This paper presents an assessment for the artificial neural network (ANN) based approach for hourly solar radiation prediction. The Four ANNs topologies were used including a generalized (GRNN), a feed-forward backpropagation (FFNN), a cascade-forward backpropagation (CFNN), and an Elman backpropagation (ELMNN). The three statistical values used to evaluate the efficacy of the neural networks were mean absolute percentage error (MAPE), mean bias error (MBE) and root mean square error (RMSE). Prediction results show that the GRNN exceeds the other proposed methods. The average values of the MAPE, MBE and RMSE using GRNN were 4.9%, 0.29% and 5.75%, respectively. FFNN and CFNN efficacies were acceptable in general, but their predictive value was degraded in poor solar radiation conditions. The average values of the MAPE, MBE and RMSE using the FFNN were 23%, −.09% and 21.9%, respectively, while the average values of the MAPE, MBE and RMSE using CFNN were 22.5%, −19.15% and 21.9%, respectively. ELMNN fared the worst among the proposed methods in predicting hourly solar radiation with average MABE, MBE and RMSE values of 34.5%, −11.1% and 34.35%. The use of the GRNN to predict solar radiation in all climate conditions yielded results that were highly accurate and efficient.
Solar radiation is the part of the Sun’s radiation which falls at the Earth’s surface. This energy is available for many applications, such as increasing water’s temperature or moving electrons in a photovoltaic cell. Moreover, it supplies energy to natural processes like photosynthesis. Solar energy is secure, clean, and available on the Earth throughout the year. Its secure and clean applications are very important to the world, especially at a time of fossil fuel high costs and the critical situation of the atmosphere resulting from fossil fuel applications. Solar radiation data provides information on how much is the Sun potential at a location on the Earthduring a specific time period. These data are very important for designing sizing solar energy systems. Due to the high cost and installation difficulties of measurement, these data are not always available. Therefore, there is a demand to develop alternative ways of predicting these data. A solar radiation database is very important part of an energy efficiency policy [
In recent years, ANNs have been used in solar radiation modeling for locations at different latitudes and with different climates using ANN. Related work has been done in countries such as Saudi Arabia, Oman, Spain, Turkey, China, Egypt, Cyprus, Greece, India, Algeria, and the UK [
However, solar prediction methods that have been developed for Malaysia are found in [
Solar radiation is classified into two main categories: extraterrestrial solar radiation (
The global solar irradiation (
Artificial neural networks, ANNs, are nonalgorithmic and intensely parallel information processing systems. They learn the relationship between the input and output variables by mastering previously recorded data. An ANN consisted of parallel elemental units called neurons. The neurons are connected by a large number of weighted links which passes signals or information. Simply, a neuron receives and combines inputs and then generates the final results in a nonlinear operation. The term ANN usually refers to a multilayer perceptron (MLP) network. However, there are many other types of neural networks, including probabilistic neural networks (PNN), general regression neural networks (GRNN), radial basis function networks (RBF), cascade correlation, functional link networks, Kohonen networks, Gram-Charlier networks, learning vector quantization, Hebb networks, Adaline networks, heteroassociative networks, recurrent networks, and hybrid networks [
In this study, the four networks used to predict hourly solar radiation for Kuala Lumpur are the generalized regression neural network (GRNN), the feed-forward back propagation neural network (FFNN), the cascade-forward back propagation neural network (CFNN), and the Elman back propagation neural network (ELMNN). These networks were selected based on the fact that they are among the most commonly used neural networks [
The generalized regression neural network (GRNN) is a probabilistic-based network. This network makes classification where the target variable is definite, while GRNNs make regression where the target variable is continuous. Figure
GRNN for solar radiation prediction.
The network consists of input, hidden, and output layers. The input layer has one neuron for each predictor variable. The input neurons standardize the range of values by subtracting the median and dividing by the inter quartile range. The input neurons then feed the values to each of the neurons in the hidden layer. In the hidden layer, there is one neuron for each case in the training data set. The neuron stores the values of the predictor variables for each case along with the target value. When presented with the vector of input values from the input layer, a hidden neuron computes the Euclidean distance of the test case from the neuron’s center point and then applies the RBF kernel function using the sigma value(s). The resulting value is passed to the neurons in the pattern layer. However, the pattern layer (summation layer) has two neurons: one is the denominator summation unit and the other is the numerator summation unit. The denominator summation unit adds up the weights of the values coming from each of the hidden neurons. Meanwhile, the numerator summation unit adds up the weights of the values multiplied by the actual target value for each hidden neuron. Finally, the decision layer divides the value accumulated in the numerator summation unit by the value in the denominator summation unit and uses the result as the predicted target value [
Figure
FFNN for solar radiation prediction.
FFNN, a type of multilayer perceptron network (MLP), has an input layer which standardizes these values so that the range of each variable is −1 to 1. The input layer distributes these values to each of the neurons in the hidden layer. In addition to the predictor variables, there is a constant input of 1.0, called “the bias,” that is fed to each of the hidden layers. The bias is multiplied by a weight and added to the sum going into the neuron. The hidden layer represents the phase where the value from each input neuron is multiplied by a weight, and the resulting weighted values are added together producing a combined value. The weighted sum is fed into a transfer function, which then outputs a value. The outputs from the hidden layer are then distributed to the output layer. The output layer is the final layer where the value from each hidden layer neuron is multiplied by a weight, and the resulting weighted values are added together producing a final combined value. The weighted sum is fed into a transfer function, which then yields the outputs of the network [
Cascade correlation neural networks are “self-organizing” networks. The network begins with only input and output neurons. It is called a cascade because the output from all of the neurons is already in the network that feeds into new neurons. As new neurons are added to the hidden layer, the learning algorithm attempts to maximize the magnitude of the correlation between the new neuron’s output and the residual error of the network that we are trying to minimize. A cascade neural network has three layers: input, hidden, and output. The input layer is a vector of predictor variable values. The input neurons do not perform any action on the values other than distributing them to the neurons in the hidden and output layers. In addition to the predictor variables, there is a constant input of 1.0, called the
CFNN for solar radiation prediction.
Elman networks are a form of recurrent neural networks that have connections from their hidden layer back to a special copy layer. This means that the function learned by the network can be based on the current inputs plus a record of the previous state(s) and outputs of the network. In other words, the Elman net is a finite state machine that learns what state to remember (i.e. what is relevant). The special copy layer is treated as another set of inputs so standard backpropagation learning techniques can be used [
ELMNN for solar radiation prediction.
To evaluate the proposed neural networks, three error statistics were used. These statistics are mean absolute percentage error (MAPE), mean bias error (MBE), and root mean square error (RMSE). MAPE is an indicator of accuracy. It usually expresses accuracy as a percentage and is defined by the following formula:
In addition, most ANN models are being evaluated using MBE and RMSE. MBE is an indicator for the average deviation of the predicted values from the measured data. A positive MBE value indicates the amount of overestimation in the predicted global solar radiation and vice versa. On the other hand, RMSE provides information on the short-term performance of the models and is a measure of the variation of the predicted values around the measured data. It indicates the scattering of data around linear lines. Moreover, RMSE shows the efficiency of the developed network in predicting future individual values. A large positive RMSE implies a big deviation in the predicted value from the measured value. MBE and RMSE are defined as follows:
The proposed networks were trained using 80% of the provided data, while the remaining 20% was used to test the trained network. Random solar radiation profiles for September 2000, March 2002, and June 2004 were used to calculate the results. The proposed ANNs predicted the solar radiation values (global and diffuse), and then the predicted results were compared with the measured data. Each neural network was tested individually using the hourly solar radiation values, and all of the proposed ANNs were compared together using the monthly average solar radiation values.
Figure
Solar radiation prediction using GRNN.
In Figure
Evaluation statistics for GRNN.
Global radiation | MABE (%) | MRSE ( |
MRSE (%) | MBE ( |
MBE (%) |
---|---|---|---|---|---|
September 2000 | 4.5 | 25.9 | 5.7 | −1.5 | −0.33 |
March 2002 | 6.3 | 34.6 | 6.8 | −2.3 | −0.44 |
June 2004 | 3.5 | 19 | 4.5 | −2.8 | −0.07 |
Average | 4.8 | 26.5 | 5.7 | −2.2 | −0.28 |
Diffuse radiation | |||||
September 2000 | 4.7 | 15.8 | 5.7 | −1.5 | −0.33 |
March 2002 | 7 | 17.8 | 7.2 | −0.32 | −0.13 |
June 2004 | 3.3 | 11.4 | 4.5 | −1.11 | −0.44 |
Average | 5 | 15 | 5.8 | −0.98 | −0.3 |
From the table, we can see that the prediction was accurate as shown by Figure
Figure
Solar radiation prediction using FFNN.
Table
Evaluation statistics for FFNN.
Global radiation | MABE (%) | MRSE ( |
MRSE (%) | MBE ( |
MRSE (%) |
---|---|---|---|---|---|
September 2000 | 22.5 | 99.6 | 22.1 | −14.6 | −3.3 |
March 2002 | 20.2 | 101.1 | 19.9 | −7.6 | −1.5 |
June 2004 | 28.7 | 99 | 23.7 | 32.9 | 7.9 |
Average | 23.8 | 99.9 | 21.9 | 3.6 | 1.03 |
Diffuse radiation | |||||
September 2000 | 20.3 | 59.1 | 21.8 | −14.8 | −5.5 |
March 2002 | 32.2 | 61.8 | 25 | −7.6 | −3.1 |
June 2004 | 18.8 | 47.7 | 19 | 2.04 |
|
Average | 23.8 | 56.2 | 21.9 | −20.4 | −2.6 |
Figure
Solar radiation prediction results using CFNN.
Table
Evaluation statistics for CFNN.
Global radiation | MABE (%) | MRSE ( |
MRSE (%) | MBE ( |
MBE (%) |
---|---|---|---|---|---|
September 2000 | 22.1 | 101.5 | 22.5 | −26.8 | −6 |
March 2002 | 21.8 | 108.2 | 21.3 | −23.12 | −4.6 |
June 2004 | 22.7 | 88.3 | 21.1 | 7.2 | 1.7 |
Average | 22.2 | 99.3 | 21.6 | −42.7 | −8.9 |
Diffused radiation | |||||
September 2000 | 20.6 | 59.3 | 21.9 | −13.6 | −5 |
March 2002 | 28.8 | 62.6 | 25.4 | −11.6 | −4.7 |
June 2004 | 18.9 | 48.1 | 19.2 |
|
|
Average | 22.8 | 56.7 | 22.2 | −24.3 | −9.4 |
Figure
Solar radiation prediction results using ELMNN.
Table
Evaluation statistics for ELMNN.
Global radiation | MABE (%) | MRSE ( |
MRSE (%) | MBE ( |
MRSE (%) |
---|---|---|---|---|---|
September 2000 | 28.1 | 131.9 | 29.3 | −34 | −8.9 |
March 2002 | 28.1 | 145.9 | 28.7 | −47.7 | −9.4 |
June 2004 | 33.4 | 128.8 | 30.8 | 9.9 | 2.4 |
Average | 29.9 | 135.5 | 29.6 | −23.9 | −15.9 |
| |||||
Diffuse radiation | MABE (%) | RMSE ( |
MRSE (%) | MBE ( |
MRSE (%) |
| |||||
September 2000 | 41 | 126.8 | 46.8 | −34.7 | −12.8 |
March 2002 | 45.5 | 96.8 | 39.2 | −7.6 | −3.1 |
June 2004 | 31.1 | 78.6 | 31.3 | −7.4 | −3 |
Average | 39.2 | 100.7 | 39.1 | −16.6 | −6.3 |
Figures
Comparison of measured and predicted values based on monthly averages of global radiation.
Comparison of measured and predicted values based on monthly averages of diffuse radiation.
Based upon Figures
Comparison of the proposed methods.
Network | MABE (%) | MRSE (%) | MBE (%) |
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GRNN |
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FFNN |
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CFNN |
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ELMNN |
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In this research, prediction of hourly solar radiation values for Kuala Lumpur was performed. This prediction was performed using the GRNN, FFNN, CFNN, and ELMNN artificial neural networks. Prediction results show that GRNN has a higher efficacy compared to the other proposed networks. The FFNN and CFNN are still efficient at predicting solar radiation but do not predict well in poor radiation conditions such as the first and final hour of the solar day. The ELMNN was the worst at predicting the solar radiation among the proposed methods. Based on our results, GRNN is recommended for such purposes in Malaysia and other nearby regions.