Liang Ma
email: liang.ma@irccyn.ec-nantes.fr

Damien Chablat

Fouad Bennis

Wei Zhang

Dynamic Muscle Fatigue Evaluation in Virtual Working Environment

Keywords: Muscle fatigue, muscle fatigue index, muscle fatigue model, virtual reality, virtual environment

Musculoskeletal disorder (MSD) is one of the major health problems in mechanical work especially in manual handling jobs. Muscle fatigue is believed to be the main reason for MSD. Posture analysis techniques have been used to expose MSD risks of the work, but most of the conventional methods are only suitable for static posture analysis. Meanwhile the subjective influences from the inspectors can result differences in the risk assessment. Another disadvantage is that the evaluation has to be taken place in the workshop, so it is impossible to avoid some design defects before data collection in the field environment and it is time consuming. In order to enhance the efficiency of ergonomic MSD risk evaluation and avoid subjective influences, we develop a new muscle fatigue model and a new fatigue index to evaluate the human muscle fatigue during manual handling jobs in this paper. Our new fatigue model is closely related to the muscle load during working procedure so that it can be used to evaluate the dynamic working process. This muscle fatigue model is mathematically validated and it is to be further experimental validated and integrated into a virtual working environment to evaluate the muscle fatigue and predict the MSD risks quickly and objectively.

Relevance to industry

Muscle fatigue is one of the main reasons causing MSDs in industry, especially for mechanical work. Correct evaluation of muscle fatigue is necessary to determine work-rest regimens and reduce the risks of MSD.

Introduction

Musculoskeletal disorder is defined as injuries and disorders to muscles, nerves, tendons, ligaments, joints, cartilage and spinal discs and it does not include injuries resulting from slips, trips, falls or similar accidents (Maier and tional disability in muscles and other tissues of human body. Hence, it becomes an important mission for ergonomists to find an efficient method to evaluate the muscle fatigue and further more to decrease MSD risks caused by muscle fatigue.

There are various tools available for ergonomists to evaluate the MSD risks, most of them are listed and compared in paper [START_REF] Li | Current techniques for assessing physical exposure to work-related musculoskeletal risks, with emphasis on posture-based methods[END_REF]. For general posture analysis, Posturegram, Ovako Working Posture Analyzing System (OWAS), posture targeting and Quick Exposure Check (QEC) were developed. Further more, some special tools are designed for specified parts of human body. For example, Rapid Upper Limb Assessment (RULA) is designed for assessing the severity of postural loading and is particularly applicable for sedentary jobs. The similar systems include HAMA, PLIBEL and so on [START_REF] Stanton | Handbook of Human Factors and Ergonomics Methods[END_REF].

In these methods, several "risk factors" of mechanical jobs are taken into consideration, like physical work load factors, psychosocial stressors and individual factors. The level of exposure to physical work load can be evaluated with respect to intensity (or magnitude), repetitiveness and duration [START_REF] Li | Current techniques for assessing physical exposure to work-related musculoskeletal risks, with emphasis on posture-based methods[END_REF]. Using these tools, MSD risks can be effectively reduced, but there are still several limitations. At first, even just for lifting job, five prevailing tools (NIOSH lifting index, ACGIH TLV, 3DSSPP, WA L & I, Snook) were developed. The evaluation results of them for a same task were different, and sometimes even contradictory (J. Russell et al., 2007). Second, most of the traditional methods have to be carried out in field environment, there is no immediate result from the observation and it is time consuming for the repetition. Further more, there are different evaluation results from different subjects even using a same method [START_REF] Lamkull | The influence of virtual human model appearance on visual ergonomics posture evaluation[END_REF]. At last,only posture information and limited working conditions are considered in these methods, and thus they are not able to estimate the MSD risks into detailed analysis and can not further enhance the safety of the work. The most significant problem is that muscle fatigue prediction and assessment tool is still in blank in conventional methods.

In order to evaluate the human work objectively and quickly, virtual human techniques have been developed to facilitate the ergonomic evaluation. For example, Jack [START_REF] Badler | Simulating Humans[END_REF], ErgoMan [START_REF] Schaub | A computer-aided tool for ergonomic workplace design and preventive health care[END_REF], 3DSSPP [START_REF] Chaffin | A computerized biomechanical modeldevelopment of and use in studying gross body actions[END_REF], Santos (VSR Research Group, 2004;[START_REF] Vignes | Modeling muscle fatigue in digital humans[END_REF] and so on, these human modeling tools are used in field of automotive, military, aerospace and industrial engineering. These human modeling tools are mainly used for visualization to provide information about body posture, reachability and field of view and so on. In paper [START_REF] Jayaram | Introducing quantitative analysis methods into virtual environments for real-time and continuous ergonomic evaluations[END_REF], a method to link virtual environment (Jack) and quantitative ergonomic analysis tools (RULA) in real time for occupational ergonomics is presented, and it allows that ergonomic evaluation can be carried out in real time in their prototype system. But until today, these is still no fatigue index available in these virtual human tools for dynamic working process. It is necessary to develop the muscle fatigue model and then integrate it into the virtual human softwares to evaluate the muscle fatigue and analyze the mechanical work into details.

For objectively predicting muscle fatigue, several muscle fatigue models and fatigue index have been proposed in publications. In a series of publications [START_REF] Wexler | A mathematical model that predicts skeletal muscle force[END_REF]Ding et al., 2000aDing et al., ,b, 2002b[START_REF] Ding | Mathematical models for fatigue minimization during functional electrical stimulation[END_REF], Wexler and his colleges have proposed a new muscle fatigue model based on Ca 2+ cross-bridge mechanism and verified the model with stimulation experiments, but it is mainly based on physiological mechanism and it is too complex for ergonomic application. Further more, there are only parameters available for quadriceps. This model was integrated into VSR system for several muscle fatigue simulations with lots of limitations [START_REF] Vignes | Modeling muscle fatigue in digital humans[END_REF]. Taku [START_REF] Komura | Calculation and visualization of the dynamic ability of the human body[END_REF], 2000) have employed a muscle fatigue model based on force-pH relationship [START_REF] Giat | A musculotendon model of the fatigue profiles of paralyzed quadriceps muscle under fes[END_REF] in computer graphics to visualize the muscle fatigue, but it just evaluated the mus-cle fatigue at a time instant and cannot evaluate the overall muscle fatigue of the working processes. Meanwhile in this pH muscle fatigue model, although the force generation capacity can be mathematically analyzed, the influences from the muscle forces are not considered enough. Rodríguez proposes a half-joint fatigue model [START_REF] Rodríguez | A joint-level model of fatigue for the postural control of virtual humans[END_REF](Rodríguez et al., , 2003a,b),b), more exactly a fatigue index, based on mechanical properties of muscle groups. The fatigue is quantified by accumulation of the proportion of actual holding time over the predicted maximum holding time. With this halfjoint model, it can adjust human posture during a working process dynamically, but it cannot predict individual muscle fatigue due to its half-joint principle. The maximum endurance equation of this model was from static posture analysis and it is mainly suitable for evaluating static postures. In [START_REF] Liu | A dynamical model of muscle activation, fatigue, and recovery[END_REF], a dynamic muscle model is proposed based on motor units principles, but there are just parameters available under maximum voluntary contraction situation which is rare in manual handling work.

In this paper, we are going to propose a dynamic muscle fatigue model and a fatigue index with consideration of muscle load history and personal factors. This fatigue model is going to be verified with comparison of the previous static endurance time models and several dynamic muscle fatigue models. At last, we are going to propose the experimental validation procedure in a virtual environment framework.

Dynamic Muscle Fatigue Model

We believe that the fatigue of muscle is closely related to the external load of the muscle with the time and the strength of the muscle. These factors can represent the physical risk factors mentioned before: the external load the muscle with the time can include the intensity (or magnitude), repetitiveness and duration; and the muscle strength can be determined individually. Thus, the muscle force history and maximum voluntary contraction (MVC) are taken to construct our muscle fatigue model. MVC is defined as "the force generated with feedback and encouragement, when the subject believes it is a maximal effort" [START_REF] Vollestad | Measurement of human muscle fatigue[END_REF]. The effect of maximum voluntary contraction on endurance time is often used in ergonomic applications to define the worker capabilities [START_REF] Garg | The effect of maximum voluntary contraction on endurance times for the shoulder girdle[END_REF]. Here, we are going to use MVC to describe the maximum force generation capacity of an individual muscle.

Our fatigue index is trying to describe the human feelings (subjective evaluation) about the fatigue and it is expected to have a close correlation between subjective evaluation and objective evaluation about muscle fatigue during mechanical work.

For ergonomic evaluation, there are several self-report methods to assess the physical load, body discomfort or work stress. These subjective assessments of body strain and discomfort have been the most frequently used form due to the ease of use and apparent face validity. But subjec-tive ratings are prone to many influences. This kind of approach has too low validity and reliability. But ergonomists have to concentrate themselves on the feeling of the workers. Several authors even insist that "If the person tells you that he is loaded and effortful, then he is loaded and effortful whatever the behavioral and performances measures may show" [START_REF] Li | Current techniques for assessing physical exposure to work-related musculoskeletal risks, with emphasis on posture-based methods[END_REF]. Thus, to combine the subjective evaluation and objective evaluation can reduce the contradictory problems between them and can rate the muscle fatigue correctly.

The general feeling of human body about fatigue is: the larger the force is, the faster people can feel fatigue; the longer the force maintains, the more fatigue; the smaller capacity of the muscle is, the more easily we can feel fatigue. Based on this description, the equation 1 is used to describe the subjective evaluation. The parameters used in the equations are listed and described in table 1. This equation can be explained as follows:

(i) F cem describes the capacity of the muscle after some contraction, the rest force generation ability. (ii) F load (t)/F cem (t) is relative load which describes the muscle force relative to the capacity of the muscle at a time instant t. (iii) M V C/F cem (t) describes the smaller capacity of the muscle, the faster the muscle get fatigued.

f M V C %M V C/100 dU (t) dt = M V C F cem (t) F load (t) F cem (t) (1)
Meanwhile, the current maximum exertable force F cem is changing with the time due to the external muscle load. It makes sense that: The larger the external load, the faster F cem decreases; the smaller F cem is, the more slowly F cem decreases. The differential equation for F cem is equation 2.

dF cem (t) dt = -k F cem (t) M V C F load (t) (2)
The integration result of equation 2 is equation 3.

F cem (t) = M V C e t 0 -k F load (u) M V C du (3)
Assume that F (t) is:

F (t) = t 0 F load (u) M V C du (4)
M V C is a constant value for an individual person, so we can change the equation 3 into equation 5. If F load /M V C is constant and equals to C, then F (t) = Ct, equation 3 can be further simplified. This constant case can occur during static posture and static load.

F cem (t) M V C = e -kF (t) = e -kCt (5)
The feeling of our fatigue is a function below and which is closed related to M V C and F load (t). M V C can represent the personal factors [START_REF] Chaffin | Occupational Biomechanics, 3rd Edition[END_REF], and F load (t) is the force exerted on the muscle along the time and it reflects the influences of external loads equation 6.

U (t) = 1 2k e 2kF (t) - 1 2k e 2kF (0) (6)
In this model, personal factors and external load history are considered to evaluate the muscle fatigue. It can be easily used and integrated into simulation software for real time evaluation especially for dynamic working processes. This model still needs to be mathematically validated and ergonomic experimental validated, and meanwhile muscle recovery procedure should also be included to make the fatigue index completed.

Static Validation

Validation result

Our dynamic muscle fatigue model is simply based on the hypothesis on the reduction of the maximum exertable force of muscle. It should be able to describe the most special case -static situations. In static posture analysis, there is no model to describe the reduction of the muscle capacity related to muscle force, but there are several models about maximum endurance time (MET) which is a measurement related to static muscular work. MET represents the maximum time during which a static load can be maintained [START_REF] Elahrache | Percentile values for determining maximum endurance times for static muscular work[END_REF]. The MET is most often calculated in relation to the percentage of the voluntary maximum contraction (%M V C) or to the relative force (f MV C = %M V C/100) required by the task. These models which are cited from [START_REF] Elahrache | Percentile values for determining maximum endurance times for static muscular work[END_REF] are listed in table 2.

In our dynamic model, suppose that F load (t) is constant, and it represents the static situation. MET is the duration in which F cem falls down until the current F load . Thus, MET can be figured out in equation 7 and 8.

F cem (t) = M V C e t 0 -k F load (u) M V C du = F load (t) (7) t = M ET = - ln F load (t) M V C k F load (t) M V C = - ln(f MV C ) k f MV C (8)
In order to analyze the relationship between MET of our dynamic model and the other models, two correlation coefficients are calculated. One is Pearson's correlation r in equation 9 and the other one is intraclass correlation ICC in equation 10. r indicates the linear relationship between two random variables and ICC can represent the similarity between two random variables. The closer r is to 1, the more the two models are linear related. The closer ICC is to 1, the more similar the models are. M S between is the mean square between different MET values in different f MV C values, M S within is the mean square within MET values in different models at the same f MV C level. p is the number of models in the comparison. In our case, we compare the other models with our dynamic model one by one, k equals to 2. The calculation results are shown in table 2 andfigure 1 to 8

. r = n (A n -Ā)(B n -B) n (A n -Ā) 2 n (B n -B) 2 (9) ICC = M S between -M S within M S between + (p -1)M S within (10)

Discussion

From the comparison results of the static validation, it is obvious that MET model derived from our dynamic model has a great linear correlation with the other experimental static endurance models, and almost all the Pearson's correlation r are above 0.97.

From ICC column, the similarity between our dynamic model and the other models in descend sequence is: elbow models, hand model, general model, shoulder models and hip/back model. For elbow models, the average ICC is approximate 0.9, but for the back/hip models, ICC varies from -0.057 to 0.9447. The explanation is: in shoulder and back/hip of human body, the anatomical structure is in a much more complex way than in the elbows and hands.

Rohmert M ET = -1.5 + 2.1 f M V C -0.6 f 2 M V C + 0.1 f 3 M V C
0.9937 0.8820

Monod and Scherrer M ET = 0.4167 (f M V C -0.14) -2.4 0.8529 0.6474 Huijgens M ET = 0.865 In this case, during these experimental models, the measurement of M V C is an overall performance of the muscle group, but not an individual muscle. Meanwhile from figure 7, the differences between the experimental models for hip/back are much greater than in the other models like in elbow models (figure 5). It can be explained as: in different working conditions (for example, different postures), the engagement of the muscles in the task in the hip/back of human body varies due to the complexity of the structure. Thus, the error between our model and the other models is closed related to the complexity of the structure and our model can fit most of the experimental models with a high similarity.

1-f M V C f M V C -
Overall, the static validation can prove that our dynamic model can be used to predict MET in static situations.

Dynamic Validation

Validation result

Static validation results have shown that our dynamic model can be used to predict the MET for general static load and even for some specific body parts. But static procedures are still quite different from dynamic situations, thus our dynamic model need to be under examination with the other dynamic models. For this objective, we are going to verify our dynamic model through comparison with some existing muscle fatigue models, quantitatively or qualitatively.

In paper [START_REF] Freund | A dynamic model of the forearm including fatigue[END_REF], a muscle fatigue model was proposed and integrated into a dynamic model of forearm. In this model, the muscle was treated like a kind of reservoir, and force production capacity S 0 reduces with the time that the muscle is contracted. S 0 varies between 0 and the upper limits of the muscle force S l . In this model, the recovery and decay rates depend on S l -S 0 and muscle force S (equation 11). The constants α and β were obtained by fitting the solution using experimental results from static endurance time test. In this model, muscle force is taken into consideration as a factor causing muscle fatigue, and further more, muscle force production capacity S 0 was proposed just like in our dynamic model F cem to describe the capacity of the muscle after performing certain task. But in this model, the force production capacity and the muscle force are decoupled with each other which is different in our model.

dS 0 dt = α(S l -S 0 ) -βS (11)
Wexler's dynamic muscle fatigue model based on Ca 2+ cross-bridge mechanism can also verify our dynamic model quantitatively. This model can be used to predict the muscle force fatigue under different stimulation frequencies. From figure 9, it is clear that the faster the stimulation frequency is, the larger the force can be generated by the muscle. If each curve is normalized into figure 10, it is obvious that: the larger the peak force is, the faster the muscle gets fatigue. But this model can only be used to predict the muscle force under a stimulation pattern and it can not predict or evaluate the muscle force generation capacity under a stimulation pattern when the muscle is getting fatigue.

In the paper [START_REF] Liu | A dynamical model of muscle activation, fatigue, and recovery[END_REF], another dynamic model of muscle activation, fatigue and recovery was presented. This model is based on biophysical mechanisms: a muscle consists of many motor units which can generate force or movement. The number of the motor units depends on the size and function of the muscle. The generated force is proportional to the activated motor units in the muscle. The brain effort B, fatigue property F and recovery property R of muscle can decide the number of activated motor units. The relationship is expressed by equation 12. The parameters in this equation is explained in table 3. [START_REF] Liu | A dynamical model of muscle activation, fatigue, and recovery[END_REF] dM

A dt = B M uc -F M A + R M F dM F dt = F M A -R M F M uc = M 0 -M A -M F (12)
When t = 0 under the initial conditions of M A = 0, M F = 0, M uc = M 0 , we can have equation 13.

M A (t) M 0 = γ 1 + γ + β (1 + γ)(β -1 -γ) e -(1+γ)F t - β -γ β -1 -γ e -βF t (13)
β B/F γ R/F
In our fatigue model, we assume that there is no recovery during mechanical work, and the workers are trying their best to finish the work which means the brain effort is quite large. In this assumption, we set γ=0 and β → ∞, then the equation 14 represents the motor units which are not fatigued in the muscle and M A (t)/M 0 represents the muscle force capacity. We can simplify the equation 13 to equation 14 which does have the same form of our dynamic model equation 5.

M A (t) M 0 = e -F t -e -βF t = e -F t (14)
This fatigue model has been experimentally verified [START_REF] Liu | A dynamical model of muscle activation, fatigue, and recovery[END_REF]. In the experiment, each subject performed an MVC of the right hand by gripping a handgrip device for 3 min. And the fitting curve from the experiment result has almost the same curve of our model in MVC condition (figure 12). In this model, F and R are assumed to be constant for an individual under MVC working conditions. There is no experiment result for F and R under the other load situations, thus this muscle fatigue model can only verify our model in MVC condition.

Discussion

Through dynamic validation, our dynamic model is quantitatively and qualitatively verified with the other existing muscle fatigue models. The fatigue model used in Overall, our dynamic model is simple and easy to use and it can evaluate the muscle fatigue during a dynamic working process.

Experimental Validation

Objective and methodology

After mathematical validation of our dynamic model, we are going to construct a virtual reality framework to verify the fatigue index in experimental environment. The objective of the experimental validation is to find the correlation between subjective fatigue evaluation results and objective fatigue evaluation results. In our hypothesis, if both results are highly linear related, that means the objective methods can represent the subjective feeling of fatigue and then it can be further integrated into virtual human simulation software to evaluate human muscle fatigue during manual handling work.

In order to realize our objective, two evaluation systems should be established: subjective evaluation system and objective evaluation system. Subjective evaluation methods have been mentioned in many papers, and here we are focusing on objective evaluation system. For objective evaluation, according to our model, muscle force at each time in-stant during the work should be calculated. It requires dynamic information like acceleration, velocity, position and external load. These information can be further input into dynamic formulas to calculate the muscle force. In order to get these information, motion capture method should be involved. As mentioned, the traditional methods have several drawbacks for ergonomic analysis, a virtual environment needs to be constructed to decrease the time cost and physical prototype cost.

System Structure

The overall objective of the framework is to evaluate human work and predict potential human MSD risks dynamically, especially for human muscle fatigue. The function structure of the framework is shown in figure 13 and discussed below.

In order to avoid field-dependent work evaluation, virtual reality techniques and virtual human techniques are used. Immersive work simulation system should be first constructed to provide the virtual working environment. Meanwhile, virtual human should be modeled and driven by the motion capture data to map the real working procedure into the virtual environment. Haptic interfaces can be used to enable the interactions between the worker and virtual environment.

For any ergonomic analysis, data collection is the first important step. All the necessary information needs to be collected for further processing. From section 2, necessary information for dynamic manual handling jobs evaluation consists of motion, forces and personal factors. Motion capture techniques can be applied to achieve the motion information. In general, there are several kinds of tracking techniques available, like mechanical motion tracking, acoustic tracking, magnetic tracking, optical motion tracking and inertial motion tracking. Each tracking technique has its advantages and drawbacks for capturing the human motion. Hybrid motion tracking techniques can be taken to compensate the disadvantages and achieve the best motion data.

Force information can be recorded by haptic interfaces. Haptic interface is the channel via which the user can communicate with virtual objects through haptic interactions, and the interaction data between the worker and the virtual environment are also significant for evaluating other ergonomic aspects. Individual factors can be achieved from anthropometrical database and some biomechanical database.

All the information, such as motion information, force history and interaction events, is further processed into Objective Work Evaluation System (OWES). The output of the framework is evaluation results of the mechanical work. There are many ergonomic aspects of a mechanical work. For each aspect, corresponding criteria should be established to assess the dynamic work process. Further more, these criteria can also be applied just into commercial hu-man simulation software to generate much more naturally and realistically human simulation. Three hardware systems are employed to construct a prototype system to realize this framework: virtual simulation system, motion capture system and haptic interfaces. Virtual Simulation system consists of graphic simulation module and display module. Simulation module executes on a computer graphic station, and display module is composed of projection system and head mounted display (HMD). Simulation module is in charge of graphic processing and display control. The projection system and HMD system can visualize the immersive environment. Motion Capture system is taken to capture the movement of the worker to collect the real working data. The Optical Motion Capture System developed by Tsinghua University VRLIB [START_REF] Wang | An integrated simulation system for human factors study[END_REF] is used, and it can work at 25 Hz data update rate. Each key joint of human body is attached by an active marker, and the overall skeletal structure of human body can be represented by 13 markers. Meanwhile, data gloves are used to capture the movement of fingers. Haptic system is also going to be integrated into this prototype, and now we are still under preparation.

Conclusion and Prospects

In this paper, we present a new muscle fatigue model and a new fatigue index based it. The mathematical validation has proved that the new model is very simple and easy to predict the MET in static postures. The dynamic validation result proves that the new model can be further extended into dynamic working process to predict the muscle fatigue. For experimental validation, a virtual reality framework is under construction to verify the linear relation between our fatigue index and subjective evaluation result.

The prototype system cannot only evaluate the fatigue, but also the other aspects of work by extending the evaluation criteria and data collection modules. If the framework can be verified in the future, it could be integrated with the other CAD system to optimize the product design and work process design.

In future works, we will apply our results to enhance the simulation software such that they will able to produce realistic simulations.

Fig. 1 .

 1 Fig. 1. Endurance time in general models

Fig. 4 .

 4 Fig. 2. ICC of general models

  M ET = 40.6092 exp(-9.7f M V C 0pull) M ET = 27.6604 exp(-4.2f M V C ) 0.9901 0.6585 Manenica (body torque) M ET = 12.4286 exp(-4.3f M V C ) 0.9911 0.9447 Manenica (back muscles) M ET = 32.7859 exp(-4.9f M V C ) 0

Fig. 7 .

 7 Fig. 5. Endurance time in elbow endurance models

Fig. 8 .

 8 Fig. 8. ICC of hip/back models

Fig. 9 .Fig. 10 .

 910 Fig. 9. Maximum exertable force and time relationship in Wexler's Model

Fig. 12 .

 12 Fig. 12. Comparison between the experimental result of the active motor model and dynamic model in the maximum effort the forearm used the same conception like in our fatigue model: the muscle force capacity is related to muscle force with time. Wexler's model based on Ca 2+ cross-bridge shows the reduction of the muscle force during the time under different stimulation frequencies, the reduction of the muscle capacity shows the same trend like in our muscle fatigue model. With comparison of the active motor model, the muscle force can be expressed in the same form under extremity situation. But in the active motor model, only parameters are available for MVC contraction case. The active motor does not supply further validation for other load situations. But we believe that the muscle load can influent the fatigue factor in the active motor model.Overall, our dynamic model is simple and easy to use and it can evaluate the muscle fatigue during a dynamic working process.

Fig. 13 .

 13 Fig. 13. The framework of the dynamic work evaluation system

Fig. 14 .

 14 Fig. 14. Scheme of Hardware system for the experimental validation

Table 2

 2 Static validation results[START_REF] Elahrache | Percentile values for determining maximum endurance times for static muscular work[END_REF]

	Model	Equation	r	ICC
	General models

Acknowlegement

This research was supported by the EADS and by the Région des Pays de la Loire (France) in the context of collaboration between the École Centrale de Nantes (Nantes, France) and Tsinghua University (Beijing, P.R.China).


A Duchesne

L Limat

Circular hydraulic jumps: where does surface tension matter?

Recently, an unusual scaling law has been observed in circular hydraulic jumps and has been attributed to a supposed missing term in the local energy balance of the flow [Bhagat et al. (2018)]. In this paper, we show that -though the experimental observation is valuable and interesting -this interpretation is presumably not the good one. When transposed to the case of a axial sheet formed by two impinging liquid jets, the assumed principle leads in fact to a velocity distribution in contradiction with the present knowledge for this kind of flows.

We show here how to correct this approach by keeping consistency with surface tension thermodynamics: for Savart-Taylor sheets, when adequately corrected, we recover the well known 1/𝑟 liquid thickness with a constant and uniform velocity dictated by Bernoulli's principle.

In the case of circular hydraulic jumps, we propose here a simple approach based on Watson description of the flow in the central region [Watson (1964)]], combined with appropriate boundary conditions on the formed circular front. Depending on the specific condition, we find in turn the new scaling by Bhagat et al. (2018) and the more conventional scaling law found long ago by Bohr et al. (1993). We clarify here a few situations in which one should hold rather than the other, hoping to reconcile Bhagat et al. observations with the present knowledge of circular hydraulic jump modeling. However, the question of a possible critical Froude number imposed at the jump exit and dictating logarithmic corrections to scaling remains an opened and unsolved question.

.1) Later, Duchesne et al. (2014) emphasized the importance of logarithmic corrections to scaling, due to viscous dissipation in the outer film, yet observed numerically by Bohr, and also showed that the prefactor was experimentally linked to the value of the Froude number at the exit of the jump, that seemed to be locked to a critical value. This phenomenon was recovered by Mohajer & Li (2015) and by Argentina et al. (2017) with a non-linear modeling of film flow equations including the first finite slope terms.

Very recently, an attempt of revision of this picture has been published by Bhagat et al.

(2018), who performed new experiments, and reported the observation of a different scaling in which surface tension 𝛾 was involved, but not gravity:

in which 𝜌 is the liquid density. To rationalize this finding, these authors claimed that most available approaches of surface tension influence lead to only small corrections [Bush & Aristoff (2003)] and that the description of the circular hydraulic jump had thus to be completely reconsidered. They introduced an energy balance, between two radii 𝑟 and 𝑟 + 𝛿𝑟, that

Introduction

Stationary axisymmetrical liquid structures formed by jet impacts, have motivated an enormous amount of literature. Three examples that will be important here are sketched on Fig. 1. First of all, the well-known circular hydraulic jump [Rayleigh (1914); Tani (1949); Watson (1964); Craik et al. (1981); Bohr et al. (1993); Bush & Aristoff (2003); Duchesne et al. (2014); Mohajer & Li (2015); Salah et al. (2018); Bhagat et al. (2018); Wang & Khayat (2019, 2021)], sketched on Fig. 1-a, with a well developed liquid film extending all around.

Its equivalent on a "dry" surface, possibly superhydrophobic [Jameson et al. (2010);Button et al. (2010); Maynes et al. (2011)], the "rim atomization" is sketched on Fig. 1-b. Finally the † Email address for correspondence: alexis.duchesne@univ-lille.fr Abstract must not spill onto p.2 [Watson (1964); Bush & Aristoff (2003)], in which the height of the outer film remains a control parameter, and the one from Bohr et al. (1993), rather devised when a liquid film extends all around at large distance, and inspired from boundary layer theories. As well known, this second approach leads to a scaling law dependence of 𝑅 𝐽 upon flow rate 𝑄 and the physical parameters (𝜈 the kinematic viscosity of the fluid, 𝑔 gravity), that reads: We find here useful to have a look on what would happen in the simplified geometry of Fig. 1-c, when applying this principle. As we shall show in section 2, this modeling leads to a velocity distribution in complete contradiction with the present knowledge of liquid sheets (and with Bernoulli's principle), which suggests that Bhagat et al argument is flawed. In fact the obtained flow field is not new, and has been proposed in the past by Bouasse (1923) who attributed the calculation to Hagen (see Hagen ( 1849)). It will be instructive here to remind the argument followed by Hagen and Bouasse, in section 3, in a Lagrangian frame, analyzing a circular expanding piece of film. We will then show, in the same section, how one can correct the argument to get the more classical and now admitted result deduced from Bernoulli's principle of a uniform radial velocity around the impact point, and how, missing some terms in the balance, one can get the flawed result of Bouasse and Hagen.

= [𝛾𝑟 ū] 𝑟+ 𝛿𝑟 𝑟 -[ 𝑝 ūℎ] 𝑟+ 𝛿𝑟 𝑟 -𝜌𝑔 ℎ 2 2 𝑟 ū 𝑟+ 𝛿𝑟 𝑟 -𝑟𝜏 𝑊 ū𝛿𝑟, (1.3
Finally, coming back to a Eulerian description, we will explain how these considerations impact the principle proposed in eq.(1.3). We will show that an extra term exactly equal and opposite to the capillary contribution should cancel this one, in a way consistent with classical thermodynamics, leading to the expression usually written from the balance of momentum.

This does not mean, however, that Bhagat et al. scaling discovery is of none interest. In section 4 and 5, we will try to precise to which capillary structures -different from the stationary hydraulic jump observed by Bohr -it could apply, and a possible way to justify its occurrence.

A look to a simple situation: the axisymmetrical liquid sheet.

Let us try to apply the principle suggested in eq.( 1.3) to the case suggested on Fig. 1-c, i.e. to a axisymmetrical sheet formed by the coaxial impact of two jets in a situation of negligible gravity. The viscous shear on the substrate having disappeared, eq.( 1.3) reduces to a very simple balance that reads:

𝜌𝑟 ℎ 𝑢 3 2 𝑟+ 𝛿𝑟 𝑟 = [𝛾𝑟𝑢] 𝑟+ 𝛿𝑟 𝑟 , (2.1)
where the horizontal velocity 𝑢 has no dependence upon the transverse direction, and coincides with any of its average values. This implies that the following quantity is constant all over the sheet:

𝜌𝑟 ℎ 𝑢 3 2 -𝛾𝑟𝑢 = Cte. (2.2)
Combined with the mass balance 𝑄 = 2𝜋𝑟 ℎ𝑢, this leads to the following expression for 𝑢:

𝑢 = 2𝜋 𝛾 𝜌𝑄 𝑟 + √ 𝑢 2 0 -4𝜋 𝛾 𝜌𝑄 𝑟 0 𝑢 0 + 4𝜋 2 𝛾 2 𝜌 2 𝑄 2 𝑟 2 , (2.3)
in which 𝑟 0 designates the jet radius at impact and 𝑢 0 the asymptotic value for 𝑢, reached when 𝑟 = 𝑟 0 , which satisfies the equality 𝑄 = 𝜋𝑟 2 0 𝑢 0 in a quasi-elastic shock approximation [Villermaux et al. (2013)]. In the limit of large jet velocity, i.e. 𝑢 2 0 2𝛾/(𝜌𝑟 0 ), this expression reduces to the slowly varying upon 𝑟 approximate:

𝑢 ≈ 𝑢 0 + 2𝜋 𝛾 𝜌𝑄 (𝑟 -𝑟 0 ), (2.4)
which is known to be false, as it has been checked experimentally that the velocity is constant all over the sheet, recovering the Bernoulli's principle (see in particular Fig. 3 in

[Villermaux et al. (2013)]).
It is however amazing to remind that a similar expression is proposed by Bouasse (1923) who attributed this result to Hagen ( 1849), but with a slight sign change, that is in fact due to a mistake on his own: Focus on Fluids articles must not exceed this page length Let us consider a piece of annular piece of film as on Fig. 2-a, convected and distorted by the flow. Mass conservation implies that, at any time ℎ𝑟𝛿𝑟 = Cte, while the balance of energy for the whole annulus reads, in the limit of 𝛿𝑟 small enough to satisfies the condition

𝑢 ≈ 𝑢 0 -2𝜋 𝛾 𝜌𝑄 (𝑟 -𝑟 0 ). ( 2
𝛿𝑟 𝜕𝑢 𝜕𝑟
𝑢 of a slowly varying velocity field :

𝜕 𝜕𝑡 2𝜋 1 2 𝜌𝑢 2 𝑟 ℎ𝛿𝑟 + 𝛾𝑟𝛿𝑟 ≈ 2𝜋𝛾𝛿𝑟𝑢. (3.1)
The first term in the left hand side of this equation stands for kinetic energy, and the second for the surface energy enclosed between 𝑟 and 𝑟 + 𝛿𝑟. The right hand term comes from the work of surface forces, and does not vanish. Indeed, the same surface tension force is pulling on a different arc length, as the external boundary has a larger perimeter than the other (note that this is the intuitive argument underlying Bhagat's analysis). Still in the limit of a slowly varying velocity field at the scale 𝛿𝑟, after noting that 𝜕 𝜕𝑡 = 𝑢 𝜕 𝜕𝑟 , eq.(3.1) reads:

𝑟 ℎ𝛿𝑟𝑢 𝜕 𝜕𝑟 𝜌𝑢 2 2 + 𝛾𝑢𝛿𝑟 ≈ 𝛾𝑢𝛿𝑟. (3.2)
In fact, the two surface tension terms are canceling each other, which means that the work To summarize, a correct treatment of the expansion of liquid annula in the flow leads to the classical result of a uniform velocity, while the approximates defended by Hagen and Bouasse would follow from neglecting a part of capillary terms. We believe that a similar problem is involved in eq.( 1.3). If we consider now a Eulerian description of the flow, as suggested on Fig. 2-b, the balance of energy should rather read: (2018). To our opinion, this would imply to redo the initial mistake of Hagen and Bouasse.

𝜌 ū2 2 ū𝑟 ℎ + 𝛾𝑟 ū 𝑟+ 𝛿𝑟 𝑟 = [𝛾𝑟 ū] 𝑟+ 𝛿𝑟 𝑟 -[ 𝑝 ūℎ] 𝑟+ 𝛿𝑟 𝑟 -𝜌𝑔 ℎ 2 2 𝑟 ū 𝑟+ 𝛿𝑟 𝑟 -𝑟𝜏 𝑊 ū𝛿𝑟, (3.6
Just as for the calculation of the size of radial liquid sheets, the solution should rather lies inside the boundary conditions written at the circle which radius is under question. We are now developing more this idea. To simplify the analysis, the "internal" flow for 𝑟 0 < 𝑟 < 𝑅 𝐽 is assimilated to the one discussed long ago by Watson (1964), in which fluid inertia is progressively dissipated by viscous friction, i. e. for 𝑟 < 𝑅 𝐽 :

Alternative explanation of unusual

𝑢(𝑟, 𝑧) = 27𝑐 3 8𝜋 4 𝑄 2 𝜈(𝑟 3 + 𝑙 3 ) 𝑓 𝑧 ℎ , (4.1)
in which 𝑐 ≈ 1.402, 𝑙 = 0.567𝑟 0 𝑅 (with 𝑅 the Reynolds number of the jet) and 𝑓 is the function:

𝑓 (𝜂) = √ 3 + 1 - 2 √ 3 1+𝑐𝑛(3 1 4 𝑐 (1-𝜂) )
. Mass conservation implies that the film thickness and the flux of momentum are given by:

𝜌ℎ < 𝑢 2 >= 27 √ 3𝑐 3 16𝜋 6 𝜌𝑄 3 𝑅 𝐽 𝜈(𝑅 3 𝐽 + 𝑙 3 ) , (4.2)
where < 𝑢 2 >= ∫ ℎ 0 𝑢 2 d𝑧. In the case of Fig. 1-a, this flow must be matched for 𝑟 > 𝑅 𝐽 to a film flow under the action of gravity, that, according to lubrication [Duchesne et al. (2014)],

has a thickness distribution 𝐻 (𝑟) given by:

𝐻 (𝑟) 4 = 𝐻 4 ∞ + 6 𝜋 𝜈𝑄 𝑔 𝑙𝑛 𝑅 ∞ 𝑟 , (4.3)
where 𝑅 ∞ designates the outer radius of the substrate, where the thickness 𝐻 reaches a value called 𝐻 ∞ that will depend on the specific geometrical conditions of the flow there (see

𝜌ℎ(𝑟) < 𝑢(𝑅 𝐽 ) 2 >≈ 𝜌𝑔𝐻 (𝑅 𝐽 ) 2 , (4.4)
In the limit of negligible values for 𝐻 ∞ and 𝑟 0 , compared to the other scales, it is easy to check that these equations lead to the following scaling law for 𝑅 𝐽 :

𝑅 𝐽 𝑙𝑛 𝑅 ∞ 𝑅 𝐽 1 8 = (3𝑐) 3 4 2 9 8 𝜋 1 1 8 𝑄 5 8 𝜈 3 8 𝑔 1 8 , (4.5)
i.e. the scaling obtained by Bohr et al. (1993) and modified by logarithmic corrections.

We now consider the regime described in

𝜌ℎ(𝑟) < 𝑢(𝑅 𝐽 ) 2 >≈ 𝛾(1 -cos 𝜃), (4.6)
with 𝜃 the static contact angle Using eq.(4.2) in the limit 𝑟 = 𝑅 𝐽 𝑟 0 , this condition yields a new scaling that reads: 𝑅 𝐽 = 27

√ 3𝑐 3 16𝜋 6 1 4
(1 -𝑐𝑜𝑠𝜃) We thus do not believe that there is a "universal" scaling that should hold for any circular "print" formed around an impacting jet. Sometimes one can find Bohr's scaling and sometimes Baghat and Button one, it is the analysis of the conditions around the impact that will matter.

Another possible occurrence of Bhagat and Button scaling.

We now show that Bahgat's scaling may also be observed in classical circular hydraulic jumps. In Bhagat et al. (2018) paper, the authors consider an intermediate regime where the liquid has not yet reached the edge of the plate (see Fig. 3). In their experimental evidence the authors consider partial wetting conditions (they use Perspex, glass and Teflon) and aqueous solutions. Given that the front propagation speed is rather small, we can consider that the liquid front height is approximately given by

ℎ 𝑐𝑎 𝑝 ≈ 𝛾 𝜌𝑔 1 2
(1cos 𝜃) 1 2 .

(5.1) Considering the eq.( 4.3) for low viscosity liquid and moderate flow rate one can conclude that:

𝐻 (𝑟) ≈ 𝐻 ∞ ≈ ℎ 𝑐𝑎 𝑝 .
(5.2)

Therefore the (simplified) shock condition (4.4) previously obtained leads to:

𝜌ℎ(𝑟) < 𝑢(𝑅 𝐽 ) 2 >≈ 1 2 𝜌𝑔ℎ 2 𝑐𝑎 𝑝 .
(5.3) Surprisingly, this argument leads again exactly to the "surface tension dominated" scaling :

𝑅 𝐽 = 27 √ 3𝑐 3 16𝜋 6 1 4 (1 -𝑐𝑜𝑠𝜃) 1 4 𝑄 3 4 𝜈 -1 4 𝜌 1 4 𝛾 -1 4 . ( 5

Conclusion

In summary, we have reconsidered the problem of scaling law selection of the "radius of influence" in the problem of vertical jet impact on a horizontal solid surface. In our opinion, the ideal law (1.1) proposed by Bohr and coworkers (to which, one should not forget to add logarithmic corrections as in Duchesne et al. ( 2014)) corresponds to the ideal situation of a stationary hydraulic jump formed inside a liquid film extending on the whole solid surface.

On the opposite, the scaling (1.2) suggested in ref. [Bhagat et al. (2018)] rather holds in different situations, some of these ones being:

-stationary impact of a jet on a dry surface, possibly superhydrophobic, without formation of the outer film (atomization ring),

-stationary impact of a jet on a dry surface in inverse gravity (impact of a jet on a ceiling),

-transient regime of circular hydraulic jump formation for low viscosity liquids in partial wetting.

It would be interesting to explore in more details these three situations, and to identify possible other ones. In our opinion, there is no need to imagine some universal extra capillary term imposing the scaling (1.2) as imagined in ref [Bhagat et al. (2018)]. Though this extra term really exists, when the control volume contains the free surface of the film instead of excluding it, it is in practice compensated by another one in a way consistent with classical thermodynamics. As usual in free surface flows there is no increase or decrease of velocity that could be due alone to the action of surface tension, except when Marangoni effects are involved [Marmottant et al. (2000)]. Going on in this direction would be just reproducing for thin film flows on a solid, the initial mistake of Hagen and Bouasse.

Figure 1 :

 1 Figure 1: Three axisymmetric film flows are discussed in the present article. (a) The classical circular hydraulic jump formed by a jet impacting a solid disk at its center, (b) atomization ring formed by a jet impacting a dry surface possibly superhydrophobic, (c) liquid sheet formed by impact of two liquid jets of opposite direction.

  ) with the notation [ 𝐴] 𝑟+ 𝛿𝑟 = 𝐴(𝑟 + 𝛿𝑟) -𝐴(𝑟), and in which ū designates the flux-average radial velocity, 𝑟 the distance to the axis, ℎ(𝑟) the thickness of the liquid layer, 𝑝(𝑟) the pressure at 𝑧 = 0 and 𝜏 𝑊 the wall shear stress. The last term on the right designates the viscous dissipation by friction on the substrate, while the first one is an additional term compared to previous approaches, that is presumed to be "at the origin" of the new scaling (1.2). This conjecture has been contested [Duchesne et al. (2019); Bohr & Scheichl (2021)] (see alsoBhagat & Linden (2020) answer), and it is also known that a scaling like (1.2) can also appear without such an assumption, as shown for instance byButton et al. (2010) for liquid bells formed below a ceiling.

  .5) Though obtained erroneously, this expression is very seductive and Bouasse used it to calculate the radius of the liquid sheet 𝑅 𝐿𝑆 assuming that the sheet border should stay at the place in which 𝑢 vanishes which leads to 𝑅 𝐿𝑆 = (𝜌𝑄𝑢 0 )/2𝜋𝛾(= 𝜌𝑟 2 0 𝑢 2 0 )/2𝛾 . Surprisingly this result coincides with the right one that is in fact obtained, now, by assuming a constant velocity, dictated by Bernoulli's principle, and the balance of momentum at the sheet perimeter, i.e. 𝜌ℎ𝑢 2 = 𝛾 [Villermaux et al. (2013)]. But on the other hand, we would like to stress out that the radial velocity is uniform in the sheet of Fig.1-c, which means that the principle proposed in eq.(1.3), and therefore the basis of the theory developed by Bhagat et al. (2018) is flawed.

Figure 2 :

 2 Figure 2: Lagrangien (a) and Eulerian (b) frame for discussing energy balance in a annular portion of a liquid film used in the text.

  provided to the annulus by surface tension of the outer interfaces is completely transformed into the surface energy stored at the free surface of the annulus, in agreement with simple thermodynamic considerations. As a result, the fluid velocity is unaffected by surface tension balance and remains constant as one would deduce from a more classical argument in terms of Bernoulli's principle, i.e. 𝑢(𝑟) is in fact independent of 𝑟:𝑢(𝑟) = 𝑢 0 = Cte. (3.3)Note here that skipping from eq.(3.1) to eq.(3.2) is not completely trivial as there is an extra 𝛾 term remaining, but this one vanishes for the constant and uniform 𝑢 0 solution.To reconnect with Bouasse, instead of this, if one would forget the internal surface energy contribution in the left hand member of eq.(3.2), one would get the following equation for 𝑢, simplifying 𝛿𝑟, and using the fact that 𝑄 = 2𝜋𝑟𝑢ℎ, this equation leads to: to eq.(2.4). Alternatively, eq.(2.5) is obtained when one forgets the work provided to the annulus by the outer parts of the liquid sheet, i.e. by neglecting the right hand member of eq.(3.2), following the intuitive but erroneous idea of Hagen (1849) that surface tension could slow down the flow. Historically Bouasse followed the first argument, but committed a sign mistake, obtaining eq.(2.5), that was physically more natural, considering presumably what Hagen said long ago.

  Fig.2-b in the left hand side of the equation. And just as what happens in a Lagrangian frame, the physics being the same in both frame, the capillary effects should exactly compensate each other in this equation, that should then reduce to the more conventional form:

  scaling: the boundary condition at the "jump" radius. Comparison with atomization rings. To interpret the occurrence of Bhagat et al. (2018) scaling, we propose an alternative approach. We just treat the two ideal situations of Fig.1-a and Fig.1-b with the same method, and see what happens. We will then see that the situation obtained in Fig.1-b may be compared to the one suggested by Bhagat et al. (2018).

Fig. 1 -

 1 Fig.1-a for the graphical definition). At 𝑟 = 𝑅 𝐽 , one has to write some matching condition, that is consistent with the approximations made on each side of 𝑟 = 𝑅 𝐽 , and stands for a shock [Bélanger (1841); Rayleigh (1914)]. If we assume ℎ 𝐻 and neglect the surface tension at the shock (i.e. for circular hydraulic jumps large enough such as the ones considered by Bhagat et al. (2018)), this shock condition reads:

  Fig.1-b that may be obtained in stationary regime with particular superhydrophobic treatment [Maynes et al. (2011)] or with inverse gravity [Jameson et al. (2010); Button et al. (2010)]. In this regime the force opposed to fluid inertia at the boundaries is dictated only by surface tension and not by gravity, there is no developed shock, no liquid "wall". In other words, the flux of momentum is only balanced by surface tension, which means that equations (4.3) and (4.4) are simply replaced now by:

Figure 3 :

 3 Figure 3: sketch of the intermediate regime for a low viscosity liquid in partial wetting.

  the same than the one suggested by Bhagat et al. (2018) and previously by Button et al. (2010). It explains why the scaling obtained by Bhagat et al. (2018) applies to the experimental data of Jameson et al. (2010) even if the theory leading to this scaling is not the right one.

  If we come back to the question of Bohr scaling we have left a bit aside the questions of the logarithmic corrections and the possible existence of a critical Froude number at the jump exit, suggested in[Duchesne et al. (2014)]. The possible existence of this critical Froude number leads to a different exponent for the Logarithmic corrections (3/8 instead of 1/8) and this question is still not solved. As told in the introduction, recent non-linear analytical treatment of the film flow suggests that such a critical Froude number could exist, but this remains to be established and convincingly explained.A specific problem of great interest where these considerations should mater is the question of jet impacts on inclined plates. It is not obvious in this kind of problem that a perfect hydraulic jump can exist, or not, and the two scaling should compete against each other in a way that merits to be investigated. The influence of a external fields, here the tangent component of gravity on a circular shock is a fundamental question of great interest. A specific effort should be done in this direction [Wilson et al. (2012); Duchesne et al. (2013)]. viscous circular hydraulic jump. APS Division of Fluid Dynamics Meeting Abstracts .

  .e., a constant Weber number that replaces the constant Froude number encountered in fully established hydraulic jump with a complete, flowing outer film.

	Considering 𝜃 = 𝜋 2 , we obtain that:
	We ≈	1 2	,	(5.6)
	which is the order of magnitude of the Weber number reported in Bhagat et al. (2018).

.4) Following now a remark from Bhagat et al. (2018), one can also denote that by defining the Weber number as We ≈ 𝜌ℎ(𝑟) < 𝑢(𝑅 𝐽 ) 2 > 𝛾 ≈ 𝑐𝑠𝑡𝑒, (5.5) i

Rapids articles must not exceed this page length


Eunika Mercier-Laurent
email: eunika.mercier-laurent@univ-reims.fr

Can Artificial Intelligence Effectively Support Sustainable Development?

Keywords: Artificial Intelligence, Sustainability, Sustainable Development, Planet Crisis, Climate Change, Data Obesity

This paper describes the role AI may play in sustainability. Sustainable development is currently among the greatest challenges. Sustainability and development are apparently opposite. The current efforts to face the Planet Crisis by separate actions generate less impact than expected. The capacity of available technology and in particular Artificial Intelligence is underexplored. Eco-innovation actions focus mainly on smart transportation, smart use of energy and water and waste recycling but do not consider the necessary evolution of behaviors and focus. The concepts such as Smart, Intelligent, Innovative, Green or Wise City invented to promote existing technology transform the IT market. Most of offers consist in data processing with statistical/optimization methods. This paper explains how the AI approach and techniques combined with adequate thinking may innovate the way of facing Planet Crisis and achieving some of 17 United Nations Sustainable Development Goals.

Introduction

Many factors affect the sustainability. One of them is quick technological progress, considered as powerful engine of economy. It provides benefits for humanity, but contributes also to Planet Crisis with waste generation, energy consumption, cooling data centers and depletion of scarce metals. The majority of computers, smartphones, IoT and other electronic devices are mostly not eco-designed and even integrate a principle of planned obsolescence. Consequently they are thrown away and replaced by the latest model. Not conceived with knowledge approach, the consecutive layers of software and frequent update for various reasons increase already existing "obesity" and creating a need for more powerful computers. The combination of various communicating software requires "up-to-date" hardware to run correctly.

Despite the large introduction of Corporate Social Responsibility, some companies still practice planned obsolescence to generate more revenues [START_REF] Cueto | Planned Obsolescence -An Economic and Cultural Anxiety[END_REF]. Is getting huge and quick revenue compatible with Planet protection?

Main conferences devoted to climate change blame coal and automotive industry as the biggest emitters of carbon dioxide. However, they seem forgot the other influencing factors and do not study the pollution systems as a whole.

According to [2 and 3] simple email without attachment generates equivalent of 4g CO2, annual google search 10 kg by only one person.

Social networks and various applications produce an exponential amount of data stored in data centers that need cooling. Fortunately, few apply circular energy to reduce environmental impact, but still those in Scandinavian countries and North America clearly contribute to the rise of temperature and melting of ice [4].

The third hype of AI has been triggered by marketing needs to sale more and quicker to largest public. The involved companies collect all available data in aim to elaborate the models and selected algorithms to generate "client experience" among others.

The advertisement companies explore the navigation data and "client experience" in aim pushing not always targeted advertisement to large population of the Internet users. It generates not only carbon footprint, but also visual pollution and certainly influence concentration.

Advertisement-based business model, invented by Google influences and mass media promote the "buy more" and "to have more and to show" mentality. "Buy more, throw away and buy new" are the engines of today business. The demand for data scientists, especially in marketing is increasing, which is good for employment.

This trend affected also the problem solving capacity among the AI programmers to the point that many apply Big Data + machine learning principle to solve all kind of problems even if the alternative methods, greener and smarter are available. Collection of data became a prerequisite. However, their quality should be adapted to the expected results without cheating aiming in influencing the results. Raw data need "cleaning" before processing.

In fact, the quality of data is not controlledthere is not "garbage collector" for outdated data, no verification of consistency, and no selection in function of target. For example, many organizations collect our personal data that are in various database instead of having just one (identity). By consequence the same data may be registered a dozen of times, contributing again to data obesity. Globalization has changed the economic landscape. Opening to business and quick development of China and other Asian and South American countries offering the low labor cost increases the relocation-out from origin countries, mainly US and Europe, in search of quick and high revenues. It requires transportation across the world by ships and airplanes, which increases pollution [START_REF]The Environmental Effects of Freight[END_REF]. Besides, the end-buyers have to recycle products, often of poor quality, made just for sale. Repairing costs often more than new product and requires the availability of spare pieces and related expertise.

Huge global business amplifies through communication technology, e-commerce, and transportation facilities. The each day of recent Suez Canal blockage disrupted more than $9 billion worth of goods, according to The Associated Press, citing estimates from Lloyd's List. The large number of ships stuck in one placeat the northern end of the Suez Canal in the Mediterranean Seacaused sulphur emissions to spike in the region [6].

The knowledge of adequate techniques of AI and expertise in applying them can help finding and optimizing the local resources in aim avoiding or minimizing transportation of many goods and enhance local economy.

Despite the provided benefits, the innovation is among contributors to planet disaster, because the inventors and designers think mostly about the functionalities, shape, look, attractiveness, and few about minimizing the use of raw materials, reducing the energy consumption, providing the remanufacturing and recycling facilities and other ways to reduce environmental impacts. "Innovation" in packaging by reducing the quantity of a given product (food) in more attractive box produces more waste.

The primary eco-innovation movement claims to generate new businesses and jobs but the use of technology in the related activities is moderate, except maybe for waste sorting [START_REF]Waste sorting[END_REF]. Instead of sorting, it is smarter to produce less waste. Corporate Social Responsibility aims in balancing environmental, economic and social impacts. The standards associated with product lifecycle management (PLM) software claim to manage environmental impact of the design [START_REF] Feng | Toward a Systemic Navigation Framework to Integrate Sustainable Development into the Company[END_REF].

The industrial renewal in Europe called Industry 4.0, initiated by German government to face Asian competition, focuses on digitalization and optimization of related processes. Therefore, eco-design is included into Industry 4.0 [START_REF] Dostatni | Automation of the Ecodesign Process for Industry 4.0[END_REF]. Future factories, such as those at Vaudreuil of Schneider Electric and Safran in France integrate a lot of AI, preserving principle of collaboration human-machine, instead of replacing humans. Cyber physical systems allow simulate and improve maintenance of existing equipment and design [10, 11, and 12].

Artificial Intelligence plays already a significant role in decision support systems, optimization, simulation, but can do better at the condition to consider the mentioned elements as an ecosystem. It requires a capacity of different thinking without the barriers between fields [START_REF] Cavalucci | [END_REF], complex problem solving, art of choosing appropriate techniques and managing available knowledge and experience that apply.

After describing the concepts of sustainability, and sustainable development we give a short overview of AI techniques useful for sustainability management. This is following by discussion on how AI can help achieving some of the 17 goals of UN. The case of Smart City demonstrates AI applied to mastering of environmental impact.

The paper ends with some perspective on alternative way of doing and on the role of intelligent technology in the transformation of society.

Sustainability and Sustainable Development

For many sustainability means economic health. Indeed sustainability depends on how human activities are in balance with natural ecosystems and how they affect biodiversity and our biosphere [START_REF] Mercier-Laurent | The Innovation Biosphere -Planet and Brains in Digital Era[END_REF].

Facing the Planet Crisis requires different approach that world conferences, agreements and separate actions. By the way, participants travel mostly by planes generating CO2 instead of using available teleconferencing technology. Nobody publish the "return on investment" in terms of tangible and intangible effects of such actions. Covid 19 however, changed the way we work; many conferences went online. Remote working generates positive impact on the environment, such as but there are also few negative often forgotten. All conferences online are recorded and stored in the data centers, nevertheless these records offer the access to knowledge to large audience. Successive lock downs have also increased shopping online and by consequence traffic on the internet and transportation of goods.

In biological systems, sustainability means long life. Systems components influence each other and the balance of the whole system is the condition to survive. Human activities and especially greedy economic system have affected the balance of natural ecosystems [14 and 15].

Sustainable development is a principle that many people claim to have invented. The definition of the European Union [16] inspired by those of Antoine de Saint Exupéry [START_REF] De | Terre des hommes[END_REF] is following:

"Sustainable Development stands for meeting the needs of present generations without jeopardizing the ability of futures generations to meet their own needs -in other words, a better quality of life for everyone, now and for generations to come. It offers a vision of progress that integrates immediate and longer-term objectives, local and global action, and regards social, economic and environmental issues as inseparable and interdependent components of human progress".

"Sustainable development will not be brought about by policies only: it must be taken up by society at large as a principle guiding the many choices each citizen makes every day, as well as the big political and economic decisions that have to be taken. This requires profound changes in thinking, in economic and social structures and in consumption and production patterns" [START_REF] Folke | Biological diversity, Ecosystems and the Human Scale[END_REF].

Sustainable development can be considered as a process for meeting human development goals while maintaining the ability of natural systems to provide the required natural resources and ecosystem services upon which the current economy and society depend.

The current greedy economic system is not compatible with sustainable development. Burning forests to plant genetically modified soybeans or remove trees to build houses just for sale destroys unnecessarily biodiversity. In this context, sustainable development is an oxymoron -it is impossible to remain sustainable without deep understanding of our natural ecosystems (multidisciplinary knowledge) and without radical change of behaviours, objectives, values, political and economic system. Sustainable development is an attitude to learn and cultivate.

Various actions aiming in changing the way of acting and doing things have been engaged since 1960 [START_REF] Folke | Biological diversity, Ecosystems and the Human Scale[END_REF]. Recently the young individuals such as for example Boyan Slat, Greta Thunberg and some NGOs are engaged in actions for planet cleaning and protection. Spreaded through social networks such actions have potential to influence behaviours. The initiatives as buy local, sharing knowledge on repairing via video and numerous applications, such as Uber, wonolo [19] and some others, connect people offering services or jobs with those who need them. It is quick and effective, but out of the current economic practices (taxes, companies…). Sometimes this way of doing raise conflicts between "traditional" and "innovative". Some platforms connecting offer and demand use AI techniques such as Case-based reasoning or deep learning for direct matching of offer and demand [START_REF] Capiluppi | Matching demand and offer in on-line provision: A longitudinal study of monster.com[END_REF][START_REF] Maher | Issues and Applications of Case-based Reasoning to Design[END_REF].

Games and serious games (with AI) have also potential to encourage people to think and act differently. For example, the game Nega-water developed by association Du Flocon à la Vague calculates the use of water when doing daily activities [22].

Introducing the environmental principles into a design of products and services is a step forward. However, the traditional PLM tools should evolve to take into consideration a new way of doing [12] by using alternative thinking, simulators before doing and optimizers. Future Factories are supposed to evolve in this direction [START_REF]Future Factory Schneider Electric[END_REF][START_REF] Schneider | [END_REF].

Technology is able to provide a considerable help in eco-design, but the way of thinking compatible with such complex problem solving should evolve to global, holistic and system [START_REF] Mercier-Laurent | The Innovation Biosphere -Planet and Brains in Digital Era[END_REF][START_REF] Mercier-Laurent | Rôle de l'ordinateur dans le processus global de l'innovation à partir de connaissances[END_REF]. For example, aerospace and automotive industries focus on lightening weight and reducing carbon footprint, while other related aspects such as route optimization for users are weakly considered. Current travel search engines works for their clients, not for travellers. The air transportation system "hub-and-spoke" in which local airports offer air transportation to a central airport where long-distance flights are available, need innovation to minimize the distance and related CO2 emission. The effort can be done through better collaboration between airlines. Three main alliances Sky Team, Star Alliance and One world do not accept combining the flight tickets between them for optimizing flights distance. This situation my change with Covid crisis.

The International Standard ISO 26000 provides guidelines on how businesses and organizations can operate in a socially responsible way [23]. While it constraints companies to integrate social and environmental aspects into their activities, for ex. design, they should also focus on balancing their economic performance. These guidelines are complex and it is very difficult for a small company to check and respect all these principles without losing business. The AI-based simulators can help checking and optimizing things. Such system has been prototyped in the framework on French national funded project Convergence [START_REF] Feng | Toward a Systemic Navigation Framework to Integrate Sustainable Development into the Company[END_REF] that delivered a game-based guide for SMEs aiming in guiding them in applying ISO 26000 requirements related to eco-design.

To remain sustainable, development requires a smart use of available AI techniques, not only trendy ones but also those effective for a given case. Combined with intensive use of available knowledgeindividual and collective, from related domains, from the past and currently gained from experience such systems can really help minimizing impact of human activity.

Artificial Intelligence and sustainability

Since years, researchers and practitioners of AI have demonstrated the AI has potential to provide valuable solutions for facing today challenges. Since 1980s, numerous applications in the fields of medicine, chemistry, industry, finance and others demonstrated that AI is able to help human in many situations [START_REF]Unimagined Futures -ICT Opportunities and Challenges[END_REF].

Third hype of AI

The third hype of AI triggered by marketing needs to sale more and to more people amplified collection of multisource data. Despite of GBDR the acceptation of cookies by users is mandatory to access most of websites. Before marketing, professionals in operational safety, reliability and feedback processing applied mathematical methods based on statistical analysis to sample of data. While engineering specialists understood that it is necessary to combine "data approach" with "knowledge -based AI, those of marketing were suddenly empowered by analytics and "machine learning" algorithms.

As deep-learning requires big data for more accurate results the marketing specialists focus mainly on gathering more data from various available sources about customers to push them more products and services. Collected data is mined using analytics and deep learning software and the results explored commercially. This approach is not sustainable, because it requires a huge amount of data (data obesity) and consequently their storage and cooling, as well as energy for processing. Third generation of AI includes also evolution of robotsnow robots are deployed in many contexts without necessarily having a need for robot capacities. Currently many various robots replace humans including military robots and drones what raise ethical questions [START_REF] Wang | Ethics and Regulation of Artificial Intelligence[END_REF]. Very few is wondering about sustainability, eco-designing of robots, their recyclability and reparability, availability of raw materials and of electronic components to build "super-robots".

While an "automated" dialog between human and machine was proposed by Turing (famous Turing test) and Weizenbaum (Eliza, 1966), today there is a trend for having a chatbot able to answer the questions of clients and visitors. The designers of "intelligent" assistants implemented this principle. The majority of chatbots explore the ready answers recorded in (again) database. Main applications of chatbotsare described in [26]. Some research groups still follow the old dream of AI founding fathers work on Artificial General Intelligence (AGI)a machine able to surpass human intelligence [27].

AI patrimony

Since over 60 years, AI researchers and practitioners invented and have experimented the various approaches and techniques. The first robot Perceptron built in the late 1960s was equipped with embedded sensors, camera, and neural networks. It was able to ride on the ground and "learn" from "observation".

The knowledge-based AI introduced object programming, expert systems, natural language understanding and processing. After neural networks (1943) other machine learning approaches has been invented, such as automated generation of decision tree (ID3, 1970), Star methodology (Michalski, 1969) implemented in AQ [27]. All existing ML methods were grouped in Multi-Strategy Machine Learning (MSML) toolbox [START_REF] Michalski | Machine Learning -An Artificial Intelligence Approach[END_REF]. ID3 laid the foundation for data mining.

Case-based reasoning developed from the works of Roger Shank and Janet Kolodner in 1982 was latter improved by adding ID3 algorithm and dynamic induction combining the best from induction and nearest neighbors' algorithms.

Voice recognition and latter face recognition (image mining) are not new neither. Virtual reality implemented the principles of image processing in the middle of the 1990s.

The Figure 1 presents an overview of main AI fields and available techniques. Fig. 1. Overview of main AI fields and techniques [START_REF] Kayakutlu | Intelligence in Energy[END_REF] All techniques shown in Figure 1 have been successfully experimented for various applications in many fields around the globe. Decision support systems, diagnosis and many others are now embedded in larger applications such as automated pilot, autonomous car, intelligent building, in drones, translation systems, personal assistants, security and many others.

AI introduced specific way of thinking and problem solving which is different from those related to exploring databases. For example, managing sustainability requires deep understanding of all influencing factors, relations between them and elements of context, such as policies and human behaviors. The approach such as KADS [START_REF] Schreiber | KADS -A Principled Approach to Knowledge-based System Development[END_REF] comb-ing Newell knowledge level, Chandrasekeran interaction hypothesis and Clancey generalization, requires defining of a goal and decomposing it into the tasks; each tasks corresponds to a specific reasoning model that will use available knowledge and consider the context to achieve a given goal.

Deep problem understanding (global, holistic and system thinking) facilitates the choice of right technique or combination of them in hybrid systems [START_REF] Mercier-Laurent | Rôle de l'ordinateur dans le processus global de l'innovation à partir de connaissances[END_REF][START_REF]Problem Solving Methods: Past, Present, and Future[END_REF]. For example, we can use constraint programming for optimizing, planning and scheduling, artificial neural networks to find similar pattern in images, text or in audio file, case-based reasoning for matching local offers of jobs and competency and in intelligent e-commerce application. Some of mentioned techniques are integrated in multi-agents systems (MAS) [START_REF] Julian | Multi-Agent Systems[END_REF]. They have been used to study and to simulate complex systems in different application domains where physical factor are present for energy minimizing, where physical objects tend to reach the lowest energy consumption possible within the physically constrained world. Furthermore, MAS have been intensively exploited for the analysis through simulation of biological and chemical systems.

In the case of sustainability the contextual knowledge on policies in a given country, base of available actions and practice/prototyping should be considered. Taking inspiration from games [35] we can imagine building a Sustainability Support System as a simulator containing various interrelated components to evaluate the impact of decisions for policy makers, planners, organizations and companies. It can be conceived as a toolbox allowing easy configuration in function of the needs and allowing verifying various constraints before doing.

AI and sustainability

AI affects the sustainability. Two aspects of AI should be investigated: negative and positive. Negative consists in being dependent of all forms of computers and of software sometimes unnecessarily complicated; the both quickly evolving for many reasons including planned obsolescence. Collecting and storing exponentially growing data related to web services, for marketing and other purposes can be optimized by alternative green and smart approach to programming, using the suited knowledge models, both for collecting relevant data (Fig 2 ) and for guidance in "learning".

Fig. 2. Collection of data guided by knowledge models

According to Eric Thivant [START_REF] Thivant | Developing of Knowledge Base on Climate Change for Metropolitain Cities[END_REF] all outdated electronic devices can be partially recycled or reused in the developing countries that lacks computers.

Repairing is a key when it is possible. However, it requires expertise and can be supported by videos or AI applications. Since over five years now, French company called Back Market has been working on revaluation of apparently outdated smartphones [37]. Repair cafés multiplies connecting people that need a service or learn reparation [38]. 3D printer services provide spare pieces if not available for sale (old equipment). Sweden government offers the tax reduction for repairing goods.

The United Nations defined the 17 Sustainable Development Goals presented in Fig. 3. Some of them can be achieved with the help of adequate AI approach and techniques.

For example the Goal 1 -"No powerty" can be partially achieved by better management of talentsfrom education to employment and entrepreneurship [START_REF]Trends and Challenges for Intellectual Capital, chapter in Intellectual Capital in Organizations[END_REF]. However it is related to human behaviors.

The Goal 2 "End hunger, achieve food security and improved nutrition and promote sustainable agriculture". AI can bring a contribution here by smart agriculture, combining past knowledge on crop rotation, natural fertilization and symbiosis between plants with various optimization techniques, forecasting, smart use of water, optimal gathering and distribution (local). French Research Center on Agriculture CIRAD initiated agroecology [START_REF] Côte | The agroecological transition of agricultural systems in the Global South, Editions Quae[END_REF] that addresses this goal by combining Knowledge Management and selected AI techniques.

We have also avoid the food waste, especially in developed countries, pushed by business. Again behaviors plays a role hereit is better to explain how to do instead of giving ready food, as says an old proverb "Give a man a fish, and you feed him for a day. Teach a man to fish, and you feed him for a lifetime".

Achieving of Goal 3 "Ensure healthy lives and promote well-being for all at all ages" requires education on how our body works and nutrition. Access to Knowledge base on healthy cooking (not just to multitude of recipes) with available local ingredients, the basic phytotherapy, gymnastic may help achieving this goal. It can be done through games combining knowledge and fun. AI brought significant contribution in health systemsearly detection of serious diseases, robot surgery, diagnosis (expert systems), elaboration of vaccines and other. Artificial human "spare pieces" such as artificial pancreas [41] are already available and research on it progresses.

The well-being strongly depends on environment; it is linked with goals 11, 13 and 15.

The Goal 4 "Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all" involves the distribution of knowledge via technology. While AI-supported online learning has been practiced from the late 1990s and many MOOCs are available, the Covid pandemics accelerated massive use of technology in education. Many conferences on various topics are online and often for free. What should be better developed is the early evaluation of talents via dialogue with intelligent systems, interaction human-machine during learning and adaptation of the program to the students' level. An advice system for matching talents and interests with the range of occupational possibilities including new professions created by AI may help young people selecting their dream education leading to this job. Education influences the results in achieving the other goals.

The contribution of AI to the achievement of the Goal 5 "Achieve gender equality and empower all women and girls" can be done through access to education and better management of talents, independently of gender. However, the biggest challenge here is to make evolve mentalities, accept and develop the women talents, attract girls to scientific and technical study and professions. Social networks and other communication media has a significant role to play in achieving this goal.

The Goal 6 "Ensure availability and sustainable management of water and sanitation for all" can be partially achieved by optimized use of water. There are the similarity with achieving of the Goal 7 "Ensure access to affordable, reliable, sustainable and modern energy for all". The IBM offer Smarter Planet launched in 2010 contains few optimizing tools, however it addresses the energy, water and transportation providers. Kayakutlu and Mercier-Laurent [START_REF] Kayakutlu | Intelligence in Energy[END_REF] addresses the energy users and propose applying of AI techniques for optimized combining of natural and fossil energy, but also making citizens aware about energy waste. The trend of bitcoin, of collecting data, posting on social networks and recent recording of conferences online is energy consuming. The addressing of this two goals requires critical thinking and capacity of finding the smartest way of performing our activities. For example a leaf blower is energy consuming, polluting and not effective.

The Goal 8 "Promote sustained, inclusive and sustainable economic growth, full and productive employment and decent work for all" remains very difficult to achieve. The biggest barrier here is human greed, desire to become rich and powerful at the expense of others and by exploring cheap workforce and people in the need. This attitude can be "corrected" by games and social networks. This goal is related to the goal 10.

The Goal 9 "Build resilient infrastructure, promote inclusive and sustainable industrialization and foster innovation" is rather easy but requires better organization of innovation ecosystems and again management of talents, promoting "local". Digital transformation has a significant role to play at the condition of innovating the whole process. AI way of thinking helps organizing and implementing it using the suited techniques. At this stage the evaluation of impacts should be considered.

The Goal 10 "Reduce inequality within and among countries" is very ambitious and requires other organization then those by countries. It is connected to the goal 8 and requires wisening and humility of the world leaders or emergence of new leaders before applying AI for global optimization. Achieving this goal requires having an effective global governance. Some examples of societal innovation are given in [START_REF] Mercier-Larent | World Class Cooking for Solving Global Challenges[END_REF].

The Goal 11 "Make cities and human settlements inclusive, safe, resilient and sustainable" will be discussed in the point 4 on Smart City. This goal is linked with the goals 3, 6, 7 and 13.

The achievement of the Goal 12 "Ensure sustainable consumption and production patterns" again AI can help preventing various impacts. Eco-innovation and eco-design approaches [START_REF] Mercier-Laurent | Innovation Ecosystems[END_REF] powered by AI and alternative thinking may lead to wise exploring of raw materials, even avoid using them, especially in electronic devices. Planned obsolescence has to be replaced by sustainable products and services.

The Goal 13 "Take urgent action to combat climate change and its impacts" addresses a very complex and interconnected problems. Dealing with this challenge requires a deep understanding and modeling of impacting components and their interrelations, before planning the actions. As in constraint programming the priority of the actions and elaboration of adequate metrics to be implemented will determine the effectiveness of footprint reduction. Complex system approach [START_REF] Leonteva | A quantum simulation algorithm for continuous optimization[END_REF] and AI-powered simulator may help in global governance of climate change. This goal is interlinked with the goals 3, 6, 7, 9, 14, 15 and 17.

The Goal 14 "Conserve and sustainably use the oceans, seas and marine resources for sustainable development". This challenge is also complex, as the ocean life that should remain sustainable is. Taking care of the oceans requires combining knowledge and expertise from related fields. It covers many actions such as removing plastic (Boyan Slat), absorbing harmful fish using robots [45] or preserving spaces actions. Fishing is regulated however, this can be managed by AI, not on the country or European level, but for each sea and ocean. Transportation amplified by globalization try to shorten the roads despite pollution and heat generated. This problem can be solved by influencing mentality (as Goal 10), producing and buying local sustainable goods. Researchers deploy other robots to understand the sea life in aim preserving the balance. The European initiative OceanGov addresses 7 components in the related multidisciplinary working groups [START_REF]Ocean Gov initiative[END_REF]. Achieving of the Goal 15 "Protect, restore and promote sustainable use of terrestrial ecosystems, sustainably manage forests, combat desertification, and halt and reverse land degradation and halt biodiversity loss" depends again of the way of doing business and searching for quick profit. AI may help in urbanization planning and optimizing. Desertification depends on managing local talents and increase the attractiveness. For example today the only way of getting benefits in France is investment into houses and buildings. Investors purchase the land for low prices and build houses or buildings for sale destroying biodiversity. If only we could change the innovation policies and make investment in innovation more attractive than investment in buildings, not always necessary. Again the AI based simulators have the potential to demonstrate such impacts.

Goal 16 "Promote peaceful and inclusive societies for sustainable development, provide access to justice for all and build effective, accountable and inclusive institutions at all levels". Achieving this goal require the change of behaviors at all levels and restoring the lost respect. Games may help, but it should be connected to politics, education and amplified by mass media.

Goal 17 "Strengthen the means of implementation and revitalize the global partnership for sustainable development" can be achieved by incentives such as investment in sustainable innovation. Global partnership has been already tried by various conference but without significant results. Interesting initiatives such as Earth Planet, agro ecology of CIRAD [START_REF] Côte | The agroecological transition of agricultural systems in the Global South, Editions Quae[END_REF], numerous projects on preserving biodiversity and other prototyping actions [may serve as inspiration for the next. Knowledge base BC3 [START_REF] Thivant | Developing of Knowledge Base on Climate Change for Metropolitain Cities[END_REF] was designed to group such experiences.

Smart city can be a playground for prototyping of sustainable development of not only cities but applying holistic approachsmart and autonomous villages, small and bigger cities and regions. Well defined and conceived such way of doing may help achieving several UN goals.

Contribution of AI -Case of Smart City

All concepts -Smart City, Intelligent City, Green and Wise City -aim in providing services to citizens of quickly growing cities. The citizens can be individual or a part of organization or company that is why holistic approach is appropriate. Actually, the raisons of this growth are job offer, access to services, to culture or immigration or search for better social conditions. Based on linear approximation in 2050 70% of world population will be living in the Megapolis [48,[START_REF]Ville intelligente[END_REF].

Another influencing factor to take into consideration is the ambition of politicians to grow their territory, to attract companies and capital in aim increasing their power and show it up. As consequence, regional economy collapses in many cases and should be reinvented using local talents and resources.

The concept of Smart City was probably born in early 2000s pushed by technology with Cisco as network provider, IBM and some others. In 2010, IBM introduced a new slogan "Smarter Planet" combining their current offer to various elements related with water, energy and transportation management.

Intelligent City tries to be different and defines integrated model of intelligent economy, green transportation, environment, governance and services for citizens [START_REF]Ville intelligente[END_REF].

The city of Nice (French Riviera) runs annually a conference on Innovative City [50]. This year AI and its benefits for the city is on the program. The other topics discussed are more traditional -mobility, energy, recycling, urbanism, wellbeing and specificities of Euro-Mediterranean area to explore. Technology is behind all items, but it lacks an overall approach for better optimization of efforts and investment.

Growing cities want to attract people and companies by offering wellbeing to citizens. Green City combines architecture, gardening and social cohesion [START_REF]ICT for Societal Challenges. Digital Agenda for Europe[END_REF]52]. The topic of societal innovation is timely in the current changing context [START_REF] Mercier-Larent | World Class Cooking for Solving Global Challenges[END_REF].

The Wise City of Hong Kong in collaboration with French Chamber of Commerce brings together large companies -Schneider Electric, Alstom, Veolia, Thales and KPMG -no room for small ones. KPMG claims to be integrator of all offers. They focus on improvement of living conditions: pollution, access to clean water, waste treatment, etc. Hong Kong with over 7 million of habitants produces 15,000 tons of waste daily and uses 60% more water than New York. Buildings are heavy consumers and air pollution is 53% local [53].

Schneider Electric being a partner of Wise City proposes an integrated offer, shown in Fig. 3. The presented offer, elaborated as a whole, improved though deployment in over hundred targeted cities includes the following components: smart energy, smart mobility, smart water, smart public services, smart buildings, smart data centers and smart integration. These components represent also the areas of Schneider expertise. Several AI techniques, optimization, maintenance, decision support and others facilities are embedded in this offer to provide solutions tailored for the city. For example, mobility module provides the real-time monitoring of system performance and detection of problems that may occur (predictive maintenance). The collected feedback allows reducing traffic and improving the network.

The energy module is in charge of providing continuous service. In the case that apply the energy offer is composed also with available sources of renewable energy.

Another module is in charge of water management and supply. Improving public safety is possible thanks to real-time analysis of video cameras (using deeplearning).

We can notice that the offers for energy and water are a part of smart buildings. Smart buildings, IoT and home automation systems helps managing machine-to-machine connections, detection of incidents, water and energy supply and optimized use of resources.

Healthcare management includes, among others AI-bases planning and scheduling of staff and devices for better service offered to patients.

Environmental footprint assessment application collects the environmental data. After validation, they are explored for improvement of performances. Data related to "users' experience" are also collected and explored for continuous improvement.

Data Center is certainly associated with city management system and we hope there is only one for all applications proposed by partners.

This integrated city management platform designed using Knowledge Management principle connects all elements and allow information and knowledge sharing, the observation of world best practices, provides decision support and incidents management. This platform communicates with city management and citizens.

The city is also in charge of the other services that citizens may need but the above system does not allow expressing the citizen (consider in holistic perspective) ideas for new services. Considering holistic approach a Future factory is a part of the city or of the region.

AI plays multiple role in Smart cityin the above-integrated offer the optimization techniques are used to manage water and energy distribution and consumption, other techniques for diagnosis, maintenance, business intelligence, optimizing transportation, collection of garbage, planning works, meetings, events and other city activities.

However, the smart city has to be managed as the whole ecosystem in its environment and not by separate modules. Cities are concerned by economic development, but also pandemics, biodiversity, climate change, pollution, education, poverty and other UN goals.

We suggest to improve this concept by connecting several UN goals and prototyping in selected region. Some examples of such prototyping are already available, but in various context, that makes difficult finding similar example [START_REF] Mercier-Larent | World Class Cooking for Solving Global Challenges[END_REF]. The project B3C [START_REF] Thivant | Developing of Knowledge Base on Climate Change for Metropolitain Cities[END_REF] ambitions in building collaborative knowledge base of best world practices.

Conclusion and Perspective

Humans are the greater generators of disasters. In the context of Planet Emergency, sustainability and sustainable development is still a big challenge for humanity. Before applying technology this complex problem requires awareness about our impact and evolution of individual and companies behaviors, radical change of focus from having more to living better in harmony with nature. AI way of thinking helps understanding better such a complex problem, finding alternative solutions. The better use of our brain capacity is mandatory.

The presented example demonstrated that AI is useful in many situations if we apply appropriate method and techniques. AI can help managing many aspects when used appropriately, but we still need to define the right metrics for correct evaluation of the effects of our actionsindividual and collective. Simulators cans help evaluating the situation, testing effect of influencing factors and consequence of decisions to take before doing. It applies in industry, city and in our lives.

The balance between the use of technology and human capacity should be preserved. Technology producers have tendency to produce software and devices that think instead of the human and take decisions for him/her. This kind of applications may replace human at the long run and reduce his cognitive capacity. That is why we have to design applications able to enhance human intelligence without switching it off. Technology alone cannot save Planet, but can help us to be smarter.

Fig. 4 .

 4 Fig. 4. Integrated services for Smart City (source https://www.slideshare.net/SchneiderElectric/schneider-electric-smart-cities-hannover-v3