3.1. Model Fitting
The CCD experiments were conducted with three parallel tests, and the AN removal rates were calculated (see Table 2). All the removal rates of AN were between 51.35% and 92.09%, and the average value was 74.48%. In center runs of the CCD experiments, AN removal rates varied from 87.05% to 92.09% with the average value of 89.26%, much higher than the ones calculated from other runs (Star and Axial), with the average value of 68.14%. The rotation and sequentiality of the experiments were well demonstrated.
Table 2. The CCD experiments and results.
Run
|
Type
|
Uncoded Level
|
AN removal rate (%)
|
C/N X1
|
pH
X2
|
HL (d-1)
X3
|
1
|
Star
|
15
|
7
|
0.5
|
65.30
|
2
|
Star
|
25
|
7
|
0.5
|
59.45
|
3
|
Star
|
15
|
8
|
0.5
|
80.35
|
4
|
Star
|
25
|
8
|
0.5
|
69.21
|
5
|
Star
|
15
|
7
|
1.5
|
57.35
|
6
|
Star
|
25
|
7
|
1.5
|
58.58
|
7
|
Star
|
15
|
8
|
1.5
|
76.89
|
8
|
Star
|
25
|
8
|
1.5
|
76.08
|
9
|
Axial
|
11.59
|
7.5
|
1
|
73.15
|
10
|
Axial
|
28.41
|
7.5
|
1
|
56.84
|
11
|
Axial
|
20
|
6.66
|
1
|
51.35
|
12
|
Axial
|
20
|
8.34
|
1
|
82.15
|
13
|
Axial
|
20
|
7.5
|
0.16
|
69.97
|
14
|
Axial
|
20
|
7.5
|
1.84
|
77.33
|
15
|
Center
|
20
|
7.5
|
1
|
87.05
|
16
|
Center
|
20
|
7.5
|
1
|
89.83
|
17
|
Center
|
20
|
7.5
|
1
|
89.50
|
18
|
Center
|
20
|
7.5
|
1
|
92.09
|
19
|
Center
|
20
|
7.5
|
1
|
88.28
|
20
|
Center
|
20
|
7.5
|
1
|
88.78
|
AN is the abbreviation of Ammonia Nitrogen.
With the assistance of Design-Expert 10.0.8.0, the predictive quadratic polynomial regression model was developed, and its coefficients were figured out with least square method. The unencoded numerical value was assigned to including constant term, the linear coefficient, the square term coefficient and the interaction coefficient respectively, forming the following prediction equation.
In this equation, η was the AN removal rate and X2 stood for pH. X1 and X3 represented the C/N and HL of the influent..
Through variance analysis, the predictive quadratic polynomial regression model of the AN removal rate (Equation 3) was evaluated the quality of the fitting degree, and the results were listed in the table 3. The F-value is the ratio of inter group mean square to intra group mean square in analysis of variance. At a certain level of confidence, it can be used to evaluate whether the difference between two sets of data comes from systematic differences or random errors. The F-value and p-value can reflect the significant impact of each control factor in the model, and the larger the F-value and the smaller the p-value, the more significant the correlation 20.The F-value of the model was 45.00 and the p-value less than 0.0001, which showed that the model was highly significant and fitted well throughout the studied regression region. Meanwhile, the P-value of the mismatch term was 0.067, and the mismatch of the model is not significant. The R2 (goodness of fit) was used to test the density of sample data points clustered around the regression line, and to evaluate the fitting degree of the regression model to the sample observation values. The R2 was 0.976, indicating that the model could explain the change in response value of 97.6%, and the variation in removal rate of less than 3% could not be explained by the model. The coefficient of variation, also known as the standard deviation, is the ratio of the standard deviation to the mean, abbreviated as CV. The CV was 3.72% less than 10%, which indicated that the results of CCD experiments were reliable 21. The Adeq precision was 18.4, much higher than 4.0, which implied that the CCD experimental results were precise 22. From the influence of variables simulated by the regression model, The effect of X2 (pH) on the AN removal rate was linearly significant (p<0.05). However, in the pairwise interaction of three variables (C/N, pH, and HL), HL-C/N effect was significant (p<0.05), others were not significant.
Table 3. The variance analysis of the fitting model.
Source
|
Sum of Squares
|
DF
|
Mean Square
|
F Value
|
P Value
|
Model
|
3110.26
|
9
|
345.58
|
45.00
|
< 0.0001
|
X1
|
141.90
|
1
|
141.90
|
18.48
|
0.0016
|
X2
|
945.73
|
1
|
945.73
|
123.15
|
< 0.0001
|
X3
|
3.56
|
1
|
3.56
|
0.46
|
0.5113
|
X1·X2
|
6.72
|
1
|
6.72
|
0.87
|
0.3717
|
X1·X3
|
37.95
|
1
|
37.95
|
4.94
|
0.0404
|
X2·X3
|
18.69
|
1
|
18.69
|
2.43
|
0.1498
|
X12
|
1024.40
|
1
|
1024.40
|
133.40
|
< 0.0001
|
X22
|
879.00
|
1
|
879.00
|
114.46
|
< 0.0001
|
X32
|
415.75
|
1
|
415.75
|
54.14
|
< 0.0001
|
Residual
|
76.79
|
10
|
7.68
|
|
|
Lack of fit
|
62.37
|
5
|
12.47
|
4.32
|
0.0670
|
Pure error
|
14.43
|
5
|
2.89
|
|
|
Cor Total
|
3187.05
|
19
|
|
|
|
Residual is the difference between the experiment result and the regression model fitting. In the regression analysis, the residuals conforming to the normal distribution is pre assumed. Therefore, conducting a normality test of residuals can ensure that the assumptions of regression analysis are valid, thereby ensuring the accuracy of model fitting. Residual plots can reveal experimental data structures and discover information that numerical results cannot provide, making them an indispensable part of model diagnosis 23.
Figure 3a showed the relationship between the cumulative frequency distribution of the AN removal rates and the cumulative probability distribution of Normal distribution. The points in the figure were distributed in an approximate straight line, indicating that the normal distribution assumption was acceptable. The distribution of residuals with predicted values exhibited significant randomness (Figure 3b), and there was no correlation between adjacent residuals. These implied that the residuals did not contain any predictable information 24. From the relationship between actual and predicted values (Figure 4), the data points distributed along the predicted diagonal. This suggested that the actual AN removal rates were highly consistent with the predicted values of the regression model.
In order to compare the influence of three factors on the AN removal rate at the same scale, three curves (Figure 5) were obtained in which, horizontal-axis was for coded variation of C/N, pH and HL, vertical-axis was for the AN removal rate. The variation characteristics of the three curves were similar, all rising first and then decreasing, showing the single-peaked trends. As each of the three factors changed in the CCD experimental range, the AN removal rate can reach the corresponding maximum value. The synergistic changes between the C/N curve and the HL curve were evident, both reaching their peaks near the CCD center point with coded level of 0. This indicated a significant interaction between C/N and HL, consistent with the results of the previous analysis of variance.
3.2. Influence Factor of AN Removal rate
The contour line diagram and 3D response surface diagram could intuitively reflect the influence of the interaction of various factors on the response value 25. Figure 6 showed the interaction between pH and C/N on the AN removal rate under the central value condition of HL. Within the same coded unit range, the removal rate variation range of the vertical-axis was larger than that of the horizontal-axis (Figure 6a), suggesting that pH had a greater impact on the AN removal rate than C/N. The curvature of the pH direction surface was higher than that of the C/N direction (Figure 6b), and the effect of pH on AN removal rate was dominant, with no significant interaction between the two.
Different situation occurred in the interaction between HL and C/N on the AN removal rate under the central value condition of HL (Figure 7). Within the same coded unit range, the change range of removal rate on the vertical-axis was close to that on the horizontal-axis (Figure 7a), implying that the effect of HL on AN removal rate was similar to that of C/N. The curvature of the surface differed slightly in the HL and C/N directions (Figure 7b), and the synergistic effect on the AN removal rate appeared between HL and C/N., with significant interaction.
Within the same coded unit range, the removal rate variation range of the vertical-axis was less than that of the horizontal-axis (Figure 8a), indicating that pH had a greater impact on the AN removal rate than HL. The curvature of the pH direction surface was higher than that of the C/N direction (Figure 8b), and the effect of pH on AN removal rate was dominant, with no significant interaction between the two.
The optimal condition for AN removal (Table 4) was obtained through model fitting: C/N of 18.95, pH of 7.78, and HL of 1.04 d-1. To verify the accuracy of the prediction model, three parallel validation experiments were conducted under optimal condition in the BF, and the average AN removal rate was calculated to be 91.37%, which was not significantly different from the predicted value (91.90%) of the model.
Table 4. The optimal solution and validation of the optimization model.
Optimum Conditions
|
AN Removal rate (%)
|
C/N
|
pH
|
HL (d-1)
|
Experimental
|
Predicted
|
18.95
|
7.78
|
1.04
|
91.37
|
91.90
|
The pH affected nitrification and denitrification processes greatly. Pramanik 26 found that for the nitrification process, the removal rate of NH3-N ranged from 61.32% to 90.24% when the pH was 6-9; When the pH of the influent was between 7.2 and 8.6, the removal rate of NH3-N reached the highest, basically maintaining around 90%; When pH<7.2 or pH>8.6, the removal rate of NH3-N decreased, and the nitrification process was inhibited. Carbon source is the largest nutrient source for microorganisms, and the C/N has a significant impact on the activity of both nitrifying and denitrifying bacteria. Through the experiment, Guo 27 investigated the effects of C/N on simultaneous nitrification and denitrification in BF. The results indicated that when the C/N was too low, the denitrification carbon source was insufficient; when the C/N is too high, a large number of carbonized heterotrophic bacteria multiply, inhibiting the growth of nitrifying bacteria, leading to a decrease in nitrification efficiency; these all could reduce the effect of nitrogen removal. Different from the first two factors, HL had a significant impact on the balance between nitrification and denitrification processes. Using actual domestic sewage as the study object, Wei et al. 28 studied the impact of HL on treatment efficiency of BF. The experimental results indicated that with the increasing of HL, the removal rate of NH3-N first increased then decreased. The above studies unilaterally confirm the results of this research in terms of their impact on the AN removal. For the BF reactor that has been constructed, HL, C/N and pH three engineering parameters should be comprehensively considered, and the interaction between them could not be ignored. In this way, the optimized parameters can effectively improve the removal rate of AN.