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Modeling of solid-phase tea waste extraction for the removal of manganese and cobalt from water samples by using PSO-artificial neural network and response surface methodology
⁎Corresponding author. Fax: +98 542 2226765. m_khajeh@uoz.ac.ir (Mostafa Khajeh)
-
Received: ,
Accepted: ,
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.
Peer review under responsibility of King Saud University.
Abstract
The aim of this research was to develop a low price adsorbent with the abundant of source to remove manganese and cobalt from water samples. Tea waste solid-phase extraction coupled with flame atomic absorption spectrometry (FAAS) was used for the extraction and determination of manganese and cobalt ions. Response surface methodology (RSM) and hybrid of artificial neural network-particle swarm optimization (ANN-PSO) have been used to develop predictive models for simulation and optimization of tea waste extraction process. The pH, amount of tea waste, concentration of PAN (complexing agent), eluent volume, concentration of eluent, and sample and eluent flow rates were the input variables, while the extraction percent of Mn and Co were the output. Two approaches for their modeling and optimization capabilities were compared. The generalization and predictive capabilities of both RSM and ANN were compared by unseen data. The results have shown the superiority of ANN compared to RSM. Under the optimum conditions, the detection limits of Mn and Co were 0.5 and 0.67 μg L−1, respectively. This method was applied to the preconcentration and determination of manganese and cobalt from water samples.
Keywords
Manganese
Cobalt
Tea waste
Artificial neural network
Particle swarm optimization
Response surface methodology
1 Introduction
Many elements are important to life, but in excess, these same substances can be toxic. The contamination of environmental waters by heavy metals is a major concern today because of their potential influences on living organisms. Heavy traffic, industrial development and urbanization lead to pollution of waters by heavy metals (Lemos et al., 2010; Beiraghi et al., 2012). For the formation of vitamin B12 cobalt is necessary, while manganese is an important element to all forms of life, which has both structural and enzymatic functions (Lemos et al., 2010). Cobalt is one of common poisonous elements that affect the environment and is present in waste water industries such as electroplating, pigments, paints and electronic. The low amounts of this element could lead to poisonous influences such as flushing and vasodilatation in animals and humans (Beiraghi et al., 2012). If humans for long period exposed to excessive levels of manganese, this element can develop emotional and mental disturbances and clumsy and slow body movements (Lemos et al., 2008). It is evident that the determination of these metals, at trace levels in natural water samples is necessary.
In this study, tea wastes have been utilized as adsorbent for the extraction of cobalt and manganese from water samples. Tea waste is a household waste available in large amount in Iran. Tea waste is an oxygen pollutant demanding and also requires a long period for biodegradation (Uddin et al., 2009). Insoluble cell walls of tea leaf are largely made up of hemicelluloses and cellulose, structural proteins, condensed tannins and lignin. One-third of the total dry matter in the tea leaf due to contain functional groups must be good potential as metal sorbent from aqueous solution (Tee and Khan, 1988).
Response surface methodology (RSM), in statistical-based methods has been usually used in extraction process optimization (Khajeh and Musavi Zadeh, 2012). In this technique, the experimental responses to experimental design are fitted to quadratic function. The effective application number of this technique proposes that second-order relation can reasonably approximate many extraction systems.
Artificial neural network (ANN), in last two decades as an attractive tool for non-linear multivariate modeling has been developed (Desai et al., 2004, 2008). ANN’s power is that it is generic in structure and has the capability to learn from historical data. The major advantages of ANN compared to RSM are (i) it does not need a prior specification of appropriate fitting function and (ii) ANN is capable of universal estimation, i.e. ANN can estimate nearly all types of non-linear functions such as quadratic functions, where RSM is suitable only for quadratic estimations (Desai et al., 2008).
Particle swarm optimization (PSO) is a stochastic optimization procedure motivated by the behavior of a bird flock or the sociological behavior of a people group (Lazzus, 2010).
The present work describes the efficiency of tea waste for the extraction of manganese and cobalt from water samples. The effects of various parameters including pH, amount of tea waste, eluent volume and concentration, concentration of PAN and sample and eluent flow rates were investigated. The aims of this study are: (i) to obtain a predictive model based on ANN and RSM techniques for prediction of the extraction percent of manganese and cobalt, (ii) to maximize the extraction percent of manganese and cobalt using RSM and ANN models, and (iii) to develop a cheap, simple and fast method for the extraction of analytes.
2 Experimental
2.1 Materials
1-(2-pyridylazo)-2-naphthol (PAN) was obtained from Merck (Darmstadt, Germany). All acids used were of the highest purity available from Merck. Reagent grade Co(NO3)2 and MnSO4 (from Merck) were of the highest purity available. A stock solution of cobalt and manganese (1000 mg L−1) was prepared by dissolving the proper amount of these elements in double distilled water in a 10 mL flask. Dilute solutions were prepared by an appropriate dilution of the stock solution in double distilled water.
2.2 Instrumentation
The measurements were performed with a Konik Won M300 (Barcelona, Spain) flame atomic absorption spectrometer (FAAS), equipped with a conventional pneumatic nebulizer. Hollow cathode lamp for the determination of manganese and cobalt were used. The most sensitive wavelengths for manganese at 279.5 nm and cobalt at 240.7 nm were used. The pH was determined with a model 630 Metrohm pH meter with a combined glass-calomel electrode.
2.3 Preparation of the adsorbent
Tea waste was taken from the tea waste leaves after the process of tea making. Colored and soluble components have been removed from tea waste with washing by boiling water. This washing was repeated until the water was virtually colorless. Then, it was immersed in 0.5 mol L−1 nitric acid about 5 h to eliminate traces of alkalinity and other impurities. The acid treated tea waste was washed with distilled water to remove excess of nitric acid and other coloring materials until wash water is colorless. Finally, the tea leaves were then washed by deionized water and were oven dried for 5 h at 105 °C. The dried tea was sieved between 400 and 500 μm and stored in sealed polythene bags.
2.4 Procedure
A plastic syringe with two filters was applied as a cartridge and then, was filled with different amounts of dried tea waste (according to experimental design). One filter was placed at the bottom of adsorbent and other to avoid disturbance during solution passage was placed on the top of adsorbent. First, the cartridge was treated with 5 mL nitric acid and then, was washed with deionized water. A portion of solution containing manganese and cobalt was prepared. After that, the solutions were adjusted to the desired pH values with dropwise addition of 0.1 mol L−1 NaOH and HCl and passed through the cartridge with various flow rates. Subsequently, manganese and cobalt retained on the tea waste adsorbent were eluted with the desired volume of nitric acid as eluent. The eluent was analyzed for the determination of manganese and cobalt concentration.
Adsorption equilibrium studies were done under optimum condition at pH 9.5 for tea waste adsorbent. Isotherm studies were performed with a constant tea waste (0.5 g) and varying initial concentration of manganese and cobalt in the range of 1–100 mg L−1. The amount of adsorption was calculated based on the difference between manganese and cobalt concentrations in sample solution before and after adsorption. According to this formula:
2.5 Response surface methodology
The relationships between the screened parameters are represented mathematically in the form of quadratic equation under RSM (Khajeh and Sanchooli, 2010; Khajeh, 2011; Khajeh et al., 2010). In this research, the experiments were conducted in the Box–Behnken experimental design and fitted with an empirical, full second order polynomial model expressing in the form of response surface over a relatively wide range of parameters. Eq. (2) is used to fit the experimental data (Table 1) of manganese and cobalt recovery to construct the RSM model.
Run
pH
Mass of adsorbent (g)
[PAN] (molL−1)
Eluent volume (mL)
Eluent concentration (molL−1)
Sample flow rate (mLmin−1)
Eluent flow rate (mLmin−1)
Experimental
Predicted (Mn)
Predicted (Co)
R % (Mn)
R (%) (Co)
R (%) (RSM)
R (%) (ANN)
R (%) (RSM)
R (%) (ANN)
1
9.5
0.3
2
2
0.1
2
2
95
92
95.4
95
93.0
91.3
2
9.5
0.3
2
5
0.1
2
2
96
91
97.1
95.6
88.0
91.4
3
9.5
0.3
2
2
1.5
2
2
95
87
96.8
95
89.9
86.5
4
9.5
0.3
2
5
1.5
2
2
96
83
96.9
96
83.4
83.9
5
9.5
0.3
2
2
0.1
6
2
98
84
97.1
98
83.6
83.6
6
9.5
0.3
2
5
0.1
6
2
97
89
95.3
96.9
86.1
89.1
7
9.5
0.3
2
2
1.5
6
2
99
87
97.9
99
90.0
85.5
8
9.5
0.3
2
5
1.5
6
2
95
92
94.6
95.1
91.0
91.3
9
7
0.3
2
3.5
0.8
2
1
93
91
91.1
93.4
97.3
90
10
12
0.3
2
3.5
0.8
2
1
89
77
88.8
89
76.3
77.3
11
7
0.3
2
3.5
0.8
6
1
93
87
94.3
93
85.5
86.7
12
12
0.3
2
3.5
0.8
6
1
88
61
88.4
88
63.0
61.1
13
7
0.3
2
3.5
0.8
2
3
86
86
85.6
86.2
84.0
86.7
14
12
0.3
2
3.5
0.8
2
3
98
67
96.8
97.8
68.5
65.8
15
7
0.3
2
3.5
0.8
6
3
85
95
85.3
85
95.7
95.7
16
12
0.3
2
3.5
0.8
6
3
91
85
92.9
91
78.7
85
17
9.5
0.1
2
3.5
0.1
4
1
98
79
97.8
97
80.9
79.6
18
9.5
0.5
2
3.5
0.1
4
1
98
93
97.4
98
89.5
90.5
19
9.5
0.1
2
3.5
1.5
4
1
99
80
99.6
99
79.8
80
20
9.5
0.5
2
3.5
1.5
4
1
98
89
98.8
98
85.9
89.4
21
9.5
0.1
2
3.5
0.1
4
3
99
74
98.3
99
77.1
74.9
22
9.5
0.5
2
3.5
0.1
4
3
99
89
98.4
99
89.2
89.2
23
9.5
0.1
2
3.5
1.5
4
3
97
79
97.6
96.8
82.5
78.9
24
9.5
0.5
2
3.5
1.5
4
3
97
94
97.3
97.1
92.1
93.3
25
7
0.1
2
2
0.8
4
2
92
84
91.3
92
81.5
84.8
26
12
0.1
2
2
0.8
4
2
94
63
93.4
95.3
61.0
64.8
27
7
0.5
2
2
0.8
4
2
92
93
92.4
92
94.0
92.7
28
12
0.5
2
2
0.8
4
2
92
71
91.1
92
73.5
71
29
7
0.1
2
5
0.8
4
2
87
84
87.9
87
81.5
84.1
30
12
0.1
2
5
0.8
4
2
95
65
94.6
95
64.0
65.2
31
7
0.5
2
5
0.8
4
2
89
85
89.6
88.8
87.0
87
32
12
0.5
2
5
0.8
4
2
92
67
92.8
92
69.5
67.1
33
9.5
0.3
1
2
0.8
4
1
97
93
97.6
97.1
91.2
93.1
34
9.5
0.3
3
2
0.8
4
1
99
92
99.3
99
90.5
91.2
35
9.5
0.3
1
5
0.8
4
1
96
91
95.8
96
91.2
91.3
36
9.5
0.3
3
5
0.8
4
1
97
89
96.4
96.7
91.0
89.3
37
9.5
0.3
1
2
0.8
4
3
94
93
94.6
94.2
91.0
92.8
38
9.5
0.3
3
2
0.8
4
3
98
98
98.3
98
97.8
97.6
39
9.5
0.3
1
5
0.8
4
3
96
85
95.8
96
86.5
85.6
40
9.5
0.3
3
5
0.8
4
3
99
92
98.4
99
93.8
92
41
7
0.3
1
3.5
0.1
4
2
87
86
86.9
87.5
86.4
86.7
42
12
0.3
1
3.5
0.1
4
2
96
63
97.6
96
64.9
60.6
43
7
0.3
3
3.5
0.1
4
2
87
89
88.6
87.3
89.7
89.6
44
12
0.3
3
3.5
0.1
4
2
94
69
94.3
94
69.7
69
45
7
0.3
1
3.5
1.5
4
2
90
87
89.8
90
86.3
86.6
46
12
0.3
1
3.5
1.5
4
2
91
69
89.4
91
68.3
68.7
47
7
0.3
3
3.5
1.5
4
2
99
90
97.4
98.8
88.1
90.2
48
12
0.3
3
3.5
1.5
4
2
92
72
92.1
92.2
71.6
72.2
49
9.5
0.1
1
3.5
0.8
2
2
96
88
95.8
96
87.2
88.4
50
9.5
0.5
1
3.5
0.8
2
2
97
97
96.9
96.2
95.3
96.8
51
9.5
0.1
3
3.5
0.8
2
2
98
95
98.4
98
92.5
95
52
9.5
0.5
3
3.5
0.8
2
2
98
99
97.6
96.8
97.6
98.3
53
9.5
0.1
1
3.5
0.8
6
2
95
83
95.4
95.1
84.4
83
54
9.5
0.5
1
3.5
0.8
6
2
96
95
95.6
96.7
97.5
94.1
55
9.5
0.1
3
3.5
0.8
6
2
99
87
99.1
99
88.7
86.8
56
9.5
0.5
3
3.5
0.8
6
2
97
98
97.3
97.1
98.8
97.8
57
9.5
0.3
2
3.5
0.8
4
2
99
94
97.2
97.2
92.5
92.4
58
9.5
0.3
2
3.5
0.8
4
2
95
89
97.2
97.2
92.5
92.4
59
9.5
0.3
2
3.5
0.8
4
2
98
97
97.2
97.2
92.5
92.4
60
9.5
0.3
2
3.5
0.8
4
2
96
95
97.2
97.2
92.5
92.4
61
9.5
0.3
2
3.5
0.8
4
2
97
88
97.2
97.2
92.5
92.4
62
9.5
0.3
2
3.5
0.8
4
2
98
92
97.2
97.2
92.5
92.4
RMSE
0.106
0.10
0.063
0.051
SEP%
0.11
0.10
0.074
0.059
Bf
1.0
1.0
1.0
0.999
Af
1.01
1.01
1.02
1.0
MPE%
1.5
1.3
2.2
0.89
2.6 Definition of the ANN model
In this work, Neural Network Toolbox V7.12 of MATLAB mathematical software was used to predict the extraction percent of manganese and cobalt from water samples.
An artificial neural network (ANN) generally consists of three layers including input, hidden and output layers. The inputs are used in the input layer and output is achieved at the output layer and the learning acquired when the associations among a specific set of input–output pairs formed. In this study, ANN was used to model the influence of seven input parameters including pH, amount of tea waste, concentration and volume of eluent, concentration of PAN and sample and eluent flow rates on extraction percent of manganese and cobalt as output. A feed-forward artificial neural network (FFANN) topology (architecture) also famous as multilayer perceptron (MLP), has been used with back propagation (BP) algorithm to build the predictive models. The neuron output signal O is known by the following Eq.
The most used transfer functions to solve non-linear and linear regression problems are log-sigmoid transfer function (logsig), hyperbolic tangent sigmoid transfer function (tansig) and linear transfer function (purelin) Khayet and Cojocaru, 2012. In this work, tansig was used as transfer function between input and hidden layers, while purelin was used as transfer function between hidden and output layers, shown by the following equations:
Different variables may have various magnitudes, and some of them could have unmerited, but favorable, and effective on the monitored quantity. In this research, all inputs and outputs are normalized within a uniform range of [0–1] according to the below equation:
The corresponding experimental values are plotted versus to the values predicted by the ANN and RSM models visualize the modeling abilities of the ANN and RSM models.
2.7 The concept of particle swarm optimization (PSO)
When the generalized ANN model is developed, its input space can be optimized by PSO method. The input vector containing input parameters of model converts the decision parameter for the PSO. Kennedy and Eberhart in 1995 (Kennedy et al., 2001; Che, 2010) proposed the PSO method. It is an evolutionary computational algorithm. PSO has been developed based on the simulation of the behavior of foraging birds and searches for optimization by updating generations (Che, 2010). Namely, the position (
) and velocity
of each particle will be changed by the particle best value (
) and global best value (
). Kennedy and Spears (Kennedy and Spears, 1998) offered the inertia weighing technique, and presented inertia weight, w, into the basic update rule to decrease the particle speed when particle swarms are searching a large area using the inertia weight [163]. Then, the particles are forced into a better search area to find better practical solution by a more effective technique. The particles’ new position and velocity are updated by the below Eq.:
2.8 Adsorption isotherms
In this study, the equilibrium data were analyzed by the Langmuir and Freundlich isotherm expression given by the following Eq.:
3 Results and discussion
3.1 Hybrid ANN-PSO optimization
3.1.1 Predictive modeling with ANN
Table 1 shows the main factors and extraction percent of manganese and cobalt. The ANN contains three processes that were training, validation and testing. The aim of training was to decide the w and b of the network; testing verifies whether the network was over-trained and validation determined whether the output values estimated using the ANN was accurate (Che, 2010). In this study, ANN with tansig transfer function at hidden layer and a purelin transfer function at output layer was used. The experimental data were randomly divided into three subsets: 76% for the training set, 12% for the validation set and 12% for the test set. The split of data into training, test and validation subsets was performed to estimate the performance of the NN for prediction of “unseen” data, which were not used for training. Network architecture has important influences on the predicted values. The number of input and output nodes is equal to the number of input and output data, respectively (7 and 1 in this work). However, the number of neurons in the hidden layer was recognized by training several FFANNs of different architectures and selecting the optimal one based on the minimization of MSE and improving generalization ability of the topology. In this study, the optimal topology of the ANN model developed involves seven inputs, one hidden layer with 13 neurons for manganese and 15 neurons for cobalt and one output layer (7:13:1 for manganese and 7:15:1 for cobalt). Fig. 1 shows the optimal topology of the developed ANN model. The RMSE, SEP (%), MPE (%), Bf and Af are shown in Table 1.
Optimal ANN structure (a) manganese and (b) cobalt.
3.1.2 PSO-based optimization of input variables in ANN
The PSO technique was utilized to optimize the input space of the ANN model with an objective of maximizing extraction percent of manganese and cobalt. The values of PSO-specific parameters used in the optimization simulation for manganese and cobalt, respectively, were number of particle in swarm = 15 and 10; cognitive component = 2; social component = 2; maximum velocity = 7; minimum inertia weight = 0.6 and 0.05; and maximum inertia weight = 0.8 and 0.1. Optimum conditions have been selected after the evaluation of PSO for 10 iterations for manganese and cobalt to achieved good extraction percent of them. The optimized process conditions are as follows: for manganese; the pH of solution is 9.8, amount of tea waste is 0.5 g, concentration of PAN is 3.0 mol L−1, eluent volume is 3.8 mL, eluent concentration is 0.1 mol L−1, sample flow rate is 3.1 ml min−1 and eluent flow rate is 1.0 mL min−1 and for cobalt; the pH of solution is 9.1, amount of tea waste is 0.35 g, concentration of PAN is 3.0 mol L−1, eluent volume is 2.0 mL, eluent concentration is 1.0 mol L−1, sample flow rate is 6.0 ml min−1 and eluent flow rate is 3.0 mL min−1. The ANN prediction of the extraction percent under the optimized process conditions is 100.2% and 100.1% for manganese and cobalt, respectively.
3.2 Response surface methodology
The below equation explains the relationship of the seven variables, that is, pH (A), amount of tea waste (B), concentration of PAN (C), eluent volume (D), eluent concentration (E), sample flow rate (F) and eluent flow rate (G) and response (Y).
For manganese
(A) pH; (B) mass of adsorbent; (C) concentration of PAN; (D) volume of eluent; (E) concentration of eluent (nitric acid); (F) sample flow rate and (G) eluent flow rate
Source
Coefficients
Sum of squares
Degree of freedom
Mean of square
F-value
p-Value
Mn
Co
Mn
Co
Mn
Co
Mn
Co
Mn
Co
Intercept or model
4.35
−2.8
828.876
5572.647
35
23.682
159.2185
11.99
12.52
<0.0001
<0.0001
A
17.91
29.78
288.798
798.2490
1
288.798
798.2490
146.27
62.76
<0.0001
<0.0001
B
12.76
73.57
1.340
44.5755
1
1.340
44.5755
0.68
3.50
0.4175
0.0725
C
3.17
−8.16
1.954
12.9217
1
1.954
12.9217
0.99
1.02
0.3290
0.3228
D
−1.52
3.03
0.957
3.8320
1
0.957
3.8320
0.48
0.30
0.4924
0.5878
E
13.09
1.88
17.882
0.3682
1
17.882
0.3682
9.06
0.03
0.0058
0.8662
F
5.35
−12.31
22.160
117.5650
1
22.160
117.5650
11.22
9.24
0.0025
0.0053
G
−13.33
−16.81
34.436
54.8040
1
34.436
54.8040
17.44
4.31
0.0003
0.0479
AB
−1.75
0
6.125
0.0000
1
6.125
0.0000
3.10
0.00
0.0899
1.0000
AC
−0.50
0.15
12.500
1.1250
1
12.500
1.1250
6.33
0.09
0.0184
0.7685
AD
0.30
0.2
10.125
4.5000
1
10.125
4.5000
5.13
0.35
0.0321
0.5571
AE
−1.57
0.5
60.500
6.1250
1
60.500
6.1250
30.64
0.48
<0.0001
0.4939
AF
−0.18
−0.075
6.125
1.1250
1
6.125
1.1250
3.10
0.09
0.0899
0.7685
AG
1.35
0.55
91.125
15.1250
1
91.125
15.1250
46.15
1.19
<0.0001
0.2855
BC
−2.50
−3.75
2.000
4.5000
1
2.000
4.5000
1.01
0.35
0.3235
0.5571
BD
0.42
−5.83
0.125
24.5000
1
0.125
24.5000
0.06
1.93
0.8033
0.1770
BE
−0.89
−4.46
0.125
3.1250
1
0.125
3.1250
0.06
0.25
0.8033
0.6243
BF
−0.63
3.12
0.500
12.5000
1
0.500
12.5000
0.25
0.98
0.6190
0.3307
BG
0.63
4.37
0.125
6.1250
1
0.125
6.1250
0.06
0.48
0.8033
0.4939
CD
−0.17
0.083
0.500
0.1250
1
0.500
0.1250
0.25
0.01
0.6190
0.9218
CE
2.14
−0.54
18.000
1.1250
1
18.000
1.1250
9.12
0.09
0.0056
0.7685
CF
0.13
−0.13
0.500
0.5000
1
0.500
0.5000
0.25
0.04
0.6190
0.8444
CG
0.50
1.87
2.000
28.1250
1
2.000
28.1250
1.01
2.21
0.3235
0.1490
DE
−0.36
−0.36
1.125
1.1250
1
1.125
1.1250
0.57
0.09
0.4571
0.7685
DF
−0.29
0.63
6.125
28.1250
1
6.125
28.1250
3.10
2.21
0.0899
0.1490
DG
0.50
−0.75
4.500
10.1250
1
4.500
10.1250
2.28
0.80
0.1432
0.3805
EF
−0.09
1.7
0.125
45.1250
1
0.125
45.1250
0.06
3.55
0.8033
0.0709
EG
−0.89
2.32
3.125
21.1250
1
3.125
21.1250
1.58
1.66
0.2195
0.2088
FG
−0.44
2.94
6.125
276.1250
1
6.125
276.1250
3.10
21.71
0.0899
<0.0001
A2
−0.93
−1.88
455.010
1870.4590
1
455.010
1870.4590
230.46
147.05
<0.0001
<0.0001
B2
14.24
−67.71
4.378
99.0234
1
4.378
99.0234
2.22
7.79
0.1485
0.0097
C2
0.19
1.6
0.510
34.7402
1
0.510
34.7402
0.26
2.73
0.6154
0.1104
D2
−0.14
−0.68
1.260
31.2246
1
1.260
31.2246
0.64
2.45
0.4315
0.1293
E2
0.91
−8.59
2.667
239.0859
1
2.667
239.0859
1.35
18.80
0.2557
0.0002
F2
−0.23
0.34
11.690
24.7559
1
11.690
24.7559
5.92
1.95
0.0221
0.1748
G2
−0.06
−0.96
0.042
12.3984
1
0.042
12.3984
0.02
0.97
0.8856
0.3326
Residual
51.333
330.7083
26
1.974
12.7196
Lack of Fit
40.500
269.2083
21
1.929
12.8194
0.89
1.04
0.6216
0.5355
Pure Error
10.833
61.5000
5
2.167
12.3000
R2
0.942
0.944
Adj-R2
0.863
0.869
3.3 Comparison of RSM and hybrid ANN-PSO
The ANN and RSM models were compared for the design of experiments. The comparison was made on the basis of different parameters including RMSE, SEP%, Bf, Af and MPE, which are shown in Table 1. For cobalt extraction, as shown in Table 1, the RMSE (0.063) and SEP (0.074%) for the RSM model are almost bigger than those 0.051% and 0.059%, respectively for the ANN model, showing that the ANN model has better modeling ability than the RSM model for the extraction of cobalt. For manganese extraction, as shown in Table 1, the RMSE and SEP are 0.106% and 0.11%, respectively for the RSM model as compared to 0.1% and 0.1%, respectively for the ANN model. These values show a good fit of the experimental data by ANN in comparison to the RSM model. Moreover, as shown in Table 1, the Bf and Af are closed to unity for both ANN and RSM models for manganese and cobalt, showing a good concordance between the predicted and experimental values. Better accuracy of predictions (MPE%) is observed by the ANN model with 0.89% and 1.3% prediction error for cobalt and manganese, respectively as compared to 2.2% and 1.5% prediction error for cobalt and manganese, respectively by RSM. Fig. 2 indicates the comparative parity plot for RSM and ANN prediction for design experiments of manganese and cobalt. The generalization capability only with completely unseen dataset can be best judged. Therefore, both the models were tested using unseen data. The experimental and predicted extraction percent are summarized in Table 3. Fig. 3 indicates the comparative parity plot for RSM and ANN prediction for unseen data. The correlation coefficients for unseen data by ANN and RSM are 0.944 and 0.902 for manganese and 0.942 and 0.912 for cobalt, respectively. Therefore, ANN has shown a higher generalization ability compared to RSM. ANN model’s upper predictive accuracy can be attributed to its universal capability of it for approximate non-linearity of the system, while the RSM model is only limited to second-order polynomial.
RSM and ANN predicted vs. experimental data for manganese and cobalt.
No
pH
Mass of adsorbent
[PAN]
Eluent volume
Eluent concentration
Sample flow rate
Eluent flow rate
R (%)
Experimental
Predicted
Mn
Co
Mn
Co
RSM
ANN
RSM
ANN
1
8
0.2
2.5
3
1
5
1.5
98.9
89.2
97.7
100.5
89.7
89.6
2
8
0.2
2.5
4
1
3
1.5
85.6
91.6
86
85
92.8
89.6
3
8
0.4
2.5
3
0.5
3
1.5
92.5
95
94.9
91.3
98.3
97.6
4
10.5
0.2
1.5
3
0.5
5
2.5
97.9
82.5
97.3
98.2
81.5
83
5
10.5
0.2
1.5
3
1
5
1.5
96.5
82.4
96
96.3
80.8
83.4
6
10.5
0.2
2.5
3
0.5
3
1.5
94
85.1
96.5
93.4
86.3
86.2
7
10.5
0.2
2.5
4
0.5
5
1.5
97
79.2
96.6
97.1
81.6
78.1
8
10.5
0.4
1.5
3
0.5
3
1.5
90.2
88.4
90.5
90.8
89.5
87.6
9
10.5
0.4
1.5
4
0.5
5
1.5
95.2
86.7
96.2
92.7
85.1
86.1
10
10.5
0.4
1.5
4
1
5
2.5
96.1
91.1
95.6
96.6
89.9
92.3
Comparison of generalization ability of RSM and ANN models for unseen data.
3.4 Adsorption isotherms
The results of adsorption isotherms of Langmuir and Freundlich for manganese and cobalt exhibited that the equilibrium data represented by the Langmuir isotherm equation were superior from the Freundlich equation. The calculated Freundlich constants, for cobalt KF and n are 29.7 and 1.75, respectively and for manganese KF and n are 8.0 and 1.4, respectively. The best fit of equilibrium data in the Langmuir isotherm equation predicts the monolayer coverage of manganese and cobalt onto tea waste. From the slope of the straight line and intercept, the qo of adsorbent and the KL for cobalt and manganese were determined to be 135.1 and 128.2 mg g−1 and 0.25 and 0.05, respectively. The correlation coefficients for Langmuir and Freundlich were 0.999 and 0.995 for cobalt and 0.982 and 0.978 for manganese, respectively.
3.5 Optimization
The comparison of the extraction of manganese and cobalt for optimized media using various methods is given in Table 4. This table clearly demonstrates that the extraction percent of manganese and cobalt predicted by hybrid ANN-PSO are much more close to the experimentally validated results than those predicted by the RSM.
Approach
Variables
R (%)
pH
Mass of adsorbent
[PAN]
Eluent volume
Eluent concentration
Sample flow rate
Eluent flow rate
Predicted
Experimentala
Mn
Before optimization
7
0.1
1
2
0.1
2
1
91.0
At center point of experimental design
9.5
0.3
2
3.5
0.8
4
2
98.2
RSM
9.5
0.1
1
3.5
0.8
6
2
95.5
98.9
Hybrid ANN-PSO
9.8
0.5
3
3.8
0.1
3.1
1
100.2
99.5
Co
Before optimization
7
0.1
1
2
0.1
2
1
88.3
At center point of experimental design
9.5
0.3
2
3.5
0.8
4
2
94.5
RSM
9.5
0.5
3
3.5
0.8
6
2
98.8
99.4
Hybrid ANN-PSO
9.1
0.35
3
2
1
6
3
100.1
99.5
3.6 Study of coexisting ions
In order to evaluate the analytical application of the present study, some foreign ions’ effects, which often accompany manganese and cobalt ions in different real samples and may interfere with the above method, under the optimized conditions were tested. For this purpose, a solution of 10 μg of cobalt and manganese in 25 mL water containing the corresponding interfere ions was prepared. The tolerance limit was defined as the foreign ions’ concentration needed to cause a ±5% error. The tolerable ratio of each foreign ions’ concentration was as below: 500-fold for Li+, Na+, K+, Cl−, NO3−, Mg2+, Ca2+, Ba2+, and CO32−, 50-fold for Cu2+, Fe3+, Pb2+ and Ni2+. The results show that the tested ions do not interference on the pre-concentration and determination of manganese and cobalt.
3.7 Evaluation of method performance
In this study, under the optimum condition, the linear range was obtained between 0.05 and 0.90 mg L−1 for manganese and cobalt with a correlation coefficient of 0.995 and 0.997, respectively. The limit of detection (LOD) for the determination of manganese and cobalt was studied under the optimum condition. The LOD is evaluated using 3(Sd)blank/m and was 0.5 and 0.67 μgL−1 for manganese and cobalt, respectively where Sd is the standard deviation of the blank signals and m is the slope of the calibration curve. The relative standard deviation (RSD%) of the ten replicate determination was <1.9% for both analytes.
In order to obtain a high pre-concentration factor, the sample volume effect on the extraction of manganese and cobalt on tea waste was investigated in the range of 25–500 mL. The results showed that the extraction percent of manganese and cobalt was quantitative (>97%) in the sample volume range of 25–250 mL. After that, the extraction percent of manganese and cobalt were decreased. In this work, the pre-concentration factor was 71 for 250 mL sample volume due to the elution volume of 3.5 mL.
3.8 Analysis of real samples
The procedure was used for separation and determines the concentration of manganese and cobalt in water samples. The results are shown in Table 5.
Analytes
Samples
Manganese and cobalt content (μg g−1 ±RSD%)
R (%)
Added
Found
Mn
Tap water
0
41.25 ± 1.2
–
50
90.9 ± 1.3
99.3
Well water
0
18.43 ± 1.3
–
50
68.83 ± 1.0
100.8
Mineral water
0
5.1 ± 1.2
–
50
53.35 ± 1.4
96.5
Co
Tap water
0
12.65 ± 1.1
–
50
62.5 ± 0.7
99.7
Well water
0
10.06 ± 1.1
–
50
60.16 ± 0.9
100.2
Mineral water
0
–
–
50
48.95 ± 1.8
97.9
4 Conclusions
In this study, hybrid ANN-PSO and RSM have been successfully used to study the modeling of the variables for maximum extraction of manganese and cobalt based experimental data using the Box–Behnken design. The modeling capability of ANN has shown its superiority over RSM with comparative less values of RMSE and SEP%. Hybrid ANN-PSO approach has predicted maximum extraction for manganese and cobalt of 100.2% and 100.1%, respectively, while, maximum extraction of 95.5% and 98.8% is reported by RSM for manganese and cobalt, respectively. The predictive and generalization capabilities of both RSM and ANN were compared using separate dataset. The correlation coefficients for ANN and RSM were 0.944 and 0.902 for manganese and 0.942 and 0.912 for cobalt, respectively, representing the superiority of ANN in capturing the non-linear behavior of the system.
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