is another important feature to bear in mind.

Overall, although many other aspects related to the milling of silica in presence of water would deserve to be investigated, these results on the hydrolysis of silica clearly highlight that (i) beyond the identification of rolling or erratic impact movements of the beads, acoustic measurements can attest of other phenomena occurring in the reactor, such as the formation of snow-balls (during which a different type of rolling movements take place), or the evolution of the aspect of the mixture (e.g. formation of a "sticky gel" inducing impact motions); and (ii) sound measurements are highly complementary to temperature measurements, as they can bring unique evidence of phenomena taking place during the milling. Finally, in order to demonstrate the utility of sound measurements for the optimization of ball milling reaction conditions, we decided to study the hydrolysis of an activated fatty acid, lauric acid, using this operando method. Indeed, during our previous work on the 17 O/ 18 O isotopic enrichment of fatty acids, 27,28 we had found that for saturated fatty acids, the hydrolysis time of the activated acylimidazole intermediates had to be systematically optimized by repeating the experiments with various milling times. Given that this hydrolysis is accompanied by a change in texture of the reaction medium, which switches from a powdery aspect to a more oily one, we suspected that acoustic measurements could be used to determine the time after which the hydrolysis is complete (Fig. 4a).

Two experimental conditions were compared: the first hydrolysis experiment was performed in a Perspex reactor with two zirconia beads (10 mm Ø) in order to allow the Raman signals to be recorded, while the second one was performed in a stainless steel reactor with two stainless steel beads (10 mm Ø), and can be seen as a "blind" experiment (as it cannot be followed by Raman spectroscopy). The changes in sound, temperature, and, in the former case, in Raman signatures, during the milling are compared in Fig. 4.

For these milling experiments, carried out at a frequency of 50 Hz, it was found that the highest contrast on the AF spectrograms appears close to the 5 th harmonic, and more specifically in the 205-245 Hz frequency region (see ESI Figures S10 -S12). For both types of milling reactors, after an initial period during which significant variations in the sound intensity are observed, there is a stabilisation of the sound intensity (see dashed red vertical line in Fig. 4b), suggesting that a final physical state of the reaction medium has been reached. When looking at the simultaneous temperature measurements, it appears that this time also corresponds to the threshold after which no strong changes in reactor's temperature are noticed. Moreover, when looking at the operando Raman data recorded for the experiment carried out in a Perspex reactor, it is clear that this threshold also corresponds to the period after which no further change in the vibration frequencies occurs, as illustrated by focussing on the 1100-1200 cm -1 spectral region. Using ex-situ analyses by FTIR spectroscopy, it was verified that after stabilization of the sound the hydrolysis is indeed complete, for reactions carried out both in Perspex and stainless steel reactors (see Figure S12). Overall, this demonstrates the utility of performing sound measurements in operando mode, in order to determine the time at which experiments are over, especially in situations when simultaneous Raman analyses are not possible, for example when working in a stainless steel reactor, or when temperature measurements may not be possible, for example in cases when dedicated temperature-regulated milling systems are used for the experiments.

Fig. 4: a) Reaction corresponding to the mechanochemical hydrolysis of activated lauric acid (CH3-(CH2)10-COOH), which was followed here using operando analyses. b) Operando experiments conducted in a Raman laser-transparent Perspex reactor (see picture in the orange rectangle, left) and in an opaque stainless steel reactor (see picture in the blue rectangle, right) with: temperature profiles of the reactor during the milling reactions, intensity of the 5 th harmonic of the AF spectrograms as a function of time obtained by an integration between 205 and 245 Hz, and Raman analyses (for the experiment in a Perspex reactor). Dotted red lines are used as visual helps for indicating the completion of the reaction.

In conclusion, we have presented here a new approach based on the study of the sound for following mechanochemical syntheses using operando methods. The potential of this approach was illustrated in three different examples, demonstrating how it can be used to draw attention to the formation of synthetic intermediates, to know when a reaction is complete, and also to follow changes in the physical state of a reaction medium. Moreover, it was shown that sound analyses can shed light

Fig. 1 :

 1 Fig. 1: Top: schematic representation of the set-up used for the operando monitoring of mechanochemical reactions, using the combination of Raman spectroscopy, thermal imaging, and the recording of an AF spectrogram. Bottom: Photo of the instrumental set-up used in this work.

Fig. 3 :

 3 Fig. 3: a) Scheme of the hydrolysis of SiO2 in a Perspex reactor using two zirconia beads. After each addition of 10 μL of H2O, the mixture was milled during 5 min at 50 Hz. b) Sound intensity variation of the 3 rd harmonic (145-155 Hz) according to the physical state of SiO2 upon addition of H2O. Associated pictures are taken just before the water addition. The red dashed line is given as a guideline to show the differences in sound intensities for motions which are predominantly impact. The blue arrows indicate the 5 minutes periods of milling when impact motions were predominant. c) Temperature profile of the reactor. Blue shaded rectangles emphasize the impact motions regions. The green arrows highlight the regions which show similar temperature profiles (but different sound signatures). d) Details of the three different bead motions detected during the experiment (on the left: pictures of the reactor, on the right: schemes of the beads motion): impact, rolling under snow-ball effect and rolling.

J. Špačková, C. Fabra, G. Cazals, M. Hubert-Roux, I. Schmitz-Afonso, I. Goldberga, D. Berthomieu, A. Lebrun, T.-X. Métro and D. Laurencin, Chem. Commun., 2021, 57, 6812-6815.

on different types of movements of the beads within the milling reactors, meaning that it is highly interesting to use such analyses to decipher the different phenomena taking place within the milling jars.

Overall, this makes sound measurements a promising addition to the toolbox of methods which mechanochemists can now use to try to understand and control the evolution of reaction media during ball-milling. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 772204; 2017 ERC-COG, MISOTOP project). We acknowledge Prof. Franziska Emmerling for providing the Perspex reactors used for some of the real-time monitoring syntheses shown here.

Author contributions

The project was conducted by CL, in close interaction with DL and TXM. GF developed the Python script to generate the AF spectrograms. PG, GF, NF, SM and CL took part in the experimental development of the operando acoustic set-up. SM and CL performed the BM syntheses for the cocrystal, NF and CL designed the experiment with SiO2, JS and CL the syntheses involving the lauric acid. CL performed the data analyses, and prepared all figures and tables. CL and DL wrote the initial draft of the manuscript. All authors discussed the results and contributed to the final preparation of the manuscript.

Conflicts of interest

There are no conflicts to declare.


Jean Raphael Richa
email: jean-raphael.richa@etud.univ-pau.fr

Data Quality Computation For Obsolescence Detection Within Connected Environments

Keywords: Connected environments, Data obsolescence, Data Quality Metrics

The unceasing growth in digital technologies has promoted the means of sensing, visualizing, and autonomously analyzing the environment encompassing us. These connected environments provide data interoperability producing and collecting a staggered quantity of information deemed forefront in better understanding the challenges our societies face. This has helped in enhancing the performance of new or existing entities with product life-cycle and smart cities being just two examples. However, making use of data is one perspective, and being able to detect which data is actually useful is a different perspective. The latter encounters a critical research gap as there is no clear procedure for identifying obsolete data. Therefore, this paper aims to clearly identify data quality metrics purposed for data obsolescence detection within a connected environment.

I. INTRODUCTION

Living in the fast tech era, the focus is mainly on data security, interoperability, and speed with less emphasis on the data integrity; namely, the data that is no longer useful. In a world itself being a fast-paced environment changing faster than our ability to comprehend, comes premature obsolescence [START_REF] Bashir | Managing obsolescence in information technology[END_REF] leading to unsustainability in information and communication technologies. Data obsolescence can have different meanings based on the context it's involved in. Focusing on the information technology sector, it is defined as antiquated data gone/going out of use, data no longer practical, or data not needed to begin with [START_REF] Bradley | An analysis of obsolescence risk in it systems[END_REF].

Obsolescence is a major cause of high cost and integrity loss; nonetheless, it is often not taken into consideration as a serious issue nor included within the planning and implementation stages [START_REF] Bradley | An analysis of obsolescence risk in it systems[END_REF]. With the gradual loss of data confidentiality runs a risk of erroneous behavior and false data representation [START_REF] Finger | Temporal data obsolescence: modelling problems[END_REF]. For instance, this causes the United States defense and aerospace sector to face an approximate loss of 750$ million annually according to the US Navy [START_REF] Romero Rojo | Obsolescence management for long-life contracts: state of the art and future trends[END_REF]. Accordingly, it is crucial to adopt a goal-oriented approach to minimize the impact of obsolescence on organizations especially for communication and sensing industries. Smart cities are increasingly integrated with various devices, systems, and sensors within a networked ecosystem; connected environments, allowing them to communicate, share, and collaborate on data seamlessly. However, with vigorous data generation comes again the need for new data integrity measures. Consequently, being the first representatives of this initiation, we will unveil which data quality parameters to use alongside computation techniques providing the basic infrastructure needed for obsolescence detection in connected environments.

Research is aiming to adequately manage, reduce and solve the negative impacts of data obsolescence; however, there is currently still no clear definition as to what data obsolescence is and how it corresponds to the new ongoing technical revolution. Its existence cannot be narrowed down only to the aspect of data no longer used; there are many more reasons behind the cause of it. It is to be a stand-alone parameter with its own definition and dimensions; the topic this paper aims to uncover in the field of connected environments. In this paper, we aim to provide data obsolescence with a clear set of metrics and definitions purposed in its detection within connected environments.

II. STATE OF THE ART

Data obsolescence can exist almost in any topic and can have various definitions based on the context it is used in. In [START_REF] Junge | Obsolescence in information and communication technology: A critical discourse analysis[END_REF], the authors focus on data obsolescence in the domain of products such as when a product becomes non-functional prematurely with a shorter life span. The authors argue that targeting obsolescence policies and interventions can contribute to more sustainable technology. In [START_REF] Bradley | An analysis of obsolescence risk in it systems[END_REF], the authors also focus on both the product, its users, and how they are affected by what they called "Technological Obsolescence". The latter afflicts almost every developed product claimed, some of which are slowly affected (e.g. roads, bridges) while others rapidly (e.g. audio industry). The authors in [START_REF] Bradley | An analysis of obsolescence risk in it systems[END_REF] further extend this to a functional definition of obsolescence describing it as a road becoming obsolete just because the destination is no longer in use. In other words, due to technological advancements, the market trends shift into something new making the old trend antiquated. The authors of [START_REF] Schulze | Obsolescence as a future key challenge for data centers[END_REF] also discuss the obsolescence of products/services, defining it as the aging of a product in means of the production process and materials. They consider a product's obsolescence can be one of four types: material, functional, psychological, or economical. While the authors managed to describe four obsolescence types, these types are limited to the product as a physical entity. In this context, the product life cycle management of data centers was the most important factor here and not treating the data centers themselves; one of the gaps this research paper aims to show. Examining life cycles as well, extending that of defense and aerospace sectors through managing obsolescence is covered by the authors of [START_REF] Rojo | Obsolescence management for longlife contracts: state of the art and future trends[END_REF]. Knowingly, aerospace uses Concept, Assessment, Demonstration (CAD) phases which can last as long as 10 years as the authors explained. This is a major issue as obsolescence may arise even before the actual development phase starts. This suggests the seriousness of data obsolescence and the need of its management in early stages to reduce the associated risks.

Contemporary Internet of Things (IoT) systems are producing fast growing volumes of data. Accordingly, while the new data is coming into storage, previously saved data becomes excessive with obsolete data. As it's unprofitable to store all original data, in [START_REF] Alieksieiev | Big data aggregation algorithm for storing obsolete data[END_REF], the authors investigate obsolescence in data storage while making use of aggregation methods to minimize the amount of it stored. Their methodology is limited to two factors, old data versus current data, whereby the latter is represented as the system's latest state. Data is then labeled as obsolete based on its probability of necessity; any data no longer requested becomes obsolete. While expressive in their application, the authors do not comprehensively consider obsolescence as their focus is more on when the sensors have collected the data. However, sensors, whether real or virtual, collect a large set of data on a real time basis, as the authors of [START_REF] Noueihed | Knowledge-based virtual outdoor weather event simulator using unity 3d[END_REF] foreground. With the digital twin becoming a growing trend, the authors develop a connected environment of a mimicked real world composed of virtual sensors and weather phenomenon to measure. Although the authors do not provide data analysis, they emphasize on the importance of the data to be collected by the sensors. Accordingly, understanding such data while detecting which is useful and which is obsolete, will help handle spatial-temporal redundancies and enhance systems' processing time. Knowingly, programmed environments intend to grow indefinitely while the users wait on standard backup discs to archive data, the authors of [START_REF] Habermann | Automatic deletion of obsolete information[END_REF] highlighted. The authors stress on the importance of removing obsolete data in order to prevent data explosion, and how it "vanishing" is a peace of mind in business. While this reflects the research attention data obsolescence is in need of, it also highlights the lack of perception this topic has. Namely, the aim is not to vanish obsolete data on the spot, but rather understand first the data itself then act accordingly. [START_REF] Chaieb | Data obsolescence detection in the light of newly acquired valid observations[END_REF] expands the importance of obsolescence highlighting that even new data can contradict existing ones. The authors focus on the contradiction detection accuracy variable "-Contradiction" to estimate any obsolescence. However, the scope was limited to two consistent databases compromising the same subject of information with criteria considered to be "perfect and fixed during processing". Also covering databases are authors of [START_REF] Finger | Temporal data obsolescence: modelling problems[END_REF] who describe how the confidence in data decays with time as we are held behind the world's fast-paced evolution. Understanding the importance of data obsolescence, the authors aim to reduce the problems faced through monitoring and controlling obsolescence. Although they categorize obsolescence metrics minimalistically, the authors highlight the amount of research needed in this area and the need for more data credibility.

In [START_REF] Bouzeghoub | A framework for analysis of data freshness[END_REF], the authors explain how information systems' success is closely related to data freshness. Even though the authors do not discuss obsolescence, they describe quality metrics (such as currency/materialization, staleness, timeliness) representing freshness level of data. Knowingly, freshness is not only about the latest data received, it's also how important that data is. For instance, old data may have a quality dimension deeming it necessary to keep while a newly received piece of data might be of no use. In this paper, we aim to incorporate the various data quality metrics into a new sector; data obsolescence. In [START_REF] Glushkov | Intellectual obsolescence detection method of spatial data using historical data[END_REF], the authors prove the close relativity between obsolete spatial information and user influence, showing how most advancing technologies are purposed to improve the users' experience and simplify their life. Knowingly, spatial data is one the sectors in need of up-to-date data on a real time basis; otherwise, a potential risk is likely when using map services due to false decision making. That's why the authors of [START_REF] Glushkov | Intellectual obsolescence detection method of spatial data using historical data[END_REF] stress on the need of geographical obsolescence identification for keeping data as complete as possible. The latter is of one the fields connected environments encompasses, and the authors agree there exist no strict metrics to evaluate obsolescence. The more the data collected, the more obsolescence is appearing as an issue requiring solutions. This being a reflection of the research gap data obsolescence encounters, in this paper, we investigate data obsolescence metrics and definitions that will help detect data obsolescence within connected environments.

III. RELATED WORK

One might confuse data obsolescence with data quality (DQ) which can explain the few to no research done on the formers' connection. DQ is a widely studied topic described as the wholeness of an entity (data) capable of satisfying the user's needs. In other words, DQ is usually subjective to its intended use, difficult to assess as the quality properties are set by the user. Each property is provided with a collective framework, named data quality dimensions (DQD), to measure data quality and assess its requirements. While DQDs are argued to be domain dependent, standard metrics include: (1) Intrinsic: comparing similar data points to locate any abnormalities, (2) Representational: sampling techniques to view, understand, and manipulate data, (3) Accessibility: where and how the user is accessing the data, and (4) Contextual: driving data based on the data contextual circumstances it belongs to. Table 1 classifies some of the data indicators contained within these four pillars [START_REF] Byabazaire | Data quality and trust: Review of challenges and opportunities for data sharing in iot[END_REF] [15] [16] [START_REF] Teh | Sensor data quality: A systematic review[END_REF].

However, when it comes to data context such as relevance, completeness, added-value, and appropriate data amount, there is still no adequate solution considered [START_REF] Byabazaire | Data quality and trust: Review of challenges and opportunities for data sharing in iot[END_REF]. DQDs have been around for quite some time, yet no consensus on a generic methodology is to be found. With the ongoing integration of both worlds, physical and virtual, there are seamless amounts of new systems heavily relying on such data yet minimal focus How reasonable the cost of collecting data is on its integrity [START_REF] Liu | Data quality and the internet of things[END_REF]. While some systems and applications consider some dimensions and leave others out [START_REF] Byabazaire | Data quality and trust: Review of challenges and opportunities for data sharing in iot[END_REF], they seem to lack the attention deemed necessary. That's why, this paper, being first in its approach, will adopt and define such crucial dimensions with a new light putting forward methodologies per indicator needed for the detection of data obsolescence in connected environments. In section 3, we delve in to these major indicators' definitions and computations, chosen as the necessities of this obsolescence detection.

Similar confusion is faced by data popularity; a parameter to track how often a piece of data is requested by the system's sites. "Most requested" is not sufficient alone as a metric to measure the data's usefulness especially that data popularity does not investigate how that data is being used by the requestor. "What about the data that are not requested? Are they not useful? What about the data that has just arrived? Might there be missing data?" are a few questions that present a gap. Data popularity is important, but it's also important to know that it's commonly used for data replication management; the stringent conditions needed for data sharing, storing and transferring within distributed systems [START_REF] Ma | A classification of file placement and replication methods on grids[END_REF]. Data management concerns, such as eliminating, duplicating, and transferring between disks and caches, are often determined by counting how many times the files have been accessed [START_REF] Beermann | Methods of data popularity evaluation in the ATLAS experiment at the LHC[END_REF].

IV. PROPOSAL

In this section, we propose formal definitions for data obsolescence and the most significant data quality measures in the field of connected environments.

A. Data obsolescence as an independent terminology

When data becomes insignificant over time and is no longer valid for its intended use, data obsolescence is the phenomenon in depiction. Technological changes are among the top factors causing obsolescence especially after the widespread use of the internet and mobile devices, which has revolutionized the way we communicate and access information. Connected environments, leading this technical revolution, are subject to data obsolescence and require treatment for the data items collected by the sensors. Therefore, in connected environments, we define:

• "Data Obsolescence" as the state wherein data, collected via devices and sensors, is no longer rendered significant, effective, and applicable in the content of its existence.

B. Definitions & preliminaries

As aforementioned, spatial-temporal redundancies face critical lack of treatment with few to none when speaking of connected environments. A number of factors, including modifications in land use, population demography, and infrastructure, can lead to obsolescence especially spatially considering dynamic sensors. This refers to the phenomena wherein information pertaining to a particular place, region, or location, becomes outdated or irrelevant ceasing to serve the original purpose. Even if the sensor was static and not moving, connected environments are subject to spatial obsolescence especially that sensors sense the encompassing surrounding and not necessarily only the data part the system is in need of. Figure 1 visualizes a simple connected environment as a group of zones (e.g. Z0) each having a group of sensors/devices (e.g. D1). Device D2 is a camera monitoring the surrounding locale; however, only space S1 is the data we are interested in. Accordingly, this depicts a spatial obsolescence since a portion of the spatial data the camera collects is outside the relevant space. Taking into consideration that the camera is rotating, at some angle, the whole data might be spatially obsolete with zero relevance. This is only one type and one scenario depicting the need of data treatment, again reflecting the existing research gap.

The aim is not only providing obsolescence with an official definition, but also formulating data estimation definitions and Us making the first step in comprehending the gap data obsolescence is facing, we focus on connected environments and choose predefined DQDs (Table I). Knowing that such DQDs do not offer computational methodologies, we put forward 19 definitions and demonstrations filling in such gap. Even though the latter are connected environments specific, many are characterized with extension capabilities making them useful for many other technological domains.

Definition 1 (Temporal characteristic.) A temporal characteristic t represents when the data was collected:

t =< f ormat, v > where :

(1)

• format is the type of the temporal stamp (e.g., date, time, datetime, interval, duration) • v is the temporal value expressed in the specified format ■ Definition 2 (Spatial characteristic.) A spatial characteristic l represents information pertaining to a particular place, region, or location: l =< P > where :

(2)

• P=[p 0 , p 1 , ..., p n ] is the list of points

• p =< longitude(decimal), latitude(decimal), order(integer) > connected based on the specified order to form the required shape (e.g., point, rectangle, square) ■ Definition 3 (Sensor.) A sensor s refers to a physical sensor capable of measuring its feature of interest:

s =< type, D, c, a, ca, l, f, f o, sr, se, mse, rrt, mnt, ST AT U S, m D > where :

• type (string) refers to the category of the sensor (e.g., temperature, proximity)

• D=[d 0 , d 1 , ..., d n ] (Data Item
• type (string) specifies whether the zone is a coveredwith at least one sensor -or uncovered -with no sensors -area • l is a spatial characteristic representing the particular shape of a zone (cf. Def 2) • S=[s 0 , s 1 , ..., s n ] is the set of sensors (cf. Def 3) deployed in z • a z (percentage) is the inference of the zone reflecting the impact on the sensors by its environmental properties ■ Definition 5 (Environment.) An environment E refers to a physical infrastructure composed of one or multiple zones:

E =< Z > where :

• Z=[z 0 , z 1 , ..., z n ] is the set of zones z (cf. Def 4) ■ Definition 6 (Individual Data.) A data d represents the measurement captured by a sensor in a particular time and location:

d =< s id, v, t, l, an, m d > where :

• s id (string) is the sensor id (e.g. temperature sensor 1)

• v (decimal) is the data value the sensor measured (e.g., 21 • C) • t the temporal property representing when the data was sensed (cf. Def 1) • l the spatial property representing where the data was sensed (cf. Def 2) • an (integer) is the number of times the individual data was accessed or requested • m d (set) is the single data's quality metrics including:

tl (percentage) is the timeliness of the data sa (percentage) is the spatial accuracy of the data ac (percentage) is the accessibility of the data pl (percentage) is the popularity of the data rl (percentage) is the relevance of the data ■ Definition 7 (Query.) q is a query received by the connected environment. It is related to three properties: q =< q id, q t, q i > where :

• q id is the query id • q t is the time at which the query is sent for execution • q i = < k, z, t > incorporates parameters that identify the query's fields of interest:

k is the attribute being searched z is the data's location being searched (cf. Def 2) t is the time of interest being searched (cf. Def 1) ■ Definition 8 (Coverage area.) A coverage area ca designates the spatial limit beyond which the sensor is not capable of catching values: ca =< l, z > where :

(8) • l represents the spatial property of the coverage area limited by the boundaries of z (cf. Defs 4, 5) ■ Definition 9 (Accuracy.) Accuracy a resembles the margin of error in the measurement of the sensor: a(s) = a E + a f ixed where :

• a f ixed is the fixed accuracy (percentage) provided by the sensor's documentation (e.g., ±2%) • a z is the additional accuracy (percentage) defect reflecting the impact of z (cf. Def 4) on the sensor ■ Definition 10 (Availability.) Availability av represents the percentage of time the sensor was available and successfully responding to the queries:

av(D) = |D| i=0 di.an | QD |
where :

• Q D = {q ∈ Q | q has S as the source of interest} is a list of all the queries that request the data item D ■ Definition 11 (Credibility.) Credibility cr provides the extent to which the sensor can be trusted with the measurements it is providing:

cr(D) = K1 * rt + K2 * rp + K3 * se | n i=0 Ki = 1 (11)
(cf. Def 3) where: is the percentage of failures/stoppages the sensor faces according to its status logs • f rf = 1-f recommended f req is the frequency with respect to the recommended one ■ Definition 14 (Format consistency.) Format Consistency fc checks how compatible and the change of compatibility in the sensor's data format: S S ← (UNION(q.q i.z, d.l)/INTERSECTION(q.q i.z, d.l));

• rt = 1 -|{d∈D|d==sr.
f c(D) = 1 - | D f d | | D | where : (13)
• D f d = {d.f ∈ D | d.f
• Q d = {q ∈ Q | q has d as the data of interest} is a list of all the queries that request the individual data d ■ Definition 18 (Popularity.) Popularity pl is the level of interest or attention that an individual data receives with respect to the data item it belongs to:

pl(d) = d.an |D| i=0 d i .an (15)
■ Definition 19 (Relevancy.) Relevancy rl is the degree to which data is within the valid expected range:

Relvancy function θ (d) =      1, d ∈ valid range 0, d / ∈ valid range similarity valid range ∈ ϕ (16)
• similarity (e.g., cosine) computes the degree to which data d is close to the respective data item and its logs ■ As noticed from Table 1, although data quality is widely investigated, it's usually covered within theoretical aspects. Data quality dimensions are refereed back to one of the four main categories aforementioned; namely, intrinsic, representational, accessibility, and contextual. In other words, when coming across a certain indicator (e.g. consistency, contradiction), we go up the hierarchy checking whether this indicator focuses on the internal consistency, data viewing, ease of access, or data significance when the focus should be more on the indicator itself and how to compute it. Detecting this gap, we create clear definitions and specifications per indicator providing the hierarchy with its infrastructure. In other words, we are providing the first step for the data quality indicators to be as independent while giving space and enlightenment for expansion towards other domains. Consequently, while our definitions and metrics are inspired by connected environments, they are applicable to many other technological domains. As an end result, all indicators work collectively to provide the connected environments with what's needed as an initial step for obsolescence detection.

V. FUTURE SCOPE

This paper investigates DQDs made helpful for data obsolescence detection within connected environments. Each indicator tackled is provided with a computation procedure producing a numerical output. However, how all these estimation will be grouped together in order to produce a single obsolescence percentage will be the role of future work. Based on the connected environment properties, each dimension should be assigned a specific weight describing its contribution to the overall obsolescence detection. Additionally, this paper shows the initial contribution towards practical DQDs quantifications; however, it is specific to connected environments. Accordingly, the future scope also includes what and how dimensions can be extended towards other domains.

VI. CONCLUSION

In the age of rapid technology, the emphasis is more on data security and interoperability with less emphasis on data integrity; namely, Data Obsolescence. Depending on the context in which it is used, data obsolescence might exist in practically any area of study and have different definitions. In connected environments, we define "Data Obsolescence" as the state wherein data, collected via devices and sensors, is no longer rendered significant in the content of its existence. In this context, we propose and characterize major data quality computational indicators offering data obsolescence the baseline needed for its detection. We put forward 19 definitions resembling metrics within the connected environment with extension capability towards other technological domains. The paper examines how each indicator is calculated, as to how they work together to provide a single obsolescence estimation, that will be within the paper's future scope.

Fig. 1 .

 1 Fig. 1. Sample connected environment metrics forming the infrastructure necessary for its detection.Us making the first step in comprehending the gap data obsolescence is facing, we focus on connected environments and choose predefined DQDs (TableI). Knowing that such DQDs do not offer computational methodologies, we put forward 19 definitions and demonstrations filling in such gap. Even though the latter are connected environments specific, many are characterized with extension capabilities making them useful for many other technological domains.Definition 1 (Temporal characteristic.) A temporal characteristic t represents when the data was collected:t =< f ormat, v > where :(1)

  ) is the set of the data measured by the sensor saved on an external data storage • c (Gigabyte) is the storage capacity of the aforementioned data storage • ca (metric unit 2 ) is the coverage area of the sensor • l is the spatial property specifying the location of the sensor (cf. Def 2) • f (Hertz) is the frequency of sensing • fo is the format of the measured data • sr = < min, max > is the sensor range (decimal values) • se (percentage) = 1 -sensor sensitivity in documentation sr.max is the sensitivity of the sensor • rp (percentage) = actual response time recommended response time is the responsiveness of the sensor • mnt is the manufacture response time of the sensor • STATUS = [st 1 , st 2 , ..., st i ] where st i =< state i , t i > is the state (e.g., stopped, active, failed) of the sensor at the respective datetime (cf. Def 1) • m D (set) is the sensor quality metrics including:a (percentage) is the margin of error of the sensor av (percentage) is the availability of the sensor cr (percentage) is the credibility of the sensor ct (percentage) is the contradiction of the sensor cn (percentage) is the correctness of the sensor fc (percentage) is the format consistency of the sensor ■ Definition 4 (Zone.) A zone z designates is a physical geolocation capable of hosting sensors:z =< type, l, S, a z > where :

/ 3 drif■

 3 max}|+|{d∈D|d==sr.min}| |D| is the resolution of the sensor resembling the percentage of D having the min and max saturation data values ■ Definition 12 (Contradiction.) Contradiction ct is the discrepancy present within the data item reflecting the percentage data drift its encountering: Algorithm 1: Contradiction Computation Via Data Drift Check Input : D Output : ct Variables: drif tpercent, i 1 drif tpercent = 0; 2 for i = 2 to i = size(D) do /* Equality_function infers similarity between two consecutive data individuals *tpercent+ = Equality f unction(di, di-1)); Definition 13 (Correctness.) Correctness cn provides the extent to which the sensor's measurements are affected by external conditions: cn(S) = K1 * sf (S) + K2 * f rf (S) | n i=0 Ki = 1 where : (12) • sf (D) = 1 -of f time on time = 1 -n i=1 (ST AT U S (i) .t-ST AT U S (i-1) .t)•I(STATUS (i) .state=active) n i=1 (ST AT U S (i) .t-ST AT U S (i-1) .t)•I(STATUS (i) .state̸ =active)

10

  avg s s = SU M (S S) COU N T (S S) ; 11 return avg s s; ■ Definition 17 (Accessibility.) Accessibility ac represents the storage means of the data and how applicable it is to access: ac(d) = d.an | Q d | where :

  appears only once in D} is a list of the distinct formats that exists in the data item D ■ Definition 15 (Timeliness.) Timeliness tl is the degree to which data has attributes that are of the right age in a specific context of use with respect to the queries: Definition 16 (Spatial accuracy.) Spatial accuracy sa is the degree to which data has attributes that are of the right location in a specific context of use with respect to the queries:

	Algorithm 2: Timeliness Calculation
	Input	: d, Q
	Output : avg t s
	Variables: T S
	1 avg t s ← 0;
	2 T S ← new_list();
	/* allen_temporal detects relation of two temporal intervals (e.g., equal,
	intersect)	*/
	3 for q in Q do
	Algorithm 3: Spatial Accuracy Calculation
	Input	: d, Q
	Output : avg s s
	Variables: S S
	1 avg s s ← 0;
	2 S S ← new_list();
	/* DE_9IM detects relation of two spatial objects (e.g., equals, contains,
	disjpoint, intersects, touches, crosses, within, overlaps)	*/
	3 for q in Q do

4

if allen temporal(q.q i.t, d.t) ∈ ["equal", "include"] then 5 T S ← 1;

6 else if allen temporal(q.q i.t, d.t) == "outside" then 7 T S ← 0; 8 else 9 T S ← (UNION(q.q i.t, d.t)/INTERSECTION(q.q i.t, d.t)); 10 avg t s = SU M (T S)

COU N T (T S) ; 11 return avg t s; ■ 4 if DE 9IM (q.q i.z, d.l) ∈ ["equals", "contains"] then 5 S S ← 1; 6 else if DE 9IM (q.q i.z, d.l) ∈ ["disjoint", "touches"] then 7 S S ← 0; 8 else 9