Karim Tabia
email: tabia@cril.univ-artois.fr

Hugues Wattez

Nicolas Ydée

Karima Sedki

Data Analytics and Visualization for Connected Objects: A Case Study for Sleep and Physical Activity Trackers

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Data analytics and visualization for connected

objects: A case study for sleep and physical activity trackers (Preprint version)

1 Introduction

Wearable connected objects that focus on health and well-being (eg connected watches, fitness wristbands, sleep trackers, etc.) are largely being used and are being democratized on a large scale [START_REF] Yuehong | The internet of things in healthcare: An overview[END_REF]. Reluctance regarding their use still exists for various considerations [START_REF] Macaulay | Chapter 8 -availability and reliability requirements in the iot[END_REF][START_REF] Lee | How and what to study about iot: Research trends and future directions from the perspective of social science[END_REF][START_REF] Ammar | Internet of things: A survey on the security of iot frameworks[END_REF] such as the lack of security of the data collected, the lack of customization, the lack of functionalities and services "intelligent" and high level, the lack of interoperability, etc.

In the last decade, more and more IoT devices and applications are dedicated to help users monitor and improve their health and well-being [START_REF] Woo | A reliable iot system for personal healthcare devices[END_REF]. Physical activity trackers (also called activity monitors or sports/fitness monitors or activity trackers) are connected devices (such as wrist bracelets or Smart watches) or Smartphone applications that measure the intensity, duration and amount of the activities performed by the user. They measure features such as walking or running distance, calory consumption and expenditure, and in some cases, heart rate and "quality" of sleep. Such devices are widely used and very popular as they aim at helping users to increase their motivation and improve their performences. Moreover, in addition to emproving well-being, the trackers allow user's awareness about physical activity, they help ensuring regular physical activity and decreasing the risks of many chronic diseases [START_REF] Durstine | Chronic disease and the link to physical activity[END_REF][START_REF] Yuehong | The internet of things in healthcare: An overview[END_REF].

Wearable activity trackers and more generally most IoT devices still have many issue regarding interoperability, security, personalization and sensors reliability to name a few [START_REF] Macaulay | Chapter 8 -availability and reliability requirements in the iot[END_REF][START_REF] Lee | How and what to study about iot: Research trends and future directions from the perspective of social science[END_REF]. The lack of "smart" features and services is due, among other things, to not taking advantage of the large amounts of data collected and generated to learn and automatically extract information that can be very useful. For example, with devices such as smart watches and connected bracelets, we can collect a lot of data of physical activities and sleep (eg distance traveled, number of steps, number of awakenings, duration of deep sleep ...). The majority of these devices are limited to displaying simple statistics describing these activities. It is clear that extracting information like correlations between factors, recurring patterns, trends, etc. from these physical activity and sleep data and possibly cross-referencing them with other factors (eg environmental factors such as temperature, noise, lumunosity, pollution, etc.) can provide interesting elements to explain for example what is strongly correlated with disturbed sleep. This type of information derived from the analysis of activity data constitutes a very interesting added value [START_REF] Wu | Adoption of big data and analytics in mobile healthcare market: An economic perspective[END_REF][START_REF] Ahmed | The role of big data analytics in internet of things[END_REF]. Now, even if useful and relevant information has been extracted, it is necessary to represent the results of the analytics in an intuitive and efficient way so that the user can directly perceive, for example, the impact of the different factors on her sleep quality. Visualization will play an important role for the effective retrieval and interpretation of results by users [START_REF] Gu | Visualizing the knowledge structure and evolution of big data research in healthcare informatics[END_REF]. Our study confirms that big data and analytics along with appropriate knowledge visualization techniques can help improve the usefulness of activity trackers and more generally IoT devices.

In this paper, we first focus on large public IoT limitations and provide a real case study in monitoring physical activities and sleep using Fitbit smart watches. Two users are hired in this study for several months and real data has been collected in real life conditions. We propose then some high level and smart functionalities by taking advantage of the large amount of data collected and using data analytics and visualization techniques. This paper is organized as follows: Section 2 recall the main limits and lack of smart functionalities in activity tracking connected objects. In Section 3 we present our case study and we provide discussions and concluding remarks in Section 4.

Main issues with activity trackers from a usefulness persective

Like many IoT devices, activity and sleep trackers still suffer from many problems and limits [START_REF] Ammar | Internet of things: A survey on the security of iot frameworks[END_REF][START_REF] Macaulay | Chapter 8 -availability and reliability requirements in the iot[END_REF]. For instance, one can mention the reliability of the sensors, the lack of security while exchanging and storing the data, lack of interoperability with other devices (especially those of other manufacturers) and of course lack of intelligent or smart functionalities. In this paper, we focus only on user-related aspects in terms of useful functionalities and efficient user interaction.

Lack of personalization

One of the challenges facing the use of IoT is personalization, especially in case of general public applications. Personalization aims to provide services tailored specifically for the user needs and preferences. For example, IoT devices aiming at improving sleep quality would provide the user personalized recommendations regarding for instance when to go to bed, temperature of the room, food/drinks to avoid, physical activity..., and trigger alerts and warnings in case of sleep deficiency/disorder, physical activity deficiency, food deficiency/excess, etc. In order to learn the factors they may have an impact on the sleep quality of the user, there is need to measure the sleep quality and learn correlations with factors associated with good/bad sleep quality to provide useful recommendations while taking into account user profile, preferences and constraints (for more details on this issue, see [START_REF] Vallee | On personalization in IoT[END_REF]).

Lack of smart functionalities

While IoT devices are capable of collecting many types of data with their sensors and potentially acquire complemnetary data from other sources, the collected data is often neither correlated nor exploited to give relevant information, pieces of knowledge, advices and recommendations to the user for improving his life style. For instance, the quality of sleep is affected by a number of factors such as physical activity, dietary habits (alcohol intake, caffeine containing beverages, smoking, etc.), environmental factors, etc. It is then possible to correlate and analyse all these data in order to highlight which factors have a positive or negative impact on the user's sleep quality. Of course, this needs making use of big data/datamining techniques and data analytics to extract useful knowledge from the large amounts of user-generated and ambient data.

Lack intuitive and interactive dashboards and user interfaces

As just mentioned above, in addition to analyzing the data of physical activities and sleep collected by connected objects, we will have to report this data and potentially pieces of knowledge to the user, through user-friendly, intelligent and interactive interfaces. Thanks to visualization techniques, the user can then see for example disorders that he may have during his sleep and the link that this may have with his physical activities or ambient factors. Unfortunately, as shown in the dashboard of Fig. 1, most activity and sleep trackers display only very basic statistics and graphs summarizing the daily activities. There for instance no analysis or interactivity. It is true that the characteristics of the screens used by the users (smartphones or connected watches) impose limits for the display but the very basic nature of the data to display does not lend itself to elaborate visualizations as we will illustrate it in our case study. In order to learn from the data relevant information (eg. the factors they may have an impact on the sleep quality of the user), there is need to use as much data as possible and extract such useful knowledge (eg. learn correlations and patterns with factors associated with good/bad sleep quality). Hence the collected data should include all i) the factors that may describe the sleep quality (eg. awakenings count, minutes asleep, etc) and ii) factors that may have an impact or influence on sleep quality (eg. physical activity, food, temperature, noise, etc.). We distinguish two types of data:

-User-generated data: Such data can be sensed by dedicated devices (ex. physical activity) or by the user through a graphical interface on a laptop or mobile phone (ex. food intake). In our study, user-generated data consists only in physical activity and sleep data collected by the used Smart watches.

-Ambient data: This refers to factors such as air quality, noise level, temperature, luminosity, etc. Such data could also be provided by some IoT devices or retrieved from special applications and sources (eg. Web sources).

In our study, we used external sources to acquire weather and air quality data corresponding to the location where the volunteers were living.

Specifications of the activity trackers used in the study

The two Fitbit Smart watches that are selected are Fitbit Blaze having the following specifications:

-Sensors: An altimeter, ambient light sensor, three-axis accelerometer, optical heart rate monitor. In addition, a connected GPS is used. -Data tracked: As detailed below, the trackers collect activity data (eg. distance, floors climbed, heart rate...) and sleep (eg. time in bed, awaikening account, etc). Some data is not sensed but derived from activity data such as the number of calories burned. -Operating system: The devices are connected with smartphones running Apple MacOS X 10.6 or later, Microsoft Windows Vista or later.

For more details on the Fitbit Blaze tracker, please see1

Raw data

Like most activity and sleep tracking tools, the Fitbit Blaze trackers just collect some data and remotely store it using a Smartphone connection in the form of log records which can be downloaded or displayed in various ways to the user. We collected the raw data on a monthly basis. Each month a .csv file is downloaded and contains only the records of activity and sleep (of course, other information could be downloaded). The following is an example of log records for activity data.

The collected files correpond to the activity tracking of two users wearing Fitbit Blaze trackers during 8 months. In the current work, the date columns are omitted since we do not mine sequential patterns. Of course, this means that we make a strong hypothesis implying that each day data is independant of the previous and following days. This hypothesis is very debatable for assessing for example the quality of sleep and physical activity (for instance, three days of bad sleep but distant from each other should be considered less serious than three days in a row of bad sleep). But with this hypothesis, we lose the dependence and relationship between the activities of successive days.). This issue is discussed in the last section and left for furture works.

Data preprocessed and enrichment

As mentioned earlier, in order to provide relevant information, there is need to enrich the tracking data provided by the trackers with other data. For instance, there is no doubt that ambient data (eg. room temperature, noise level, luminosity, etc.) has an impact on the sleep quality but such data is not provided by the used Fitbit trackers. In our study, we used APIs for getting i) weather data (eg. temperature, humidity, wind, etc.) from http://www.meteociel.fr/, ii) air quality data from http://www.atmo-hdf.fr dedicated to monitoring and assessment of air quality in Hauts-de-France (location where the two volunteers hired in this study live) and from http://www.openhealth.fr/.

Many technologies and techniques are used to process and mine the data and display the results. First, the csv files containing tracking data are organized by day and by user. Each raw contains both activity and sleep data. Then the data is enriched with ambient data for that day. For visualization, data is first put into a relational database such that the visualization scripts needing complex SQL queries could run efficiently in real time to allow user interactivity.

Analytics and high level feature definition

This is the part where the added value is expected to be mined from the data collected from the trackers and other sources. In this study, we addressed two types of relevant information that can be automatically extracted from data:

-Correlations among basic features: The goal here is to extract meaningful correlations among the features of the data. For instance, one could be interested to know how and to which extent the intensity of physical activity is related the number of awakenings. In this study, we extract different types of statistical correlations such as Pearson, Spearman and Kendall correlations.

-High level correlations: Since the correlations among basic features are somewhat limited from a user's point of view, we need to define high level features such that the user finds the provided information really relevant. For instance, in order to learn the factors they may have a negative/positive impact on the sleep quality of the user, there is need to "assess" the sleep quality from the basic features then learn correlations with factors associated with good/bad sleep quality (what is formally a good or bad sleep?). Sleep quality could automatically be estimated based on sleep tracking data (ex. awakenings count) or through forms answered each day by the user assessing his sleep quality. Note that there is to the best of our knowledge no high level sleep measure in the litterature that could be directly computed from the basic features 2 . In this study, we simply relied on an existing score called sleep efficiency assessing sleep quality as the number of minutes of sleep over the number of minutes spent in bed which is obviously not satisfactory. The definition of sleep quality measures should be done by experts or subjectively rated by the user herself.

Visualization

Once relevant informations extracted from the data, there remains to display it for the user. One of the goals here is to display the results in an intuitive and interactive way while most of the time users monitor their activities through smartphones or directly on smart watches having very limited display possibilities. The following provides few examples illustrating how relevant information (eg. correlations) could be displayed.

In order to display statitistical correlations existing among some features of interest, a very easy way is to superpose the graphs of features of interest as illustrated in Fig. 2. The superposed graphs when appropriately scaled visually display some inter-relationships between the chosen features (here, the number of burned calories, the weight and the number of awakeneings).

Fig. 2. Example of superposed plots displaying inter-relationships among features of interest

One could also use a simple correlogram (see of Fig. 3) where respectively colors and cercle diameters tell about the positive/negative nature of the correlations and the strength of these correlations. In order to give a more global view on the user activity and sleep over time, one could superpose the plots of activity or sleep of successive weeks (Fig. 5 Fig. 4. Example of a chord diagram displaying inter-relationships among some features left) or successive months (Fig. 5 right). Doing so, the user could recognize some repeating patterns due to working days/weekend rythm of life, holidays, seasons or any repeated events and cycles. The intuition underlying this point is that the weekly/monthly/annual, etc. organization of daily life has an impact on the activity and the sleep of the users. This visualization will show some phenomena such as the Sunday blues that negatively affects sleep the days before the beginning of each working week.

Many other visualizations could be used and many other forms of knowledge could be extracted and displayed. As for implementation, for the analytics part, we used R packages while we use many Web-based technologies (eg. D3.js) for the visualization part. Following section focuses on the main issues encountered in our case study. This paper focused on a practical application combining data analytics and visualization to improve activity and sleep trackers. We showed that even with very limited sensed data, it is possible to extract relevant information and pieces of knowledge and display the results in a more intuitive and interactive way to the user. The following are the main concluding remarks of our study.

-Missing and noisy data: While collecting data over time, we realized that missing data for whole days can affect the collected data. Indeed, it is not rare that the users forget to wear their smart watches or forget to recharge them. This could be a real issue if sequential patterns were to be mined from the collected data. Techniques to be used should also cope with the limited reliability of some sensors and also some derived data such as calories burned. The users themselves realized that some measures are not exact and this may affect the correlations and more generally the relevant information we want to extract. Hence, one would make use of techniques that are robust and less sensitive to noise or use smoothing techniques for example to cope with this issue.

-Sequential dimension: In the current study, no sequential patterns are mined and no extracted information needs to take into account the sequencial dimension of data. It is obvious that physical activity and sleep in last few days influence those of the following ones. Moreover, most people's physical activity and sleep is influenced by weekly rythm... as pointed out above.

-Beyound statistical correlations: The problem here is that the interpretation (hence the utility) of the statistical correlations between the basic attributes which is quite limited. For example, knowing that there is a correlation between the number of minutes spent in bed and the number of active minutes of physical activity is not very meaningful for a user. What would be really useful is to define quality indicators of good sleep and good physical activity. For this latter, for example, an indicator can be defined if the number of steps or the number of minutes of recommended activities per day is exceeded. Same for sleep. We believe that such indicators are still limited and that a good quality of sleep and activities depends on several parameters and its evaluation must take into account the history of activities. For example, the quality of physical activity and sleep over several days should be evaluated instead of days separately. What can also be very useful is to mine cause-effect relationships instead of just statistical correlations. Cause-effet relations could help the user to make changes in his actitvities to improve his well-being.

-Beyond user-generated data: Through our case study it becomes obvious that in order to provide smart functionalities there is need to use the data collected by the sensors but also some other user-generated data (ex. food intake, smoking or user profile can be provided by the user through a graphical interface on a laptop or mobile phone). Other sources of information are ambient data (ex. weather, pollution, ...). The main issues here are the one heterogeneous data provided by different sources and the one of interoperability between different IoT devices such as connected scales, connected thermometers... that could be used in our case study.

-Towards more interactivity and smartness: Many smart functionalities could be added based on the knowledge that can be extracted form the available data. For example, it is possible to design prediction models such supervised classifiers and regression models that could answer some user queries or make recommendations. One could for example predict her sleep quality given her physical activity and other data for a given day. An example of recommendattion would be to advice at what time it is best to go sleep, which food to avoid or set the temperature of the room to a given level to have optimal sleep. To increase interactivity along with such functionalities, one could for example want to know what will be her sleep quality if she exercises a given amount of physical activity. Such prediction models could be built using history data of physical activity and sleep of the user. This latter will have a friendly user interface to set any parameter of interest for her and see what will be the impact of the fixed parameters on his sleep quality or any other parameter of interest to her.

To sum up, this preliminary work focused on the high-level functionalities that can be implemented to improve the usefulness of physical activity and sleep trackers. Our approach is to exploit the data collected by the connected objects possibly enriched with other data to extract relevant information and display it to the user in a visual and interactive way. We presented a real case study where we highlighted the problems encountered and built a prototype for demonstration. We finally propose several tracks for future works. This will require relying on big data techniques and analytics as well as exploiting the power of visualization techniques for better interaction with the user.

Fig. 1 .

 1 Fig. 1. Example of a Fitbit tracker dashboard

Fig. 3 .

 3 Fig. 3. Example of a correlogram displaying Pearson correlations among some features

Fig. 5 .

 5 Fig. 5. Example of superposed plots of sleep

Fitbit Blaze User Manual https://staticcs.fitbit.com/content/assets/help/manuals/manual_blaze_ en_US.pdf

Polysomnography (PSG) is the main method of sleep monitoring used to detect sleep disorders in a medical context. It is performed during a whole night in a hospital by placing on the patient different signals (electrodes on the scalp, eyelids, and chin, etc.). Such a method is efficient but it is obtrusive, costly and cannot be conducted frequently on a large number people.


Elmehdi Bahri

Rémus Pusca

Raphael Romary
email: raphael.romary@univ-artois.fr.

Driss Belkhayat

A new approach for torque ripple reduction in a faulty Surface Permanent Magnet Synchronous Motor by inverse current injection

Keywords: Permanent magnet synchronous motor, torque ripple, vibrations, winding asymmetry gap thickness. h : mmf space harmonic rank

The aim of this paper is to present a new method to generate stator currents supplying a Surface Permanent Magnets Synchronous Motor (SPMSM) presenting an asymmetry of the stator windings. This asymmetry may be due to a lack of turns in one of the stator windings or to an inter-turns short circuit. An analytical model of the SPMSM is developed to calculate the current which allows minimizing the torque ripple generated by the asymmetry. This model is based on the combination of the space harmonics of the flux densities of stator and rotor for the generation of the torque. Our study leads to define a stator inverse current system able to compensate the harmonic torque component at the double of the supply frequency. In the experimental tests, several cases of supply were applied and the results confirmed those obtained by the analytical study essentially concerning the amplitude of the inverse current.

Introduction

The Permanent Magnet Synchronous Motor (SPMSM) is widely used in various fields such as industry, electric vehicles, aircraft, etc. This is mainly due to its high performance, high torque density, robust brushless construction, etc. [START_REF] Li | Disturbance rejection control method for permanent magnet synchronous motor speed-regulation system[END_REF][START_REF] Borghi | Reduction of the torque ripple in permanent magnet actuators by a multi-objective minimization technique[END_REF]. The tangential vibrations generated by the SPMSM and the iron losses in the rotor are factors that reduce its performance and efficiency and consequently its use [START_REF] Mohamed | Designed instantaneous-torque Ccntrol of direct-drive PMSM servo actuator with improved torque estimation and control characteristics[END_REF][START_REF] Pellegrino | Core losses and torque ripple in IPM machines: dedicated modeling and design tradeoff[END_REF][START_REF] Mademlis | Loss minimization in vector-controlled interior permanent-magnet synchronous motor drives[END_REF].

The occurrence of a fault such as a winding unbalance, a rotor demagnetization, an inter-turns shortcircuit or an eccentricity results in the increase of the tangential vibrations and also the losses [START_REF] Ebrahimi | Configuration impact on eccentricity fault detection in permanent magnet synchronous motors[END_REF][START_REF] Byong | Dynamic modeling and control for SPMSMs with internal turn short fault[END_REF][START_REF] Urrestyj | Shaft trajectory analysis in a partially demagnetized permanent-magnet synchronous motor[END_REF][START_REF] Brudny | Rotor design for reducing the switching magnetic noise of ac electrical machine variable-speed drives[END_REF]. Significant lack of reliability of the global system may occur if the power supply control does not take into account the fault [START_REF] Leboeuf | Inductance calculations in permanentmagnet motors under fault conditions[END_REF][START_REF] Romeral | Modeling of surface-mounted permanent magnet synchronous motors with stator winding interturn faults[END_REF]. This is especially true for applications such as electric vehicles and aerospace systems [START_REF] Xu | A modular control scheme for pmsm speed control with pulsating torque minimization[END_REF].

The reduction of tangential vibrations in a healthy synchronous machine has been studied in several researches and numerous strategies have been proposed in this field [START_REF] Ait-Gougam | Inverse modeling and pulsating torque minimization of salient pole non-sinusoidal synchronous machines[END_REF]. The best known strategy is to control the stator currents to compensate the torque ripple as indicated in [START_REF] Hasanien | Torque ripple minimization of permanent magnet synchronous motor using digital observer controller[END_REF][START_REF] Espanetc | Reduction of the torque ripples in brushless PM motors by optimization of the supplytheoretical method and experimental implementation[END_REF][START_REF] Hung | Design of currents to reduce torque ripple in brushless permanent magnet motors[END_REF]. These currents are determined by several methods. Some of these methods use the Fourier series decomposition of the electromotive force to obtain a limited number of current harmonics. Others use the finite element method to determine harmonic currents [START_REF] Favre | Permanent-magnet synchronous motors: a comprehensive approach to cogging torque suppression[END_REF][START_REF] Jia | Torque ripple suppression in flux-switching pm motor by harmonic current injection based on voltage space-vector modulation[END_REF][START_REF] Lee | Torque ripple reduction of interior permanent magnet synchronous motor using harmonic injected current[END_REF]. Other control strategies are based on the analytical modeling of the machine to obtain the harmonic currents by performing an optimization test [START_REF] Holtz | Identification and compensation of torque ripple in high-precision permanent magnet motor drives[END_REF].

Concerning the faulty SPMSM, numerous studies have been carried out for its modeling and control especially for multiphase motors. Some methods use a vector approach to calculate the optimal current reference [START_REF] Kestelyn | A Vectorial Approach for generation of optimal current references for multiphase permanent-magnet synchronous machines in real time[END_REF]. In this work the calculation of the currents is based on maintaining a smooth torque and minimal joule losses. The electromotive force vectors allow the determination of the current reference in real time. Other methods for three phase motor [START_REF] Byong | Dynamic modeling and control for SPMSMs with internal turn short fault[END_REF] are based on the dynamic modeling of the faulty machine using the mathematical equations of the flux. The separation of voltages and currents in direct and inverse components are also taken into account. The purpose of the control strategy is to cancel the inverse component using two current controllers. There is also a control method for a three phase motor with special stator winding architecture where all the phases are electrically isolated and able to support twice the rated current, so that the motor can provide the nominal torque even if only 2 phases are supplied [START_REF] Bennett | Fault-tolerant control architecture for an electrical actuator[END_REF]. In [START_REF] Cintron-Rivera | Mitigation of Turn-to-Turn Faults in Fault Tolerant Permanent Magnet Synchronous Motors[END_REF], it is proposed to change the supply in faulty conditions in order to mitigate the short circuit current. But none of these works studies the electrical motor with the objective to find the real origin of the fault and to give a method to estimate its magnitude, that can be used in the control system.

The aim of this work is to define a control strategy to compensate the effect of the stator winding asymmetry and therefore to minimize the torque ripple. The analytical method is based on the cancellation of the negative sequence of the air gap flux density. As reported in [START_REF] Byong | Dynamic modeling and control for SPMSMs with internal turn short fault[END_REF], the principle of many researches is to cancel the negative sequence current, but this method is not sufficient for the torque ripple. It will be shown that the faulty winding generates negative sequence of air gap flux density even when the motor is supplied by a positive sequence current. In this paper, the asymmetry will be generated, at first, by a lack of turns of approximately 11% of a stator phase winding.

This paper is organized as follows: in the first part, the used analytical approach is presented. Then, the effects giving rise to torque harmonics, especially those generated by the space harmonics are identified. The relationship between these harmonics and the torque is expressed in a condensed equation depending on the parameters of the SPMSM. In the second part, a comparative study of the torque harmonics generated in the two cases (healthy SPMSM and faulty SPMSM) is performed. The simulation results concerning the control law to minimize the torque ripple are presented in the next part. Finally, experimental results are provided to validate the effectiveness of the proposed supply strategy in case of faulty winding by a lack of turns.

SPMSM analytical modeling

According to previous works [START_REF] Toda | Rotor Eddy current loss in permanent magnet brushless machines[END_REF], stator and rotor flux densities include fundamental components which generate the average torque and space harmonics responsible for the iron losses and the torque ripple [START_REF] Dajaku | Air-gap flux density characteristics of salient pole synchronous permanent-magnet machines[END_REF][START_REF] Bianchi | Impact of MMF space harmonic on rotor losses in fractional-slot permanent-magnet machines[END_REF][START_REF] Ko | Characterization of noise and vibration sources in interior permanent-magnet brushless DC motors[END_REF]. In our analytical model a simplified method is presented to show the link between the torque harmonics and the flux density space harmonics relative to the stator and the rotor. Fig. 1.a shows the geometry of the studied machine. Here the stator yoke of the SPMSM contains 36 slots. The rotor yoke is smooth and has two pole pairs.

Stator flux density

In this study, the analytical modeling is based on the calculation of the torque using stator and rotor flux densities. The stator flux density is given by multiplying the stator magnetomotive force with the air gap permeance [START_REF] Gaussens | Analytical armature reaction field prediction in field-excited flux-switching machines using an exact relative permeance function[END_REF]. The permeance is proportional to the inverse of the air gap thickness and depends only on the shape of stator slots (Fig. 1.a). Adopting a simplified fictitious model for the slots (Fig. 1.b) resulting from the hypothesis that the rotor is smooth, the tooth has a rectangular shape and the slot depth is equal to one fifth of its width, the air gap permeance can be expressed as follows :

) α N k cos( P P P s s t s 1 k k 0 s s      (1) with )
         1 h s j s h s j e s j h ) β h(α sin Γ δ) (π i n ε (2) with s t s d s t s d h N / ) r h(1 ] /N ) r sin[h(1 Γ     
The main advantage of using the slot mmf s j ε is that the machine can be easily modeled in faulty case.

The total mmf generated by all the slots can be written as:

   s t N 1 j s j s ε ε (3)
A coil of a 4 pole stator winding is shown in Fig. 2. It is composed of two coils; one has a side inserted into slot 1 and the other side inserted into slot 2. The mmf generated by the strands inserted in slots 1 and 2, and the resulting mmf is shown in Fig. 3.a. A zoom of the mmf created by slot 1 is shown in Fig. 3.b. A linear evolution of mmf over the slot opening can be observed. Thus the stator flux density is given by:

s s s Pε ) (α b  (4)
ε P ) (α b  and ) α N k cos( P ε ) (α b s s t s 1 k k s s s k s s s     Therefore, it leads to: h )] (hβ hα t cos[ω Γ δ) (π 2 I n P ) (α b j s j s N 1 j 0) (h h h s j e 0 s s 0 s t               and                         s t s s s N 1 j 0) (h h k s s t s j s j s s s t s j s j s k h s j e s s k )] α N k ) (hβ hα t cos( ω ) α N k ) (hβ hα t [cos( ω P Γ δ) h(π 2 2 I n ) (α b
The stator flux density can be expressed with the following concise equation:

         0) (h h s h s s h s s ) hα t cos(ω B ) (α b ( 6
)
where B the magnitude and s h

 the phase of the stator flux density space harmonic, are calculated using numerical implementation. Each harmonic of rank h rotates at the angular speed of ω/h.

Rotor flux density

The rotor flux density of a synchronous machine can be expressed as: [START_REF] Zhu | Analytical prediction of the cogging torque in radial-field permanent magnet brushless motors[END_REF] 

     1,3,5 n r n s r n s r ) npθ cos(npα B ) (α b  (7)
where r n B is the magnitude of rotor flux density space harmonic.

Torque

The torque generated by a SPMSM [START_REF] Proca | Analytical model for permanent magnet motors with surface mounted magnets[END_REF] is of three types: the cogging torque, the reluctant torque, and the main electromagnetic torque produced by the interaction between the stator and rotor flux densities. The latter is the most important one. In this paper, only the electromagnetic torque is considered. It is given, using the magnetic co-energy Wmag, as:

  mag W θ C    It comes:             2π 0 s r s 0 dα b b μ V θ C ( 8
)
where V is the total volume of the air gap. Considering Equ. ( 6) and ( 7), the electromagnetic torque C becomes:

                                π s n,h r n s h r n s h ) t ( ) t ( θ C 2 0 s s s h r n 0 dα np θ np) α (h cos np θ np) α (h cos B B 2 1 μ V      
For this expression the integral is zero excepted for h=np and h=-np. Consequently, the torque can be divided into two terms according to the two conditions: -h+np=0 and -h-np=0. So the electromagnetic torque can be written as:

0 = np + h 0 = np + -h C C C   with                             5 3 1 0 s h r n 0 0 npθ cos B B μ Vπ , , n h ) (h h r n s h -h+np= ) t ( θ C    (a) (b)                             5 3 1 0 s h r n 0 0 npθ cos B B μ Vπ θ , , n h ) (h h r n s h h+np= ) t ( C   
At steady state operation, the rotor position  is:

0 θ ωt/p θ  
where 0 θ is the initial rotor position and the above torque equations become:

               5 3 1 0 0 0 0 1 sin , , n h ) (h h r n s h s h r n -h+np= ) npθ t n) (( B nB μ Vpπ C    (9) and                5 3 1 0 0 0 0 1 sin , , n h ) (h h r n s h s h r n h+np= ) npθ t n) (( B nB μ Vππ C    (10)

Simulation of the stator flux density and torque ripple

To evaluate the impact of spatial harmonics on torque ripple, the theoretical equations of the stator and rotor flux densities for SPMSM, presented in Fig. 1, and also its torque are numerically implemented. Here, a SPMSM with two pole pairs (p=2) will be considered. Motor parameters and harmonics of the rotor flux density are given in Tables A.1 and A.2 (Appendix A). In practice, the magnitudes of rotor flux density harmonics are determined by an open-circuit test in generator mode. The measured line-to-neutral back force electromotive force (emf) is decomposed in Fourier series, and then the rotor flux density harmonics are calculated according to the method used in [START_REF] Simon-Sempere | Spatial filtering: a tool for selective harmonics elimination in the design of permanent -magnet synchronous motors[END_REF]. Some of rotor flux density harmonics are attenuated by the distribution of the stator winding and others are cancelled. Therefore, these harmonics will not appear in the back emf. In this study, it is sufficient to take into account the harmonics that produce the emf and are also responsible for torque ripples [START_REF] Simon-Sempere | Spatial filtering: a tool for selective harmonics elimination in the design of permanent -magnet synchronous motors[END_REF]. The calculation of the torque will be obtained by Equs. ( 9) and ( 10), considering the motor running at no load.

Simulation results in a healthy case

The space harmonics of the stator flux density in healthy case are presented in Fig. 4. In this case it is assumed that the SPMSM is supplied by a by three phase current system. This supply system is a direct balanced one which provides sine currents with Id=1.7A rms value at 50Hz frequency. In addition to the fundamental, which corresponds to the rank h = p =2, there are space harmonics caused by the non-sine distribution of the winding and by the slots. It can be noticed that the ranks of the harmonics are distributed with respect to h=p(6k+1) (k varies from -∞ to +∞). In Fig. 4, these ranks correspond to h=-10 and h=14. This case corresponds to mode 1 in Table 1.

Simulations results in faulty case

The considered fault model is shown in Fig. 5 where a part of the stator winding is short circuited. This approach allows one to consider both stator inter-turn short-circuit fault and lack of turn fault: if

0 I 0, I f a1  
there is an inter-turn short circuit fault, and if

0 I 0, I f a1  
there is a lack of turns fault. Therefore, both faults can be modeled through one model because the torque delivered by the machine depends only on Ia1. To simplify the study, only the lack of turns will be analyzed below, with two different situations: the SPMSM is supplied by balanced and by unbalanced currents Case 1: balanced current system supplying the faulty SPMSM For this case, Fig. 6.a shows the space harmonics of the stator flux density where a lack of turns in a stator winding is practically obtained by removing the two thirds of an elementary section in one winding (Fig. 10), corresponding to 5.5% of one phase winding. The machine is still supplied by a sine direct balanced three phased current system of magnitude Id=1.7A rms and 50Hz frequency. It can be noticed that many space flux density harmonics appear, even ones non multiple of p, contrary to a healthy case. The amplitude of stator flux density space harmonic at h=-2 is The torque frequency spectrum in faulty case computed with Equ. ( 9) and ( 10) is shown in Fig. 6.b. The harmonic component at 100 Hz corresponding to -h-np = 0 is largely provided by the stator space harmonics flux density at h = -2 and by the rotor space harmonics flux density at n=1. The calculated magnitude of torque harmonic at 100Hz is 0.5Nm. It can be also observed very low magnitude for harmonic at 200Hz, 300Hz, 400Hz generated by combination of rotor harmonic flux density with stator ones. As the amplitudes of flux density harmonics are low, the resulting torque harmonic will have a very low magnitude. The presence of the torque harmonics is baneful for motor because they increase its vibrations and noise [START_REF] Sun | Effect of pole and slot combination on noise and vibration in permanent magnet synchronous motor[END_REF]. This case corresponds to mode 3 presented in Table 1.

Case 2: unbalanced current system supplying the faulty SPMSM:

Another tested faulty case is presented in Fig. 7, where the faulty SPMSM is supplied by an unbalanced current system. Fig. 7.a shows the increase of the amplitude of the flux density space harmonics and Fig. 7.b the torque harmonics. In this case, space harmonic of stator flux density at h=-2 is

T 048 . 0 B s 2 
 and the magnitude of the torque harmonic at 100 Hz is 1.2 Nm, are greater compared to the results presented in Fig. 6.b. The unbalanced current system is obtained by supplying the SPMSM with voltage source without current regulation. In this case, the lack of turns presented in Phase A (Fig. 10) leads to different current values in each phase. These values are reported in mode 2 (Table 1). 4 Control procedure for minimizing torque ripples

In order to cancel the torque ripple at 100 Hz frequency, the control is carried out by adding an inverse three phase current system with Ii rms value to the initial direct one. This inverse system will mainly create a space harmonic component of rank h = -2, able to compensate the one generated by the asymmetry.

The strategy for calculation of stator currents able to cancel the space harmonic of the stator flux density at rank h = -2 for a lack of turns fault leads to a relationship between the direct current Id and the inverse current Ii. The method starts with the knowledge of the currents in the wires in each slot, then the additional inverse system is computed in order to cancel the mmf component at h=-p=-2. The details of the computation leading to the inverse current characteristics are given in Appendix B. Let's assume that the faulty slots are the N°3 and 10, and that 2/3 of the wires in this slot are missing, then Equ. B.7 has to be considered with p=2, K=2/3 and Ia1=0, leading to: and for Id =1.7A rms and Ii=0.064A rms (mode 4 in Table 1). The injection of the inverse current calculated previously allows the reduction of the harmonic at rank h=-2 of stator flux density as shown in Fig. 8.a.

In Fig. 8.b the torque spectrum after injection of the inverse current is presented. It can be seen that there is a strong decrease of the 100Hz harmonic torque, whereas the other harmonics still have low values. Torque harmonic at 100Hz is 1.2Nm

Experimental results

Experiments are performed on a laboratory test bench. A block diagram and a picture of the test bench are presented in Fig. 9. The used SPMSM is the same machine studied in the theoretical analysis with the following electrical characteristics: 4.4 kW rated power, 1500 rpm rated speed, 4-pole. The stator windings are concentric, with 3 elementary sections per pole per phase that can be used to generate faults such as a lack of turns or a short-circuit of a part of an elementary section (Fig. 10). The machine is supplied by a power amplifier (Model 390-ASX -Pacific Power Source), controlled by a PC such that magnitudes and phase angles of the voltages can be adjusted. Supply currents can be adjusted indirectly by tuning these variables. The torque is not directly measured but the presence of torque harmonics is evaluated through the tangential vibrations they generate. An accelerometer with 0.01mV/mms -2 sensitivity is suitably placed in order to measure the tangential vibrations of the machine. It is connected to a frequency analyzer (Brüel&Kjaer 3560).

The aim of the experiments is to test the impact of the new reference current on the reduction of the tangential vibrations at 100 Hz generated by the faulty SPMSM. The considered fault is, according to the theoretical analysis, a lack of turns of 2/3 from the elementary section located in phase A (Fig. 10). Voltages, currents, and tangential vibrations are recorded for 4 operating modes of the SPMSM, as presented in the simulation:

-mode 1: healthy SPMSM supplied by a balanced voltage and current systems.

-mode 2: faulty SPMSM supplied by a balanced voltage and an unbalanced amplitude currents system.

-mode 3: faulty SPMSM supplied by balanced currents system -mode 4: faulty SPMSM supplied by unbalanced currents system, minimizing the 100Hz harmonic torque component. Demagnetization and eccentricity faults produce vibration at [START_REF] Ebrahimi | Configuration impact on eccentricity fault detection in permanent magnet synchronous motors[END_REF], [START_REF] Ebrahimi | Advanced eccentricity fault recognition in permanent magnet synchronous motors using stator current signature analysis[END_REF] and [START_REF] Urrestyj | Shaft trajectory analysis in a partially demagnetized permanent-magnet synchronous motor[END_REF]; this assumption can justify the presence of vibration spectral lines at 25 Hz, 50 Hz, and 75 Hz.

) 1 ( 2 p k f    .... 3 , 2 , 1  k as reported in
When a fault occurs, three cases are analyzed. The first one considers the faulty SPMSM supplied by a balanced voltage system. This case leads to unbalanced currents in the motor phases (mode 2) as shown in Fig. 13. In the winding with lack of turns (in phase A), it can be observed that the amplitude of a I is greater than the amplitudes of c b I I , . In this case, the amplitude of tangential vibrations at 50 Hz and 100 Hz (Fig. 14) become respectively 23.8 mV and 8.94 mV, and are greater than the ones relative to the healthy machine shown in Fig. 12. In the second faulty case, supply voltages are adjusted in order to provide balanced currents in the three phases (mode 3) of the SPMSM (Fig. 15).The results, regarding the tangential vibration spectrum, are presented in Fig. 16. It can be seen that the harmonic amplitude at 100Hz is more reduced (3.84 mV) compared to the value relative to mode 2 (Fig. 14). The third analyzed case corresponds to mode 4 (Fig. 17) where the phase and the amplitude of the currents are adjusted in order to reduce the tangential vibrations. For that, Ia, Ib and Ic are computed from the inverse current Ii and the direct current Id using the following transform. Actually, Id is imposed and the phase and amplitude of Ii are adjusted in order to minimize the 100Hz tangential vibration harmonic. The frequency spectrum of tangential vibrations measured by the accelerometer is presented in Fig. 18. The currents become unbalanced and it can be seen that the amplitude of the harmonic at 100Hz is more reduced (3.19 mV) than the amplitude relative to the mode 2 (Fig. 14 -8.94mV) and the value obtained in the mode 3 (Fig. 16 -3.84mV). Computed and measured values of the currents (amplitude, phase), the 100Hz harmonics torque component and the 100Hz tangential vibration are reported in Table 1. In order to compute the direct and inverse current from measurements, Equ. ( 13) and Equ. ( 14) are used :

) I a I a I ( 3 1 I c 2 b a d    ( 13
) ) I a I a I ( 3 1 I c b 2 a i    (14)
It can be noticed a good concordance between simulations results in mode 4 when an inverse current is injected to decrease the amplitude of harmonic at 100 Hz. This case is denoted by "inj" parameter in Table 1.

Conclusion

In this paper, a method for analyzing the stator flux density in faulty conditions has been presented. The role of the space harmonics in torque harmonics generation is brought to the fore. As far as stator winding asymmetry is considered, a method for reducing the torque harmonic at 100 Hz frequency, based on the reduction of the stator flux density harmonic of rank h= -2, has been studied analytically. Actually, the torque harmonic at 100 Hz is generated by an inverse current system or by a stator winding asymmetry. Each one creates a significant harmonic flux density of rank h = -p, and the approach presented in this paper aims at using the inverse stator current to compensate the flux density harmonic h = -p generated by the winding asymmetry. The case of stator lack of turns is illustrated in the paper as stator asymmetry but actually the computation can also be applied in the case of a stator inter-turns short circuit. The experimental results confirm the analytical study and shows that the tangential vibrations caused by torque ripples can be reduced by unbalancing the current system supplying the faulty SPMSM.

APPENDIX B

The strategy for calculation of stator currents consists in cancelling the space harmonic of stator mmf of rank h = -p in the case of a stator fault in one phase winding. The computation of a mmf space harmonic component is done by considering the currents in each slot. The following developments consider p pole pair machine with an inter-turn short circuit fault that occurs in slots j1 and j2. K is the ratio of faulty windings in the faulty slots, Ia1 is the rms value of the current in the faulty turns.

Let us consider the mmf s ε can be written with a Fourier series as follows:

               1 h s h , j 1 h s j s h s j e s j h ) β h(α sin Γ δ) (π i n ε
The analytical computation is performed using the complex notation of the mmf components when the SPMSM is assumed to be supplied with sine currents:

) t sin( I 2 i j s j s j     Then, the complex quantity s h , j  is defined such that              ) h t ( i s h , j s h , j s e
And the rank h of mmf harmonic generated by all the slots can be expressed as :

                       s t s t s N 1 j s h , j ) h t ( i N 1 j s h , j s h e
Case of inter-turn short circuit fault in stator winding:

The stator winding mmf at h=-p is computed in two cases:

 healthy stator winding supplied by direct current of d I rms value, in this case the mmf harmonic at h=p is null, because in healthy case only the ranks h=p(6k+1) exist. For the stator winding supplied by inverse current of i I rms value, it is supposed that the inverse current does not flow through the fault resistance rf, the stator winding mmf at h=-p can be expressed as follows:

                         

Fig. 1 .

 1 Fig.1. Model of the considered machine (a) Geometry with N = 36 and p=2, (b) simplified model adopted for stator slots.

(

  The point M in the air gap can be identified by its angular abscissa s α related to the stator referential s d and also its angular abscissa r α related to the rotor referential r d . So the angle θ related to the rotor position is Fig.1.b). The magnetomotive force generated by n conductors located in the slot j and flowed through by a

Fig. 2 .

 2 Fig.2. Coil configuration in the stator yoke.

Fig. 3 .

 3 Fig.3. Evolution of the magnetomotive force created by: (a) the conductors into two slots and the resulting component. (b) the conductors housed in slot 1.

Fig. 4 .

 4 Fig.4. Representation of space harmonic of stator flux density in healthy case

Fig. 5 .

 5 Fig.5. Faulty SPMSM model.

Fig. 6 .

 6 Fig.6. Representation of :(a) space harmonic of stator flux density (b) frequency spectrum of the torque, for the faulty SPMSM supplied by balanced current system.

Fig. 7 .

 7 Fig.7. Representation of: (a) space harmonic of stator flux density, (b) frequency spectrum of the torque for the faulty SPMSM supplied by unbalanced current system.

Fig. 8 .

 8 Fig.8. Representation of: (a) space harmonic of stator flux density (b) frequency spectrum of the torque in faulty case after injection of inverse current.

Fig. 9 .

 9 Fig.9. Experimental test bench: (a) block diagram (b) picture of the laboratory test bench.

Fig. 10 .

 10 Fig.10. Stator winding In mode 1, the recorded voltages of each phase ( c b a V , V , V ) and current ( c b a I I I , , ) supplying the SPMSM are shown in Fig.11. It can be noticed that the corresponding three phase systems are balanced. All measured values are reported in Table1. The torque harmonics of the healthy SPMSM are evaluated by measuring the tangential vibrations. The spectrum measured is given in Fig.12. The cursor gives 2.97mV amplitude for the 100Hz

Fig. 11 .

 11 Fig.11. Voltages and currents delivered by balanced system supplying the healthy SPMSM (mode 1).

Fig. 12 .

 12 Fig.12. Spectrum of tangential vibrations signal generated by the healthy SPMSM supplied by balanced current system (mode 1), 0.01mV/mms -2 .

Fig. 13 .

 13 Fig.13. Unbalanced currents delivered by balanced voltage system supplying the faulty SPMSM (mode 2).

Fig. 14 .

 14 Fig.14. Spectrum of tangential vibrations signal generated by the faulty SPMSM supplied by unbalanced currents system (mode 2) 0.01mV/mms -2 .

Fig. 15 .

 15 Fig.15. Balanced currents delivered by unbalanced system in voltage amplitude supplying the faulty SPMSM (mode 3).

Fig. 16 .

 16 Fig.16. Spectrum of tangential vibrations signal generated by the faulty SPMSM supplied by balanced system in current amplitude(mode 3).

Fig. 17 .

 17 Fig.17. Voltages and currents delivered by unbalanced system in voltage amplitude and phase supplying the faulty SPMSM (mode 4).

Fig. 18 .

 18 Fig.18. Spectrum of tangential vibrations signal generated by the faulty SPMSM supplied by unbalanced system in voltage amplitude and phase (mode 4).

j ε generated by

  Fig. B.1 -mmf generated by the wires in one slot



  faulty stator winding supplied by direct current of d I rms value. In this case Kn e wires of the slots j1 an j2 are flowed through by a current of Ia1 magnitude and the other wires of the both slots ((1-K)n e wires) are flowed through by the line current of Id magnitude. :

3 )

 3 To cancel the harmonic h = -p, the mmf generated by the inverse and direct current must satisfy the following equation:

  simplification, the relationship between the direct current and the inverse current used to compensate the harmonic of rank h=-p is given by:

Table 1 .

 1 Summary table with experimental and simulation results for healthy and faulty case of the SPMSM supplied by balanced (b) and unbalanced (u) currents. Vibration variation obtained by injection of inverse current (inj).

						Experimental results				Simulation results
		Case		Healthy			Faulty			Healthy		Faulty
							u		b	inj			u	b	inj
		Mode		1		2		3	4		1	2	3	4
	Torque harmonic									0	1.2	0.5	0.0014
	at 100 Hz [Nm]
	Amplitude of vibration	12.8		23.8		9.21	8.03
	harmonic at 50 Hz
	[mv]
	Amplitude of vibration	2.97		8.94		3.83	3.19
	harmonic at 100 Hz
	[mv]
	Ia [A]			1.69		2.43		1.70	1.86	1.7	2.43	1.7	1.76
	Ib [A]			1.70		1.73		1.70	1.84	1.7	1.73	1.7	1.66
	Ic [A]			1.71		1.89		1.70	1.84	1.7	1.893	1.7	1.66
	φa Phase A			0°		0°		0°	0°		0°	0°	0°	0°
	φbPhase B			240°		240°		241.21°	248.66°	240°	240°	240°	239°
	φc Phase C			120°		120°		122.2°	120.89°	120°	120°	120°	121°
	Id				0.0044i 1.70 +		0.0044i 1.9460 +		0.0340i 1.6994 +	0.1019i 1.8395 +	1.7	0.0044i 1.9460 +	1.7	1.7
	Ii				0.0022i 0.0038 -	0.0022i 0.2498 -		0.0166i 0.0126 -	0.0513i -0.0732 -	0	0.0022i 0.2498 -	0	0.0630
	I	d			390.65		7.50		81.37	20.61		7.50	26.57
	I	i
								APPENDIX A
					Table.A.1. SPMSM parameter simulation
	Rotor flux density space harmonic magnitudes (Tesla)
	r 1 B		B	r 3	B	r 5		B	r 7	B	r 9	r 11 B		r 13 B	B	r 15
	0.5711	0.0080	0.0966	0.0668	0.0030	0.0350	0.0308	0.0026
					Table.A.2. Rotor flux density space harmonic
		SPMSM parameters
		p	n	N Ω (rad/s)	K		l (cm) l (cm)	p	e(mm)
		2 36 36 157		1/3		0.27	0.7368	l /5 0.5


Sustainable and degradable plastics

Sophie M. Guillaume Plastics developed from renewable resources and able to be recycled are highly environmentally desirable alternatives to current petroleum-based non-degradable polymers. Now, an effective and robust industrially relevant strategy towards high performance biomass-derived degradable poly(thiobutyrolactone)s has been developed.

While plastics are omnipresent in our daily life, one current major objective in polymer science is to tackle the production of plastic waste -through both the synthesis of high performance polymers derived from renewable non-edible resources or wastes rather than from fossil feedstocks, and the design of polymers with improved end-of-life options enabling a more circular economy. [START_REF] Abel | Chemically recyclable thermoplastics from reversible-deactivation polymerization of cyclic acetals[END_REF][START_REF] Coates | Chemical recycling to monomer for an ideal, circular polymer economy[END_REF] New generations of eco-friendly polymer materials thus ideally have to be sustainable and recyclable while remaining economically viable. In this regard, polymers that are degradable back into their original monomer, or into other smaller valuable molecules that can be subsequently used to synthesize new materials, are highly desirable.

Sulfur-containing functional polymer materials have recently attracted increasing interest thanks to their valuable properties. Typically, polythioesters -in comparison to their oxoester analogues, polyesters -exhibit significantly enhanced thermal and mechanical properties as well as biological and chemical resistance, degradability and/or recyclability, thereby offering multi-faceted applications. [START_REF] Shi | High-performance pan-tactic polythioesters with intrinsic crystallinity and chemical recyclability[END_REF][START_REF] Xiong | Geminal dimethyl substitution enables controlled polymerization of penicillamine-derived -thiolactones and reversed depolymerization[END_REF] While the thiocarbonyl moiety has been extensively exploited in radical ring-opening polymerization (ROP) to insert a sulfur-based functional group along the polymer backbone, it is only recently that cyclic monomers containing thionoester functionality ((C=S)O) -that is, thionolactones -have been explored for their ability to afford degradable (thanks to thioester functions) polymers by radical ROP. [START_REF] Plummer | radical polymerization: an interesting tool to insert weak bonds into poly(vinyl esters)[END_REF][START_REF] Bingham | [END_REF][START_REF] Pesenti | 100th anniversary of macromolecular science viewpoint: degradable polymers from radical ring-opening polymerization: latest advances, new directions, and ongoing challenges[END_REF][START_REF] Smith | Radical approach to thioester-containing polymers[END_REF] Miao Hong and colleagues have now synthesized, for the first time, sustainable and degradable poly(-thiobutyrolactone)s by the irreversible ring-opening polymerization (IROP) of challenging five-membered thionolactone monomers. This innovation relies on an effective and robust sulfur/oxygen (S/O) isomerization-driven IROP strategy that converts these non-strained cyclic -thionobutyrolactones -often referred to as "non-polymerizable" -into high-molar-mass and degradable polythiolactones -containing thioester functionality ((C=O)S) -, at industrially relevant temperatures of 80-100 °C (Figure 1). The primary feature of -butyrolactones is that their ROP is generally thermodynamically forbidden at ambient conditions due to insufficient ring-strain in the five-membered cycle of the monomer to drive the polymerization. One approach to overcome this limitation is to perform the ROP at a temperature lower than the ceiling temperature -that is, below the temperature at which the equilibrium between polymerization and depolymerization is reached. However, the usually negative ceiling temperature of unstrained five-membered lactones would require performing the ROP below ambient temperature that is not ideally compatible with industrial implementation.

Starting from succinic, itaconic and levulinic acids that are among the US Department Of Energy top 10 value-added biomass-derived compounds, Hong and co-workers prepared a series of sustainable five-membered (-, -, or -methyl-substituted) -thionobutyrolactones in high yields (80-92%) on multi-gram scales (ca. 20 g) via the one-step sulfurization of the corresponding fivemembered butyrolactones using Lawesson's reagent. The subsequent controlled ROP of the γthionobutyrolactones -catalyzed by the commercially available phosphazene strong organic base t Bu-P4 in the presence of an alcohol initiator (Ph2CHOH) -typically proceeds in toluene at 80 °C within a few hours (15 min at 100 °C) affording poly(thiobutyrolactone)s with a high selectivity (up to 97%). This is in sharp contrast to the commonly observed non-polymerizability of such non-strained five-membered rings at ambient conditions, and to the organocatalytic ROP of larger thionolactones which affords polythionolactones without S/O scrambling. [START_REF] Kalana | Organocatalytic ring-opening polymerization of thionolactones: anything O can do, S can do better[END_REF] Remarkably, the recovered polythioesters display absolute number-average molar mass (Mn,SEC) up to 178.5 kg/mol with relatively narrow dispersity (Đ = Mw/Mn < 1.6), while previously reported values, following another approach, did not exceed 6.3 kg/mol (50% yield).

Further mechanistic insights were gained from computational density functional theory (DFT) studies. In addition to confirming the exclusive cleavage of the oxygenalkyl bond of the thionobutyrolactone rather than of the more commonly opened oxygenacyl bond, in silico evaluation of the energy profile of the ROP evidenced the formation of the thermodynamically advantageous S/O isomerization product, which provides an overall thermodynamic driving force for the polymerization of non-strained -thionobutyrolactones at room temperature or above. Furthermore, DFT calculations clearly indicated that the polymerization is selectively initiated via a kinetically favorable proton-transfer pathway facilitated by Ph2CHOH mediated deprotonation, while Ph2CHOH also effectively suppresses back-biting side reactions during propagation by acting as a Hbonding donor to stabilize the -COS -propagation species together with [ t Bu-P4H]  , thereby accounting for the controlled polymerization.

The typical polythiolactone obtained from -thionobutyrolactone (Mn,SEC = 162.6 kg/mol) revealed a semicrystalline thermoplastic (glass-transition and crystallisation temperatures of Tg ~ 49 °C and Tc ~ 74 °C, respectively) with a high melting (Tm ~ 100 °C) and degradation (Td 5% ~ 230 °C) temperature, and a hard, rigid and hydrophilic material (Young's modulus E = 296.5 MPa, yield strength σy = 15.7 MPa, tensile strength σb = 29.8 MPa, elongation at break εB = 412.5%, and static contact angle  = 78.4°). Rewardingly, the polyester thus showcases high performances with key thermal and mechanical properties that are advantageously competitive to commercial petroleum-based low-density hydrophobic polyethylene (so called LDPE; Tm ~ 105 °C, E ~ 280 MPa, σy ~ 8 MPa, σb ~ 10 MPa, εB ~ 200%, ~ 102°) that is commonly used for flexible bottles, as packaging or as an insulator. Interestingly, the commercially available 1,5,7-triazabicyclo[4.4.0]dec-5-ene (TBD) organocatalyst ( 0.2 mol%) efficiently prompts the ultrafast degradation (within 15 s) of this poly(thiobutyrolactone) sample at room temperature, quantitatively converting it into the parent thiobutyrolactone.

Hong and coworkers have thus enriched the polythioesters domain by demonstrating the irreversible ROP of -thionobutyrolactones as being thermodynamically driven by the S/O isomerization instead of ring strain relief. Catalysis played a seminal role in this achievement. The judicious choice of the highly active t Bu-P4/Ph2CHOH catalytic system in which the alcohol favorably plays an essential dual role, combined with a beneficial high operating temperature of 80 °C, enabled the first successful straightforward rapid and selective ROP of these five-membered cyclic thionoester-based monomers. The external organocatalyst-triggered ultra-rapid degradation of the poly(-thiobutyrolactone) into its corresponding cyclic thioester further bestows a valuable end-oflife to such polymers. Starting from monomers derived from renewable resources, the implementation of this remarkably simple and effective out-of-the-box polymerization strategy towards the preparation of robust yet easily degradable polythioesters, holds great promise for the expansion, within a circular economy model, of the next generation of eco-friendly polymer materials with a wide range of notable properties and potential applications.

Figure 1 .

 1 Figure 1. Synthesis and subsequent S/O isomerization-driven irreversible ring-opening polymerization (IROP) of -thionobutyrolactones (R = H, Me) and degradation of poly(-thiobutyrolactone) (R = H).γ-Thionobutyrolactones can be prepared by sulfurization of the corresponding biomass-derived γ-butyrolactones. Poly(γ-thiobutyrolactone) -a potential substitute for commercial petroleum-based low-density polyethylene -can be degraded to γ-thiobutyrolactone in the presence of TBD.

Sophie M. Guillaume is at the CNRS, University of Rennes, Institut des Sciences Chimiques de Rennes, UMR 6226, F-35042 Rennes, France. e-mail: sophie.guillaume@univ-rennes1.fr

The author declares no competing interests