Modeling of Trivalent Chromium Sorption onto Commercial Resins by Artificial Neural Network

Figures & data

Figure 1. Structure of artificial neural network for removal efficiency.

Table 1. Transfer functions used in algorithms.

Transfer function	Algorithm
Tansig	tansig(n) = 2/(1 + exp (−2n)) – 1
Purelin	purelin(n) = n, for all n
Logsig	logsig(n) = 1(1 + exp (-n))

Table 2. The ranges of data set and their statistic.

	Data Statistic
Parameters	Ranges	Mean ± S.D.	Unit
Input Layer
Adsorbent Dosage	0.01–0.1	0.04 ± 0.01	mg
Concentration	4.60–31.7	27.76 ± 7.48	ppm
pH	2.00–7.0	2.52 ± 1.37
Contact Time	5.00–240.0	73.15 ± 57.53	min
Output Layer (r.e)
Amberjet 1200H	27.50–95.6	66.13 ± 19.95	%
Diaion CR11	17.66–99.6	70.41 ± 23.32	%

Table 3. Results of training and transfer functions used for removal efficiency for Amberjet 1200H.

Training Functions	Transfer Functions	R^2test	R^2simulated	MSE
Trainscg	Logsig	0.89	0.52	0.0030382
	Purelin	0.83	0.38	0.0030462
	Tansig	0.92	0.45	0.0916780
Trainlm	Logsig	0.98	0.50	0.0431500
	Purelin	0.98	0.55	0.0428900
	Tansig	0.93	0.12	0.0129560
Traingdm	Logsig	0.96	0.08	0.0780680
	Purelin	0.95	0.42	0.0288049
	Tansig	0.95	0.12	0.0880420
Traincgp	Logsig	0.96	0.03	0.0780680
	Purelin	0.97	0.15	0.0157380
	Tansig	0.83	0.52	0.0015453
Trainrp	Logsig	0.95	0.18	0.0630900
	Purelin	0.93	0.28	0.0335720
	Tansig	0.97	0.18	0.0212760

Figure 2. Simulated data and experimental data for removal efficiency of Amberjet 1200H.

Table 4. Comparison of 20 neurons in the hidden layer for Amberjet 1200H.

Number of neurons	R^2test	R^2simulated	MSE
1	0.97	0.62	0.016273
2	0.99	0.43	0.041402
3	0.98	0.51	0.019986
4	0.99	0.48	0.049786
5	0.98	0.55	0.042890
6	0.92	0.47	0.029075
7	0.99	0.85	0.006162
8	0.99	0.72	0.070079
9	0.99	0.81	0.077377
10	0.94	0.24	0.026626
11	0.98	0.36	0.013237
12	0.95	0.67	0.080641
13	0.97	0.45	0.040617
14	0.96	0.33	0.044566
15	0.98	0.16	0.051126
16	0.95	0.06	0.037436
17	0.96	0.82	0.055593
18	0.98	0.77	0.056530
19	0.96	0.85	0.006367
20	0.96	0.84	0.037163

Figure 3. Relationship between MSE and number of neurons in the hidden layer for Amberjet 1200H.

Table 5. Results of training and transfer functions used for Diaion CR11.

Training Functions	Transfer Functions	R^2test	R^2simulated	MSE
Trainscg	logsig	0.94	0.26	0.0119000
	purelin	0.97	0.03	0.0314000
	tansig	0.97	0.66	0.0086272
Trainlm	logsig	0.97	0.18	0.0089458
	purelin	0.93	0.20	0.0072744
	tansig	0.96	0.08	0.0026474
Traingdm	logsig	0.85	0.23	0.0091143
	purelin	0.87	0.02	0.0572870
	tansig	0.84	0.02	0.0186180
Traincgp	logsig	0.97	0.95	0.0075858
	purelin	0.89	0.02	0.0236190
	tansig	0.84	0.62	0.0170590
Trainrp	logsig	0.97	0.58	0.0404380
	purelin	0.85	0.95	0.1025100

Figure 4. Simulated data and experimental data for Diaion CR11.

Figure 5. The relationship between MSE and number of neurons in the hidden layer.

Table 6. Comparison of 20 neurons in the hidden layer for Dıaıon CR11.

Number of neurons	R^2test	R^2simulated	MSE
1	0.96	0.74	0.013907
2	0.92	0.51	0.031044
3	0.94	0.45	0.028884
4	0.93	0.67	0.010767
5	0.97	0.95	0.007585
6	0.92	0.78	0.010585
7	0.98	0.97	0.006684
8	0.97	0.66	0.060933
9	0.90	0.75	0.016150
10	0.93	0.38	0.002578
11	0.90	0.43	0.001192
12	0.93	0.89	0.052404
13	0.93	0.81	0.022233
14	0.97	0.48	0.003129
15	0.94	0.24	0.014677
16	0.95	0.12	0.006286
17	0.98	0.89	0.009004
18	0.96	0.79	0.028021
19	0.89	0.87	0.012133
20	0.90	0.91	0.076181