Abdullah M Shaheen

M A Hamida

Ragab A El-Sehiemy
email: elsehiemy@eng.kfs.edu.eg

Ehab E Elattar

Optimal Parameter Identification of linear and non-linear models for Li-Ion Battery Cells

Keywords: Li-Ion Battery Cells, Non-linear models, Equilibrium Optimizer, Three stage parameter identification, State of charge estimation

This study proposes a reduced model based on the state space representation for identifying an accurate electric equivalent circuit of Lithium-Polymer Battery Cells. The parameter extraction process is formulated as non-linear optimization problem via three-stage procedure. The first stage estimates the state of charge (SoC) based on the non-linear characteristics associated with the battery current and the initial SoC condition. In the second stage, the open circuit voltage is estimated in terms of the resulted SoC that is employed in the first stage with varied linear and non-linear models. In the third stage, an Equilibrium Algorithm (EA), a recent optimizer, is developed for optimally identifying the battery parameters. The EA's parameters are adjusted based on Taguchi's design of experiment approach to reduce the computational time as well as the number of experiments that are required to get the optimum possible parameter arrangement. Numerical simulations associated with experimental implementation are emulated on Li-Ion Battery to prove the high capability of the proposed EA an as efficient identification procedure. In Addition, the proposed EA is characterized with high accuracy compared with several recent optimization algorithms for ARTEMIS driving cycle profile. The solution quality improvement of the proposed reduced model is achieved with high closeness to the experimental measurements for battery voltage and SoC. Furthermore, 16 % less computational times 12 % more accuracy are obtained by the proposed reduced model compared with linear and non-linear models.

Open circuit voltage

V ex Experimental voltage F i (u)
is the objective function iand u is the estimated parameters of the battery N is the number of the estimated u min , u max are the accepted parameter bounds of control variable's vector u , nobf is the number of objective functions. Vbat and V bat refer to the estimated and experimental battery voltages, respectively. w 1 and w 2 weighting factors to reflect the degree importance of objectives, F 1 and F 2 . min and max refer to the minimum and maximum operators of the extracted parameters. X * and X are the new and current vectors of the particle concentration, respectively. X r,eq is a random extracted individual from the four best-so-far concentrations in equilibrium pool. λ

The random factor and its range is within [0, 1]; F is an exponential term Gr is the rate of generation rate.

1. Introduction

Motivation

Energy storage systems act important role in facilitating the inclusion of different types of renewable resources such as wind, fuel and solar energies into the electrical power grids while the network reconfiguration is carried out with the existence of renewable distributed generation units [START_REF] Rowden | Estimating lithium-ion battery behavior from half-cell data[END_REF]. Added to that, Energy storage can be used to manage the maximum load affecting on the power grids [START_REF] Abou El-Ela | Pv and battery energy storage integration in distribution networks using equilibrium algorithm[END_REF] as one of the important devices in the renewable energy resources [START_REF] Ginidi | Supply demand optimization algorithm for parameter extraction of various solar cell models[END_REF]. Parameter estimation of battery is an urgent issue in recent years for efficient modeling of these elements on the overall system operation [START_REF] Xiong | Co-estimation of state of charge and capacity for lithium-ion batteries with multi-stage model fusion method[END_REF]. Finding the most accurate model for emulating the battery is still rich research field. Estimation of the battery parameters of various models is carried out based on the utilization of experimental methods. But this estimation procedure suffers from several demerits as cost expensive, high computational capacity, is needed in addition it consumes more time because the existence of repeated computation tasks In [START_REF] Yuan | A new technique for optimal estimation of the circuitbased pemfcs using developed sunflower optimization algorithm[END_REF].

Literature Review

Several efforts have been employed for finding the optimal parameters of battery and to extract the state of charge. In [START_REF] De Fatima Brondani | Parameter estimation of lithium ion polymer battery mathematical model using genetic algorithm[END_REF],the parameters of the Lithium Ion Polymer are optimized by using the genetic optimization algorithm. In [START_REF] Brondani | Battery model parameters estimation using simulated annealing[END_REF], another optimization method was developed by using the Simulated Annealing optimization method In [START_REF] El-Sehiemy | Parameter identification and state-of-charge estimation for lithium-polymer battery cells using enhanced sunflower optimization algorithm[END_REF]. The sunflower optimizer was developed for extracting the battery parameters and estimating the SoC of lithium ion battery. The proposed method is employed with aid of the state space model and the SoC with battery voltage relationship is represented by a linear equation which is not the case in reality. The model based methods are largely investigated especially for SoC estimation [START_REF] Wei | Noise-immune model identification and state of charge estimation for lithium-ion battery using bilinear parameterization[END_REF], [START_REF] Sun | Combined internal resistance and state-of-charge estimation of lithium-ion battery based on extended state observer[END_REF]. An online extraction of the SoC based on the equivalent circuit with offer high accuracy and robustness [START_REF] Zhao | Lithium-ion battery state of charge estimation with model parameters adaptation using hâ extended kalman filter[END_REF]. A number of these methods includes parameters identification problem to deal in particular the internal resistance uncertainties. The authors in Ref. [START_REF] Wei | Noise-immune model identification and state of charge estimation for lithium-ion battery using bilinear parameterization[END_REF] proposes to use a Lunberger observer to estimate the SoC of Lithium-ion battery by considering the effect of the measurement noises on the parameter identification. The problem is solved by considering two linear models, the first one to estimate the SOC and the second one to identify the parameters. As it is well known, linear model can give an accurate estimation in limited operation conditions. Using the same approach, [START_REF] Ning | Adaptive sliding mode observers for lithium-ion battery state estimation based on parameters identified online[END_REF] proposed the real-time battery SoC is extracted based on the adaptive sliding observer. Firstly, an online parameter estimator was developed and then a sliding mode observer is designed based on the estimated parameters. The developed solution offers good results but it is very hard for real time implementation in particular when low cost embedded systems are employed. [START_REF] Yu | Lithium-ion battery parameters and state-of-charge joint estimation based on h-infinity and unscented kalman filters[END_REF] propose to combined observer for parameter and SoC estimation. A H-infinity filter was employed for on-line parameter identification and a modified version of Kalman observer is employed for SoC estimation. Thanks to the online parameter identification, the proposed solution allows an accurate estimation of SoC in different operation conditions but the stability of the both observers cannot be guaranteed which limit its scope.

The electrochemical model was the crucial tool which allows to analyse the dynamic behaviour of lithium battery because it allows the analysis of the dynamic behavior of batteries [START_REF] Hu | Condition monitoring in advanced battery management systems: Moving horizon estimation using a reduced electrochemical model[END_REF]. Several SoC estimation methods have been implemented based on the electrochemical model, such that last-square fitting method, Kalman filtering and electromotive force method [START_REF] Li | Li-ion dynamics and state of charge estimation[END_REF]. These methods offer an accuracy estimation in particular when the model impedance is updated. However, the estimation accuracy is affected by the aging of the battery and the related variations in the battery temperature.

The Open Circuit Voltage (OCV) was employed for estimating the SoC of lithium battery based on approximate linear relationship model to express the open circuit voltage in terms of the state of charge as presented in Refs. [START_REF] Meng | Comparative study of lithium-ion battery open-circuit-voltage online estimation methods[END_REF]. This relationship varies from a battery to another because it depends on the battery capacity and material. Moreover, it is not easy to express the OCV measurement in real time because that is needs cutting off the power and the battery rest for long period [START_REF] Hannan | A review of lithium-ion battery state of charge estimation and management system in electric vehicle applications: Challenges and recommendations[END_REF]. Another approach was considered for the estimation of the lithium battery SoC [START_REF] Xiong | A systematic model-based degradation behavior recognition and health monitoring method for lithium-ion batteries[END_REF] on the basis of Ampere-hour counting method was also employed. This method offers an estimation in particular when the initial SoC is known. Moreover, the battery capacity should be not considered constant since it is affected with the battery lifetime [START_REF] Hu | An enhanced multi-state estimation hierarchy for advanced lithium-ion battery management[END_REF]. The estimation of the Li-ion batteries SOC was the focus of great number of researchers in recent 10 years. The dynamic model is considered with for formulating the parameters estimation problem. But, the rate of changes of the battery parameters is not considered in the previous studies of estimation process. The work in [START_REF] Safwat | A novel methodology for estimating state-of-charge of li-ion batteries using advanced parameters estimation[END_REF] discussed the change of rate of the estimated parameters. With the development of the computing systems, the intelligent mathematical tools become good candidate for SoC estimation of lithium battery system. Among these tools one can find neural network [START_REF] Yang | State-of-charge estimation of lithium-ion batteries based on gated recurrent neural network[END_REF] fuzzy logic [START_REF] Hu | Reliable state of charge estimation of battery packs using fuzzy adaptive federated filtering[END_REF], adaptive neuro-fuzzy interface [START_REF] Singh | Hardware-in-the-loop implementation of anfis based adaptive soc estimation of lithium-ion battery for hybrid vehicle applications[END_REF] and support vector machine [START_REF] Sahinoglu | Battery state-of-charge estimation based on regular/recurrent gaussian process regression[END_REF].

These methods allow to meet the of accurate estimation requirements to represent the SoC independently to the battery internal circuit with the initial value of SoC by using the trained data and to work when the battery is operated in nonlinear conditions. The artificial intelligence method can be combined with other estimation methods such as model-based method as in [START_REF] Chen | Neural network-based state of charge observer design for lithium-ion batteries[END_REF] where a neural network is combined with a nonlinear observer to obtain an accurate estimation of SoC. However, the artificial intelligence methods require large memory to store a large data which is not always possible. Reference [START_REF] Wang | A novel consistency evaluation method for seriesconnected battery systems based on real-world operation data[END_REF] presented an evaluation and assessment model for batteries that were connected in series into the grid. The assessment system is developed on the basis of the operation data in real domain. In Ref. [START_REF] She | Battery aging assessment for real-world electric buses based on incremental capacity analysis and radial basis function neural network[END_REF], the aging issue of battery assessment in real world was carried on incremental capacity analysis accomplished with neural network as a radial training mechanism. In Ref. [START_REF] Zhang | Hybrid electrochemical energy storage systems: An overview for smart grid and electrified vehicle applications[END_REF] presented the electrochemical energy based on combined mechanism storage systems. References it was presented a survey about the electrical vehicle application in smart grid environments. Reference [START_REF] Liu | Feature analyses and modelling of lithium-ion batteries manufacturing based on random forest classification[END_REF] presented Random Forest Classification Feature for Analysis and Model the Li-Ion batteries. In Ref. [START_REF] Liu | An evaluation study of different modelling techniques for calendar ageing prediction of lithium-ion batteries[END_REF] the machine learning method was developed for identifying the aging of Li-Ion batteries as an assessment study.

The optimization techniques with their excellent global search abilities were used for the parameter identification and SoC estimation of lithium batteries [START_REF] Zheng | State-of-charge inconsistency estimation of lithium-ion battery pack using mean-difference model and extended kalman filter[END_REF]. These techniques presented excellent tools to identify with high accuracy the parameters of the developed battery models. The optimization algorithms are generally combined with other estimation tools such as genetic algorithm [START_REF] Chen | A novel state-of-charge estimation method of lithium-ion batteries combining the grey model and genetic algorithms[END_REF], model-based method [START_REF] Zheng | State-of-charge inconsistency estimation of lithium-ion battery pack using mean-difference model and extended kalman filter[END_REF], battery equivalent circuit method [START_REF] Sangwan | Estimation of battery parameters of the equivalent circuit model using grey wolf optimization[END_REF]. The estimation obtained by using the optimization algorithms depend also on the employed model. The using of the nonlinear models lead to more accuracy estimation [START_REF] Mesbahi | Dynamical modelling and emulation of li-ion batteriesâsupercapacitors hybrid power supply for electric vehicle applications[END_REF] compared to the linear models. However, the nonlinear models are more complicated and require more computing time even when the battery is operated in linear conditions. Recently, the equilibrium optimization algorithm was proposed by A. Faramarzi et al. in [START_REF] Faramarzi | Equilibrium optimizer: A novel optimization algorithm[END_REF]. The EA has a straightforward optimization framework with adaptive controlling parameters. It simulates the dynamic equilibrium states that describe and characterize the mass balance patterns. In the EA, each search individual mimics the concentration of a particle which is randomly initialized and updated in respect of attaining the optimal fitness that mimics the final equilibrium state. Later, some EA applications are noticed in the literature for solving engineering problems of image segmentation [START_REF] Abdel-Basset | A novel equilibrium optimization algorithm for multithresholding image segmentation problems[END_REF], vehicle components design [START_REF] Özkaya | The equilibrium optimization algorithm and the response surface-based metamodel for optimal structural design of vehicle components[END_REF], parameters extracting of fuel cell [START_REF] Menesy | Extracting model parameters of proton exchange membrane fuel cell using equilibrium optimizer algorithm[END_REF], and economic dispatch [START_REF] Agnihotri | Equilibrium optimizer for solving economic dispatch problem[END_REF]. As further successful applications of EA the following references can cited: distributed generation (DG) allocation with network reconfiguration [START_REF] Shaheen | A forensic-based investigation algorithm for parameter extraction of solar cell models[END_REF], Feature Selection [START_REF] Gao | An efficient binary equilibrium optimizer algorithm for feature selection[END_REF], Optimal Power Flow (OPF) of hybrid grids [START_REF] Abdul-Hamied | Equilibrium optimizer based multi dimensions operation of hybrid AC/DC grids[END_REF], OPF with Renewable Energy [START_REF] Nusair | Application of equilibrium optimizer algorithm for optimal power flow with high penetration of renewable energy[END_REF], and biomass DGs placement in power systems [START_REF] El-Ela | Optimal coordination of static VAR compensators, fixed capacitors, and distributed energy resources in egyptian distribution networks[END_REF].

Research Gap

Many issues are considered for modeling the battery parameters identification and SOC estimation. Actually, no assessment for the impact non-linear modeling were considered the previous studies in the literature. Also, most of the models presented in the literature are based on a complex state space model. The linear model doesn't need lot of computation time for parameter identification. However, it can not give a good accuracy for parameter identification because the Lion-Ion Battery is a nonlinear system. From the other side, nonlinear model can give a good accuracy for parameter estimation, but it requires longer computation time. The proposed strategy has produced a reduced nonlinear model which give a good identification accuracy with less computation time compared to classical nonlinear models. Then, the parameter estimation are greatly effected by the solution method. To overcome this problem, the proposal of the reduced model with enough accuracy for parameter estimation becomes an absolute necessity The current study is concerned with the previous raised research gaps in the literature. In this regard, linear and non-linear representation of the relation between open circuit voltage and the state of charge are considered.

Paper Contributions

The salient features of this study are summarised as follows:

1. The state space model is divided into three separated models that enhance the solution methodology and find the accurate relation for each stage. 2. in this study, an assessment between the various linear and non-linear models, that are employed the relation between open circuit voltages and the battery state of charge. 3. An new solution methodology based on Enhanced Equilibrium Optimization Algorithm (EA) is proposed considering statistical indices that reflect the proposed method capability. 4. The EA's parameters are designed based on Taguchi's design of experiment approach.

5. The proposed procedure is initially applied on real Li-Ion Battery Characteristics then dynamic verification study is carried out on ARTEMIS driving cycle. 6. Less computational time is achieved by using the reduced model at acceptable level of accuracy compared with linear and non-linear models.

Paper Organization

The rest sections of this study are organised as follows: Section 2 presents the problem formulation of the considered parameters estimation problem of the Li-IOn battery. In Section 3, the proposed battery parameters and SoC estimation is introduced. The experimental results are presented in Section 4. This study conclusions are reported in Section 6.

Problem Formulation

The problem of battery parameters estimation is still of interest for many researchers . The proposed formulation describes the way to compute the battery voltage and state of charge. According to [START_REF] El-Sehiemy | Parameter identification and state-of-charge estimation for lithium-polymer battery cells using enhanced sunflower optimization algorithm[END_REF], the battery voltage and the state of estimation are modelled by state space model as:

Modeling of Lithium Ion Battery

The general equivalent circuit model is constructed with a number of n times RC elements denoted by nRC-model [START_REF] Lai | A comparative study of global optimization methods for parameter identification of different equivalent circuit models for li-ion batteries[END_REF], normally it is extended up to 3 RC elements [START_REF] Orcioni | Lithium-ion battery electrothermal model, parameter estimation, and simulation environment[END_REF]. The RC group is considered as relaxation part to avoid the complexity raised for the extraction the battery parameters. In the sequel,the state space model for the battery dynamics is represented in the following form:

Ẋ = AX + Bu (1) y = CX + Du + b 0 (2)
where,

X = SOC V rc , A = 0 0 0 -1 RC , B = 1 Q R 1 C , C = b 1 1 , D = R 0 .
To describe the static characteristic of the battery under predetermined conditions of temperature and age, Equation (3) presents a linear relationship between the V oc and SoC is assumed as [START_REF] Rahimi-Eichi | Online adaptive parameter identification and state-ofcharge coestimation for lithium-polymer battery cells[END_REF] as:

V OC = f (SOC) = b 0 + b 1 SOC. (3)
The nonlinear relation that describes the open circuit voltage versus the state of charge can be expressed in exponential form as:

V OC = f (SOC) = a O + N i=1 a j e a j+1 (1-SOC) i +a j+2 e a j+3 (SOC) i (4)
where

j = i + 3 × (i -1)
Based on Eq. ( 4), the variable N can control the number of terms that is used to describe the nonlinear relation between V OC and SOC.

In the current work,the state space dynamic model is used to describe the terminal voltage (V T ) versus current (I L ). Both the temperature and ageing of the battery effects are not considered in this work.

Parameterization model development

To optimize the parameters of the Li-ion battery model, The dynamic model of the battery described in the previous section is used. An objective function has to be set for fitting the estimated output voltages with the corresponding recorded voltage in the experimental tests. This objective function aims at minimizing the Squares Error Sum (SSE) between the estimated and experimental data. The common form of this optimization form is:

min u F i (u), i = 1, 2..nobf (5) u min ≤ u ≤ u max
The parameters extraction model is dependent on the battery experimental data. In the proposed method, two cases studied are considered. A multi-objective M oF fittness function that aims at minimizing the aggregation of the root mean square of the normalized deviation between both the estimated and experimental battery voltage and the estimated and experimental state of charge is proposed. This function M oF combines two objectives which are:

F 1 (u) = ( V bat -V ex V max bat ) 2 ; (6)
F 2 (u) = ( ŜOC -soc soc max ) 2 ; (7)
The first objective function (F 1 (u)) represents the normalized deviation between extracted and experimental voltage of the battery while the second one represents the normalized deviation of the state of charge (F 2 (u)). Then, the combined objective function of the battery model identification can be expressed as:

M oF (u) = w 1 × n i=1 ( V bat -V ex V max bat ) + w 2 × n i=1 | ( ŜOC -soc soc max ) | (8)
Then, the combined objective function,Eq. ( 8), is optimized with respecting the following inequality constraints for each control parameter (u) within their boundaries as:

R min ≤ R ≤ R max (9) R 0 min ≤ R 0 ≤ R 0max (10)
C min ≤ C ≤ C max (11) b 0 min ≤ b 0 ≤ b 0max (12) b 1 min ≤ b 1 ≤ b 1max (13) Q r min ≤ Q r ≤ Q rmax (14)
N Model V OC = f (SOC) Parameters Number 1 =a 0 + a 1 e a 2 (1-SOC) + a 3 e a 4 SOC
a 0 , a 1 , ... a 4 5 2 =a 0 + a 1 e a 2 (1-SOC) + a 3 e a 4 SOC + a 5 e a 6 (1-SOC) 2 + a 7 e a 8 SOC 2 a 0 , a 1 , ... a 8 9 3 = a 0 + a 1 e a 2 (1-SOC) + a 3 e a 4 SOC +a 5 e a 6 (1-SOC) 2 + a 7 e a 8 SOC 2 + a 9 e a 10 (1-SOC) a o , a 1 , ... a 24 25

Proposed Battery Parameters Procedure based EA

The parameter extraction problem is represented as non-linear three-stage procedure based optimization problem. The first stage estimates the SoC based on its non-linear relation defined by equations with the battery current (1)-( 2) considering the initial SoC condition. It can be computed by equation [START_REF] Li | Li-ion dynamics and state of charge estimation[END_REF]. In this equation, η refers to the battery efficiency and SoC int refers to the initial condition of the SoC. In the second stage, the open circuit voltage is estimated in terms of the resulted SoC that is employed in stage 1 with varied linear and non-linear models. Equation (4), represents these several models that describe the nonlinear relation between V OC and SOC by varying the number of the control parameters that are required to be identified as reported in the Table 1. From this table, 6 non-linear models are used to express the open circuit voltage and SoC

SoC = 100 (SoC int - 1 Q n ηI b dt) (15)
In the third stage, the recent optimizer called equilibrium algorithm is employed for optimally identifying the battery parameters. In EA [START_REF] Faramarzi | Equilibrium optimizer: A novel optimization algorithm[END_REF], the initial concentrations with a particular number (Npr) are iteratively generated

X * = X r,eq + Gr λ (1 -F) + (X -X r,eq ) • F (16) F = A 1 sign(B -0.5).(e -λ(1-Z Zmax ) A 2 Z/Zmax -1) (17)
Gr = 0.5r 1 (X r,eq -λX) F if r 2 ≥ GP 0 if r 2 < GP (18)
where, the constants A1 and A2 equal 2 and 1 , respectively. the vector B, r 1 and r 2 are is random within range [0, 1]; Z and Z max are the current and the maximum number of the iterations, respectively. are random numbers within range [0, 1]; GP is the probability of generation that is set to 0.5. As shown [START_REF] Meng | Comparative study of lithium-ion battery open-circuit-voltage online estimation methods[END_REF], the updating process of each particle concentration is mainly based on the effect of three parts. The first is the extracted individual from the four best-so-far concentrations in the equilibrium pool. The second and third parts is dependent on the variation measure between the extracted equilibrium concentration and the current one. These two parts have a randomized vector of exponential behavior that is responsible for exploitation and exploration characteristics of the EA in the search space to optimally find the outcome. The main steps of the EA can be written as follows:

1. Create the initial population of the particle's concentrations randomly.

2. Check the bounds of the control variables (u) and set any violated one to its nearest bounds (( 9)-( 14)). 3. Estimate the fitness function in Equation ( 8) of each concentration in the population. 4. Pick out the four best-so-far concentrations to form the equilibrium pool using Equation( 16). 5. Update the exponential term (F) and the generation rate (Gr) using Equations [START_REF] Hannan | A review of lithium-ion battery state of charge estimation and management system in electric vehicle applications: Challenges and recommendations[END_REF] and ( 18), respectively. 6. Update each particle concentration X * using Eq. ( 16). 7. Go to step 2 until reaching the maximum iteration number which is considered as the stopping criteria.

Experimental Results

In this study, the 40 Ah Li-ion battery cell is an example of the commercial batteries that achieve high improvements in the drive performance and its accompanied reliability [START_REF] Affanni | Battery choice and management for new-generation electric vehicles[END_REF]. The pertinent specifications that can be found in the data -sheet are: nominal voltage equals 3.7 V, internal resistance is 0.9 mΩ, the capacity 40 Ah, specific energy is 167 Wh/kg of weight 0.885 kg and both charging/discharging currents are 40A. In this study, the proposed estimation procedure is employed for two cases. These cases are considered to emulate linear and non-linear representation for the relation between V OC and SoC as follows:

1. Case study 1: Consideration of Linear relation between V OC and SoC 2. Case study 2: Consideration of Non-Linear relation between V OC and SoC Added to these two cases, the proposed estimation procedure is developed for Artemis driving cycle. Table 2 presented the considered boundaries of the estimated parameters of the battery cells. In the first case, the relation between V OC and SOC is taken in its linear form as 3) [START_REF] Affanni | Battery choice and management for new-generation electric vehicles[END_REF]. The proposed EA is applied for minimizing the aggregation of the root mean square of the normalized difference between both battery voltage and state of charge for the experimental and estimated values. Table 3 shows the obtained optimal parameters and their corresponding results.

Simulation results of Case study 2

In the second case, the relation between V OC and SOC is taken in its non-linear form as described in Eq. ( 4) [START_REF] Mesbahi | Dynamical modeling of li-ion batteries for electric vehicle applications based on hybrid particle swarm-neldermead (pso-nm) optimization algorithm[END_REF]. Similar to Case 1, the proposed EA is applied effectively, and the optimal results is tabulated in Table 3. In this case, the identified parameters are more than double the parameters in Case 1. However, the considered objective, in this case, is greatly minimized to 0.00765 compared to 0.0292 in Case 1. Both indexes are minimized where the root mean square of the normalized difference of the battery voltage between both the estimated and experimental records is declined to 0.0072 and the estimated and experimental state of charge is declined to 0.0135 as well.

Effect of exponential terms in the Non-Linear relation between V OC and SOC

As discussed previously, the non-linear form that describes the relation between V OC and SOC has better performance than the linear form. In this subsection, the effect of increasing and decreasing the exponential terms in the Non-Linear relation of Eq. ( 5) between V OC and SOC is considered. This effect is discussed by controlling the number (N) in Eq. ( 5). Table 4 summarizes the optimal parameters based on EA for different N values which is specified at 5, 9, 13, 17, 21, and 25, respectively. The proposed EA can reach the minimum MOF in all cases of 0.00775, 0.00764, 0.00764, 0.00784, 0.00765, and 0.00767 at N values of 5, 9, 13, 17, 21, and 25, respectively. As shown, no significant improvement in the accuracy by increasing N values more than 9. On the other side, the more increasing of the value of N, the more increasing in the parameters that are required to be optimally identified. Consequently, the computational complexity is increased and so it needs more calculation time. between V OC and SOC In this subsection, several recent optimization algorithms are applied to show the capability and robustness of the proposed EA in consideration of Non-Linear relation between V OC and SOC. Beside the EA, 2020, the compared algorithms are Forensic-based investigation algorithm (FBI), 2020 [START_REF] Shaheen | Equilibrium optimization algorithm for network reconfiguration and distributed generation allocation in power systems[END_REF], grey wolf optimizer GWO, 2021 [START_REF] Shaheen | Optimal coordinated allocation of distributed generation units capacitor banks voltage regulators by egwa[END_REF], efficient particle swarm optimization (PSO), 1995, backtracking search algorithm (BSA), 2013 [START_REF] Shaheen | Enhanced feeder reconfiguration in primary distribution networks using backtracking search technique[END_REF]. These algorithms are applied with the same number of individuals of 100 and maximum number of iterations of 500. Their obtained parameters and results are tabulated in Table 5. This table elucidates the high capability of the proposed EA in finding the global minimal as it obtains the minimum MOF with 0.007654 where GWO, FBI, PSO and BSA acquire 0.008614, 0.009216, 0.00974, and 0.5774, respectively. Furthermore, a robustness test for these algorithms is executed by running them 10 times and recording the Best, Mean, Worst, and standard deviation (Std) in Table 5. It is clear that the proposed EA is distinguished with high robustness minimum indices, Best, Mean, Worst, and Std, of 0.007654, 0.00861, 0.011873, and 0.001248, respectively.

For any meta-heuristic optimization method, there really is no promise to say that the gained response is the optimal option except it is identified [START_REF] Elsakaan | An enhanced moth-flame optimizer for solving non-smooth economic dispatch problems with emissions[END_REF]. This returns to the probability of such optimization methods to be trapped in a local optima and, subsequently, stop developing. As described in [START_REF] El-Ela | Optimal coordination of static VAR compensators, fixed capacitors, and distributed energy resources in egyptian distribution networks[END_REF], the continuity in developing the best solution in the convergence curve declares a good indicator for avoiding local minimal area. Fig. 8 describes the EAâs convergence curve of ten separate runs. This figure demonstrates the significant development of the best solution by non-stick iterations at a local minimum. Added to that, Fig. 9 illustrates the box and Whiskers plot for the competitive optimization algorithms, MPO, FBI, GWO and EA, which demonstrates the high effectiveness of the EA in finding the minimum MOF compared with the others. Furthermore, a robustness test for these algorithms is executed by running them 10 times and recording the Best, Mean, Worst, standard deviation (Std) and the computation time per iterationin Table 6. It is clear that the proposed EA is distinguished with high robustness minimum indices, Best, Mean, Worst, and Std, of 0.007654, 0.00861, 0.011873, and 0.001248, respectively. In terms of The EA employed is defined by its adaptive framework. However, there seem to be the size of the population (Ps) and the maximum number of iterations show high effect on results.

Parameter Tuning of Competitive Algorithms

In this subsection, the all competitive parameters are adjusted based on Taguchi's design of experiment approach, which reduces computational time and the number of experiments required to get the optimum possible parameter arrangement [START_REF] Hossain | Energy management of community energy storage in grid-connected microgrid under uncertain real-time prices[END_REF]. The orthogonal array L É¡(32) is used to execute the parameter combinations listed in Table 7, as the number of parameters is 2 and each one has 3 levels. The array results in 9 treatments. Table 8 shows the orthogonal array with the MOF value. Table 9 tabulates and depicts the response score and meaningful ranking of the parameters. The maximum number of iterations, rated first, has a significant impact on the performance of the EA in minimizing the MOF value, followed by the population size, ranked second. As a result, the following arrangement from Fig. 10 is chosen: The population size is set to 100, and the maximum number of iterations is set to 500. Similarly, for each of the examined methods, the parameter determination curves by means of the Taguchi methodology are depicted in Figs. [START_REF] Xiong | Co-estimation of state of charge and capacity for lithium-ion batteries with multi-stage model fusion method[END_REF].5 and 12. Similar conclusions may be derived, as the optimum tuning settings are supplied where the population size is set to 100, and the maximum number of iterations is set to 500. For the PSO, two other control parameters must be specified whereas the cognitive and social learning factors are required. Considering the maximum number of iterations is fixed at 500, Taguchi method is applied where the orthogonal array L É¡ [START_REF] Sangwan | Estimation of battery parameters of the equivalent circuit model using grey wolf optimization[END_REF] is used to execute the parameter combinations and it is reduced to 8 treatments as the number of parameters is 3 and each one has 3 levels as listed in Table 10. Thus, the best values of the cognitive and social learning factors are 2 and 2, respectively.

DESIGN OF EXPERIMENTS

In this paper, the design of experimental tests is dependent on classification constraints. The objective aims at reducing the cycling times with preserving the important test features, such as the maximum current intensity and the amount of charge exchanged [START_REF] Rizoug | Aging of high power li-ion cells during real use of electric vehicles[END_REF], [START_REF] Mesbahi | Dynamic model of li-ion batteries incorporating electrothermal and ageing aspects for electric vehicle applications[END_REF]. The ARTEMIS driving cycle is selected for extracting the battery parameters using a dynamics model of the urban electric vehicle (Bollor é Bluecar).

Driving cycle

Recently, several normalized/non-normalized driving cycles are suggested to evaluate the pollution emissions and fuel consumption of gasoline-powered engines for examples the ECE, NEDC, UDC, ARTEMIS, FTP75,WLTC and NYCC [START_REF] Torres | Energy management strategy for plug-in hybrid electric vehicles. a comparative study[END_REF]. The modeling of the tested driving cycle is employed based on speed-time sequences that emulates the traffic conditions and driving behavior in a specific area. In this paper, the Assessment and Reliability of Transport Emission Models Inventory Systems (ARTEMIS) driving cycle is chosen for its real-world driving behavior. ARTEMIS has three driving cycles called urban, rural and highway. In this work, the ARTEMIS cycle selected to represent the urban and the rural cycle. Recently, various types of batteries have been developed to meet the main requirements of electric and hybrid vehicles with enhancing the drive performance and high reliability such as a commercial 40 Ah Li-ion battery [START_REF] El-Sehiemy | Parameter identification and state-of-charge estimation for lithium-polymer battery cells using enhanced sunflower optimization algorithm[END_REF] and [START_REF] Affanni | Battery choice and management for new-generation electric vehicles[END_REF], . This battery under reference of HED-SLPB90216216 that is produced by Kokam manufacturer is selected study.

Verification study on Artemis driving cycle

The ARTEMIS, Assessment and Reliability of Transport Emission Models Inventory Systems, driving cycle is generally represented in terms of their speed-time sequences which are originally based on the driving behavior and traffic conditions in a particular area. In the current paper, this driving cycle is performed by the urban and the rural cycle with the average distance of 22 km in 2075 seconds. The average and maximal speeds are 38.4 and 111.5 km/h, respectively. The proposed EA is applied to optimally identify the battery parameters considering the linear and non-linear relation between V OC and the SOC as described in the previous sections. For both cases, Table 11 shows the obtained optimal parameters and their corresponding results. Similar conclusion is drawn where the linear consideration is unsuitable that it creates bad accuracy compared to the non-linearity relation. The considered objective, in the non-linear form, is greatly minimized to 0.00445 compared to 0.012 in the linear form. The root mean square of the normalized deviation between the estimated and experimental battery voltage is reduced from 0.0119 to 0.00437. preference of both models on the second objective of the root mean square of the normalized deviation between estimated and experimental state of charge as shown in Figs. 15 and 16 depicts the error response of the state of charge, respectively. From these figures, both models demonstrate the high accuracy in tracking the state of charge.

Efficient simplified nonlinear model of lithium-ion battery

A linear model of lithium-ion battery has been proposed in [START_REF] El-Sehiemy | Parameter identification and state-of-charge estimation for lithium-polymer battery cells using enhanced sunflower optimization algorithm[END_REF], this model is quite simple but it couldn't give precise identification because it doesn't take into account the nonlinear dynamics of the lithium-ion battery. The nonlinear model of lithium-ion battery presented in [START_REF] Mesbahi | Dynamical modeling of li-ion batteries for electric vehicle applications based on hybrid particle swarm-neldermead (pso-nm) optimization algorithm[END_REF] is efficient but it is too complicated and requires more computation time to identify its parameters and to estimate the SoC. The proposed simplified model is presented with keeping the same performance obtained in [START_REF] Mesbahi | Dynamical modeling of li-ion batteries for electric vehicle applications based on hybrid particle swarm-neldermead (pso-nm) optimization algorithm[END_REF]. This reduced model contains only 5 parameters instead of 13 as it can be shown in Table 1. The proposed model is compared with 13 th parameter to show their performance. The obtained results are shown by Figs. 17 and 18 As shown, no significant difference is noticed between both models in evaluating the battery voltage and the state of charge. Furthermore, the simplified model (N=5) has less computational time than the high accurate one of (N=13) since the simplified model has 16.31% decrease in the computation time. An improved procedure for lithium ion battery parameter estimation has been proposed in this paper based on an enhanced equilibrium optimization algorithm. The significant contributions can be concluded as follows:

• A good compromise between state space model and nonlinear model is obtained and the estimation problem is divided into three steps that enhance the solution methodology and find the accurate relation for each stage.

• An assessment between various non-linear models, to represent the dependency between open circuit voltages and the battery state of charge, has been employed compared with linear models.

• An enhanced equilibrium optimization algorithm considering has been employed, the statistical indices reflect that the proposed method improve the accuracy by 12% compared to competitive methods.

• Comparison with other state-of-the-art solutions have shown that the proposed give more precise results with less computation time (16 % improvement).

• Dynamic verification study has been carried out on ARTEMIS driving cycle to prove the capability of the proposed solution.

• Tuning the parameters of all competitive algorithms to assign the optimal modeling method at the best algorithm parameters. The future trends of this study can be classified into two main categories:

• Considering the thermal impacts for single battery or a set of batteries especially for varied environmental conditions and for electrical vehicles applications.

• Considering the uncertainty of measurements and the shift noises from sensors and the battery aging.

• Developing new solution modeling for real time applications of the different types of batteries

  a 1 .....a 2 4 -100 100 Q R (As) 13000 170000

Figure 1 :

 1 Figure 1: Response of the voltage drop over the internal resistance for ARTEMIS driving cycle

Figure 2 :

 2 Figure 2: Response of the capacitor voltage for ARTEMIS driving cycle

Fig. 3 Figure 3 :

 33 Fig. 3 depicts the estimated battery voltage versus the corresponding experimental voltage for Cases 1 and 2. Great improvement is shown in the estimated battery voltage in Case 2 compared to Case 1. This improvement is originally due the accurate high nonlinearity consideration between the open circuit voltage and the state of charge as shown in Fig. 4. This figure clearly illustrates the curved relationship in Case 2 that makes accurate tracking to the experimental battery voltage. Fig. 5 depicts the estimated battery voltage versus the corresponding experimental voltage in both forms. As shown, great improvement

Figure 4 :

 4 Figure 4: Relation between estimated open circuit voltage and SOC for Cases 1 and 2

Figure 5 : 2 Figure 6 :

 526 Figure 5: Responses of the estimated open circuit voltage for Cases 1 and 2

Figure 7 :

 7 Figure 7: (a) Laboratory current profile with 150 km ARTEMIS driving cycle (b) Experimental and modeling responses of battery voltage

Figure 8 :

 8 Figure 8: Convergence curve of the employed EA for Case 1

Figure 9 :Table 7 :

 97 Figure 9: Box and Whiskers plot for MPO, FBI, GWO and EA for Case 1

Figure 10 :

 10 Figure 10: Parameters selection for EA based on Taguchi method

Figure 11 :Figure 12 :

 1112 Figure 11: Parameters selection based on the Taguchi method for FBI, GWO and BSA methods

Fig. 13 Figure 13 :Figure 14 :

 131314 Figure 13: Error response of the battery voltage

Figure 15 :Figure 16 :

 1516 Figure 15: State of charge experimental and modeling responses

Figure 17 :Figure 18 :

 1718 Figure 17: Comparison between 5 th and 13 th parameters models

  List of Symbols and Nomenclature

	SoC	State of charge
	OCV	Open circuit voltage
	EA	Equilibrium Algorithm
	V T	Battery terminal voltage
	I L	Battery terminal current
	R 0	Internal resistance
	Q r	Nominal battery capacity
	C i	Equivalent circuit capacitors
	R i	Equivalent circuit resistances
	V oc

Table 1 :

 1 The nonlinear relation between V OC and SOC

  3 + a 11 e a 12 SOC 3 a o , a 1 , ... a 1213 4 = a O + +a 1 e a 2 (1-SOC) + a 3 e a 4 SOC + a 5 e a 6 (1-SOC) 2 + a 7 e a 8 SOC 2 + a 9 e a 10 (1-SOC) 3 + a 11 e a 12 SOC 3 + a 13 e a 14 (1-SOC) 4 + a 15 e a 16 SOC 4 a o , a 1 , ... a 16 17 5 = a o + a 1 e a 2 (1-SOC) + a 3 e a 4 SOC + a 5 e a 6 (1-SOC) 2 + a 7 e a 8 SOC 2 + a 9 e a 10 (1-SOC) 3 + a 11 e a 12 SOC 3 + a 13 e a 14 (1-SOC) 4 + a 15 e a 16 SOC 4 + a 17 e a 18 (1-SOC) 5 + a 19 e a 20 SOC 5 a o , a 1 , ... a 20 21 6 = a o + a 1 e a 2 (1-SOC) + a 3 e a 4 SOC + a 5 e a 6 (1-SOC) 2 + a 7 e a 8 SOC 2 + a 9 e a 10 (1-SOC) 3 + a 11 e a 12 SOC 3 + a 13 e a 14 (1-SOC) 4 + a 15 e a 16 SOC 4 + a 17 e a 18 (1-SOC) 5 + a 19 e a 20 SOC 5 +a 21 e a 22 SOC 6 ++a 23 e a 24 SOC 7

Table 2 :

 2 Bounds of battery parameters[START_REF] El-Sehiemy | Parameter identification and state-of-charge estimation for lithium-polymer battery cells using enhanced sunflower optimization algorithm[END_REF]

Table 3 :

 3 Optimal parameters based on EA for Linear and Non-linear Models

	Parameter Linear	Non-Linear
	R (mΩ)	0.13120618	0.000568
	R 1 (Ω)	0.74081781	0.000954
	C 1 (F)	0.0001026851 0.036197
	R 2 (Ω)	0.033796674	0.000946
	C 2 (F)	0.0022340423 0.059282
	Q r (As)	144000	147964.2
			a 0 =3.7480	a 7 =-0.1236
			a 1 =0.3658	a 8 =-1.5833
	Coefficients	b 0 = 3.36673 b 1 = 0.74081	a 2 =-3.0791 a 9 =-0.06919 a 3 =-0.2624 a 10 =0.7384 a 4 =-14.4221 a 11 =0.0228
			a 5 =0.1348	a 12 =-3.2842
			a 6 =-10.8373 a 13 =-0.1626
	F1	0.015985615	0.007243354
	F2	0.013588193	0.0004103893
	MOF	0.029239027	0.0076537439
	described in Eq. (

Table 4 :

 4 Optimal parameters based on several algorithms for Case 2

	N	5	9	13	17	21	25
	R 0	0.000313	0.00092	0.00115	0.00025	0.00087	0.00058
	a 0	3.44539	2.90216	2.95816	3.04743	3.86027	1.53556
	a 1	0.71692	-0.01987	-0.25092	-0.17554	-0.11100	3.08155
	a 2	-2.09764	-71.41551 -10.28074	-2.50577	-0.33987	-0.29232
	a 3	-0.27755	-0.32546	-0.30660	-0.3110	-0.56280	0.01156
	a 4	-15.19273 -12.19807 -13.39952	-15.64221 -5.86341	2.32518
	a 5	23.26866	0.05772	0.06925	3.11795	-0.46976	0.00942
	a 6		-11.4172	-1.91169	-5.23991	-5.11693	-26.91067
	a 7		0.68162	0.40582	0.32992	0.35757	0.40626
	a 8		0.5718143 1.22954	-6.09220	-20.68999	-2.88182
	a 9		27.92645	-0.03106	-2.68465	2.18453	-0.07038
	a 10			-82.95173	-14.23189 0.04824	1.58637
	a 11			0.18982	0.19827	-1.74397	-0.04575
	a 12			-2.43041	-1.04874	0.0047	0.23968
	a 13			22.27915	0.75288	0.39776	-0.0105
	a 14				-34.4296	-1.22888	3.63572
	a 15				-0.01623	-1.05411	-0.03389
	a 16				-6.10648	-2.00274	-0.37811
	a 17				46.01661	0.18642	0.01262
	a 18					-2.41969	0.08977
	a 19					0.05885	-0.1899
	a 20					-30.62175	-1.71234
	a 21					-0.07887	0.27886
	a 22						0.88715
	a 23						-0.67662
	a 24						0.04349
	a 25						-0.38525
	Q r	147963.94 147964.49 147964.1	147962.72 147963.53	147963.15
	R 1	0.00162	0.00029	0.00123	0.00210	0.00068	0.00034
	C 1	0.06704	0.02097	0.02714	0.06499	0.02596	0.05867
	R 2	0.00053	0.00125	8.86633E-05 0.00011	0.00091	0.00156
	C 2	0.05142	0.03845	0.03241	0.04186	0.072524062 0.04877
	MOF	0.00775	0.00764	0.00764	0.00783	0.00765	0.00766
	Calculation
	Time (sec) 357.12	392.86	426.73	461.535	501.15	539.81

Table 5 :

 5 Optimal parameters based on several algorithms for Case 2

		EA	FBI	GWO	PSO	BSA
	Ro	0.000568 0.000719 0.002335 0.00001	0.000588
	a 0	3.748055 2.635103 3.644386 5	2.44061
	a 1	0.365885 -0.38412 -0.00064 -1.0927	13.09921
	a 2	-3.0791	1.030771 -46.5625 0.394574 -9.06146
	a 3	-0.2624	0.090911 -0.29748 100	-13.4491
	a 4	-14.4221 0.131675 -7.09734 -100	-34.0529
	a 5	0.134894 0.367197 0.833493 0.094509 -1.96034
	a 6	-10.8373 -0.33207 -12.1331 -100	-97.1077
	a 7	-0.1236	0.762054 -0.16797 -0.97144 15.44068
	a 8	-1.58334 0.336337 -38.5273 -100	-27.0616
	a 9	-0.06919 0.359072 -0.3547	0.14212	-7.11499
	a 10	0.738454 -0.32747 -57.1836 -100	-72.6671
	a 11	0.022825 0.355903 0.098728 -0.0308	-6.20173
	a 12	-3.28428 -10.8378 -99.4059 -100	-55.0202
	a 13	-0.16269 -1.16718 19.04225 -100	33.63797
	Q r	147964.2 147876.7 147949.6 170000	149654.8
	R 1	0.000954 0.001705 6.11E-06 0.000001 0.004249
	C 1	0.036197 0.059723 0.047881 0.1	0.088662
	R 2	0.000946 0.000169 3.37E-06 0.000001 0.02417
	C 2	0.059282 0.059705 0.017428 0.000001 0.079619
	MOF 0.007654 0.009216 0.008614 0.097418 0.577422
	4.4. Comparison of several optimization algorithms in Consideration of Non-Linear relation

Table 6 :

 6 Robustness test of several optimizers for Case 2 per iteration, the proposed EA consumes 0.6048 sec compared with FBI, GWO, PSO and BSA which consume 1.2069 sec, 0.5716 sec, 0.7507 sec and 0.998 sec, respectively. It is cleared that the fast optimizer is GWO then the proposed EA.

		EA	FBI	GWO	PSO	BSA
	Best	0.007654 0.009216 0.008614 0.097418 0.577422
	Mean	0.00861	0.01084	0.019526 0.556035 1.272247
	Worst	0.011873 0.013717 0.026385 1.150793 2.879003
	Std	0.001248 0.001342 0.006806 0.452099 0.757069
	Time/Iteration (sec) 0.6048	1.2069	0.5716	0.7507	0.9980
	the computation time

Table 8 :

 8 Orthogonal table based on Taguchi method for the compared algorithms

	Population Size Maximum number of iterations	MOF
	25	100	0.023716523
	25	300	0.00783557
	25	500	0.007732807
	50	100	0.007966795
	50	300	0.000768923
	50	500	0.0007697034
	100	100	0.007732807
	100	300	0.007697034
	100	500	0.0007653744

Table 9 :

 9 Response table of means for the EA.

	Item	Population Size Maximum number of iterations
	Level 1 0.01309496667	0.01313870833
	Level 2	0.0031684738	0.005433842333
	Level 3 0.005398405133	0.003089294933
	Delta 0.009926492869	0.0100494133970
	Rank	2	1

Table 10 :

 10 Combination of parameters for the PSO

	Parameters	Level 1 Level 2 Level 3
	Population Size	25	50	100
	Cognitive learning factor	1	2	4
	Social learning factor	1	2	4

Table 11 :

 11 Optimal parameters based on EA for Linear and Non-Linear relation for ARTEMIS driving cycle -24.78047 a 2 -4.77465 a 9 0.34301 a 3 -0.24291 a 10 -0.87348 a 4 -5.25495 a 11 0.65556 a 5 0.23610 a 12 -58.29117 a 6 -14.74987 a 13 13.

	Parameter Linear	Non-Linear (N=5) Non-Linear (N=13)
	R (mΩ)	0.002334072394	0.0003068363818	0.00131930343899999
	R 1 (Ω))	0.001244251137	0.00037837	0.001630968
	C 1 (F)	0.08266382139	0.06375762	0.019172327
	R 2 (Ω))	0.0006059282676 0.003494296	0.001234919
	C 2 (F)	0.068005188	0.099650938	0.032159331
	Q r (As)	144000	143999.998	144000.234499999
	Coefficients	b 0 3.248043 b 1 0.873431	a 0 3.40327 a 1 0.80028 a 2 -2.3124 a 3 -33.35991 a 4 -30.68399 a 5 -46.75711	a 0 3.33767 a 1 0.27462	a 7 -1.16956 a 8 48667
	F1	0.01192552947	0.004577236303	0.004378931369
	F2	0.000077476147	0.00007747614742 0.00007747937708
	MOF	0.01200300562	0.00465471245	0.004456410746
	Calculation
	time (sec)	584.15	668.22	842.371
	6.2. Future work

ACKNOWLEDGMENT

This work was supported by Taif University Researchers Supporting Project number (TURSP-2020/86), Taif University, Taif, Saudi Arabia.


M.D. Nolwenn Lavagen
email: nolwennlavagen@hotmail.fr

Lara Nokovitch

Amandine Algrin

Stéphanie Dakpe

Sylvie Testelin

Bernard Devauchelle

Cica Gbaguidi

Efficiency of advanced-PRF usage in the treatment of alveolar cleft with iliac bone graft: a retrospective study

Keywords:

The aim of this study was to evaluate the efficiency of a new alveolar bone grafting protocol using advanced-PRF (a-PRF) by comparing the volume of newly formed bone after a bone graft combining autogenous iliac crest bone with either PRF or a-PRF.

Patients presenting an uni-or a bilateral alveolar cleft were included retrospectively in 2 groups: one group was grafted using cancellous iliac crest bone with PRF (group PRF), whereas a-PRF was used for the other group (group a-PRF). Pre-operative (3 months) and post-operative (6-months) CBCT were performed. The volume of newly formed bone was measured by subtracting the post-operative to the pre-operative cleft volume. The mean volume of newly formed bone was compared between the 2 groups using a student's t-test.

Twenty-four patients were included, twelve allocated to each group. Forty-eight CBCT were analysed. The mean volume of newly formed bone was 0,29 (± 0,09) cm 3 in the a-PRF group, versus 0,20 (± 0,08) cm 3 in the PRF group (student's t-test, p= 0,024). The percentage of newly formed bone was 60,4 (± 10,4) % in the a-PRF group versus 51,4 (±18,4) % in the PRF group (student's t-test, p = 0,165).

The present study is in favour of improved bone regeneration in group a-PRF. Within the limitations of the present study, this procedure should be adopted in cleft bone grafting whenever possible.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

INTRODUCTION:

Alveolar bone grafting is currently considered the gold standard for the reconstruction of maxillary alveolar defect [START_REF] Kang | Current Methods for the Treatment of Alveolar Cleft[END_REF] in cleft patients. Although the literature is inconclusive regarding the perfect timing for alveolar bone grafting, secondary bone grafting seems to be preferred in order to limit maxillofacial growth disturbances [START_REF] Brudnicki | Cephalometric comparison of early and late secondary bone grafting in the treatment of patients suffering from unilateral cleft lip and palate[END_REF]. It is usually performed before permanent canine eruption, between 5 and 11 years-old [START_REF] Seifeldin | Is alveolar cleft reconstruction still controversial? (Review of literature)[END_REF][START_REF] Brudnicki | Secondary alveolar bone grafting in cleft lip and palate: A comparative analysis of donor site morbidity in different age groups[END_REF], with a current tendency to early bone grafting around 5-6 years-old [START_REF] Dissaux | Evaluation of success of alveolar cleft bone graft performed at 5 years versus 10 years of age[END_REF][START_REF] Garcia | Ideal Versus Late Secondary Alveolar Bone Graft Surgery: A Bone-Thickness Cone-Beam Computed Tomographic Assessment[END_REF][START_REF] Fahradyan | Optimal Timing of Secondary Alveolar Bone Grafting: A Literature Review[END_REF], and involves for most teams the grafting of autogenous bone [START_REF] Farronato | How various surgical protocols of the unilateral cleft lip and palate influence the facial growth and possible orthodontic problems? Which is the best timing of lip, palate and alveolus repair? literature review[END_REF][START_REF] Dao | Cleft Palate Repair, Gingivoperiosteoplasty, and Alveolar Bone Grafting[END_REF][START_REF] Shirani | Comparison between autogenous iliac bone and freeze-dried bone allograft for repair of alveolar clefts in the presence of plasma rich in growth factors: A randomized clinical trial[END_REF]. Cancellous iliac crest bone is usually the preferred donor material, due to its easy surgical access and great osteogenic potential [START_REF] Rawashdeh | Secondary alveolar bone grafting: the dilemma of donor site selection and morbidity[END_REF]. There is, however, no clear international consensus about any of these points, and each team continues to follow its own specific protocol [START_REF] Shaw | The Eurocleft project 1996-2000: overview[END_REF][START_REF] Urbanova | The Slav-cleft: A three-center study of the outcome of treatment of cleft lip and palate. Part 1: Craniofacial morphology[END_REF].

Platelet-rich fibrin (PRF) was first introduced in 2001 by Choukroun and his team, and comes as a gel like material that can be used in conjunction with bone substitutes [START_REF] Dohan | Platelet-rich fibrin (PRF): a second-generation platelet concentrate. Part I: technological concepts and evolution[END_REF]. PRF is a second generation of platelet concentrate produced by simple blood centrifugation without biochemical manipulation, unlike platelet-rich plasma (PRP) which is obtained with use of anticoagulants. PRF is made of an autologous bio scaffold of a dense fibrin matrix with integrated growth factors, which are released from the scaffold over a sustained period of time to promote healing of hard and soft tissues [START_REF] Clark | Advanced platelet-rich fibrin and freeze-dried bone allograft for ridge preservation: A randomized controlled clinical trial[END_REF][START_REF] Canellas | Platelet-rich fibrin in oral surgical procedures: a systematic review and meta-analysis[END_REF]. A modification of the centrifugation protocol was proposed in 2017 [START_REF] Ghanaati | Advanced platelet-rich fibrin: a new concept for cell-based tissue engineering by means of inflammatory cells[END_REF], the new formulation of advanced-PRF (a-PRF) obtained releasing in vitro significantly higher quantities of growth factors when compared to traditional PRF [START_REF] Kobayashi | Comparative release of growth factors from PRP, PRF, and advanced-PRF[END_REF].

At our institution, the use of PRF combined to autogeneous iliac crest bone grafting was integrated in 2013 for gingivoperiosteoplasty procedures, with very satisfying results in terms of bone integration and mucosal healing. Due to the promising results of a-PRF on bone osteogenesis [START_REF] Caruana | From Platelet-Rich Plasma to Advanced Platelet-Rich Fibrin: Biological Achievements and Clinical Advances in Modern Surgery[END_REF], the alveolar bone grafting protocol was modified in cleft patients in 2018, and switched from using PRF to a-PRF.

The aim of this study was to evaluate the efficiency of this new protocol by comparing the volume of newly formed bone after alveolar bone grafting combined with either PRF or a-PRF.

MATERIALS AND METHODS:

1/ Patients population:

In this monocentric study, patients who underwent alveolar bone grafting for an unior bilateral alveolar cleft, and for whom a pre-and post-operative cone beam computed tomography were available, were included retrospectively in the study. This study was conducted in accordance with the Helsinki Declaration of 1975, as revised in 2013, and registered at our institution under PI2021 843 0074.

All patients had been managed and operated since their birth by the same experienced surgeon. The surgical timetable was as follow:

-2-3 weeks: use of a passive alveolar plate to enable the realignment of the maxillary arch.

-6 months: cheiloplasty according to Malek's modified Tennison technique, rhinoplasty according to Mac Comb and Talmant, and intravelar veloplasty according to Sommerlad.

-18 months: two planes uranoplasty in residual cleft palate < 15 mm, or calvarial periosteal graft after closure of the nasal plane in residual cleft palate > 15 mm.

-4-5 years or 9-10 years (if early management was not possible): pre-surgical expansion with a quadhelix or rapid maxillary expander, followed by alveolar bone grafting with an autogenous anterior iliac crest bone graft.

Patients were allocated into 2 groups according to the adjunction of PRF (Group PRF) or a-PRF (Group a-PRF) to the grafting material.

A CBCT was performed 3 months pre-operatively, and 6 months post-operatively for each patient. The DICOM files were treated with the Planmeca Romexis Viewer 5.2.1.R software. The volume of the alveolar cleft was segmented cut by cut from the piriform aperture to the alveolar crest of the teeth adjacent to the cleft in a cephalocaudal direction, and from the anterior border of the alveolar bone to the mesial surface of the teeth adjacent to the cleft in an anteroposterior direction (Figure 1). The volume of newly formed bone in each group was measured by subtracting the post-operative cleft volume to the pre-operative cleft volume. To assess osseous integration, the absolute value of newly formed bone volume was expressed as a percentage of the initial cleft volume.

To ensure the reliability and reproducibility of the results, all measures were taken twice by the same operator, and their mean value calculated.

2/ Surgical procedure:

The patient was installed on a supine position, with hyperextension of the head and neck. Venous blood was withdrawn under general anaesthesia, via venipuncture with a butterfly needle. Four sterile plastic tubes of 10 mL without external anticoagulants were used to collect 40 mL of blood, immediately placed in the centrifuge (Adip'spin®, Adip'sculpt).

-PRF group: centrifugation at 2700 rpm during 12 minutes. Careful removal of the clot, and separation from the red blood cell fraction with scissors (Figure 2).

a-PRF group: centrifugation at 1300 rpm during 5 minutes, collection of 1 cc of the supernatant, and centrifugation at 1300 rpm during 3 minutes. Careful removal of the clot, and separation from the red blood cell fraction with scissors.

Meanwhile, cancellous iliac crest bone was harvested following the usual surgical procedure.

For patients of group a-PRF, it was mixed with 1 cc of the supernatant previously collected, in order to obtain a cohesive bone graft, easier to manipulate.

The oral mucosal lining was closed, and a membrane of PRF (PRF group) or a-PRF (a-PRF group) was put over the suture line. The alveolar cleft was then filled with cancellous iliac crest bone along its entire height. A new membrane of PRF (PRF group) or a-PRF (a-PRF group) was placed over the bone graft, in order to enclose and protect it (Figure 3). Finally, muco-periosteal flaps were advanced and sutured without tension over the alveolar crest.

3/ Statistical analysis:

Descriptive statistics were produced using the MS Excel 2016 software (MICROSOFT, Redmond, USA) and the R 3.5.2 software (Foundation for Statistical Computing, Vienna, Austria). A χ 2 test was performed to assess the comparability between groups. A student's t-test was performed to compare the pre-and post-operative volume of the alveolar cleft, and the volume of newly formed bone between groups. A p-value less than 0,05 was considered statistically significant. The Pearson correlation coefficient (r) was measured to evaluate intra-observer reliability.

RESULTS:

Twenty-four patients presenting uni-or bilateral alveolar cleft were included. Twelve were allocated to group PRF, and 12 to group a-PRF. Both groups were comparable regarding the sex, the age (mean age 7,7 ± 1,96 years), and the type of alveolar cleft (unilateral or bilateral). Patients characteristics are described in Table 1.

A total of 48 CBCT (24 pre-operative, and 24 post-operative) were analysed. The results are presented in Table 2, and an example of pre and post-operative CBCT is shown in Figure 4. The mean pre-operative volume of the alveolar cleft was comparable in both groups (0,41 cm 3 (± 0,11) for the PRF group, 0, 47 cm 3 (±0,16) for the a-PRF group, p = 0,248).

The mean volume of newly formed bone was 0,29 cm 3 (±0,09) in the a-PRF group, and 0,20 cm 3 (± 0,08) in the PRF group, this difference being statistically significant (t-test, p = 0,024) (Figure 5). The percentage of newly formed bone was also greater in the a-PRF group (60,4% ±10,4) than in the PRF group (51,4% ±18,4), with an increase of almost 10% of newly formed bone, although this result was not statistically significant (t-test, p = 0,165).

The distribution of results in both groups is presented in figure 4. Intra-observer reliability was good, with a Pearson correlation coefficient of 0,96 (Figure 6).

DISCUSSION:

PRF and a-PRF membranes present a vast regenerative potential by releasing a broad spectrum of cytokines, chemokines, growth factors and other mediators [START_REF] Dohan | Platelet-rich fibrin (PRF): a second-generation platelet concentrate. Part I: technological concepts and evolution[END_REF][START_REF] Ghanaati | Advanced platelet-rich fibrin: a new concept for cell-based tissue engineering by means of inflammatory cells[END_REF]. Unlike PRP membranes, PRF and a-PRF membranes do not require the use of anticoagulants that might interfere with the natural healing process [START_REF] Kobayashi | Comparative release of growth factors from PRP, PRF, and advanced-PRF[END_REF]. Changing the centrifugation protocol in terms of centrifugation time and speed also leads to a different distribution pattern for neutrophilic granulocytes and growth factor release, in favour of a-PRF membranes compared to PRF and PRP-membranes [START_REF] Ghanaati | Advanced platelet-rich fibrin: a new concept for cell-based tissue engineering by means of inflammatory cells[END_REF][START_REF] Bagdadi | Reduction of relative centrifugal forces increases growth factor release within solid platelet-rich-fibrin (PRF)-based matrices: a proof of concept of LSCC (low speed centrifugation concept)[END_REF]. The increased cell distribution of neutrophilic granulocytes of the a-PRF membrane might indeed be the basis for a better functionality of the transplanted monocytes/macrophages and lymphocytes, and their deployment to support tissue regeneration [START_REF] Ghanaati | Advanced platelet-rich fibrin: a new concept for cell-based tissue engineering by means of inflammatory cells[END_REF]. Furthermore, the increased growth factor release of the a-PRF membrane might influence positively wound healing and biomaterial-based tissue regeneration [START_REF] Kobayashi | Comparative release of growth factors from PRP, PRF, and advanced-PRF[END_REF][START_REF] Bagdadi | Reduction of relative centrifugal forces increases growth factor release within solid platelet-rich-fibrin (PRF)-based matrices: a proof of concept of LSCC (low speed centrifugation concept)[END_REF].

However, if the literature regarding PRF is rich and tends to support its beneficial effects on bone regeneration [START_REF] Zumarán | The 3 R's for Platelet-Rich Fibrin: A "Super" Tri-Dimensional Biomaterial for Contemporary Naturally-Guided Oro-Maxillo-Facial Soft and Hard Tissue Repair, Reconstruction and Regeneration[END_REF][START_REF] Canellas | Platelet-rich fibrin in oral surgical procedures: a systematic review and meta-analysis[END_REF][START_REF] Karayürek | Combining platelet rich fibrin with different bone graft materials: An experimental study on the histopathological and immunohistochemical aspects of bone healing[END_REF], a standardization of PRF protocols is required in order to perform reproducible studies with a higher scientific level of evidence [START_REF] Ghanaati | Fifteen Years of Platelet Rich Fibrin in Dentistry and Oromaxillofacial Surgery: How High is the Level of Scientific Evidence?[END_REF]. PRF efficiency on bone formation in maxillary alveolar cleft reconstruction is also debated, with conflicting results in the literature [START_REF] Marukawa | Reduction of bone resorption by the application of platelet-rich plasma (PRP) in bone grafting of the alveolar cleft[END_REF][START_REF] Shawky | Does Platelet-Rich Fibrin Enhance Bone Quality and Quantity of Alveolar Cleft Reconstruction? Cleft Palate-Craniofacial[END_REF][START_REF] Saruhan | Evaluating of Platelet-Rich Fibrin in the Treatment of Alveolar Cleft With Iliac Bone Graft By Means of Volumetric Analysis[END_REF][START_REF] Omidkhoda | Efficacy of Platelet-Rich Fibrin Combined with Autogenous Bone Graft in the Quality and Quantity of Maxillary Alveolar Cleft Reconstruction[END_REF]. As for a-PRF, due to its recent description, its efficiency on bone regeneration has yet to be proven for that indication.

Although this is a retrospective study, this modification of the gingivoperiosteoplasty procedure shows promising results, and the adjunction of a-PRF to the grafting material seems to increase the volume of newly formed bone compared to PRF (t-test, p = 0,024). The gain of almost 10% of newly formed bone in the a-PRF group, although not statistically significant (t-test, p = 0,165), is also in favour of the superiority of the new a-PRF protocol.

The use of PRF and a-PRF membranes might also improve soft tissue healing, as there was no wound dehiscence to declare in this small cohort of patients.

It was unfortunately not possible to dispose of a control group in this study owing to its retrospective character. Indeed, PRF membranes started to be used at our institution in 2013, and a-PRF membranes in 2018, and no CBCT evaluation was available for patients grafted without PRF before 2013. Yet, if a new prospective study with a control group was to be considered, it might represent a potential loss of opportunity for the patients that would not benefit from the use of PRF or a-PRF membranes. To date, only one other study is available comparing the use of a-PRF versus no PRF with iliac crest bone graft (Dayashankara [START_REF] Rao | A comparative evaluation of iliac crest bone graft with and without injectable and advanced platelet rich fibrin in secondary alveolar bone grafting for cleft alveolus in unilateral cleft lip and palate patients: A randomized prospective study[END_REF], and is in favour of less bone resorption in the a-PRF group. However, this study only used two-dimension radiography to assess bone loss, thus not taking into account the whole volume of grafted bone.

CBCT is an efficient tool to evaluate bone remodelling [START_REF] Spin-Neto | Exploring CBCT-based DICOM files. A systematic review on the properties of images used to evaluate maxillofacial bone grafts[END_REF]. It allows the delivery of lower radiation doses with short scanning times (10-70 seconds) compared to medical CT scanning [START_REF] Feragalli | Cone beam computed tomography for dental and maxillofacial imaging: technique improvement and lowdose protocols[END_REF], these two points being essentials when it comes to the paediatric population. CBCT is also capable of providing a 3dimensional representation of the maxillofacial skeleton, with minimal distortion and submillimetre resolution [START_REF] Kamperos | A novel success scale for evaluating alveolar cleft repair using cone-beam computed tomography[END_REF]. It provides satisfactory information about linear distances and volumes, and was used in this study to measure the pre-and post-operative alveolar cleft volume, and the volume of newly formed bone [START_REF] Stasiak | Current methods for secondary alveolar bone grafting assessment in cleft lip and palate patients -A systematic review[END_REF]. Intraobserver reliability was good (Pearson correlation coefficient = 0,96) and supports the validity of the measures taken pre-and post-operatively.

Autogenous cancellous iliac crest bone was used in the current study, as it is considered the gold standard to stimulate bone healing and fill bone defects, and is associated with a higher success rate [START_REF] Seifeldin | Is alveolar cleft reconstruction still controversial? (Review of literature)[END_REF]. Particulate cancellous iliac grafts were used as they are more readily incorporated and remodel to the adjacent alveolus. For all patients in a-PRF group, particulate bone grafts were also mixed with liquid PRF supernatant in order to secure the bony particles, this modification of protocol having been proposed by Choukroun in his first description of a-PRF. As this study is a retrospective one, it was not possible to standardize this technique in both groups. However, this should not represent any bias in term of volume added as only a minimal amount of liquid was used to this extent.

CONCLUSION:

A-PRF membranes combined with cancellous iliac grafts seem to improve bone regeneration compared to PRF. Within the limitations of the present study, a-PRF should be adopted in cleft bone grafting whenever possible..

FIGURE LEGENDS:

Table 1: Patients characteristics of group PRF and a-PRF. SD: standard deviation.

Figure 1 :

 1 Figure 1: Segmentation of the cleft volume (in blue) with the Planmeca Romexis Viewer

Figure 2 :

 2 Figure 2: Removal of the PRF clot after centrifugation.

Figure 3 :

 3 Figure 3: Alveolar cleft bone grafting technique. A PRF or a-PRF membrane is placed over

  Figure 4:

Figure 5 :

 5 Figure 5: Box-plot showing the distribution of results in group PRF and a-PRF.

Figure 6 :

 6 Figure 6: Measure of Pearson correlation coefficient to evaluate intra-observer

Table 2 : Volume of newly formed bone in group PRF and a-PRF

 2 . SD: standard deviation.

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