Amir Rahmaniab,
Alireza Khataee*bc,
Baris Kaymak*a,
Behrouz Vahidd,
Mehrangiz Fathiniab and
Mahsa Dindarsafaa
aDepartment of Environmental Engineering, Middle East Technical University, 06800 Ankara, Turkey. E-mail: bkaymak@metu.edu.tr; Fax: +90 3122102646; Tel: +90 3122105873
bResearch Laboratory of Advanced Water and Wastewater Treatment Processes, Department of Applied Chemistry, Faculty of Chemistry, University of Tabriz, 51666-16471 Tabriz, Iran. E-mail: a_khataee@tabrizu.ac.ir; Fax: +98 41 33340191; Tel: +98 41 33393165
cDepartment of Materials Science and Nanotechnology, Near East University, 99138 Nicosia, Mersin 10, North Cyprus, Turkey
dDepartment of Chemical Engineering, Tabriz Branch, Islamic Azad University, 51579-44533 Tabriz, Iran
First published on 17th August 2016
Natural martite microparticles (NMMs) were prepared with a high energy planetary ball mill to form a nanocatalyst for a Fenton-like process. Martite nanoparticles (MNs) of different scales are formed when the milling time ranges from 1 to 5 h at the milling speed of 300 rpm. The catalytic performances of MNs are higher than the NMMs for the degradation of acid blue 5 (AB5) in a heterogeneous Fenton-like process. The NMMs and the MNs were characterized by SEM, EDX, BET, XRD and FT-IR analyses. The size distribution of the 5 h milled martite nanoparticles (MN3) is in the range of 20 nm to 100 nm, and these have the highest surface area (19.23 m2 g−1). The influence of the main operational parameters, including initial pH, MN3 dosage, H2O2 and initial dye concentration, were investigated on the AB5 degradation. The treatment process obeys pseudo first order kinetics and some of the degradation intermediates were recognized by the GC-MS method. The environmentally-friendly production of the MNs, low amount of leached iron and repeated catalyst usage are the significant advantages of this research. Finally, an artificial neural network (ANN) is expanded to estimate the degradation efficiency of AB5 on the basis of the experimental results, which indicates the appropriate performance (R2 = 0.955).
The development of novel and highly efficient methods like advanced oxidation processes (AOPs) for the treatment of wastewaters, which can degrade and mineralize the pollutants whilst producing no secondary waste, is vital from an environmental viewpoint.8–10 Among AOPs as green treatment technologies, the homogenous Fenton process has been extensively applied for the degradation of different contaminants in aquatic media.11–14 However, this process has some drawbacks including the formation of iron-containing sludge and the deactivation of catalyst by intermediates generated during oxidation.15–18
Usage of heterogeneous Fenton process without need for the catalyst segregation and low released iron to the solution is the practical method to decline the mentioned problems.19 Reactive species, particularly hydroxyl radicals (˙OH), have the main function in the AOPs owing to unselective oxidation of contaminants into inorganic mineral salts, water and carbon dioxide.20 Superficial solid Fe ions in the heterogeneous Fenton-type catalysts such as iron-substituted zeolites,21 LAPONITE®,22 pyrite,23 magnetite,15,24,25 goethite26 and pillared clays27 catalyze the formation of ˙OH radicals. Martite (Fe2O3) which yielded upon conversion of magnetite (Fe3O4) into hematite (Fe2O3) indicates the physical properties of the latter.28,29 It is a mineral, which can also be used as the potential Fenton-like catalyst. Since, generation of hydroxyl radicals from the decomposition of hydrogen peroxide is initiated in the presence of ferric ions from martite, it is commonly referred as “Fenton-like” although ferrous iron and ferric ions are both present in the cycle of reactions.30
However, the heterogeneous Fenton process has also some restrictions including limited active reaction sites and low mass transfer. The heterogeneous catalytic performance can be enhanced by applying of nano-sized particles due to providing of a short diffusion path and more active sites for organic pollutants.31–33 Production of nanoparticles by chemical syntheses require expensive and toxic reactants.34 Recently, mechanical ball milling (MBM) via high energy planetary ball mill has been used for formation of nanoparticles owing to its cost effectiveness and simplicity.27–29 Moreover, the ball milling method is a suitable method for large scale industrial productions from an economical viewpoint since the process takes place at ambient temperature in a reasonable processing time.31,32 For instance, diverse nanomaterials such as ZnS,34 LiF,33 FePt35 and Cu2O36 have been produced using the high energy MBM process.
Since the heterogeneous Fenton process is influenced by various operational parameters, it is hard to simulate and model this process applying conventional mathematical models. The Artificial Neural Networks (ANNs) are recently employed in various science and engineering fields, which are effective method owing to their logical prediction, modelling and simulation.35–37 Furthermore, the main advantages of this modelling over other techniques are no requirement for customary mathematical training and ability to predict the results with less number of tests resulted in saving money and time.38
In this study, first, the MBM is applied for production of martite nanoparticles by varying the milling time from 1 h to 5 h. Then, the properties of the NMMs and as-prepared samples were characterized by scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), Brunauer, Emmett and Teller (BET), X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FT-IR). Next, the catalytic performance of the NMMs and MNs was determined in the heterogeneous Fenton-like process for degradation of AB5 as a model triarylmethane pollutant. The influence of experimental parameters including the solution pH, catalyst dosage, H2O2 concentration, initial AB5 concentration, and hydroxyl radical scavengers were investigated on the degradation efficiency (DE%) of the dye. Gas chromatography-mass spectrometry (GC-MS) was employed for the identification of the generated byproducts through the AB5 degradation. Finally, the artificial neural network modelling was applied as a helpful method to estimate the degradation efficiency of AB5 in heterogeneous Fenton-like process.
Table 1 demonstrates the size distribution of the NMMs, MN1, MN2 and MN3. 46.23% of size distribution of the MN3 is in the range of 40–60 nm. In other words, it proves that the particle size of the martite has been increased by passing the ball milling time.
Frequency (%) | ||||
---|---|---|---|---|
Microparticles size distribution (μm) | 30–50 | 50–70 | 70–90 | 90–140 |
NMM | 21.43 | 38.57 | 25.71 | 14.29 |
Nanoparticles size distribution (nm) | 20–40 | 40–60 | 60–80 | 80–100 |
---|---|---|---|---|
MN1 | 13.11 | 36.24 | 17.79 | 32.86 |
MN2 | 20.00 | 41.50 | 21.50 | 17.00 |
MN3 | 29.50 | 46.23 | 15.61 | 8.66 |
Fig. 3 displays the nitrogen adsorption–desorption isotherms of catalysts samples observed at 77.38 K.42,43 According to the IUPAC classification, a simple review indicates that the experimental isotherms are of type IV. However, a more detailed observation of the figure reveals that it is a combination of type IV and V isotherms which characterize mesoporous structure for the martite sample. Therefore, the isotherms can be appropriately defined by the BET surface area method.44 Besides, the hysteresis shaping started from nearly 0.55 and extended almost to 0.95 demonstrating their large porosity.45 Table 2 presents the specific surface area, pore diameter and pore volume of the catalysts. As seen in the table, after 5 hours of MBM process, specific surface area, pore diameter and pore volume of the catalysts have been increased from 5.675 to 19.23 m2 g−1, from 17.20 to 32.24 Å and from 7.961 × 10−3 to 2.984 × 10−2 cm3 g−1, respectively. It is because of increase in collisions between balls and martite particles in the planetary ball milling process by passing time. Therefore, under effect of this collision, pore diameter, pore volume and surface area of martite nanoparticles increase.46,47
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Fig. 3 N2 adsorption–desorption isotherm of (a) NMMs, (b) MN1, (c) MN2 and (d) MN3 samples achieved from the BET test. |
Sample | Primary martite | 1 h-milled martite | 3 h-milled martite | 5 h-milled martite |
---|---|---|---|---|
Specific surface area (m2 g−1) | 5.675 | 15.28 | 16.47 | 19.23 |
Pore diameter (Å) | 17.20 | 21.36 | 25.83 | 32.24 |
Pore volume (cm3 g−1) | 7.961 × 10−3 | 1.425 × 10−2 | 2.201 × 10−2 | 2.984 × 10−2 |
Fig. 4 shows XRD patterns of the NMMs, the 1 h (MN1), 3 h (MN2) and 5 h (MN3) milled martite nanoparticles. The obtained peaks at 2θ values of 24.13, 33.2, 35.44, 40.96, 49.46, 53.87, 57.19, 62.23, and 64.04° are related to the characteristic (0 1 2), (1 0 4), (1 1 0), (1 1 3), (1 2 4), (1 1 6), (1 2 2), (2 1 4), and (3 0 0) planes. The observed XRD patterns are very close to the hematite (JCPDS no. 33-664). This is a rational finding because the martite is hematite pseudomorphs after magnetite and its physical properties is similar to the hematite.48,49Also, observation of identical peaks indicate that the primary martite sample is maintained after the MBM process. In addition, the peaks at 2θ values of 43.10 and 57.08° are relevant to the (4 0 0) and (5 1 1) reflection planes of the magnetite (JCPDS no. 19-0629), respectively.50 The reduction in XRD peak intensity takes place with increase in ball milling time. It is owing to the crystallinity decrease of the as-obtained nanosized martite.51
The FT-IR analyses indicated in Fig. 5 were carried out to find the existing bonds and functional groups of the NMMs (curve (a)) and the milled samples (curves (b–d)). The peaks at 2854.69 and 2923.42 cm−1 are attributed to the symmetric and asymmetric C–H bonds, respectively.52,53 The O–H vibration peak at 3436.58 cm−1 indicates the presence of O–H group.54 The peaks of the –COO– vibration (1386.19 and 1598.89 cm−1), the Si–O vibration (1094.96 cm−1) and the Fe–O vibration (467.42 and 552.64 cm−1) are also found in all samples.55–57 Thus, the functional groups on the martite nanoparticles are identical to the ones in unmilled sample. Moreover, the vibration peak intensity of the Fe increases after passing time of ball milling process which is due to the surface oxidation of the martite nanostructures.51 On the other hand, the –COO– vibration peak, symmetric and asymmetric C–H bonds intensity reduces which is owing to the partial oxidation of the compounds.58
Fe3+–martite + H2O2 → Fe–martite–OOH2+ + H+ | (1) |
Fe–martite–OOH2+ → Fe2+–martite + HO2˙ | (2) |
Fe2+–martite + H2O2 → Fe3+–martite + HO− + ˙OH | (3) |
The DE% for the Fenton-like process during 70 min of contact time are shown in Fig. 6. The experiments containing martite catalyst shows higher degradation efficiency compared to the ones without the catalyst. The highest degradation efficiency is observed when MN3 is used as a catalyst.
The inset of Fig. 6 shows that the heterogeneous Fenton-like process obeys the pseudo-first order kinetic, which is comparable to the other Fenton studies.60 The straight lines with appropriate coefficient of determinations (R2), which are more than 0.99, verify the validity of suggested kinetic. The apparent pseudo-first order rate constants (kapp) for the AB5 degradation are given in Table 3. The kapp increases by using the martite catalyst and increasing ball milling time.
No. | Process | kapp (min−1) | Normalized kapp (min m2 g−1)−1 | Coefficient of determination (R2) |
---|---|---|---|---|
1 | Adsorption | 0.0010 | — | 0.9988 |
2 | H2O2 | 0.0030 | — | 0.9950 |
3 | NMMs | 0.0120 | 2.11 × 10−3 | 0.9989 |
4 | MN1 | 0.0269 | 1.76 × 10−3 | 0.9973 |
5 | MN2 | 0.0344 | 2.09 × 10−3 | 0.9982 |
6 | MN3 | 0.0415 | 2.16 × 10−3 | 0.9991 |
In order to consider the degradation kinetic of the AB5 through different processes, experimental data are fitted with the pseudo-first order kinetic equation (eqn (4)):61
![]() | (4) |
The apparent pseudo-first order constants are directly correlated with the specific surface area and pore volume. The highest kinetic rate is observed with the catalysts that has the highest specific surface area and pore volume. Also as seen in Table 3, when the apparent pseudo-first order reaction constant is normalized with the specific surface area of catalysts, the rate constants are very close to each other, indicating the importance of specific surface area of the catalyst on the AB5 oxidation. The catalyst MN3 has the highest apparent pseudo-first order reaction constant (Table 3), specific surface area and pore volume (Table 2) among unmilled catalyst and catalyst milled for a shorter period of time. Also, at the end of 70 minutes contract time, the highest degradation ratio of 94.5% was observed in the reactor containing MN3. As a consequence, the MN3 is chosen as the desired nanocatalyst for the rest of experiments in the degradation process. The modified NMMs by the mechanical ball milling leads to more surface area and active sites owing to the production of nano-sized particles and thus its enhanced performance.38,54,57
One of the most significant operational parameters in the Fenton-like process is pH. Hence, its effect on the degradation of AB5 was studied, and the results are displayed in Fig. 7. The inset plot shows the pseudo-first order kinetic (kapp) for different pHs. As it is seen, the amount of kapp increases as pH decreases. At low pHs, higher degradation efficiency is achieved, and the DE% diminishes with the enhancement of pH.62 This can be attributed to more oxidation potential of the ˙OH radicals in acidic condition;63 moreover, the dissolved iron concentration increases in lower pHs determined by AAS (Fig. 8). The highest DE% is achieved when the pH is adjusted to 3 after 70 min of treatment. It should be noticed that, the total leached iron concentration is lower than 1 mg L−1 after heterogeneous Fenton-like process in the presence of MN3 for the pH range of 3 to 9. As mentioned in the other similar studies, at this low level of iron concentration, the ˙OH radicals generation is almost owing to the heterogeneous process on the catalyst surface compared to the homogeneous one in the bulk solution for the AB5 degradation.60,64
Fig. 9 shows the DE% as a function of process time for the different MN3 dosages. The DE% increases over the initial dosage range of 0 to 2.5 g L−1; this is due to the further available sites for radicals formation and AB5 adsorption.65 Afterwards, an inverse trend is seen, and the DE% reduces. This observation is due to the scavenging effect of ferrous ions on the hydroxyl radicals (eqn (5)).66–68 Also, the inset plot demonstrates the degradation of AB5 in the presence of the martite nanocatalysts following pseudo-first order kinetic. As the MN3 dosage increases, kapp increases. However, it reduces beyond 2.5 g L−1 of the catalyst.
˙OH + Fe2+ → OH− + Fe3+ | (5) |
It is essential to optimize the H2O2 concentration because a main expense of the Fenton-like process is the cost of H2O2. In addition, an excessive oxidant amount decreases the process efficiency.69 Fig. 10 shows that the DE% increases by H2O2 addition up to 2 mM. This observation is due to the extra reactive radicals generation from the H2O2 decomposition in the presence of catalyst (eqn (1)–(3)). But, more oxidant addition leads to decline in the DE%;61 hydrogen peroxide scavenging effect on hydroxyl radicals declines the dye degradation (eqn (6)).70–74 The inset plot presents that kapp increases up to 2 mM, but over 2 mM it diminishes.
H2O2 + ˙OH → H2O + HO2˙ | (6) |
Increasing the AB5 concentration reduces the DE% (Fig. 11). In the same operational conditions, the generated active radicals amount and the MN3 accessible surface area are constant even with enhancement of the AB5. Besides, because of the competitive consumption of the ˙OH radicals through the formed by-products at higher dye concentration, the DE% diminishes.67,75–77 Even though the DE% of AB5 reduced with increasing initial dye concentration, the absolute dye removal has increased. For instance, as the dye concentration is increased from 10 to 40 mg L−1, the degradation of AB5 has been increased after 50 min from 9.91 to 17.48 mg L−1, respectively.77 Also, as observed from the inset plot in Fig. 11, the pseudo-first order kinetic (kapp) is reduced with increasing initial AB5 concentration from 10 to 40 mg L−1.
The influence of inorganic salts and organic compounds such as NaCl, Na2SO4, Na2CO3, ethanol and chloroform were investigated on the AB5 degradation. Chloride, sulfate and carbonate are common observed anions in the textile wastewaters. They affect the efficiency of the treatment, which is named the salting-out effect.60 As can be observed in Fig. 12, the DE% reduces by the addition of these scavengers to the AB5 solution. The ions with negative charges are adsorbed on the martite nanocatalysts surface and active superficial sites of the catalyst are occupied by them inhibiting the Fenton reaction.41,78 Therefore, this reduces the amount of hydroxyl radicals generation. The impact of NaCl over the degradation of AB5 is higher than that of Na2CO3 and Na2SO4. The reason can be ascribed to the scavenging of ˙OH by chloride and the generation of reactive radicals with low oxidation potential instead of ˙OH only given by the eqn (7)–(9).41,60,79 Also, ˙Cl produced in eqn (9) has a high tendency to react with H2O2, which decreases ˙OH concentration in the process (eqn (10)).80
Cl− + ˙OH → ˙ClOH− | (7) |
˙ClOH− + H+ → H2O + ˙Cl | (8) |
Cl− + ˙Cl → ˙Cl2− | (9) |
˙Cl + H2O2 → H+ + Cl− + HO2˙ | (10) |
Carbonate ion reacts with ˙OH through eqn (11) and results in the production of CO3˙−. It has lower oxidation potential than that of ˙OH; so, the degradation efficiency is reduced.
CO32− + ˙OH → CO3˙− + OH | (11) |
Sulfate ion can also react with ˙OH (eqn (12)) and decreases its concentration in the solution. But, according to Fig. 12, the scavenging effect of sulfate ion is less than the others. It is because of peroxydisulfate anion (S2O82−) produced by eqn (13). Its oxidation potential is 2.01 eV.81 which is less than the oxidation potential of ˙OH.
SO42− + ˙OH → SO4˙− + OH− | (12) |
SO4˙− + SO4˙− → S2O82− | (13) |
Furthermore, ethanol and chloroform as organic compounds can scavenge ˙OH in the solution. Due to eqn (14) and (15), the reduction in the degradation efficiency of AB5 occurs.82,83
˙OH + CH3CH2OH → CH3˙CHOH + H2O | (14) |
˙OH + CHCl3 → ˙CCl3 + H2O | (15) |
The inset plot shows the gradient of kapp in the presence of different scavengers. As it can be seen, the kapp decreases in the presence of ethanol more than the other scavengers. On the other hand, it reduces in the presence of sodium sulfate less than the others. The reaction rate constants for eqn (12) and (14) are (0.95 ± 0.08) × 1010 M−1 s−1 and (0.16 ± 0.02) × 1010 M−1 s−1, respectively.84,85
In all runs, the degradation rate also obey the pseudo-first order kinetic and the apparent reaction rate constants and the corresponding coefficient of determination are estimated from the inset plots of Fig. 7–12 and presented in Table 4.
Operational parameters and amounts | kapp (min−1) | Coefficient of determination (R2) |
---|---|---|
a Experimental conditions: [AB5]0 = 10 mg L−1, [MN3] = 2.5 g L−1 and [H2O2]0 = 3 mM.b Experimental conditions: [AB5]0 = 10 mg L−1, pH = 3 and [H2O2]0 = 3 mM.c Experimental conditions: [AB5]0 = 10 mg L−1 [MN3] = 2.5 g L−1 and pH = 3.d Experimental conditions: [MN3] = 2.5 g L−1, pH = 3 and [H2O2]0 = 2 mM.e Experimental conditions: [AB5]0 = 1.46 × 10−5 N, [MN3] = 2.5 g L−1, [H2O2]0 = 2 mM and pH = 3. | ||
pHa | ||
3 | 0.0490 | 0.9996 |
4 | 0.0197 | 0.9988 |
5 | 0.0126 | 0.9987 |
7 | 0.0093 | 0.9990 |
9 | 0.0058 | 0.9982 |
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||
Catalyst dosageb (g L−1) | ||
1 | 0.0167 | 0.9995 |
1.5 | 0.0191 | 0.9996 |
2 | 0.0415 | 0.9991 |
2.5 | 0.0490 | 0.9996 |
3 | 0.0281 | 0.9985 |
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||
H2O2 concentrationc (mM) | ||
0 | 0.0010 | 0.9988 |
1 | 0.0195 | 0.9966 |
2 | 0.0960 | 0.9975 |
3 | 0.0490 | 0.9996 |
4 | 0.0263 | 0.9981 |
5 | 0.0215 | 0.9983 |
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||
AB5 concentrationd (mg L−1) | ||
10 | 0.0960 | 0.9975 |
20 | 0.0317 | 0.9988 |
30 | 0.0180 | 0.9989 |
40 | 0.0118 | 0.9978 |
Scavengerse | Concentration (N) | kapp (min−1) | Coefficient of determination (R2) |
---|---|---|---|
NaCl | 1.71 × 10−4 | 0.0327 | 0.9987 |
Na2CO3 | 1.88 × 10−4 | 0.0216 | 0.9962 |
Na2SO4 | 1.41 × 10−4 | 0.0394 | 0.9993 |
CH3CH2OH | 2.17 × 10−4 | 0.0102 | 0.9965 |
CHCl3 | 8.38 × 10−5 | 0.0272 | 0.9990 |
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Fig. 13 Reusability of the martite nanocatalyst for five successive cycles. Experimental conditions: [AB5]0 = 10 mg L−1, [MN3] = 2.5 g L−1, [H2O2]0 = 2 mM and pH = 3. |
The UV-vis spectra along with GC-MS analysis were performed to specify the gradient in the AB5 amount over the Fenton-like process under optimum achieved condition. Fig. 14 shows the dye absorption peaks decline with time passing owing to the dissociation of AB5 molecular structure in the heterogeneous Fenton-like process. Besides, the identified intermediates of the dye degradation by the Fenton-like process are given in Table 5. The AB5 conversion into the smaller compounds occurred by breaking of chemical bonds including C–C, C–N, or NN.86 However, all intermediates identification is not conceivable due to their slight accumulation and limitations of the GC-MS analysis.87
![]() | ||
Fig. 14 UV-vis spectra changes of AB5 solution during the Fenton-like process under the optimized conditions. |
No. | Compound | Structure | tr (min) | Main fragments (m/z) |
---|---|---|---|---|
a Value corresponding to the trimethylsilyl derivative.b Value corresponding to the bis-trimethylsilyl derivative. | ||||
1a | 2-Hydroxy-succinic acid | ![]() |
9.41 | 147 (100%), 73 (53.46%), 148 (15.42%) |
2a,b | 1-Aminoethanol | ![]() |
9.81 | 73 (100%), 147 (59.71%), 261.1 (21.12%), 113 (19.83%) |
3a | 1,4-Benzenediol,2,5-bis(1,1-dimethylethyl)- | ![]() |
21.93 | 207.10 (100%), 221.1 (59.43%), 193 (18.66%) |
4a | 2-Hydroxyacrylic acid | ![]() |
6.05 | 147 (100%), 73 (74.07%), 217.1 (23.885), 148 (15.73%) |
5a | 1,5-Naphthalenediol | ![]() |
18.21 | 304 (100%), 73 (48.67%), 305.1 (26.92%) |
6a | 2-[(Trimethylsilyl)oxy]-5-methylacetophenone | ![]() |
36.18 | 273 (100%), 73 (75.63%), 147 (58.62%), 363.1 (23.57%), 347.1 (21.83%) |
7a | 4-Hydroxybutyric acid | ![]() |
13.99 | 147 (100%), 73 (49.45%), 75 (33.92%), 117 (33.28%) |
Variable | Range |
---|---|
Input layer | |
Time (min) | 0–70 |
Initial pH | 3–9 |
Catalyst dosage (g L−1) | 0–3 |
Dye concentration (mg L−1) | 10–40 |
H2O2 concentration (mM) | 0–5 |
![]() |
|
Output layer | |
Removal efficiency (%) | 0–97 |
Various topologies were used to obtain the optimal number of neurons in hidden layers 1 and 2. The number of neurons were ranged from 3 to 11 for the first hidden layer and 0 to 9 for the second one. Fig. 16 illustrates the MSE achieved from different topological runs, where h2 is the number of neurons in the second layer. Each topology was reiterated four times to prevent random correlation owing to random initialization of the weights. The MSE demonstrates a network performance according to eqn (16):
![]() | (16) |
![]() | ||
Fig. 16 Effect of number of neurons in the hidden layers on the performance of the ANN model; h2 demonstrates the number of neurons in the second hidden layer. |
Q represents the number of test data point, Xi,pred and Xi,exp are relevant to the predicted and experimental responses, respectively.89,91,92 The lowest value of MSE is obtained as 3.3249 × 10−5 through 7 neurons in first hidden layer and 9 neurons in the second one.
The training function used was trainscg, and the tan-sigmoid transfer function was employed as a transfer function in first and second hidden layers. This function is commonly applied and it is given in eqn (17):93
![]() | (17) |
Among several data point, 165 experimental data were applied to feed the ANN model. The samples were separated into training, validation and test subsets included 99, 36 and 30 sets, respectively. In order to evaluate the ability of validation and modelling of the developed ANN, the validation and test data were chosen by chance. In view of the fact that the transfer function applied in the hidden layers was sigmoid, all of the data should be in the range of 0.2–0.8. Therefore, each data (Xi) including the training, validation and test series was converted into a new value Xnorm as follows:
![]() | (18) |
Xi,min and Xi,max are minimum and maximum amount of Xi variable.94 After running, all outputs were turned back to their original value in order to figure out training, validation and test errors according to the eqn (18). Then, the comparison between the experimental replies and predicted outputs were conducted (Fig. 17). As it is seen in this figure, the coefficient of determination is 0.955 which exhibits the credibility of the obtained model. Also, the results prove that the ANN model regenerated the degradation efficiency in this process, within experimental ranges adopted in the fitting model.89,95
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Fig. 17 Comparison between experimental and predicted values via the ANN modelling for the test data. |
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