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

Table 2

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

Number of inputs	%performance (MAE)			%training		%forecasting		Year	Delay	Neurons	Column	Row	Ranking
	Training	Validation	Testing	MSE	RMSE	MSE	RMSE
3^*	3.61^*	4.63^*	3.98^*	3.89^*	19.72^*	1.4^*	25.25^*	12^*	27^*	190^*	1^*	3^*	1^*
4^**	3.14^**	4.63^**	4.08^**	3.63^**	19.04^**	1.06^**	25.97^**	12^**	22^**	190^**	2^**	1^**	2^**
5^***	2.52^***	5.21^***	4.12^***	3.38^***	18.38^***	0.92^***	25.64^***	12^***	1^***	250^***	2^***	2^***	3^***
7	2.13	5.05	4.17	3.12	17.68	1.33	27.27	12	3	130	3	1	4
8	1.9	5.56	4.34	3.12	17.66	1.02	24.57	12	1	40	3	2	5
6	2.49	4.91	4.66	3.41	18.46	1.47	27.53	12	1	10	2	3	6
9	1.42	6.02	4.86	3.03	17.39	1.36	26.14	12	26	220	3	3	7
10	1.47	5.71	4.92	3.01	17.34	1.38	29.15	11	23	10	1	1	8
12	1.63	5.35	5.01	3.05	17.47	1.85	31.25	11	26	40	1	3	9
11	1.46	5.17	5.27	2.97	17.22	1.46	28.03	11	7	70	1	2	10
2	5.97	6.41	5.6	5.98	24.46	1.16	24.04	12	1	40	1	2	11
14	1.28	5.97	5.68	3.1	17.6	2.57	33.4	11	23	10	2	2	12
17	1.04	8.63	5.83	3.52	18.76	3.9	35.03	11	0	40	3	2	13
13	1.5	5.72	5.97	3.24	18	2.1	33.36	11	4	190	2	1	14
16	1.08	6.72	6.18	3.23	17.97	2.1	31.22	11	29	40	3	1	15
15	1.22	6.82	6.27	3.35	18.3	2.24	33.32	11	2	100	2	3	16
24	1.13	9.21	6.73	3.87	19.67	2.06	31.33	10	15	190	2	3	17
20	1.11	7.35	6.8	3.5	18.7	2.34	33.16	10	7	10	1	2	18
22	0.98	6.54	6.87	3.27	18.08	2.73	34.22	10	8	160	2	1	19
19	1.38	7.71	7	3.77	19.41	2.1	35.34	10	23	40	1	1	20
18	1.63	7.8	7.11	3.96	19.9	1.95	33.83	11	25	70	3	3	21
25	0.77	7.61	7.27	3.44	18.55	2.46	31.66	10	21	160	3	1	22
23	1.03	8.58	7.32	3.8	19.48	3.13	35.56	10	26	10	2	2	23
1	8.63	9.64	7.4	8.59	29.3	1.23	24.56	12	24	100	1	1	24
21	0.99	6.74	7.51	3.44	18.55	2.84	34.87	10	26	40	1	3	25
26	1.49	8.47	7.55	4.1	20.25	3.2	37.13	10	19	190	3	2	26
27	1.07	7.76	8.13	3.82	19.55	2.88	37.07	10	11	160	3	3	27
30	0.59	8.98	8.6	3.87	19.67	5.54	39.24	9	14	40	1	3	28
33	0.56	9.06	8.88	3.93	19.81	4.65	39.12	9	15	70	2	3	29
28	0.69	9.13	8.92	4.02	20.06	4.57	38.17	9	20	280	1	1	30
32	1.54	8.91	9.15	4.54	21.3	4.3	40.59	9	15	130	2	2	31
31	0.7	9.1	9.29	4.1	20.24	3.12	34.99	9	27	70	2	1	32
29	0.55	9.02	9.3	3.99	19.98	3.49	36.37	9	7	40	1	2	33
35	1.11	10.36	9.83	4.71	21.69	3.48	38.8	9	21	70	3	2	34
34	1.11	9.39	9.89	4.52	21.27	4.43	40.55	9	23	10	3	1	35
36	0.52	11.23	9.89	4.53	21.29	4.29	38.3	9	3	40	3	3	36
38	0.93	11.2	10.77	4.95	22.26	8.21	44.5	8	10	190	1	2	37
37	1.97	12.4	11.1	5.88	24.25	6.9	45.45	8	2	70	1	1	38
39	0.76	11.5	11.2	4.99	22.35	4.97	40.14	8	23	40	1	3	39
41	0.83	10.73	11.54	4.95	22.25	3.94	38.95	8	25	40	2	2	40
40	1.31	13.36	12.32	5.92	24.33	7.38	46.38	8	7	130	2	1	41
42	0.16	14.69	13.62	5.76	23.99	8.07	45.3	8	20	250	2	3	42
43	1.34	16.11	14.92	7.01	26.47	7.08	46.3	8	7	70	3	1	43
45	0.42	17.75	15.56	6.91	26.29	4.44	39.67	8	23	130	3	3	44
44	1.18	17.51	15.82	7.38	27.16	7.8	44.42	8	3	10	3	2	45
46	0.18	17.25	16.9	6.94	26.34	7.67	44.37	7	17	160	1	1	46
49	0.53	19.18	16.9	7.53	27.45	7.41	45.44	7	7	10	2	1	47
88	0.18	17.25	16.9	7.93	28.15	7.67	44.37	3	17	10	3	1	48
50	0.16	19.08	18.23	7.56	27.49	8.13	46.83	7	12	40	2	2	49
48	0.29	20.01	19.13	8	28.28	8.71	46.84	7	23	40	1	3	50
90	0.29	20.01	19.13	7.53	27.45	8.71	46.84	3	23	10	3	3	51
47	0.12	20.08	19.2	7.93	28.15	9.49	47.3	7	1	10	1	2	52
89	0.12	20.08	19.2	8	28.28	9.49	47.3	3	1	40	3	2	53
52	0.68	18.12	19.5	7.93	28.16	9.09	47.95	7	5	10	3	1	54
51	0.68	23.05	19.68	8.95	29.92	8.77	48.03	7	0	10	2	3	55
54	0.08	21.86	19.73	8.36	28.92	11	47.76	7	4	100	3	3	56
53	0.55	17.38	20.36	7.87	28.06	8.02	45.79	7	22	40	3	2	57
55	0.87	24.57	22.69	9.97	31.58	10.3	49.56	6	8	10	1	1	58
59	0.25	26.97	23.02	10.2	31.86	17.9	54.05	6	15	40	2	2	59
56	0.29	26.5	23.88	10.3	32.02	14.2	49.96	6	29	10	1	2	60
57	0.28	23.74	24.18	9.75	31.23	15.3	52.12	6	8	100	1	3	61
60	1.27	28.78	25.18	11.6	33.99	20.8	57.46	6	0	10	2	3	62
58	0.46	26.42	27.7	11.1	33.32	15.3	54.03	6	10	10	2	1	63
61	0.83	33.84	29.19	13.1	36.2	20.3	58.13	6	1	100	3	1	64
62	0.87	39.29	35.88	15.6	39.44	29	61.93	6	25	100	3	2	65
64	0.34	37.43	36.82	15.1	38.79	20.7	57.98	5	28	10	1	1	66
63	0.19	39.91	39.17	15.9	39.91	22.7	58.54	6	5	40	3	3	67
65	0.71	41.55	39.73	16.7	40.84	22.7	58.99	5	25	40	1	2	68
67	0.27	38.23	43.05	16.4	40.51	16.8	55.46	5	22	10	2	1	69
66	0.86	46.81	45.66	19	43.6	33.1	65.04	5	28	10	1	3	70
72	0.33	49.37	46.61	19.4	44.04	48.8	71.06	5	5	40	3	3	71
68	0.15	44.15	46.88	18.3	42.77	20.2	58.32	5	23	40	2	2	72
71	0.47	52.86	47.01	20.3	45	36.5	64.64	5	3	10	3	2	73
69	0.04	45.92	48.93	19	43.58	27.4	62.44	5	25	10	2	3	74
70	0.13	54.96	52.36	21.5	46.41	32.3	64.95	5	10	10	3	1	75
73	0.3	60.39	57.24	23.7	48.69	33.7	65.57	4	28	10	1	1	76
74	0.13	61.7	59.4	24.3	49.29	50.6	72.01	4	15	220	1	2	77
75	0.19	72.76	67.71	28.2	53.11	51.7	72.36	4	12	100	1	3	78
76	0.34	95.94	83.47	36.1	60.07	103	84.87	4	5	40	2	1	79
78	0.66	87.31	84.02	34.7	58.87	56.2	74.84	4	4	10	2	3	80
77	0.31	94.98	90.5	37.3	61.06	65.4	78.53	4	25	10	2	2	81
84	0.32	102.57	95.5	39.8	63.09	51.2	73.22	3	24	130	1	3	82
80	0.85	99.43	95.94	39.6	62.91	63.8	75.11	4	12	10	3	2	83
86	0.59	111.68	97.12	42.1	64.89	110	89.42	3	6	130	2	2	84
79	0.97	95.18	98.15	39.2	62.64	69.5	79.25	4	28	40	3	1	85
82	0.19	102.8	98.39	40.3	63.52	68.9	78.37	3	11	40	1	1	86
87	0.61	102.77	99.64	40.9	63.91	71.1	78.49	3	12	160	2	3	87
81	0.78	101.58	100.87	41	64	62.6	75.64	4	24	40	3	3	88
85	0.81	113.12	101.42	43.4	65.87	61.4	76.05	3	17	10	2	1	89
83	0.22	97.83	102.08	40.1	63.33	64	77.16	3	15	160	1	2	90