Spatial Approach of Artificial Neural Network for Solar Radiation Forecasting: Modeling Issues

Table 3

Radiation forecasting; spatial comparison of ANN models with time delay, neurons and transfer function.

Number of inputs	%performance (MAE)			%training		%forecasting		Year	Delay	Neurons	Transfer; function	Column	Row	Ranking
	Training	Validation	Testing	MSE	RMSE	MSE	RMSE
11^*	2.14^*	4.32^*	3.04^*	2.76^*	16.61^*	0.78^*	24.3^*	11^*	7^*	70^*	satlins^*	1^*	2^*	1^*
7^**	2.86^**	4.22^**	3.08^**	3.18^**	17.83^**	0.73^**	24.51^**	12^**	3^**	130^**	compet^**	3^**	1^**	2^**
6^***	3.12^***	3.41^***	3.13^***	3.18^***	17.83^***	0.63^***	22.2^***	12^***	1^***	10^***	hardlims^***	2^***	3^***	3^***
9	2.47	3.46	3.25	2.82	16.8	0.86	24.16	12	26	220	hardlim	3	3	4
15	2.14	3.6	3.29	2.66	16.31	1.35	27	11	2	100	purelin	2	3	5
29	1.63	4.76	3.33	2.6	16.12	0.69	25.05	9	7	40	compet	1	2	6
14	2.31	3.41	3.34	2.73	16.53	1.18	26.59	11	23	10	purelin	2	2	7
8	2.4	4.32	3.39	2.98	17.26	0.59	22.29	12	1	40	satlin	3	2	8
17	1.98	4.09	3.44	2.7	16.42	0.94	26.29	11	0	40	poslin	3	2	9
10	2.24	3.44	3.45	2.72	16.5	0.8	23.47	11	23	10	logsig	1	1	10
25	1.78	4.29	3.5	2.63	16.21	0.97	24.57	10	21	160	purelin	3	1	11
19	2	4.14	3.51	2.73	16.52	1.61	27.84	10	23	40	tansig	1	1	12
3	4.21	3.9	3.52	4.01	20.03	0.53	20.96	12	27	190	poslin	1	3	13
12	2.05	4.01	3.56	2.74	16.56	1.1	25.59	11	26	40	hardlims	1	3	14
5	2.79	4.52	3.59	3.29	18.15	0.44	21.05	12	1	250	poslin	2	2	15
26	1.82	4.31	3.6	2.68	16.36	1.6	29.29	10	19	190	compet	3	2	16
18	1.91	3.78	3.62	2.62	16.2	1.11	26.58	11	25	70	satlins	3	3	17
32	1.69	4.56	3.65	2.65	16.29	1.25	27.4	9	15	130	satlins	2	2	20
28	1.74	4.43	3.65	2.66	16.3	1.41	28.09	9	20	280	purelin	1	1	19
16	2.04	3.74	3.65	2.7	16.44	0.77	23.57	11	29	40	purelin	3	1	18
4	3.22	4.4	3.66	3.55	18.83	0.68	22.41	12	22	190	satlin	2	1	21
13	2.07	3.88	3.69	2.76	16.61	1.43	28.84	11	4	190	poslin	2	1	22
21	1.64	4.65	3.71	2.65	16.29	1.08	25.53	10	26	40	logsig	1	3	23
30	1.69	4.39	3.71	2.64	16.24	1.45	27.97	9	14	40	tansig	1	3	24
33	1.71	5.3	3.71	2.83	16.82	1.47	28.26	9	15	70	satlin	2	3	25
27	1.69	4.15	3.75	2.59	16.1	1.63	29.64	10	11	160	hardlims	3	3	26
34	1.69	3.98	3.86	2.58	16.07	1.1	25.55	9	23	10	tansig	3	1	28
23	1.72	4.29	3.86	2.67	16.33	1.35	26.66	10	26	10	satlin	2	2	27
35	1.68	4.36	3.94	2.67	16.34	1.24	27.56	9	21	70	purelin	3	2	29
20	1.64	4.4	3.96	2.66	16.3	0.99	25.71	10	7	10	purelin	1	2	30
31	1.65	4.15	4	2.62	16.2	1.39	28.13	9	27	70	poslin	2	1	32
22	1.7	4.1	4	2.64	16.25	1.41	28.43	10	8	160	satlins	2	1	31
38	1.7	5.8	4.03	2.98	17.27	2	30.4	8	10	190	compet	1	2	33
24	1.56	4.15	4.05	2.58	16.06	0.78	24.45	10	15	190	compet	2	3	34
37	1.62	4.39	4.1	2.67	16.33	1.83	29.63	8	2	70	hardlims	1	1	35
36	1.55	4.93	4.11	2.74	16.56	2.06	30.85	9	3	40	tansig	3	3	36
39	1.33	5.09	4.35	2.69	16.39	1.47	28.58	8	23	40	hardlims	1	3	37
40	1.29	5.51	4.54	2.78	16.68	1.48	30.01	8	7	130	tansig	2	1	38
44	1.24	5.79	4.56	2.81	16.77	2.06	32.39	8	3	10	compet	3	2	39
47	1.02	6.39	4.61	2.81	16.76	2.37	33.24	7	1	10	logsig	1	2	40
46	1.16	5.94	4.71	2.83	16.82	1.47	29.4	7	17	160	poslin	1	1	41
42	1.12	5.52	4.72	2.72	16.5	1.29	28.96	8	20	250	hardlim	2	3	42
41	1.21	5.62	4.75	2.8	16.73	0.99	28.11	8	25	40	hardlim	2	2	43
43	1.21	5.36	4.78	2.75	16.59	1.96	31.28	8	7	70	tansig	3	1	44
45	1.16	6.66	4.9	3.01	17.34	2.03	31.28	8	23	130	hardlims	3	3	45
52	1.09	5.36	5.04	2.74	16.54	1.71	31.25	7	5	10	compet	3	1	46
51	1.03	6.14	5.05	2.86	16.91	1.79	31.64	7	0	10	satlin	2	3	47
48	1.13	5.4	5.11	2.78	16.68	1.35	29.22	7	23	40	compet	1	3	48
57	0.88	6.31	5.12	2.82	16.78	2.15	32.84	6	8	100	tansig	1	3	50
50	1.16	5.7	5.12	2.86	16.92	2.65	33.98	7	12	40	purelin	2	2	49
49	1.12	5.89	5.19	2.89	16.99	2.77	33.92	7	7	10	compet	2	1	51
56	1.01	6.75	5.38	3.03	17.41	2.04	31.21	6	29	10	compet	1	2	52
55	0.9	6.13	5.45	2.86	16.91	2.77	33.86	6	8	10	purelin	1	1	53
54	0.98	6.54	5.48	2.99	17.29	2.48	33.87	7	4	100	satlins	3	3	54
59	0.96	6.58	5.51	3	17.31	2.08	32.38	6	15	40	logsig	2	2	55
53	1	9.49	5.62	3.62	19.02	1.2	27.62	7	22	40	logsig	3	2	56
61	0.83	6.91	5.63	3	17.33	3.46	36.2	6	1	100	tansig	3	1	57
60	0.91	6.52	5.75	3	17.32	3	36.7	6	0	10	tansig	2	3	58
2	5.85	6.76	5.91	6.05	24.59	1.34	25.05	12	1	40	poslin	1	2	59
58	0.9	6.48	6.03	3.04	17.43	3.16	35.41	6	10	10	tansig	2	1	60
62	0.75	8.21	6.09	3.31	18.19	2.5	34.12	6	25	100	satlin	3	2	61
65	0.67	6.9	6.44	3.07	17.53	3.46	36.21	5	25	40	poslin	1	2	63
63	0.71	6.49	6.44	3.01	17.36	3.31	35.07	6	5	40	logsig	3	3	62
66	0.69	7.08	6.45	3.12	17.66	2.52	34.33	5	28	10	hardlim	1	3	64
69	0.6	7.6	6.5	3.18	17.83	3.15	35.33	5	25	10	logsig	2	3	65
67	0.68	6.93	6.68	3.13	17.69	2.84	34.2	5	22	10	satlins	2	1	66
71	0.74	7.55	6.68	3.29	18.13	4.45	38.71	5	3	10	tansig	3	2	67
70	0.69	7.41	6.69	3.23	17.97	3.04	34.97	5	10	10	logsig	3	1	68
64	0.69	7.06	6.76	3.18	17.82	3.08	34.94	5	28	10	hardlim	1	1	69
68	0.74	6.56	6.9	3.14	17.71	3.39	36.01	5	23	40	poslin	2	2	70
72	0.79	6.72	7.31	3.28	18.11	2.77	34.86	5	5	40	compet	3	3	71