domain: chim sde

text:
Nasma Bouchelkia
email: nasmabouchelkia@gmail.com.

Hichem Tahraoui
email: tahraoui.hichem@univ-medea.dz

Abdeltif Amrane
email: abdeltif.amrane@univ-rennes1.fr

Hayet Belkacemi
email: belkacemihayet903@gmail.com

Jean-Claude Bollinger
email: jcbollinger@unilim.fr

Abdelkrim Bouzaza
email: abdelkrim.bouzaza@ensc-rennes.fr

Abdelhalim Zoukel
email: ab.zoukel@lagh-univ.dz

Jie Zhang
email: jie.zhang@newcastle.ac.uk

Lotfi Mouni
email: l.mouni@univ-bouira.dz.url

Jean- Claude Bollinger

activated carbon for methylene blue adsorption: Kinetics and isotherms modeling, thermodynamics and mechanism study, optimization via response surface methodology and machine learning approaches

Keywords: Activated carbon, Bootstrap Aggregation_Bag, Box-Behnken design, Dragonfly algorithm, Gaussian Process Regression, Methylene blue adsorption

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

experimental validation of the optimal conditions of the GPR_DA_Bootstrap model (X 1 = 700 mg/L, X 2 = 0.6 g/L, X 3 = 540 min, X 4 = 11, and X 5 =50°C) led to an MB uptake (501.01 mg/g) significantly higher than that of BBD (456.00 mg/g). In addition, the very low error between the experimental and the predicted values given by the GPR_DA_Bootstrap model (8.64 mg/g) compared to that of the BBD model (22.19 mg/g), should be highlighted. This clearly shows the efficiency and the performance of the GPR_DA_Bootstrap model on the one hand; as well as the effectiveness of activated carbon prepared from jujube stones (PJAC) as a lowcost adsorbent on the other hand.

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Introduction

Wastewater provided by human activities generates a variety of hazardous substances that degrade and pollute the environment. The discharge of dye-loaded wastewater into the ecosystem affects harmfully the human's health and ecological environment [START_REF] Abdulhameed | Modeling and mechanism of reactive orange 16 dye adsorption by chitosan-glyoxal/TiO 2 nanocomposite: application of response surface methodology[END_REF]. Water characteristics are impacted by the color caused by some dyes which can be visible even at concentrations lower than 1 ppm (Li et al. 2022), and can also provoke toxicity in aquatic environment if they contain metals or some aromatic compounds [START_REF] Mashkoor | Magsorbents: Potential candidates in wastewater treatment technology-A review on the removal of methylene blue dye[END_REF]. Moreover, dyes are not easy to degrade chemically, biologically, and by the light because of their origin and complex structure [START_REF] Postai | Adsorption of rhodamine B and methylene blue dyes using waste of seeds of Aleurites Moluccana, a low cost adsorbent[END_REF]Li et al. 2022). It is therefore crucial to treat them before their evacuation into the ecosystem (Jawad et al. 2020a) Methylene Blue is a cationic dye widely used in the industrial field to dye wool, cotton and many other fabrics in the textile industry. It is also used as a coloring agent in the paper J o u r n a l P r e -p r o o f industry and in cosmetics for artificial hair dyeing [START_REF] J O U R N A L P R E -P R O O F Pandey | Efficient and rapid adsorption characteristics of templating xanthan gum-graft-poly (aniline) and silica nanocomposite toward removal of toxic methylene blue dyes[END_REF]. High exposure to methylene blue poses serious health hazards for the environment and humans. It may provoke nausea, vomiting, breathing difficulties, allergy, heart rhythm disturbances, tissue necrosis, skin irritation, mental confusion and even cancer and dysfunction of brain, liver and central nervous system [START_REF] J O U R N A L P R E -P R O O F Pandey | Efficient and rapid adsorption characteristics of templating xanthan gum-graft-poly (aniline) and silica nanocomposite toward removal of toxic methylene blue dyes[END_REF]Jawad et al. 2018a). Researchers have, over the years, successfully developed a wide range of techniques for the methylene blue elimination such as electrochemical treatment [START_REF] Teng | Performance and mechanism of methylene blue degradation by an electrochemical process[END_REF], ion exchange [START_REF] J O U R N A L P R E -P R O O F Su | Significant enhancement of pesticide and organic dyes degradation by ion-exchange within a metal-organic framework[END_REF], photocatalytic degradation [START_REF] González-Crisostomo | iraldo L, Moreno-ira n C. 201 . Simple and competitive adsorption study of nickel (II) and chromium (III) on the surface of the brown algae Durvillaea antarctica biomass[END_REF], membrane filtration [START_REF] Bangari | Boron nitride nanosheets incorporated polyvinylidene fluoride mixed matrix membranes for removal of methylene blue from aqueous stream[END_REF], coagulation-flocculation [START_REF] Ihaddaden | Removal of methylene blue (basic dye) by coagulation-flocculation with biomaterials (bentonite and Opuntia ficus indica)[END_REF], and Fenton process [START_REF] Ye | Magnetic sludge-based biochar derived from Fenton sludge as an efficient heterogeneous Fenton catalyst for degrading Methylene blue[END_REF].

Adsorption, among other techniques, has consistently shown to be one of the most effective and reliable technology for wastewater treatment. It offers the advantages of being simple to use, environmentally friendly and economically efficient with great performance and selectivity (Jawad et al. 2018c;Jawad et al. 2022;[START_REF] Ma | Biomass derived nitrogen and sulfur co-doped porous carbons for efficient CO 2 adsorption[END_REF]. Activated carbon is the most commonly used adsorbent thanks to its characteristics, such as a big specific surface area, presence of diverse surface functional sites, developed porous structure and thermostability, high mechanical strength, as well as its capability of adsorbing huge types of dyes in a wide range of pH [START_REF] Khoo | Removal of basic dyes from aqueous solution using sugarcane bagasse: optimization by Plackett-Burman and Response Surface Methodology[END_REF][START_REF] Mammar | Modeling and optimization of process parameters in elucidating the adsorption mechanism J o u r n a l P r e -p r o o f of Gallic acid on activated carbon prepared from date stones[END_REF]. The expense of the commercial activated carbon restricted its utilization due to the need for expensive and unsustainable non-renewable raw materials such as coal [START_REF] Bouchelkia | Removal of lead (II) from water using activated carbon developed from jujube stones, a low-cost sorbent[END_REF]). Hence, low-cost precursors derived from agricultural wastes and characterized by their low organic content and high carbon content are used to prepare an inexpensive efficient activated carbon [START_REF] Ghani | Optimization of preparation conditions for activated carbon from banana pseudo-stem using response surface methodology on removal of color and COD from landfill leachate[END_REF]) such as jujube stones [START_REF] Bouchelkia | Removal of lead (II) from water using activated carbon developed from jujube stones, a low-cost sorbent[END_REF], banana pseudo-stem (Ab [START_REF] Ghani | Optimization of preparation conditions for activated carbon from banana pseudo-stem using response surface methodology on removal of color and COD from landfill leachate[END_REF], apricot stone [START_REF] Abbas | Modeling of adsorption isotherms of heavy metals onto Apricot stone activated carbon: two-parameter models and equations allowing determination of thermodynamic parameters[END_REF], artichoke leaves [START_REF] Bencheikh | The use and the performance of chemically treated artichoke leaves for textile industrial effluents treatment[END_REF], bamboo [START_REF] Khuongab | Activated carbon produced from bamboo and solid residue by CO 2 activation utilized as CO 2 adsorbents[END_REF], pistachio-nut shell [START_REF] Cheng | The adsorption properties of microporous activated carbon prepared from pistachio nut shell for low-concentration VOCs under low-medium temperatures[END_REF], and many others.

J o u r n a l P r e -p r o o f

In this research, the potential and effectiveness of a non-expensive activated carbon made by chemical activation of locally collected jujube stones using phosphoric acid was tested for the methylene blue (MB) dye sorption. The chemical activation has been chosen because of its advantages over physical activation, including a higher surface area, a comparatively shorter preparation time, and a higher product yield [START_REF] Jawad | High surface area and mesoporous activated carbon from KOH-activated dragon fruit peels for methylene blue dye adsorption: Optimization and mechanism study[END_REF]. Several experiments have been carried out to examine new efficient chemically activated carbons [START_REF] Ferreira | Adsorption performance of activated charcoal from castor seed cake prepared by chemical activation with phosphoric acid[END_REF][START_REF] Giraldo | Experimental and theoretical insights on methylene blue removal from wastewater using an adsorbent obtained from the residues of the orange industry[END_REF]Wang et al. 2021;[START_REF] De Souza | Activated carbon of Coriandrum sativum for adsorption of methylene blue: Equilibrium and kinetic modeling[END_REF].

The use of Phosphoric acid (H 3 PO 4 ) as activating agent has been found efficient in activated carbon preparation because it offers the decomposition of the lignocellulosic precursor at relatively low activation temperatures with minimal corrosion to the activation equipment. It also presents itself as a low-cost and environmentally friendly dehydration catalyst allowing the development of microporous and/or mesoporous material with high surface area [START_REF] Benadjemia | Preparation, characterization and Methylene Blue adsorption of phosphoric acid activated carbons from globe artichoke leaves[END_REF]Jawad et al. 2020a;Jawad et al. 2020b). Mbarki et al., [START_REF] Mbarki | Low-cost activated carbon preparation from Corn stigmata fibers chemically activated using H 3 PO 4 , ZnCl 2 and KOH: Study of methylene blue adsorption, stochastic isotherm and fractal kinetic[END_REF]) demonstrated that the specific surfaces area of activated carbon prepared with H 3 PO 4 were greater than those of ACs generated by activation with ZnCl 2 and KOH. Mansouri et al., [START_REF] Mansouri | Elaboration of novel adsorbent from Moroccan oil shale using Plackett-Burman design[END_REF]) have also proved the efficiency of activated carbon prepared by chemical activation with phosphoric acid in comparison with H 2 SO 4 .

In our previous paper [START_REF] Bouchelkia | Removal of lead (II) from water using activated carbon developed from jujube stones, a low-cost sorbent[END_REF], the classical method, named one-factor-at-atime (OFAT), has been used in the adsorption study. Its principle is based on the optimization of a given parameter, while all the other ones are fixed. The OFAT method is time-consuming and does not consider the interactive aspects between the various factors involved; it supposes that all factors are independent [START_REF] Mansouri | Elaboration of novel adsorbent from Moroccan oil shale using Plackett-Burman design[END_REF]. Such issues could be solved by using statistically designed experiments. Response surface method (RSM) is a combination of statistical and mathematical approaches used for modeling and analyzing different processes in order to depict the main and interaction effects and estimate correlations between J o u r n a l P r e -p r o o f experimental factors and responses. It is a simple and economical optimization method with a few number of experiments, resulting in faster and more effective experiment performance [START_REF] Asfaram | Statistical experimental design, least squares-support vector machine (LS-SVM) and artificial neural network (ANN) methods for modeling the facilitated adsorption of methylene blue dye[END_REF][START_REF] Mansouri | Elaboration of novel adsorbent from Moroccan oil shale using Plackett-Burman design[END_REF][START_REF] Alhalili | Green synthesis of copper oxide nanoparticles CuO NPs from Eucalyptus Globoulus leaf extract: Adsorption and design of experiments[END_REF]). In the same context, machine learning has also been widely used to solve complex adsorption problems and to provide a better understanding of the adsorption process [START_REF] Lakshmi | Artificial intelligence (AI) applications in adsorption of heavy metals using modified biochar[END_REF]. It is a collection of techniques for generating predictive models from databases of training examples [START_REF] Schneider | Machine learning and artificial intelligence[END_REF]). The experiential "learning" related to human intelligence is exhibited by machine learning, which has the ability to learn from its analysis by using computational algorithms.

These algorithms train the machine to make recommendations or autonomous decisions by using large amounts of data as inputs and outputs to successfully and effectively recognize patterns and essentially "learn." The machine can take an input and predict an output once has been trianed [START_REF] Helm | Machine learning and artificial intelligence: definitions, applications, and future directions[END_REF]. Machine learning allows to better understanding of the adsorption phenomena while reducing the workload, needed space, costs, and time required [START_REF] Lakshmi | Artificial intelligence (AI) applications in adsorption of heavy metals using modified biochar[END_REF]. Several researchers have performed adsorption modeling and optimization studies by comparing and combining the RSM and machine learning approaches.

The main goal of the research study of [START_REF] Onu | Comparative analysis of RSM, ANN and ANFIS and the mechanistic modeling in eriochrome black-T dye adsorption using modified clay[END_REF] was to apply response surface methodology (RSM), adaptive neurofuzzy inference system (ANFIS), and artificial neural network (ANN) to simulating the uptake of Eriochrome black-T (EBT) dye from aqueous solution using Nteje clay. The EBT dye's adsorption was predicted with great accuracy by the ANFIS, ANN, and RSM models. The results showed that ANFIS was the best predictive model and RSM the least effective for EBT dye adsorption. Ghosh et al., [START_REF] Ghosh | Modeling of biosorption of Cu (II) by alkali-modified spent tea leaves using response surface methodology (RSM) and artificial neural network (ANN)[END_REF] compared the RSM and the ANN for the simulation and optimization of the biosorption process of Cu(II) by alkali-modified spent tea leaves. The obtained results suggest that RSM had better prediction performance as compared to ANN.

J o u r n a l P r e -p r o o f

In this study, an experimental approach of RSM, the Box-Behnken Design (BBD), and some machine learning models; Gaussian Process Regression coupled with Bagging (Bootstrap Aggregation_Bag) and Dragonfly optimization algorithm (GPR_DA_Bootstrap), were used to optimize the MB adsorption onto the prepared activated carbon. The models created for the independent variables were optimized for their influence on the dependent variables using the BBD. The initial concentration of methylene blue (400-700 mg/L), the adsorbent dosage (0.6-1.6 g/L), the contact time (30-540 min), the pH (7-11) and the temperature (20-50°C) and response (MB uptake) were taken into account to find the best circumstances. Then, a Gaussian process regression model with Bagging (Bootstrap Aggregation_Bag) and Dragonfly (GPR_DA_Bootstrap) optimization algorithm was used to predict the outputs using the BBD database. After than, optimization by two techniques, dragonfly (DA) and particle swarm (PSO) was caried out to find the optimal for the two models. Finally, an application was created using the MATLAB guide to provide an easy way to implement optimization and prediction of MB uptake. To our knowledge, optimizing the efficiency of activated carbon based on jujube stones used for the treatment of MB from BBD and GPR_DA_Bootstrap has never been attempted before. Moreover, such a comparison has never been made before in this context.

The remaining part of this paper is organised as follows. The method of preparation and activation of activated carbon as well as its characterization are presented in Section 2, where a detailed explanation of the MB uptake isotherms, Kinetics, thermodynamic study and adsorption mechanism are also provided. Furthermore, the experimental design method BBD, the modelling method of GPR_DA_Bootstrap, and the optimization analysis based on two algorithms are also presented in Section 2. Section 3 presents the interpretation of BBD. In addition, the modeling results of GPR_DA_Bootstrap and the optimization results followed by experimental validation are also presented. The last section concludes the paper.

J o u r n a l P r e -p r o o f

Materials and methods

All reactants were of analytical grade and used without additional purification.

Preparation of the methylene blue stock solution

The methylene blue used (Mw=319.85 g.mol -1 ) is a cationic dye (C 16 H 18 N 3 SCl) purchased from Sigma-Aldrich. Its maximum absorption wavelength is 665 nm (determined by a UVvisible spectrophotometer, Agilent Cary 60). The 2000 mg/L stock solution was prepared by dissolving the adequate amount of MB in 1 L of bidistilled water. It was further diluted to prepare the required concentrations.

Preparation of activated carbon

The jujube used in this research was picked from Bouira, Algeria. It was harvested between September to December. The stones were first separated from the pulp by heating in boiling water, rinsed with tap water repeatedly, then with distilled water. After that, the stones were dried to constant weight. Crushed stones were sieved and the fraction of 1-2 mm was chemically activated with 85 % phosphoric acid (H 3 PO 4 ) at an impregnation rate of 1/1 by weight. The mixture was refluxed for two hours at the temperature of 200 °C, then carbonized in a furnace (WiseTherm, Witeg Wisd) at 600 °C for one hour. The obtained activated carbon (hereafter named PJAC) was finally neutralized with distilled water and dried at 60°C to constant weight, sieved on a 100 µm sieve, and stored in desiccators.

Characterization of PJAC

The approximate analysis of the PJAC composition permitted the determination of the ash content (according to ASTM D2866-70), the moisture content (according to ASTM D2867-70), the volatile matter content (according to ISO 562-1981) and the fixed carbon content (according to ASTM D3172) [START_REF] Bahnes | Preparation of a novel activated carbon from jujube stones (Ziziphus jujuba) for the removal of basic and acid dyes[END_REF]. The true density (ρ t ) was measured by the pycnometer method using methanol as a solvent [START_REF] Heschel | On the suitability of agricultural by-products for the manufacture of granular activated carbon[END_REF]. The bulk J o u r n a l P r e -p r o o f density (ρ a ) was calculated as described by El Nemr et al. [START_REF] El Nemr | Evaluation of Cationic Methylene Blue Dye Removal by High Surface Area Mesoporous Activated Carbon Derived from Ulva lactuca[END_REF]. The porosity ε (%) was then calculated using equation (1) [START_REF] Heschel | On the suitability of agricultural by-products for the manufacture of granular activated carbon[END_REF] 1 100

a t          (1)
The pore volume (V p ) was determined using the following equation [START_REF] Tarbaoui | Elaboration, caractérisation et évaluation des performances d'un nouveau matériau adsorbant à base des éponges marines: application dans l'adsorption des composés organiques volatils (Elaboration, characterization and evaluation of the performance of a new adsorbent material based of marine sponges: application in adsorption of volatile organic compounds)[END_REF] 11

P a t a V        (2)
The iodine number was determined as described in the standard method AATM 1112-01 [START_REF] Ahmed | Equilibrium isotherms and kinetics modeling of methylene blue adsorption on agricultural wastes-based activated carbons[END_REF].

To determine the methylene blue index and the specific surface area available to methylene blue, it was assumed that its adsorption occurs in a monolayer following the Langmuir equation [START_REF] Bahnes | Preparation of a novel activated carbon from jujube stones (Ziziphus jujuba) for the removal of basic and acid dyes[END_REF]. A mass of 0.02 g of studied activated carbon was stirred with 20 mL of methylene blue solution at concentrations ranging from 100 to 1000 mg/L, the mixture was stirred for 24 hours at room temperature, then centrifuged and analyzed by UV-visible spectroscopy (Agilent Technologies, Cary 60). The amount of MB adsorbed for each initial dye concentration was determined by the equation (3)

  0 e e CC qV m   (3)
Where, V (L) is the volume of the treated solution, m (g) is the mass of activated carbon used, C 0 (mg/L) represents the concentration of the MB solution at t=0, and C e (mg/L) is the MB concentration at equilibrium time.

The methylene blue index, represented by q max , was then determined from the Langmuir isotherm. The area available to methylene blue is determined by the following equation [START_REF] Douara | Sawdust-based activated carbon ability in the removal of phenol-based organics from aqueous media[END_REF][START_REF] Bahnes | Preparation of a novel activated carbon from jujube stones (Ziziphus jujuba) for the removal of basic and acid dyes[END_REF] max .

MB

q N S S M  (4)

J o u r n a l P r e -p r o o f

Where S MB (m 2 .g -1 ) is the specific surface area, q max is the MB index which represents the maximum adsorption capacity (mg/g) determined from the Langmuir isotherm, N (mol -1 ) is Avogadro's number (6.023.10 23 mol -1 ), S (Å 2 ) represents the surface occupied by a methylene blue molecule (130 Å 2 ) [START_REF] Hang | Methylene blue absorption by clay minerals. Determination of surface areas and cation exchange capacities (clay-organic studies XVIII)[END_REF], and M (g.mol -1 ) is the molecular weight of methylene blue (319.85 g.mol -1 ).

The Boehm titration was performed according to the method described in our previous work [START_REF] Bouchelkia | Removal of lead (II) from water using activated carbon developed from jujube stones, a low-cost sorbent[END_REF].

The variable pH pzc defines the pH value for which the net charge of the adsorbent surface is zero. First of all, a series of bottles containing 50 mL of 0.1 M NaCl solutions, whose pH was previously adjusted by the addition of 0.1 M NaOH or 0.1 M HCl aqueous solutions to be in the range of 2-10, were prepared. Then, 0.15 g of dried PJAC was then added to each bottle. The suspensions were stirred at a speed of 150 rpm for 48 hours at room temperature. Each solution was then filtered and a new pH measurement was performed using a Mettler Toledo pH meter and named pH final . The curve representing pH final = f (pH initial ) was drawn. The pH pzc corresponds to the pH of the solution for which the curve crosses the first bisector (pH final = pH initial ) [START_REF] Bohli | Evaluation of an activated carbon from olive stones used as an adsorbent for heavy metal removal from aqueous phases[END_REF][START_REF] Thangappan | Surface characterization and methylene blue adsorption studies on a mesoporous adsorbent from chemically modified Areca triandra palm shell[END_REF].

FTIR analysis was performed on a PerkinElmer Spectrum, to assess the functional groups present on the surface of the raw jujube stone (hereafter named Raw J) and PJAC before and after adsorption. The activated carbon powder was not pre-treated before being analyzed. The spectra were recorded in the range of 4000 and 400 cm -1 .

The X-ray diffraction (XRD) analysis of the samples was performed to investigate their structural features. The X-ray diffraction patterns on powders were collected at room temperature on a Malvern Panalytical X'pert Pro analyzer. The structure analysis of the raw material and the activated carbon was investigated between 2θ angles of 10° -80° employing a 0.02° step.

J o u r n a l P r e -p r o o f

To investigate the morphological characteristics of the Raw J and PJAC before and after adsorption of the MB, the samples were analyzed by Scanning Electron Microscopy (SEM) using Thermoscientific Quattro S Microscope.

N 2 adsorption-desorption technique was used to determine the Surface area and pore distribution of the Raw J and PJAC. The isotherms were carried out on a Micromeritics ASAP 2020 Plus surface area analyser at 77K which corresponds to the liquid nitrogen temperature.

The specific area was estimated using Brunauer-Emmett-Teller (BET) method (Labied et al.

2018)

Batch adsorption experiments

Adsorption tests were performed by stirring 20 mL of methylene blue of determined concentration with PJAC under magnetic stirring at 200 rpm using a multi-stirrer system (Selecta Multimatic-5N). The pH was adjusted using 0.1 M NaOH and 0.1 M HCl solutions.

After the adsorption time, the mixture was centrifuged at 3000 rpm for 15 min using a LW Scientific EZ Swing centrifuge, the supernatant was then analyzed spectrophotometrically at a wavelength of 665 nm. Equations 3 and 5 were used to determine the amount of methylene blue adsorbed at equilibrium time, and at any time t onto the PJAC, respectively.

 

0 t t CC qV m   (5)
Where, V (L) is the volume of the treated solution, m (g) is the mass of activated carbon used, C 0 and C t, (mg/L) are the MB concentration at t=0 and any time t, respectively. q t (mg/g) is the amount of adsorbed MB per PJAC mass unit at any time t.

Adsorption kinetics

Studying adsorption kinetics is an important step in elucidating the rate-determining steps, reaction pathways, and dominant mechanisms in the adsorption process [START_REF] Tan | Insight into the adsorption kinetics models for the removal of contaminants from aqueous solutions[END_REF][START_REF] Dao | Natural core-shell structure activated carbon beads derived from Litsea glutinosa seeds for removal of methylene blue: Facile preparation, characterization, and adsorption properties[END_REF]. To determine the kinetics of MB adsorption by PJAC, we examined J o u r n a l P r e -p r o o f pseudo-first-order, pseudo-second-order kinetic equations, and intraparticle diffusion models.

The corresponding equations are shown in Table 1 [START_REF] Tran | Mistakes and inconsistencies regarding adsorption of contaminants from aqueous solutions: a critical review[END_REF]

Adsorption isotherms

Adsorption isotherm is the equilibrium relationship between the concentrations of the adsorbed pollutant (solid phase) and its concentration in the solution (liquid phase) at a given temperature [START_REF] Panadare | Adsorptive removal of copper (II) from aqueous solution onto the waste sweet lime peels (SLP): equilibrium, kinetics and thermodynamics studies[END_REF]. The isotherm study provides crucial information on the mechanism of the adsorption process and maximum adsorption capacity [START_REF] Baidya | Adsorption of brilliant green dye from aqueous solution onto chemically modified areca nut husk[END_REF]. In this work, Langmuir, Freundlich and Temkin isotherms have been applied to investigate the methylene blue distribution between the liquid and solid phases. Table 1 shows the non-linear forms of the three used models [START_REF] Tran | Mistakes and inconsistencies regarding adsorption of contaminants from aqueous solutions: a critical review[END_REF]).

The experimental conditions were pH = 7.0, and the PJAC dosage = 1g/L. The initial dye concentration was varied between 100 and 1000mg/L and the temperature of experiments was around 25°C. The agitation rate was fixed to 200rpm. q q e   K 1 : the pseudo-first-order kinetic rate constant (min -1 )

Pseudo-second- order model 2 2 2 1 e t e q K t q q k t   K 2 : the pseudo-second-order kinetic rate constant (g•mg -1 •min -1 ) Intraparticle diffusion model 1/2 tp q K t C  K p : intra-particle diffusion rate constant (mg•g -1 •min -1/2 ) C a constant related to the boundary layer thickness (mg•g -1 )
.

Adsorption isotherms

Langmuir model 1

m L e e Le q K C q KC   T: the absolute adsorption temperature (K), R: the gas constant (8.314 J/mol.K).

Box-Behnken design

The Box-Behnken design (BBD) is a statistical model of response surface methodology (RSM) [START_REF] Box | Some new three level designs for the study of quantitative variables[END_REF]. Empirical and of second-order, it allows the estimation of the parameters of the quadratic model by establishing a relation between the experimental factors and the obtained results [START_REF] Ferreira | Box-Behnken design: an alternative for the optimization of analytical methods[END_REF][START_REF] Witek-Krowiak | Application of response surface methodology and artificial neural network methods in modelling and optimization of biosorption process[END_REF][START_REF] Sadhukhan | Optimisation using central composite design (CCD) and the desirability function for sorption of methylene blue from aqueous solution onto Lemna major[END_REF]. The total number of experiments (N) needed to a BBD is given by the relation: N = 2K.(K-1)+C 0 where C 0 represents the number of repetitions of the center point and K is the number of factors [START_REF] Ferreira | Box-Behnken design: an alternative for the optimization of analytical methods[END_REF]). All factors have three coded levels of values, low (-1), medium (0), and high (+1). Non-linear regression was carried out to fit the experimental data with the second-order polynomial given by equation ( 6) and to determine the relevant model terms:

J o u r n a l P r e -p r o o f 2 0 k k k i i ii ij i j i i ij Y x x x x E             (6)
Where Y is the MB uptake (the dependent variable), k is the number of independent variables (factors), x i is the ith independent variable in coded level, β 0 is the regression coefficient at the center point. B i is the linear coefficient for the ith independent variable, B ii is the ith quadratic coefficients, B ij is the second-order interaction coefficient between the ith and jth independent variables (linear by linear), and E is the error [START_REF] Das | Optimization of parameters for cerium (III) biosorption onto biowaste materials of animal and plant origin using 5-level Box-Behnken design: Equilibrium, kinetic, thermodynamic and regeneration studies[END_REF][START_REF] Shahbazi | Low-cost activated carbon: characterization, decolorization, modeling, optimization and kinetics[END_REF].

The relation between the actual values and the coded values is described in equation ( 7)

0 i i i XX x X    (7)
Where X i is the actual value of the ith variable; x i is the coded value of X i ; X 0 is the actual value of X i at the center point, and ΔX i is the step change [START_REF] Han | The optimization of As (V) removal over mesoporous alumina by using response surface methodology and adsorption mechanism[END_REF][START_REF] Moussa | Optimization of ultrasound-assisted extraction of phenolic-saponin content from Carthamus caeruleus L. rhizome and predictive model based on support vector regression optimized by dragonfly algorithm[END_REF].

In this work, the BBD technique, of the RSM approach, was used to optimize the studied process. Regarding the determination of the independent factors, the initial concentration of dye (X 1 ), the dose of PJAC (X 2 ), the contact time (X 3 ), the pH (X 4 ) and the temperature (X 5 )

were chosen as independent variables; while the MB uptake was chosen as the dependent variable. The JMP program (JMP® Pro 13.0.0) was used to perform the statistical analysis.

Interval parameters were determined based on MB uptake as shown in Table 2. J o u r n a l P r e -p r o o f

Gaussian Process Regression coupled with the Dragonfly algorithm

Gaussian Process (GP) is a stochastic process with a series of random variables. Any finite range of those random variables has a joint Gaussian distribution. The probabilistic illustration of a goal function can be used for regression and classification (Tahraoui et al. 2022b;Tahraoui et al. 2022c).

Gaussian Process Regression (GPR) provides a probabilistic, nonparametric strategy for solving nonlinear regression problems. GPR assumes that the measurements of the output variable y are generated in the following way [START_REF] Park | Gaussian process regression (GPR) representation in predictive model markup language (PMML)[END_REF][START_REF] Liu | Modeling of subway indoor air quality using Gaussian process regression[END_REF] :

    y f x k   (8)
where x stands for the measurements of input variables, f is the unknown functional dependence and  is a Gaussian noise with variance 2 n  . GPR uses GP as a prior to describe the distribution on the target function   fx (Park et al. 2017; Tahraoui et al. 2022b). In GPR, the function values

  1: 1 ,..., nn f f f  corresponding to the input   1: 1 ,..., nn x x x 
are treated as random variables, where [START_REF] Park | Gaussian process regression (GPR) representation in predictive model markup language (PMML)[END_REF]Tahraoui et al. 2022b). GP is defined as a collection of random variables (stochastic process), any finite number of which is assumed to be jointly Gaussian distributed [START_REF] Park | Gaussian process regression (GPR) representation in predictive model markup language (PMML)[END_REF]Tahraoui et al. 2022b). GP can fully describe the distribution over an unknown function

  ii f f x  (

 

fx by its mean function

    m x E f x    and a kernel function   ,' k x x that approximates the covariance             '' E f x m x f x m x    .
The kernel (covariance) function represents a geometrical distance measure assuming that the more closely located inputs would be more correlated in terms of their function values [START_REF] Park | Gaussian process regression (GPR) representation in predictive model markup language (PMML)[END_REF]Tahraoui et al. 2022b). That is, the prior on the function values is represented as [START_REF] Park | Gaussian process regression (GPR) representation in predictive model markup language (PMML)[END_REF]Tahraoui et al. 2022b): In GPR, the kernel (covariance) function describes the structure of the target function. Thus, the type of kernel function   ,' k x x used to build a GPR model and its parameters can strongly affect the overall representability of the GPR model and affect the accuracy of the prediction model. A wide variety of kernel functions can be used [START_REF] Williams | Gaussian processes for machine learning[END_REF].

J o u r n a l P r e -p r o o f         1: ,, n f GP m k     (
In this article, the uptake of MB was also predicted using a GPR model developed from the experimental data under BBD. In order to obtain a better model and better performance, the database was normalized from the beginning in the interval [-1.1], and then it was divided into two sets: 75% for learning and 25% for validation. Then, ten Kernel functions were optimized (exponential, exponential squared, matern32, matern52, quadratic rational, exponential ard, exponential squared ard, ardmatern32, ardmatern52, and quadratic rational ard) with the basis function (constant, linear and zero). The functions of the ten used kernel were given in the supplementary materials section (equations S1 to S10). The knowledge of each Kernel function was also optimized for their specific parameters (Kernel Scale [sigmaM, sigmaF] and sigma) (see Figure 1). For this, the dragonfly algorithm was used to optimize the specific parameters of each Kernel function, since this optimization algorithm has been used to solve a wide variety of optimization problems including solving different machine learning optimization problems [START_REF] Moussa | Optimization of ultrasound-assisted extraction of phenolic-saponin content from Carthamus caeruleus L. rhizome and predictive model based on support vector regression optimized by dragonfly algorithm[END_REF]. Numerous studies have proved that machine learning performance has been improved when the hyper-parameters were optimized using the Dragonfly algorithm [START_REF] Moussa | Optimization of ultrasound-assisted extraction of phenolic-saponin content from Carthamus caeruleus L. rhizome and predictive model based on support vector regression optimized by dragonfly algorithm[END_REF].

J o u r n a l P r e -p r o o f

Statistical evaluation criteria

Statistic analysis and ANOVA were used to investigate the statistical abilities of the model generated with a confidence level of 95%. The statistical adequacy of the model was assessed using a variety of variables, including the P-value, the value F, the coefficient of variance (C.V), the coefficient of determination (R 2 ), the adjusted determination of the coefficient (R adj 2 ), and the Root Mean Square Error (RMSE) for BBD model (Tahraoui et al. 2021b;Tahraoui et al. 2022a;Tahraoui et al. 2022b). The value F describes the variation of the responses, which can be checked by a regression equation, while the value P determines the statistical adequacy of the developed model. For a model to be significant, the P-value must be less than 5%, and the P-value for the inadequacy test must be greater than 5% (Kıvanç and Yönten 2020; Singh and Kumar 2020).

On the other hand, the Correlation Coefficient (R), R 2 , R adj 2 , and RMSE, were used to evaluate the performance of each GPR_DA model. These are calculated using the equations S11-S13 (supplementary materials) [START_REF] Belsley | Regression diagnostics: Identifying influential data and sources of collinearity[END_REF][START_REF] Hong | Monitoring of sequencing batch reactor for nitrogen and phosphorus removal using neural networks[END_REF]; Tahraoui et al.

Results and discussion

Characterization studies

In this work, activated carbon was prepared by chemical activation of Jujube stones (Ziziphus lotus L) using 85 % phosphoric acid at a carbonization temperature of 600 °C. The prepared PJAC was characterized by FTIR for the study of its chemical structure and the functional groups present on its surface. Actually, the surface of the activated carbon does not only contain carbon atoms, but also other hetero-elements such as sulfur and nitrogen, etc. linked to the carbon atoms, which form the chemical composition of the surface of the activated carbon [START_REF] Prahas | Activated carbon from jackfruit peel waste by H3PO4 chemical activation: Pore structure and surface chemistry characterization[END_REF].

Figure 2 reports the N 2 adsorption-desorption isotherms for the Raw J and the PJAC.

Figure 2a shows a type II isotherm according to the IUPAC classification [START_REF] Peñafiel | Comparative adsorption of ciprofloxacin on sugarcane bagasse from Ecuador and on commercial powdered activated carbon[END_REF]. This type of isotherm characterizes non-porous or high pore diameter materials (Jawad et al. 2022). Table 3 shows that the Raw J is characterized by a specific surface area of 2.0788 m²/g, which confirms its non-porous character. The rapid rise in adsorption that exhibits the Raw J at high pressure (P/Po > 0.95) suggests the retention of macropores (Jawad et al. 2022).

On the other hand, the PJAC isotherm was found to be similar to Type I isotherm according to the IUPAC classification (Figure 2b), indicating that the PJAC is microporous and the adsorption process involves the primary filling of microspores at low relative pressure P/P 0 [START_REF] Selmi | Physical meaning of the parameters used in fractal kinetic and generalised adsorption models of Brouers-Sotolongo[END_REF][START_REF] Daoud | Adsorption ability of activated carbons from Phoenix dactylifera rachis and Ziziphus jujube stones for the removal of commercial dye and the treatment of dyestuff wastewater[END_REF]. The isotherm also showed that no horizontal plateau was clearly reached, indicating pore enlargement [START_REF] Selmi | Physical meaning of the parameters used in fractal kinetic and generalised adsorption models of Brouers-Sotolongo[END_REF]. The formation of hysteresis loops indicates the existence of mesopores [START_REF] Mbarki | Low-cost activated carbon preparation from Corn stigmata fibers chemically activated using H 3 PO 4 , ZnCl 2 and KOH: Study of methylene blue adsorption, stochastic isotherm and fractal kinetic[END_REF]). As can be seen in Table 3, the specific surface area of the PJAC was 685m²/g with a total volume in pore of J o u r n a l P r e -p r o o f 0.425 cm²/g, while the Raw J was characterized by a specific surface area of 2.0788 m²/g and a total volume in pore of 0.00192 cm²/g. The scanning electron microscopy (SEM) is used as a valuable tool for examining the morphology, the porosity development and the surface structure of the Raw J, PJAC and MB-PJAC. Fig. 3 shows the obtained SEM images for the three samples. The surface of the Raw J is presented in Figure 3(a), which shows a compact, irregular surface with no discernible pore structure. FTIR spectrum of the Raw J is shown in Figure 4. The band at 3436 cm -1 corresponds to the stretching vibrations of the -OH groups (hydroxyl groups) [START_REF] Daoud | Adsorption ability of activated carbons from Phoenix dactylifera rachis and Ziziphus jujube stones for the removal of commercial dye and the treatment of dyestuff wastewater[END_REF][START_REF] Shahrokhi-Shahraki | High efficiency removal of heavy metals using tire-derived activated carbon vs commercial activated carbon: Insights into the adsorption mechanisms[END_REF]. The peaks at 2924 and 2852 cm -1 may be assigned to the C-H stretching vibration in the saturated aliphatic groups (alkyl/alkane). The presence of the band at around 1740cm -1 can be ascribed to the C=O stretching in aldehyde, ketone esters and acetyl [START_REF] Shamsuddin | Synthesis and characterization of activated carbon produced from kenaf core fiber using H 3 PO 4 activation[END_REF][START_REF] Li | Adsorption of congo red and methylene blue dyes on an ashitaba waste and a walnut shell-based activated carbon from aqueous solutions: Experiments, characterization and physical interpretations[END_REF][START_REF] Shahrokhi-Shahraki | High efficiency removal of heavy metals using tire-derived activated carbon vs commercial activated carbon: Insights into the adsorption mechanisms[END_REF]. The peak at 1653cm -1 is attributed to the vibration of C=C in aromatic rings [START_REF] Boudechiche | Comparative study on removal of two basic dyes in aqueous medium by adsorption using activated carbon from Ziziphus lotus stones[END_REF].

The weak peaks at 1544 and 1459 cm -1 may be attributed to the existence of C=H bending and C=C cycle stretching mode of aromatic rings [START_REF] Daoud | Adsorption ability of activated carbons from Phoenix dactylifera rachis and Ziziphus jujube stones for the removal of commercial dye and the treatment of dyestuff wastewater[END_REF][START_REF] Shahrokhi-Shahraki | High efficiency removal of heavy metals using tire-derived activated carbon vs commercial activated carbon: Insights into the adsorption mechanisms[END_REF][START_REF] Teong | Vatica rassak wood waste-derived activated carbon for effective Pb (II) adsorption: Kinetic, isotherm and reusability studies[END_REF]). Band at around 1382 cm -1 correspond to phenolic O-H bending in the Raw J (Üner et al. 2016). Peaks at 1253, 1168, and 1045 cm -1 indicate the existence of stretching vibrations band of C-O and/or C-O-C in phenols, acids, alcohols, ester, and/or ethers groups (Jawad et al. 2018c;[START_REF] Jawad | Conversion of Malaysian low-rank coal to mesoporous activated carbon: structure characterization and adsorption properties[END_REF].

FTIR spectrum of the PJAC is also shown in Figure 4. It can be noticed that the intensity of the peak at around 3400 cm -1 decreased in comparison with the Raw J. The graphs also show that the peaks at around 2900 and 2800 cm -1 almost disappeared. This diminution J o u r n a l P r e -p r o o f

indicates that phosphoric acid (H 3 PO 4 ) acted as a dehydrating agent; it also removed a significant amount of hydrogen from the Raw J [START_REF] Kundu | Taguchi optimization approach for production of activated carbon from phosphoric acid impregnated palm kernel shell by microwave heating[END_REF]. The band at 1740 cm -1 disappeared, due to the complete removal of ketones and aldehydes groups that are thermally unstable [START_REF] Shamsuddin | Synthesis and characterization of activated carbon produced from kenaf core fiber using H 3 PO 4 activation[END_REF], and also to the breaking of many bonds in aliphatic and aromatics species. The comparison shows an almost complete disappearance of some peaks in the PJAC, at 1653, 1544, 1459, and 1168 cm -1 , and some peaks were slightly shifted to low wavenumber due to the effect of carbonization and chemical activation [START_REF] Daoud | Adsorption ability of activated carbons from Phoenix dactylifera rachis and Ziziphus jujube stones for the removal of commercial dye and the treatment of dyestuff wastewater[END_REF].

The activation at high temperature degraded some functional groups that were originally present in the raw material structure [START_REF] Li | Adsorption of congo red and methylene blue dyes on an ashitaba waste and a walnut shell-based activated carbon from aqueous solutions: Experiments, characterization and physical interpretations[END_REF]. The spectra also showed the appearance of a new peak in the PJAC at 1589 cm -1 , indicating the C=O stretching vibration of carbonyl and lactone groups [START_REF] Hesas | Preparation and characterization of activated carbon from apple waste by microwave-assisted phosphoric acid activation: application in methylene blue adsorption[END_REF].

The spectra of prepared activated carbon before and after MB adsorption are shown in The characteristics of the raw jujube stones (Raw J) and the prepared activated carbon PJAC are summarized in Table 4. The pH pzc of the prepared activated carbon was found to be 5.00, indicating that the surface of PJAC is acidic. The surface charge becomes net negative J o u r n a l P r e -p r o o f above pH pzc and MB adsorption is enhanced at higher solution pH [START_REF] Thangappan | Surface characterization and methylene blue adsorption studies on a mesoporous adsorbent from chemically modified Areca triandra palm shell[END_REF].

The H 3 PO 4 treatment of the Raw J led to the diminution of the pH pzc of the produced PJAC.

The analysis of the global characteristics of the raw material (Table 4) showed that it had a high amount of volatile matter (75.25 %) and a low amount of ash (0.86 %), which are desired for the production of adsorbents [START_REF] Rozada | Activated carbons from sewage sludge and discarded tyres: production and optimization[END_REF]. The carbonization and activation processes lead to the release of volatile matter as gas and liquid; the produced activated carbon is then characterized by a low volatile matter content and high fixed carbon content [START_REF] Msaada | Industrial wastewater decolorization by activated carbon from Ziziphus lotus[END_REF]. As shown in Table 4, the volatile matter in the PJAC decreased from 75.25 % to 45.06 % compared with the raw material. Fixed carbon indicates char carbon [START_REF] Bahnes | Preparation of a novel activated carbon from jujube stones (Ziziphus jujuba) for the removal of basic and acid dyes[END_REF]; and the results showed that chemical activation induced an increase in carbon content, this is due to the release of volatiles, leading to the elimination of non-carbon content and the enrichment of carbon [START_REF] Daoud | Adsorption ability of activated carbons from Phoenix dactylifera rachis and Ziziphus jujube stones for the removal of commercial dye and the treatment of dyestuff wastewater[END_REF]). Similar results have been reported in previous work [START_REF] Daoud | Adsorption ability of activated carbons from Phoenix dactylifera rachis and Ziziphus jujube stones for the removal of commercial dye and the treatment of dyestuff wastewater[END_REF]. Ash content is a measurement of non-combustible substances and the non-volatile components of the material [START_REF] Angın | Effect of pyrolysis temperature and heating rate on biochar obtained from pyrolysis of safflower seed press cake[END_REF]) and good activated carbon must be characterized by a low ash content [START_REF] Kibami | Preparation and characterization of activated carbon from Fagopyrum esculentum Moench by HNO 3 and H 3 PO 4 chemical activation[END_REF]. Accordingly, the prepared PJAC was found to have 1.03 % of ash content.

Bulk density, porosity, iodine, and methylene blue adsorption and Surface area are some of the parameters usually examined while evaluating the performance and the porosity structure of produced activated carbons. Table 5 shows the obtained results. Bulk or apparent density defines the weight of material contained in a given volume. This volume includes not only the skeletal solid's volume, but also the pores of the particles and the voids between them [START_REF] Yeganeh | Effect of raw materials on properties of activated carbons[END_REF]). The prepared PJAC was found to have a bulk density of 0.84 g/cm 3 and a porosity of 71.33 %. ( [START_REF] Abdulhameed | Statistical modeling and mechanistic pathway for methylene blue dye removal by high surface area and mesoporous grass-based activated carbon using K 2 CO 3 activator[END_REF], via chemical activation of biomass of grass waste using a K 2 CO 3assisted pyrolysis approach. The Boehm titration is employed as a chemical approach for identifying oxygen surface groups on carbon compounds. It is built on the concept that different acidities of oxygen groups on carbon surfaces can be neutralized by varying strengths of bases [START_REF] Bouchelkia | Removal of lead (II) from water using activated carbon developed from jujube stones, a low-cost sorbent[END_REF] . For the PJAC, the number of basic groups was measured as 0.15 mmol.g -1 , while those of acidic groups were 0.25, 0.51, and 0.60 mmol.g -1 for lactonic, phenolic and carboxylic groups, respectively. The total acidic amount on the J o u r n a l P r e -p r o o f PJAC surface was therefore 1.36 mmol.g -1 , indicating the predominance of acidic functional groups on the PJAC surface. Total basic (mmol/g) 0.15 X-ray diffraction patterns of the Raw J and PJAC are given in Figure 5. No significant sharp peaks were observed, which indicated that the Raw J and the activated carbon are amorphous materials [START_REF] Tang | Extremely efficient and rapidly adsorb methylene blue using porous adsorbent prepared from waste paper: Kinetics and equilibrium studies[END_REF]). The Raw J pattern showed one broad and intense peak at around 21.5°, indicating typical amorphous carbon [START_REF] Wu | Hydrothermal synthesis of N-doped spherical carbon from carboxymethylcellulose for CO 2 capture[END_REF]). The peak disappeared when the Raw J was activated with H 3 PO 4 and carbonized at 600 °C and two broad diffraction peaks at 2θ=25° and 43° appeared, corresponding to the reflection of (0 0 2) and (1 0 0) planes, indicating the presence of dehydrated hemicelluloses [START_REF] Liou | Development of mesoporous structure and high adsorption capacity of biomassbased activated carbon by phosphoric acid and zinc chloride activation[END_REF][START_REF] Rezma | Microporous activated carbon electrode derived from date stone without use of binder for capacitive deionization application[END_REF]. At the same time, there are noise signals related to the carbon powder, indicating a predominantly amorphous structure of PJAC [START_REF] Bouchelkia | Removal of lead (II) from water using activated carbon developed from jujube stones, a low-cost sorbent[END_REF].

Adsorption kinetics

In this study, three of the most commonly used kinetic models were applied to investigate the kinetic data of the MB adsorption on the PJAC adsorbent, including pseudo-first-order, pseudo-second-order kinetic equations, and intraparticle diffusion model.

The fitting of the kinetic models to the experimental data is represented in Figure 6, and the calculated kinetic parameters are shown in table 6. As can be observed in Table 6, the pseudosecond-order model gave the highest correlation coefficient (R 2 > 0.99) compared to the pseudo-first order model, and the calculated q ecal values from this model were also in good The application of the intraparticle diffusion model (Figure 6) showed three linear segments implying the involvement of three stages during the MB adsorption process; (1) surface or film diffusion, (2) pore or intraparticle diffusion, and (3) sorption on the interior sites of the adsorbent [START_REF] Teong | Vatica rassak wood waste-derived activated carbon for effective Pb (II) adsorption: Kinetic, isotherm and reusability studies[END_REF]). In the first step, the dye diffused quickly through the liquid film to the external activated carbon surface. This step is characterized by the highest values of intraparticle diffusion rate constant (K p ) and the lowest value of the constant C (Table 6).

In the second stage, the MB molecules diffused into the internal pores of the PJAC. The third stage represents the final equilibrium step where the low residual MB concentration left in the solution moved slowly from larger pores to micropores. It is characterized by the lowest value of K p and the highest value of C which provides information about the boundary layer thickness, i.e. higher C value implies greater the effect of the boundary layer, reducing then the diffusion of the dye modules due to the occupation of the majority of the adsorption sites [START_REF] Han | High adsorption of methylene blue by activated carbon prepared from phosphoric acid treated eucalyptus residue[END_REF]. The intraparticle diffusion is considered as the rate determining step when the fitted linear relationship plot passed through the origin [START_REF] El Nemr | Evaluation of Cationic Methylene Blue Dye Removal by High Surface Area Mesoporous Activated Carbon Derived from Ulva lactuca[END_REF]. However, in J o u r n a l P r e -p r o o f this study, the fitted lines do not pass through the origin, which proves that intraparticle diffusion is involved but not the only rate-limiting step.

Adsorption isotherms

Langmuir, Freundlich and Temkin adsorption isotherms are plotted in Figure 7 and the computational parameters are listed in the Langmuir isotherm could be more suitable to describe the behavior of MB adsorption on the prepared PJAC. The Langmuir model supposes that adsorption process is monolayer and occurs on a homogeneous surface and that there is no interaction between the adsorbed molecules (Aminu et al. 2020). The value of the Langmuir parameter K L is between 0 and 1, indicating that the PJAC tends to adsorb MB [START_REF] Ren | Study on adsorption of ammonia nitrogen by iron-loaded activated carbon from low temperature wastewater[END_REF]. The essential characteristics of a Langmuir isotherm can be expressed in terms of a constant (dimensionless) separation factor, R L that is used to predict whether an adsorption system is "favorable" or "unfavorable". The separation factor R L is defined by the following equation (Weber and Chakravorti 1974)

0 1 1. L L R KC   ( 10
)
Where C 0 (mg/L) is the maximum initial concentration of dye. The isotherm is unfavorable when R L >1 and it is favorable when 0 < R L <1. The calculated value of R L was found to be 0.016 indicating the favorability of the adsorption process. Similarly, the adsorption capacity constant n of the Freundlich isotherm is 5.051 confirming the favorability of the process [START_REF] Baidya | Adsorption of brilliant green dye from aqueous solution onto chemically modified areca nut husk[END_REF].

Table 7.

Isotherm parameters for MB adsorption onto PJAC (Adsorbent dosage=1.00g/L, Time=540min, T=25°C and pH=7, agitation rate=200 rpm) Time=540min, T=25°C and pH=7, agitation rate=200 rpm).

The BBD analysis

The optimization of Methylene blue adsorption on the PJAC was performed by the BBD approach. The effect of Initial MB concentration (500-700 mg/L), PJAC dosage (0.6-1.6 g/L),

J o u r n a l P r e -p r o o f

Contact time (30-540 min), pH (7-11), and temperature (20-50 °C) were studied using the Box Behnken design. The statistical analysis of the data was performed using JMP program (version 13 pro). Table 9 reports the regression analysis (ANOVA) response surface quadratic model for the methylene blue adsorption. Results showed an F-value of 41.611, a P-value of < 0.0001, a coefficient of variance C.V. of 3.742 %, a lack of fit of 0.067 and an R² of 0.971, namely very close de the value of the R² adj (0.948). This confirmed the high significance of the model and the accuracy and the reliability of the experiments.

The suitability of the model can be judged by plotting the predicted values versus the actual values [START_REF] Zhong | Multiparameter optimization of bromate sorption on anion exchange resin by a two-step statistical strategy: Plackett-Burman and Box-Behnken experimental design[END_REF]. The relationship between the measured and predicted values is Where the second-order polynomial model can be written as follows:

J o u r n a l P r e -p r o o f

x x x x x x x x x x x x x x x x x x x x xx x                                        1 4 2 4 3 4 1 5 3 5 4 5
0.45 11.32 7.37 5.2 0.45

x x x x x x x x x x x x                 (11)
Independent variables with high explanatory power for the dependent variable were taken; the five independent variables significantly affected the MB uptake (P-value < 0.0001). The quadratic contact time (x 3 ²) and quadratic temperature (x 5 ²) terms had also significant effects on the adsorption. The methylene blue elimination by the PJAC was also significantly affected by some interaction terms; x 1 *x 3 (initial BM concentration and contact time) and

x 2 *x 5 (PJAC dosage et temperature). Contrarily, all other terms were insignificant (P-value > 0.05). So the relationship could be reduced to equation 12:

 

x x x x x x x x x x x x x                        (12)
The value of the coefficient of determination decreased slightly (R 2 = 0.957), the equation became simpler after removing the low explanatory power variables from the dependent variable.

Response surface analysis

The Box Behnken design was used to study the effect of the operating parameters (contact time, pH, Temperature, PJAC dosage and initial dye dosage) on the adsorption of methylene blue on activated carbon. The response surface analysis is a relevant way to determine the effects and interactions between the 5 selected parameters. The individual effects and the interactions of process variables are discussed below.

Effect of contact time

J o u r n a l P r e -p r o o f

The contact time between adsorbent and adsorbate can be used to determine the potential initiation of binding and the optimum time for contaminant confiscation adsorption.

Furthermore, it is a crucial factor governing the kinetics of the adsorption process and overseeing the use of an adsorbent for industrial application and influencing its costeffectiveness [START_REF] Mashkoor | Magsorbents: Potential candidates in wastewater treatment technology-A review on the removal of methylene blue dye[END_REF].

Figures 9b,9c, 10b and 11a show the 3D simulation diagrams of the combined effects of contact time with initial MB concentration, temperature, PJAC dosage, and pH, respectively.

In each combination, all other parameters were set to their respective mean values. It can be seen from the surface response plots that MB adsorption initially progressed at a high rate due to the availability and accessibility of vacant surface sites. Adsorption sites become inaccessible and the remaining vacant surface sites are difficult to occupy due to the repulsive forces between the molecules of BM on the surface of the solid (adsorbed) and those of the aqueous phase (free) [START_REF] Bouchelkia | Removal of lead (II) from water using activated carbon developed from jujube stones, a low-cost sorbent[END_REF]). In addition, the molecules have to pass deeper and farther through the pores, which slow down the adsorption rate. Finally, the adsorption process reaches equilibrium.

Effect of the initial dye concentration

The MB adsorption was carried out at initial dye concentrations ranging from 400 to 700 mg/L. The 3D simulation diagrams of the combined effects of initial BM concentration and PJAC dosage, contact time, pH and temperature are represented in Figures 9a,9b, 9d and 10a, respectively. In each combination, all other parameters were set to their respective mean values. It can be depicted from the plots that the variation of the initial dye concentration from 400 to 700 mg/L induced an increase of the adsorbed quantity whatever the value of the other factors. This can be explained by the increase of the driving forces between the two phases; liquid and solid, i.e. an increase in the concentration gradient in the medium [START_REF] Mehmood | Efficient removal of crystal violet and eosin B from aqueous solution using Syzygium cumini leaves: a comparative study of acidic and basic dyes on a single adsorbent[END_REF]. Same results have been reported by [START_REF] Baidya | Adsorption of brilliant green dye from aqueous solution onto chemically modified areca nut husk[END_REF].

J o u r n a l P r e -p r o o f

Table 5 shows that the interaction between contact time and initial MB concentration was significant with a p-value of 0.0079. The plot represented in Figure 9b was obtained for an initial MB concentration range of 400 to 700 mg/L and varying contact time from 30 to 540 min at a fixed temperature, pH, and PJAC dosage of 35°C, 9 and 1.1 g/L (middle values), respectively. As discussed above, the dye uptake increased with the adsorbent contact time until the equilibrium; and at a given time, the removal of methylene blue increased with the increase of MB initial concentration.

Effect of pH

Figures 9d, 10c, 11a and 11b show the 3D simulation diagrams of the combined effects of pH with initial MB concentration. PJAC dosage, contact time, and temperature, respectively. In each combination, all other parameters were set to their respective mean values. It can be noticed from the response surface plots that MB uptake increased with the increase of pH from 7 to 11. As previously mentioned, the pH pzc of the PJAC was 5.00. When the solution pH is lower than the pH pzc , the net surface charge is positive, which favors the adsorption of anions. On the other hand, solution pH higher than the pH pzc favors the adsorption of cations;

and the net surface charge becomes more negatively charged while increasing the pH (Jawad et al. 2018b). This explains the enhancement in the elimination of methylene blue with the increase of the pH of the solution. A similar trend was found by Dotto et al. [START_REF] Dotto | Adsorption of methylene blue by ultrasonic surface modified chitin[END_REF] in the adsorption of MB onto Ultrasonic Surface Modified Chitin.

Effect of PJAC dosage and temperature

Table 9 shows that the interaction between PJAC dosage and temperature was the most significant as compared to all the other interactions with a p-value of 0.0002. Figure 10d shows the 3D simulation diagrams of the combined effects of PJAC dosage and temperature.

Experiments were carried out within the PJAC dosage range (0.6 -1.6 g/L) and temperature range (20 -50 °C) at a fixed initial MB concentration, contact time and pH of 550 mg/L, 285

J o u r n a l P r e -p r o o f min and 9 (middle values), respectively. The response surface plot shows that, at a fixed temperature, MB uptake decreased with the increase in PJAC dosage due to the decrease in adsorbate to adsorbent ratio [START_REF] Baidya | Adsorption of brilliant green dye from aqueous solution onto chemically modified areca nut husk[END_REF]. The plot also shows that the MB uptake increased while increasing the temperature from 20 to 50°C. A similar trend was observed in the response surface diagrams shown in Figures 9c,10a, and 11b where the increase in temperature increased the dye elimination, which indicates that the MB is favorably adsorbed by PJAC at high temperatures. This could be explained by the increase in the mobility and diffusion of the methylene blue molecules due to the reduction of the viscosity of the solution [START_REF] Li | Adsorption of congo red and methylene blue dyes on an ashitaba waste and a walnut shell-based activated carbon from aqueous solutions: Experiments, characterization and physical interpretations[END_REF]). The temperature rise may also increase the porosity of the PJAC pore and improves the accessibility of active sites. The increase of the BM uptake by increasing the temperature suggests that the adsorption may be an endothermic process [START_REF] Baidya | Adsorption of brilliant green dye from aqueous solution onto chemically modified areca nut husk[END_REF]. This can be explained by the calculation of thermodynamic parameters based on the Van't Hoff equation. These parameters were developed assuming that the adsorbate is uniformly distributed on the surface of the adsorbent. The adsorption thermodynamic parameters, such as Gibbs free energy change (∆G 0 , kJ/mol), enthalpy change (∆H 0 , kJ/mol) and entropy change (∆S 0 , kJ/mol.K), were determined according to following equations: [START_REF] Huang | Preparation of porous graphene/carbon nanotube composite and adsorption mechanism of methylene blue[END_REF][START_REF] Han | High adsorption of methylene blue by activated carbon prepared from phosphoric acid treated eucalyptus residue[END_REF]Jawad et al. 2022)

ln d SH K R RT      (13) e d e q K C  (14) . ( ) G RT Ln K     (15) G H T S         (16)
Where K d is the equilibrium constant, qe is the amount of MB adsorbed at equilibrium (mg/L), Ce is the concentration of MB remaining in the solution at equilibrium (mg/L), T is J o u r n a l P r e -p r o o f the absolute adsorption temperature (K), and R is the gas constant (8.314 J/mol.K). The plot of ln(K d ) vs. 1/T (figure not shown) was used to determine the values of ΔH 0 and ΔS 0 from the slope and the intercept of the Van't Hoff equation 13, respectively. ΔG 0 was calculated at different temperatures using equation 16 [START_REF] Gao | A promising and cost-effective biochar adsorbent derived from jujube pit for the removal of Pb (II) from aqueous solution[END_REF] The obtained results are shown in Table 10. The reported results show that the ∆G 0 is negative revealing that the adsorption process was spontaneous in nature and occurred automatically [START_REF] Ren | Study on adsorption of ammonia nitrogen by iron-loaded activated carbon from low temperature wastewater[END_REF]. The negative value of ∆G 0 decreased with increasing adsorption temperature, indicating that the adsorption process was stimulated at high temperature [START_REF] Gao | A promising and cost-effective biochar adsorbent derived from jujube pit for the removal of Pb (II) from aqueous solution[END_REF]. The enthalpy change ∆H 0 confirms that the process was endothermic [START_REF] Huang | Preparation of porous graphene/carbon nanotube composite and adsorption mechanism of methylene blue[END_REF]. The ΔH 0 value is less than 40 kJ/mol, indicating that the adsorption of MB on the PJAC is mainly of physical nature [START_REF] Peñafiel | Comparative adsorption of ciprofloxacin on sugarcane bagasse from Ecuador and on commercial powdered activated carbon[END_REF]. ∆S 0 was also positive which reflect the random disorder nature of the interface between the solid and the liquid during the MB adsorption process [START_REF] Gao | A promising and cost-effective biochar adsorbent derived from jujube pit for the removal of Pb (II) from aqueous solution[END_REF]Jawad et al. 2022). J o u r n a l P r e -p r o o f

Gaussian Process Regression model

In this work, as previously indicated to develop the GPR model (Figure 1), ten kernel functions (exponential, exponential squared, mother32, mother52, rational quadratic, exponential ard, exponential squared ard, ardmatern32, ardmatern52 and rational quadratic ard) were optimized with the basis function (constant, linear and zero).

The best model, which was obtained by optimizing kernel function, basis function and specific parameters (kernel scale and sigma), is presented in Table 11.

Table 11 shows the results of the GPR model. The experimental and predicted values are graphically schematized in Figure 12.

Figure 12. Comparison between experimental and predicted values

The results obtained by the GPR model show a very good performance in the learning phase and also for all the data, looking at their statistical coefficients and their errors. Indeed, the coefficients in the learning phase were 1 (R= 1.000, R 2 = 1.000 and R adj 2 = 1.000) and also the RMSE which was very low (RMSE= 0.385). Similarly, for all the data the coefficients were very close to 1 (R= 0.994, R 2 = 0.987 and R adj 2 = 0.985) and also the RMSE which was very low (RMSE= 5.866).

J o u r n a l P r e -p r o o f The experimental and predicted values have been graphically schematized in Figure 13. From the results, it is evident that the DA optimization algorithm has improved the performance efficiency. This clearly shows the benefit of using DA algorithm.

Despite the results have been improved and have become acceptable in the validation phase (R= 0.968. R 2 = 0.940, R adj 2 = 0.879 and RMSE = 7.511), but this requires even more an evolution of the validation phase performance in particular.

3.7.

Performance development of the GPR_DA Model using Bagging (Bootstrap Aggregation_Bag):

In order to develop the validation performance of the GPR_DA model, the Bagging (Bootstrap Aggregation_Bag) technique was considered. This technique resamples the original training data set to form n different training data sets (Tahraoui et al. 2022a;Tahraoui et al. 2022b). Consequently, some of the original data points may appear more than once, while others do not appear at all in a particular replication (Tahraoui et al. 2022a;Tahraoui et al. 2022b). After training and creating the model of each training dataset that was created by GPR_DA, validation datasets were tested (Tahraoui et al. 2022a;Tahraoui et al. 2022b). represents the predicted output from the GPR_DA_Bootstrap. and n is the number of IGPR_DA models.

The results of the training data which have been resampled for n from 1 up to 30 and the results of their validation are collected in the following table in terms of correlation coefficient and the statistical error RMSE. J o u r n a l P r e -p r o o f owing to the result that was obtained (456.00 mg/g) under optimal conditions (X 1 = 700 mg/L, X 2 = 0.6 g/L, X 3 = 490.65 min, X 4 = 11 and X 5 = 47.89°C).

Interface for optimization and prediction

To provide a simple way to implement optimal optimization and predict MB uptake, an interface was designed using the MATLAB guide for optimization and prediction (Figure 15).

Adsorption mechanism

The thermodynamics parameters study revealed that MB adsorption capacity was positively influenced by temperature, this may be due to the decrease in the viscosity of the solution and the increment of the MB molecules mobility with increasing temperature, leading to an J o u r n a l P r e -p r o o f increase in the adsorption [START_REF] Khan | Surface oxidized and un-oxidized activated carbon derived from Ziziphus jujube Stem, and its application in removal of Cd (II) and Pb (II) from aqueous media[END_REF][START_REF] Li | Adsorption of congo red and methylene blue dyes on an ashitaba waste and a walnut shell-based activated carbon from aqueous solutions: Experiments, characterization and physical interpretations[END_REF]. The results also showed that the adsorption of MB on the PJAC followed a physisorption mechanism. the main suggested interactions between PJAC and MB were electrostatic, dipole-dipole interactions and hydrogen bonding (Üner et al. 2016). Figure 16 influenced by the pH of the solution and pH pzc . The PJAC surface is negatively charged at solution pH higher then pH pzc , which enhances the MB adsorption simply by electrostatic forces onto negatively charged PJAC surface as shown in Figure 16. The Methylene blue can also be easily adsorbed onto PJAC by the π-π stacking interaction that occur between the πelectron system of the activated carbon and the aromatic rings of the MB dye molecules (Jawad et al. 2020b). The third type of interaction that can be expected to occur is the hydrogen bonding between the nitrogen of MB molecules and the hydrogen band of phenolic and carboxylic functions [START_REF] Mbarki | Low-cost activated carbon preparation from Corn stigmata fibers chemically activated using H 3 PO 4 , ZnCl 2 and KOH: Study of methylene blue adsorption, stochastic isotherm and fractal kinetic[END_REF]. Similar findings regarding the MB adsorption by activated carbon-based adsorbents were proposed in the literature [START_REF] Üner | Adsorption of methylene blue by an efficient activated carbon prepared from Citrullus lanatus rind: kinetic, isotherm, thermodynamic, and mechanism analysis[END_REF][START_REF] Jawad | Conversion of Malaysian low-rank coal to mesoporous activated carbon: structure characterization and adsorption properties[END_REF]Jawad et al. 2020b;[START_REF] Jawad | High surface area and mesoporous activated carbon from KOH-activated dragon fruit peels for methylene blue dye adsorption: Optimization and mechanism study[END_REF]Jawad et al. 2022;[START_REF] Mbarki | Low-cost activated carbon preparation from Corn stigmata fibers chemically activated using H 3 PO 4 , ZnCl 2 and KOH: Study of methylene blue adsorption, stochastic isotherm and fractal kinetic[END_REF].

J o u r n a l P r e -p r o o f Time=540min, T=25°C and pH=7, agitation rate=200 rpm). The pseudo-second order model has better described the sorption phenomenon. The thermodynamic and mechanism studies revealed that the MB adsorption was spontaneous, endothermic and mainly of physical nature and carried out by surface interactions, such as electrostatics, H-bonds and π-π stacking interactions. The response surface approach with Box Behnken design method and Gaussian process regression coupled with bagging (Bootstrap Aggregation_Bag) and Dragonfly optimization algorithm (GPR_DA_Bootstrap) were used to improve the independent process parameters. The optimal conditions using the BBD model were found to be an initial methylene blue concentration of 700 mg/L, adsorbent dose of 0.6 g/L, contact time of 490.65 min, pH of 11 and a temperature of 47.89°C, leading to an adsorption of 456.00 mg/g of MB.

On the other hand, the efficiency of the GPR_DA_Bootstrap model led to 501.01 mg/g MB uptake for an initial MB amount of 700 mg/L, 0.6 g/L adsorbent dosage, 540 min contact J o u r n a l P r e -p r o o f

  mean function capturing the overall trend in the target function value, and   to approximate the covariance.

Figure 1 .

 1 Figure 1. Organization chart for the development and optimization of the GPR_DA model

  J o u r n a l P r e -p r o o f 2020;[START_REF] Bousselma | Artificial intelligence and mathematical modelling of the drying kinetics of pre-treated whole apricots[END_REF] Tahraoui et al. 2021a; Tahraoui et al. 2021b; Tahraoui et al. 2022a; Tahraoui et al. 2022b; Tahraoui et al. 2022c).

Figure 2 .

 2 Figure 2. N 2 adsorption-desorption isotherms for (a) Raw J, and (b) PJAC

  Figure 3(b) shows a porous and irregular rough structure of PJAC in comparison with Raw J due to the chemical activation with phosphoric acid and carbonization leading to the release of volatile maters such as lignin and some other organic compounds and to the formation of the porous structure of the activated carbon (Labied et al. 2018; de Souza et al. 2022). The porosity of PJAC facilitates the adsorption of BM as shown in Figure 3(c) in J o u r n a l P r e -p r o o f which the surface seems more charged and the pores are less remarkable due to the deposition of MB dye molecules all over the surface.

Figure 3 .Figure 4 .

 34 Figure 3. SEM micrographs of samples (A) Raw J, (B) PJAC and (C) MB-PJAC

Figure 4 .

 4 Figure 4. Both spectra showed a few changes in the frequencies and intensities of some bands after methylene blue adsorption. The peak at around 1382 cm -1 , was almost unchanged, but its

Figure 5 .

 5 Figure 5. X-ray diffraction pattern of the Raw J and PJAC

Figure 6 .

 6 Figure 6. Adsorption kinetic models (a) pseudo-first-order kinetic model, (b) pseudo-second-

Figure 7 .

 7 Figure 7. Isotherm models for MB adsorption onto PJAC (Adsorbent dosage=1.00 g/L,

shown in Figure 8 .Figure 8 .

 88 Figure 8. Plot of the predicted vs. actual values for MB uptake on the PJAC

Figure 9 .Figure 10 .

 910 Figure 9. Response surface plot for methylene blue uptake onto the PJAC showing variable

  It shows the coefficients (R, R 2 and R adj 2 ) and the RMSE statistical error for training, validation and all data according to specific parameters (Kernel Scale [sigmaM. sigmaF] and sigma). It also shows kernel functions with base function. a b J o u r n a l P r e -p r o o f

Figure 13 .

 13 Figure 13. Comparison between experimental and predicted values Despite the slight decrease in statistical coefficients and errors (R= 0.999, R 2 =0.998, R adj 2 =

Finally, an optimization

  number of learning Bootstrap cycle (10:30) was performed by calculating the average of predicted values of each validation by equation 17 (Tahraoui et al. r n a l P r e -p r o o f Where, GPR_DA_Bootstrap represents Gaussian process regression coupled with Bootstrap Aggregation-Bag and Dragonfly Algorithm. IGPR_DA represents Individual Gaussian process regression (IGPR) coupled with Dragonfly Algorithm,

  This interface was converted into an executable application on Windows. This powerful application for direct use allows to predict the outputs by selecting the input values by BBD, as well asby GPR__DA_Bootstrap. Moreover, the application is also an optimization solution, allowing finding the optimal ones for each type of model (BBD and GPR_DA_Bootstrap) by two methods (DA and PSO).

Figure 15 .

 15 Figure 15. MATLAB Interface for optimization analysis (DA and PSO) and prediction of

  represents the main interactions and MB possible adsorption mechanisms involved in the sorption process. Boehm titration and FTIR analysis showed the presence of functional groups on the surface of PJAC and their involvement in the adsorption process (O-H, COOH, N-H, C-O-C and C-O bands). It has also confirmed in this study that the adsorption of methylene blue on the PJAC was highly

Figure 16 .

 16 Figure 16. Illustration of the possible interaction between PJAC and MB molecules dye

Table 1 :

 1 Adsorption kinetics and isotherms models

	Model	Equation	Parameters
	Pseudo-first-order	(1	)
	model
	Adsorption
	kinetics

l Kt te

Table 2 .

 2 Coding and real levels for the BBD model.

	Factors

Table 3 :

 3 Textural properties of Raw J and PJAC materials.

	Raw J	PJAC

Table 4 .

 4 Characteristics of Raw J and PJAC

	J o u r n a l P r e -p r o o f
	Parameter	Raw J	PJAC

activated carbon under specified conditions. A high iodine value indicates a good activation of the adsorbent used and proves its reliability in the removal of small-size pollutants (microporous)

[START_REF] Du | Determination of iodine number of activated carbon by the method of ultraviolet-visible spectroscopy[END_REF]

. The PJAC was characterized by a high iodine number; 867.54 mg/g which confirmed a good development of the microporous surface. The methylene blue index is another fundamental parameter for the characterization of the efficiency and activity of an adsorbent. It is defined as the quantity of MB (in milligrams) adsorbed by one gram of carbon

[START_REF] Bahnes | Preparation of a novel activated carbon from jujube stones (Ziziphus jujuba) for the removal of basic and acid dyes[END_REF]

. The methylene blue index found for PJAC was 387.61 mg/g. The MB index of PJAC is higher than the 299 mg/g obtained via chemical activation of the jujube stone by KOH (700 °C activation temperature for a 3 hours carbonization time), by

[START_REF] Bahnes | Preparation of a novel activated carbon from jujube stones (Ziziphus jujuba) for the removal of basic and acid dyes[END_REF]

, and the value of 364.2 mg/g obtained by

Abdulhameed et al.

Table 5 .

 5 Porosity structures of the PJAC

	parameter	value
	True density (g/cm 3 )	2.93
	Bulk density (g/cm 3 )	0.84
	porosity (%)	71.33
	Pore volume (g/cm 3 )	0.85
	Iodine number (mg/g)	867.54
	Methylene blue index (mg/g)	387.61
	S MB (m²/g)	948.84
	Carboxylic groups (mmol/g)	0.60
	Lactonic groups (mmol/g)	0.25
	Phenolic groups (mmol/g)	0.51
	Total acid (mmol/g)	1.36

Table 6 .

 6 Adsorption kinetic parameters of MB dye adsorption onto PJAC (Adsorbent

	dosage=1.00 g/L, Time=540min, T=25°C and pH=7, agitation rate=200 rpm)

Pseudo-first order kinetic Pseudo-second order kinetic

				First stage				Second stage		Third stage
	C 0 (mg/L)	K P1	(mg.g -1 •min -1/2 )	C 1 (mg.g -1 )	R²	K P2	(mg.g -1 •min -1/2 )	C 2 (mg.g -1 )	R²	K P3	(mg.g -1 ) -1/2 •min	C 3 ) -1 (mg.g	R²
	100		8.811	43.314	0.972	0.828	86.368	0.994	0.019	92.774	0.925
	250	25.276	18.209	0.993	4.870	143.977	0.998	0.256	224.730	0.982
	C 0 (mg.L -1 ) 400 550 700	qe exp (mg.g -1 ) 26.462 25.165 J o u r n a l P r e -p r o o f qe cal (mg.g -1 ) K 1 (min -1 ) R² RMSE qe cal (mg.g -1 ) K 2 (g•mg -1 •min -1 ) 14.593 0.999 7.142 178.711 0.971 0.895 52.869 0.995 5.526 235.793 0.991 0.779 27.090 59.760 0.996 5.541 254.684 0.988 1.607	R² 304.880 329.780 334.148	RMSE 0.985 0.972 0.771
		93.268	92.184	0.188	0.985	2.841	95.029	0.004		0.994	1.736
		230.198	223.171	0.027	0.967	12.886	242.326	1.639.10 -4	0.991	6.331
		324.457	303.746	0.026	0.951	21.619	332.948	1.098. 10 -4	0.987	10.789
		347.426	330.715	0.029	0.959	20.975	357.956	1.201. 10 -4	0.993	8.937
		370.751	350.227	0.031	0.956	22.777	377.838	1.235. 10 -4	0.992	9.999
						Intraparticle diffusion model

Table 7 .

 7 The results indicate that the Langmuir model

	(R²=0.984, RMSE=3.134) fits the experimental data better than the Freundlich and Temkin
	isotherms (R²=0.811, RMSE=6.114 and R²=0.896, RMSE=5.305 respectively) suggesting that

Table 8 .

 8 Table 8 reports the experimental runs for examining MB adsorption on PJAC, as well as the experimental results and predicted values. The number of experiments was set to 46. MB uptake with experimental and predicted value according to BBD

	RUN 1 J o u r n a l P r e -p r o o f Initial MB concentration (mg/L) PJAC dosage (g/L) Contact time (min) pH Temperature (°C) MB uptake (mg/g), experiment values 550 1.1 285 7 20 225.82 ± 4.79	MB uptake (mg/g), predicted values 236.66
	2	550	1.1	30	9	20	202.55 ± 1.44	201.07
	3	550	0.6	285	9	20	321.43 ± 5.77	328.02
	4	400	1.1	285	9	20	260.09 ± 5.26	243.40
	5	700	1.1	285	9	20	299.26 ± 7.67	299.73
	6	550	1.6	285	9	20	198.65 ± 4.56	205.60
	7	550	1.1	540	9	20	302.26 ± 9.97	303.23

Table 9 .

 9 ANOVA of the BBD for the optimization of the elimination of the MB onto PJAC

	Source Model Linear x 1 x 2 x 3 x 4 J o u r n a l P r e -p r o o f Degree of freedom Sum of squares Mean Squares F-value P-value Prob.>F 20 117319.310 5865.970 41.611 <0.0001 6911.013 6911.013 49.024 <0.0001 19342.551 19342.551 137.210 <0.0001 33682.343 33682.343 238.931 <0.0001 10818.080 10818.080 76.740 <0.0001
	x 5	37538.094	37538.094	266.283	<0.0001
	Quadratic
	x 1 * x 1	22.058	22.058	0.157	0.6958
	x 2 * x 2	87.435	87.435	0.620	0.4384
	x 3 * x 3	2772.987	2772.987	19.671	0.0002
	x 4 * x 4	526.580	526.580	3.735	0.0647

RMSE:

Root Mean Square Error. C.V.: Coefficient of variance. lack of fit a : non-significant (> 0.05)

Table 10 .

 10 Thermodynamic parameters of the MB adsorption on the PJAC

	Adsorbent	T (K)	∆G° (kJ/mol) ∆H° (kJ/mol)	∆S° (kJ/mol.K)	R²
		293	-0,687
	PJAC	303 313	-1,442 -2,196	21,414	0,075	0,998
		323	-2,950

Table 11 .

 11 Performance of the different GPR_DA models tested

	Kernel	Basis	Kernel Scale	Sigma Quantite		R/R 2 /R 2	adj	RMSE
	function	Function
			SigmaM SigmaF			Train	Val	ALL Train Val ALL
			42.218	123.399 2.064	35	1.000	0.916	0.994	0.385 11.977 5.866
	ARD-		41.830				1.000	0.840	0.987
	GPR	Constant	32.731				1.000	0.680	0.985
	Exponential		51.663
			32.166

Table 12 .

 12 Performance of the different GPR_DA models tested

	DA

Table 13 .

 13 Structures of the optimized IGPR coupled with DA

	DA

J o u r n a l P r e -p r o o f

The problem was in the validation phase. Indeed, despite the somewhat acceptable results obtained at the level of the coefficients (R= 0.916, R 2 = 0.840 and R adj 2 = 0.680) and also of the RMSE (RMSE= 11.977), this remains the weak point of this model and requires further development.

3.6.

Gaussian process regression model coupled with Dragonfly Algorithm (GPR_DA)

In order to improve the performance of the previously developed model, especially in the validation phase, the GPR model was coupled to the Dragonfly (DA) algorithm, which was used to optimize the specific parameters of each Kernel function, since this optimization algorithm has been used to solve a wide variety of optimization problems [START_REF] Moussa | Optimization of ultrasound-assisted extraction of phenolic-saponin content from Carthamus caeruleus L. rhizome and predictive model based on support vector regression optimized by dragonfly algorithm[END_REF]). Among these solving different machine learning optimization problems, fundamental values and penalty parameters were optimized by the DA using training data [START_REF] Moussa | Optimization of ultrasound-assisted extraction of phenolic-saponin content from Carthamus caeruleus L. rhizome and predictive model based on support vector regression optimized by dragonfly algorithm[END_REF]. It was confirmed by numerous studies that machine learning performance was improved when hyper-parameters were optimized using the Dragonfly algorithm [START_REF] Moussa | Optimization of ultrasound-assisted extraction of phenolic-saponin content from Carthamus caeruleus L. rhizome and predictive model based on support vector regression optimized by dragonfly algorithm[END_REF].

In this work, the same steps that were designed in figure 1 were performed, except that a range of optimization of number of dragonfly research agents and number of iteration (max iteration = 100 up to 500 and search agents =20 up to 50) to optimize the specific parameters of each kernel function.

The best model, which was obtained by optimizing kernel function, basis function and DA specific parameters (kernel scale and sigma) is presented in Table 12.

Table 12 shows the results of the GPR_DA model. It shows the coefficients (R, R 2 and R adj 2 )

and the RMSE statistical error for training, validation and all data according to specific parameters (Kernel Scale [sigmaM. sigmaF] and sigma). It also shows kernel functions with base function. Note to mention, the number of dragonfly agents and the number of iterations.

J o u r n a l P r e -p r o o f

In order to obtain the best result, the optimization of the average calculation of the predicted values by each number of learning Bootstrap cycle using equation 17, showed that the average of the predicted values which were obtained by the industrial models from 1 to 13 gave a very interesting result (R= 0.995, R 2 = 0.991, R adj 2 = 0.982 and RMSE =2.949). This result is presented graphically in Figure 14. GPR_DA and GPR_DA_Bootstrap, it can be concluded that the Bootstrap technique developed is appropriate to enhance the performances of the GPR_DA model.

Optimization the optimal analysis

An optimization method was run using the Dragonfly Algorithm (DA in MATLAB code) and the Particle Swarm Algorithm (PSO in MATLAB code) which are available in the MATLAB

J o u r n a l P r e -p r o o f

Optimization Toolbox to find the optimum of the independent parameters to obtain maximum MB uptake. The resulting solution values of this optimization are given in Table 14.

Table 14. Results of MB uptake under optimal conditions

The optimization analysis methods used (DA and PSO) gave the same optimization results for each model (BBD and GPR_DA_Bootstrap). This shows the reliability of the models and the quality of the experimental results obtained.

On the other hand, by comparing the results of optimization using the BBD model and the GPR_DA_Bootstrap model, it can be noted the results obtained for X 1 , X 2 and X 4 are identical for the two models; while there was some difference for X 3 and a slight difference for X 5 .

Indeed, the contact time (X 3 ) in the BBD model was 490.65 min and in the GPR_DA_Bootstrap model it was 540 min. Likewise, for the temperature (X 5 ) it was 47.89°C

and 50°C for GPR_DA_Bootstrap.

In addition, by comparing the optima obtained from each model, the GPR_DA_Bootstrap model gave a predicted value of MB uptake (492.37 mg/g) higher than that obtained by BBD (433.81 mg/g). This shows the superiority of the GPR_DA_Bootstrap model over the BBD.

To confirm these results, an experimental validation method was applied.

BBD

 DA and PSO: (X 1 = 700 mg/L. X 2 = 0.6 g/L. X 3 = 490.65 min. X 4 = 11. and X 5 =47.89°C)

MB uptake (mg/g). predicted values 433.81

GPR_DA_Bootstrap  DA and PSO: (X 1 = 700 mg/L. X 2 = 0.6 g/L. X 3 = 540 min. X 4 = 11. and X 5 =50°C)

MB uptake (mg/g). predicted values 492.37

J o u r n a l P r e -p r o o f

Validation of the optimum conditions

To validate the optimization results, experiments were performed under the obtained optimal conditions to test the effectiveness of the optimization based on BBD and GPR_DA_Bootstrap. These results are presented in Table 15 in order to compare them to the predicted values and to express the error between them.

Where:

Table 15. Comparison between actual and predicted responses at optimum conditions.

From Table 15, it was found that the optimal conditions of the GPR_DA_Bootstrap model (X 1 = 700 mg/L, X 2 = 0.6, X 3 = 540, X 4 = 11 and X 5 =50) gave a result of MB uptake (501.01 mg/g), which is significantly higher than that given by the BBD model (456mg/g). In addition, the error obtained by the GPR_DA_Bootstrap model (8.64 mg/g) was lower than that obtained by the BBD (22.19 mg/g). This clearly shows the superiority of the GPR_DA_Bootstrap model. However, the BBD model was also effective and performing, BBD  X 1 = 700 mg/L. X 2 = 0.6 g/L. X 3 = 490.65 min. X 4 = 11. and X 5 = 47.89°C

MB uptake (mg/g J o u r n a l P r e -p r o o f time, a pH of 11 and a temperature of 50°C. From the obtained results, it can be deduced that the GPR_DA_Bootstrap model is more efficient than the BBD model, and also that the Jujube stone based prepared activated carbon can be effectively used as an available, economical adsorbent with high adsorption capacity and good affinity to cationic dyes.

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐ The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: