Hybrid neural network–particle swarm method to predict global radiation over the Norte Chico (Chile)

Hybrid neural network–particle swarm method to predictglobal radiation over the Norte Chico (Chile)

Alejandro A. Perez Ponce, Juan A. Lazzus,a) and Luis O. Palma ChillaDepartamento de Fısica, Universidad de La Serena, Casilla 554, La Serena, Chile

(Received 23 January 2012; accepted 4 March 2012; published online xx xx xxxx)

Solar energy estimation procedures are very important in the renewable energy field

for development of mathematical models, optimization, and advanced control of

processes. Solar radiation data provide information on how much of the sun’s energy

strikes a surface at a location on earth during a particular time period. These data are

needed for effective research into solar-energy utilization. Due to the cost and diffi-

culty in measurement, these data are not readily available. Therefore, there is the

need to develop alternative ways of generating these data. In this study, an artificial

neural network (ANN) was used for the estimation of daily global solar radiation

(RG) over the Norte Chico using 17 552 data measured from 21 meteorological

stations (years 2004–2010) located in the south area of the Atacama Desert. The

ANN was developed with particle swarm optimization. Six input parameters were

used to train the network. These parameters were elevation, longitude, latitude, air

temperature, relative humidity, and wind speed. The network that obtained the lowest

deviation during the training was one with 6 neurons in the input layer, 18 and 6 neu-

rons in the hidden layers, and one neuron in the output layer. The results show that

the ANN can be accurately trained and that the chosen architecture can estimate the

RG with acceptable accuracy: average absolute relative deviation less than 10% for

the training and for the validation step. The low deviations found with the proposed

method indicate that it can estimate RG with better accuracy than other methods

available in the literature. VC 2012 American Institute of Physics.

[http://dx.doi.org/10.1063/1.3699616]

I. INTRODUCTION

Energy is essential for the economic and social development and improved quality of life

in Chile and principally on the Norte Chico zone, located in the hyper-arid Atacama Desert.

This zone is under the influence of the south-eastern Pacific subtropical anticyclone affected by

the cycles of La Nina with periods of drought prolonged, and El Nino with abnormal increase

of the quantity of precipitation and of its temporary extension.1–3 The Norte Chico is one of the

most sensitive areas in South America.2 Recent studies of oceanic and atmospheric variability

have confirmed the implications of the dynamics of El Nino-southern oscillation (ENSO) cycle

on the climate of coast cities.4 Ecosystems in arid climates react very sensitively to changes

caused by these phenomena.3 The major feature of El Nino is periodic water scarcity due to

highly variable rainfall and runoff. This may result in severe economic problems when the

water scarcity appears during several consecutive years. Therefore, the energy resources are of

vital importance both economically and environmentally. Solar energy is being seriously con-

sidered for satisfying a significant part of energy demand in this arid zone. The importance of

knowing the temporal and spatial variations of solar radiation (energy) in arid climates have

been explored in several papers.5 Given the growing concern about energy use and its adverse

a)Author to whom correspondence should be addressed. Electronic mail: [email protected]. Tel.:þ 56 51-204128. Fax:þ 56

51-206658.

1941-7012/2012/4(2)000000/10/$30.00 VC 2012 American Institute of Physics4, 000000-1

JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 4, 000000 (2012)

impact on the environment, this could have far-reaching energy and without environmental

problems.

Solar energy estimation procedures are very important in the renewable energy field for de-

velopment of mathematical models, optimization, and advanced control of processes. Solar radi-

ation data provide information on how much of the sun’s energy strikes a surface at a location

on earth during a particular time period. These data are needed for effective research into solar-

energy utilization.6 Due to the cost and difficulty in measurement, these data are not readily

available.7 Therefore, there is the need to develop alternative ways to generate these data.6

Many models have been developed to predict the solar radiation such as Angstrom8 and

Hottel.9 Comparative studies of artificial neural networks (ANNs) and the traditional regression

approaches in modeling global solar radiation (RG) have been shown that ANN methodology

offers a promising alternative to the traditional approach.6,10 The relationship between radiation

and meteorological data is highly non-linear, and consequently an ANN can be a suitable alter-

native to model the underlying radiation properties.

In this work, global radiation data taken from years 2001–2007 were used to train a neural

network. But to obtain still more effective and fast discrimination, particle swarm optimization

(PSO) technique has been introduced to train the ANN architecture. PSO algorithm is preferred

because of its successful implementation to solve many complex optimization problems.11 To

distinguish between the different values of daily RG, and so the ANNþ PSO method can dis-

criminate and learn in an optimum form, geographical and meteorological data were used.

II. DATABASE USED

A data set of 17 552 points of daily RG of 6 years (2004–2010) was used to develop the

ANN method. This work used a leave-25%-out cross-validation method to estimate the predic-

tive capabilities of the model. This approach was applied to each station. Then, 14 042 data

points were used to train the network and 3510 data points (not used in the training process)

were predicted. All data points were taken from CEAZA-MET database.12 To distinguish between

the different values of daily RG, so the ANN can discriminate and learn in optimum form, me-

teorological data were used as input parameters. Twenty one meteorological stations located in

the valleys of the south area of the Atacama Desert were used to obtain the meteorological

data: air temperature TA (�C), relative humidity RH (%), and wind speed WS (m�s� 1). Figure 1

shows the geographical locations of the meteorological stations. Table I shows the basic infor-

mation for weather stations and the data ranges of the properties of interest.

As seen in Table I, daily RG cover wide ranges going from 2 to 12 (kWh/m2day). Exam-

ples of wide range for the input variables that the ANN must treat for training and prediction

are air temperature from 2 to 29 (�C), relative humidity from 20 to 100 (%), and wind speed

from 0.1 to 6 (m�s� 1). The influence of the selected meteorological data over the climate of

this zone of the Atacama Desert has been revised in other communications.1,2

For all stations, a Li-Cor #LI-200 Pyranometer is used. Table II shows the technical data

of these instruments.

III. NEURAL NETWORK AND PARTICLE SWARM OPTIMIZATION

A feed-forward neural network was used to represent non-linear relationships among varia-

bles.10 This ANN was implemented replacing standard back-propagation with PSO.

PSO is a population-based optimization tool, where the system is initialized with a popula-

tion of random particles and the algorithm searches for optima by updating generations.11 In

each iteration, the velocity for each particle is calculated according to the following formula13:

vpi tþ 1ð Þ ¼ xvp

i tð Þ þ c1r1 wpi tð Þ � xp

i tð Þ� �

þ c2r2 wg tð Þ � xpi tð Þ

� �; (1)

where t is the current step number, x is the inertia weight, c1 and c2 are the acceleration con-

stants, and r1, r2 are element from two random sequences in the range (0,1). xpi tð Þ is the current

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FIG. 1. Geographical locations of the meteorological stations involved in this study.

TABLE I. Solar radiation database and basic information for weather stations.

No. Location Valley

Elevation

(m)

Longitude

(�W)

Latitude

(�S)

TA

(�C)

RH(%)

WS

(m�s�1)

RG

(kWh/m2day)

Period

(yr)

No.

data

1 El Romeral Elqui 162.0 71.250 29.750 8–21 36–94 0–3 2–10 2005–2010 1807

2 Coquimbo Elqui 122.0 71.400 30.000 8–21 32–96 0–5 2–10 2005–2010 1804

3 Gabriela Mistral Elqui 204.0 71.083 29.983 4–21 36–95 0–5 2–12 2004–2010 1926

4 Illapel Choapa 275.0 71.169 31.648 5–27 31–89 0–2 2–12 2009–2010 290

5 Pan de Azucar Elqui 135.0 71.233 30.067 4–22 34–99 0–5 2–10 2004–2010 1914

6 Pisco Elqui Elqui 1212.0 70.483 30.117 2–27 39–82 0–3 2–12 2007–2010 954

7 Vicuna Elqui 657.0 70.700 30.033 3–27 39–97 0–5 2–12 2005–2010 1810

8 Tongoy Elqui 1.0 71.552 30.254 8–21 32–96 0–6 2–10 2009–2010 363

9 Bodeguilla Huasco 239.0 70.978 28.527 8–29 38–94 0–6 2–11 2007–2010 959

10 Imperial Huasco 494.0 70.709 28.618 4–26 27–95 0–3 2–11 2007–2010 838

11 Las Tablas Huasco 57.0 71.030 28.550 8–29 35–90 0–5 2–11 2009–2010 363

12 Longomilla Huasco 336.0 70.894 28.552 6–29 42–99 0–6 2–11 2007–2010 726

13 Nicolasa Huasco 179.0 71.029 28.520 8–29 47–93 0–5 2–11 2007–2010 811

14 Santa Juana Huasco 557.0 70.658 28.670 8–26 30–90 0–4 2–12 2007–2010 913

15 Chiguinto Huasco 1063.0 70.330 28.835 4–26 20–80 0–3 2–11 2009–2010 300

16 La Arena Huasco 1209.0 70.278 28.911 4–27 20–80 0–4 2–12 2009–2010 297

17 La Huerta Huasco 872.0 70.473 28.776 4–27 25–85 0–3 2–12 2009–2010 280

18 La Mesilla Huasco 961.0 70.435 28.837 5–27 20–80 0–3 2–12 2009–2010 298

19 La Pampa Huasco 1363.0 70.220 28.975 4–26 20–80 0–3 2–12 2009–2010 303

20 Ramadilla Huasco 880.0 70.437 28.772 5–27 20–80 0–5 2–12 2009–2010 296

21 San Felix Huasco 1220.0 70.457 28.940 4–26 20–83 0–3 2–12 2009–2010 300

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position of the particle, wpi is the best one of the solutions that this particle has reached, and wg

is the best solutions that all the particles have reached. In general, the value of each component

in v can be clamped to the range [–vmax,vmax] control excessive roaming of particles outside the

search space.11,13 After calculating the velocity, the new position of every particle is

TABLE II. Technical specifications of the pyranometers used in this study.

Specification Range

Input signal Sensor type Total solar radiation sensor-cosine corrected

Sensor range 0 W/m2 to 3000 W/m2

Output signal Signal type Microamp current proportional to total solar radiation

Transfer function Typical is 90 lA per 1000 W/m2

Accuracy Maximum deviation of 1% for sensor range

Output signal range 0 lA to 270 lA (typical)

Drift 6 2% change over a 1 year period

Response characteristics Threshold 0.1 W/m2

Environmental Operating temperature range �40 �C to 65 �C

Operating humidity range 0% to 100%

FIG. 2. Flow diagram for training of the ANN using PSO algorithm.

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xp tþ 1ð Þ ¼ xp tð Þ þ vp tþ 1ð Þ; (2)

where x and v denote a particle position and its corresponding velocity in a search space,

respectively.

The total steps to calculate the output parameter, using the input parameters, were as

follows.14

The data were normalized using the following equation:

pi ¼ Pi � Pmini

� � 2

Pmaxi � Pmin

i

� 1; (3)

where Pi is the input variables i, Pmini and Pmax

i are the smallest and largest value of the data.

Next, the net inputs (N) are calculated for the hidden neurons coming from the inputs neurons.

For a hidden neuron

Nhj ¼

Xn

i

whijpi þ bh

j ; (4)

where pi is the vector of the inputs of the training, j is the hidden neuron, wij is the weight of

the connection among the input neurons with the hidden layer, and the term bj corresponds

to the bias of the neuron j of the hidden layer reached in its activation. Starting from these

inputs, the outputs (y) of the hidden neurons are calculated using a transfer function fh associ-

ated with the neurons of this layer

yhj ¼ f h

j

Xn

i

whijpi þ bh

j

!: (5)

To minimize the error, the transfer function f should be differentiable. In the ANN, the hyper-

bolic tangent function (tansig) was used as

FIG. 3. Average absolute relative deviation found in the correlation the RG as function of the number of neurons in the hid-

den layers (1st HL¼first hidden layer and 2nd HL¼ second hidden layer). Black circle is the training error and grey rhom-

bus is the prediction error.

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f Njk

� �¼ eNjk � e�Njk

eNjk þ e�Njk: (6)

All the neurons of the ANN have an associated activation value for a give input pattern; the

algorithm continues finding the error that is presented for each neuron, except those of the input

layer. After finding the output values, the weights of all layers of the network are actualized by

PSO using Eqs. (1) and (2).13

The PSO algorithm is very different than any of the traditional methods of training.11 Each

neuron contains a position and velocity. The position corresponds to the weight of a neuron.

The velocity is used to update the weight. The velocity is used to control how much the posi-

tion is updated. On each pass through a data set, PSO compares each weight’s fitness. The net-

work with the highest fitness is considered the global best. The other weights are updated based

on the global best network rather than on their personal error or fitness.11 In this study, network

fitness was determined to be the mean square of errors for the entire training set

F ¼X

Recorded Value� Network Predicted Valueð Þ2: (7)

This process repeats for the total number of patterns to training. For a successful process,

the objective of the algorithm is to modernize all the weights minimizing the total mean

squared error (e)

TABLE III. Overall minimum, maximum, and average deviations for the calculated RG using the ANN.

ANN model Training set Prediction set Total set

Experimental data

No. data points 14 042 3510 17 552

Deviations

AARDmin 0.01 0.01 0.01

AARDmax 21.88 21.71 21.88

AARD 9.31 9.63 9.47

No. AARD> 20 636 171 807

R2 0.9204 0.9212 0.9210

FIG. 4. Comparison between experimental values (grey) and calculated values (black) of daily RG (kWh/m2day) as a func-

tion of the number of data per year 2004–2010 for all stations.

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e2 ¼ 1

2

XF2: (8)

Figure 2 presents a block diagram of the program developed and written in MATLAB.

The most basic architecture normally used for this type of application involves a neural net-

work consisting of three or four layers.14 The input layer contains one neuron (node) for each

input parameter. The output layer has one node generating the scaled estimated value of the RG.

The number of hidden neurons needs to be sufficient to ensure that the information contained in

the data utilized for training the network is adequately represented. There is no specific approach

to determine the number of neurons of the hidden layer, and many alternative combinations are

possible. The optimum number of neurons was determined by adding neurons in systematic form

and evaluating the deviations of the sets during the learning process.11 Several network architec-

tures were tested to select the most accurate. The accuracy was checked using the average abso-

lute relative deviation (AARD) between the calculated values (calc) and experimental data (exp)

of RG during the training and the prediction steps. The deviations were calculated as

AARD ¼ 100

n

Xn

i¼1

RcalcG � Rexp

G

RexpG

��������i

: (9)

Figure 3 shows the average absolute relative deviation found in correlating the RG as func-

tion of the number of neurons in the hidden layers (1st HL¼ first hidden layer and 2nd

HL¼ second hidden layer).

TABLE IV. Comparison of the method proposed in this work with other

methods found in the literature to estimate RG.

Method AARD Accuracy (%)

Ref. 6 10.3–11.8

Ref. 10 82–92

Ref. 15 92

Ref. 16 74–92

Ref. 17 90

This work 9.6 93

FIG. 5. Deviations found in the prediction of RG using artificial neural network with particle swarm optimization ( ), and

artificial neural network with standard back-propagation (�).

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IV. RESULTS AND DISCUSSION

The results of the ANNþPSO model are presented using Eq. (9). Table III shows the over-

all minimum, maximum, and average deviations for all data using the proposed ANNþ PSO.

These results show that the ANN can be accurately trained and that the chosen architecture can

estimate the RG with acceptable accuracy (AARD less than 10% for the training and for the vali-

dation step).

Figure 4 shows a comparison between experimental and calculated values of RG as a func-

tion of the number of data per year (2004–2010). Note that for the training set (14 042 data

points), the correlation coefficient R2 is 0.9204. For the prediction set (3510 data points), the

correlation coefficient R2 is 0.9212. And for the total set, R2 is 0.9210.

FIG. 6. Comparison between experimental values (black line) and predicted (grey line) values of daily RG (kWh/m2day) of

year 2009 for each station used. In this figure, the stations are listed as in Table I.

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Table IV shows a comparison between some ANN models found in the literature6,10,15–17

and the ANNþ PSO method proposed in this work. The low deviations found with the pro-

posed method indicate that it can estimate the RG with better accuracy than other methods. Sev-

eral authors10,15–17 present ANN models with accuracy of 74% to 90%. The prediction with the

proposed ANNþ PSO method shows an AARD less than 10% with accuracy of 93%, and the

maximum deviations are a little higher than 20%.

Another comparison was made with a neural network with standard backpropagation

(BPNN) and similar architecture and database. This BPNN shows results of AARD of 18%,

with AARDmax greater than 90% and accuracy of 60%. Figure 5 shows the relative deviations

found in the prediction of RG using the BPNN and the proposed model. Note that in a previous

work, these authors obtained good results for a net BPNN with data of this same area but only

considering a meteorological station.

Figure 6 shows another comparison between experimental and calculated values of RG for

year 2009 and for all stations involved in this study. In this year, the ANNþPSO method shows

an accuracy of 93%. All these results represent a tremendous increase in the accuracy to predict

this important property and show that the uses of the geographical and meteorological data have

influential effects on the good training and predicting capabilities of the chosen network.

A total prediction for the year 2011 has made with the ANNþPSO method for the Chi-guinto location in the Huasco Valley (Atacama Desert). Figure 7 shows the prediction values

of RG for each day of year 2011 over this location.

V. CONCLUSIONS

Based on the results and discussion presented in this study, the following main conclusions

are obtained: (i) The results show that the ANNþPSO method proposed in this work can be

properly trained and that the chosen architecture (6–18-6–1) can estimate the daily solar radia-

tion with acceptable accuracy and (ii) the geographical and meteorological data used have influ-

ential effects on the good training and predicting capabilities of the chosen network.

ACKNOWLEDGMENTS

The authors thank the Direction of Research of the University of La Serena, through the

research Grant DIULS-PR11102, and the Department of Physics of the University of La Serena for

the special support that made possible the preparation of this paper. Special thanks to CEAZA-MET

FIG. 7. Prediction of values of daily solar radiation (kWh/m2day) for year 2011 over Chiguinto (randomly selected from

database) using the ANNþPSO method development in this work.

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by the meteorological data set. L. O. Palma Chilla is supported by the Doctoral Program in Physics

of the University of Tarapaca. A. A. Perez Ponce is supported by the project MECESUP-2–0703.

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