ARTIFICIAL NEURAL NETWORK AND WAVELET DECOMPOSITION IN THE FORECAST OF
               GLOBAL HORIZONTAL SOLAR RADIATION

This paper proposes a method (denoted by WD-ANN) that combines the Artificial Neural Networks (ANN) and the Wavelet Decomposition (WD) to generate short-term global horizontal solar radiation forecasting, which is an essential information for evaluating the electrical power generated from the conversion of solar energy into electrical energy. The WD-ANN method consists of two basic steps: firstly, it is performed the decomposition of level p of the time series of interest, generating p + 1 wavelet orthonormal components; secondly, the p + 1 wavelet orthonormal components (generated in the step 1) are inserted simultaneously into an ANN in order to generate short-term forecasting. The results showed that the proposed method (WD-ANN) improved substantially the performance over the (traditional) ANN method.

wavelet decomposition; artificial neural networks; forecasts

Authorship

Luiz Albino Teixeira Júnior

Latin American Institute of Technology, Infrastructure and Territory, Federal University of Latin American Integration - UNILA, Foz do Iguaçu, PR, Brazil. E-mail: luiz.a.t.junior@gmail.com Federal University of Latin American IntegrationBrazilFoz do Iguaçu, PR, BrazilLatin American Institute of Technology, Infrastructure and Territory, Federal University of Latin American Integration - UNILA, Foz do Iguaçu, PR, Brazil. E-mail: luiz.a.t.junior@gmail.com

Rafael Morais de Souza

Department of Accounting, Federal University of Minas Gerais - UFMG, Belo Horizonte, MG, Brazil. E-mail: rafael.morais.souza@gmail.com Federal University of Minas GeraisBrazilBelo Horizonte, MG, BrazilDepartment of Accounting, Federal University of Minas Gerais - UFMG, Belo Horizonte, MG, Brazil. E-mail: rafael.morais.souza@gmail.com

* Corresponding author.

Moisés Lima de Menezes

Department of Statistics, Fluminense Federal University - UFF, Rio de Janeiro, RJ, Brazil. E-mails: moises lima@msn.com; keilamath@hotmail.com Fluminense Federal UniversityBrazilRio de Janeiro, RJ, BrazilDepartment of Statistics, Fluminense Federal University - UFF, Rio de Janeiro, RJ, Brazil. E-mails: moises lima@msn.com; keilamath@hotmail.com

Keila Mara Cassiano

José Francisco Moreira Pessanha

Institute of Mathematical and Statistics, State University of Rio de Janeiro - UERJ, Rio de Janeiro, RJ, Brazil. E-mail: professorjfmp@hotmail.com State University of Rio de JaneiroBrazilRio de Janeiro, RJ, BrazilInstitute of Mathematical and Statistics, State University of Rio de Janeiro - UERJ, Rio de Janeiro, RJ, Brazil. E-mail: professorjfmp@hotmail.com

Reinaldo Castro Souza

Department of Electrical Engineering, Pontifical Catholic University of Rio de Janeiro - PUC-Rio, Rio de Janeiro, RJ. E-mail: reinaldo@ele.puc-rio.br Pontifical Catholic University of Rio de JaneiroBrazilRio de Janeiro, RJ, BrazilDepartment of Electrical Engineering, Pontifical Catholic University of Rio de Janeiro - PUC-Rio, Rio de Janeiro, RJ. E-mail: reinaldo@ele.puc-rio.br

*
Corresponding author.

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables | Formulas

Figures (9)
Tables (2)
Formulas (10)

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Figure 1
Multilayer perceptron artificial neural network. (a) ANN's Architecture; (b) Phases of backpropagation algorithm.

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Figure 2
Setting of the training set.

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Figure 3
Combination of wavelet decomposition + ANN.

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Figure 4
Daily profiles of solar radiation.

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Figure 5
(a) Global horizontal solar radiation at Cuiabá.

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Figure 5
(b) Global horizontal solar radiation at Cuiabá.

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Figure 6
Scatter plot between observed and forecasted values by ANN method.

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Figure 7
Wavelet components of normalized time series of global horizontal solar radiation.

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Figure 8
Scatter plot between observed and forecasted values by WD-ANN method.

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Table 1
Mean and standard deviation of the global horizontal solar radiation

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Table 2
Types of ANN, RMSE and R² for each time series' modeling.

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Figure 1 Multilayer perceptron artificial neural network. (a) ANN's Architecture; (b) Phases of backpropagation algorithm.

Figure 2 Setting of the training set.

Figure 3 Combination of wavelet decomposition + ANN.

Figure 4 Daily profiles of solar radiation.

Figure 5 (a) Global horizontal solar radiation at Cuiabá.

Figure 5 (b) Global horizontal solar radiation at Cuiabá.

Figure 6 Scatter plot between observed and forecasted values by ANN method.

Figure 7 Wavelet components of normalized time series of global horizontal solar radiation.

Figure 8 Scatter plot between observed and forecasted values by WD-ANN method.

Table 1 Mean and standard deviation of the global horizontal solar radiation

Meteorological station	MeanW/m2	Standard Deviation W/m2
Brasília 2011	219,20	304,15
Caicó 2003	253,82	339,08
Campo Grande 2007	213,34	299,37
Cuiabá 2010	204,51	290,98
Florianópolis 2011	171,77	270,09
Joinville 2011	128,72	210,37
Natal 2011	241,13	334,09
Palmas 2010	220,46	304,90
Petrolina 2010	220,41	302,75
São Martinho 2010	196,04	296,06

Source: The authors.

Table 2 Types of ANN, RMSE and R² for each time series' modeling.

Local	With wavelet?	Window length	Neurons in the hide layer		RMSE Wm^-2			R²
				Training	Validation	Test	Training	Validation	Test
	without	12	8	77,90	102,40	107,88	0,9352	0,8772	0,8707
Brasília	db32	15	8	6,03	15,76	91,29	0,9996	0,9971	0,9074
		Naive predictor		129,00	134,64	143,34	0,8302	0,7992	0,7848
	without	15	19	65,13	57,82	66,58	0,9616	0,9756	0,9648
Caicó	db20	15	8	28,91	54,45	37,61	0,9924	0,9784	0,9888
		Naive predictor		130,31	135,72	134,68	0,8523	0,8704	0,8611
	without	15	10	70,59	90,36	120,07	0,9416	0,9225	0,865
Campo Grande	db20	12	8	4,43	9,25	76,06	0,9998	0,9992	0,9458
		Naive predictor		121,14	132,95	154,21	0,8354	0,8394	0,7898
	without	10	19	62.8789	88.1219	106.2804	0.951	0.9199	0.8908
Cuiabá	db38	10	12	8.354	20.4286	26.1382	0.9991	0.9957	0.9934
		Naive predictor		113,55	129,76	144,84	0,8465	0,8340	0,8076
	without	10	10	73.4169	96.9041	109.7201	0.9134	0.9114	0.8958
Florianópolis	db40	8	15	4.8984	7.1704	50.12	0.9996	0.9995	0.9783
		Naive predictor		107,10	130,99	143,29	0,8240	0,8447	0,8302
	without	11	5	64.2913	88.226	92.2426	0.892	0.8883	0.8625
Joinville	db32	12	10	2.8592	6.4026	84.3426	0.9998	0.9994	0.885
		Naive predictor		87,77	111,23	111,58	0,8087	0,8304	0,8089
	without	15	5	76.9716	58.2249	57.3206	0.9434	0.9751	0.9759
Natal	db20	15	13	4.3326	5.2023	75.9577	0.9998	0.9998	0.9577
		Naive predictor		129,73	133,72	133,36	0,8459	0,8728	0,8738
	without	15	10	71.2284	105.5357	101.7703	0.946	0.8849	0.8727
Palmas	db40	10	13	5.5671	11.1399	60.3	0.9997	0.9987	0.9553
		Naive predictor		126,70	149,35	138,54	0,8362	0,7829	0,7780
	without	15	9	64.1714	69.3586	75.1056	0.9526	0.9605	0.9423
Petrolina	db15	9	20	3.6199	7.7754	82.5086	0.9998	0.9995	0.9303
		Naive predictor		115,59	130,42	121,63	0,8520	0,8651	0,8543
	without	15	20	56.2227	71.8829	98.875	0.9562	0.9601	0.9329
São Martinho	db13	20	14	5.5941	10.4779	19.6784	0.9996	0.9992	0.9973
		Naive predictor		100,11	126,80	140,37	0,8662	0,8798	0,8694

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ARTIFICIAL NEURAL NETWORK AND WAVELET DECOMPOSITION IN THE FORECAST OF GLOBAL HORIZONTAL SOLAR RADIATION

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[1] *
Corresponding author.