J. Cent. South Univ. (2021) 28: 507-526

DOI: https://doi.org/10.1007/s11771-021-4618-9

A hybrid decomposition-boosting model for short-term multi-step solar radiation forecasting with NARX neural network

HUANG Jia-hao(黄家豪), LIU Hui(刘辉)

Institute of Artificial Intelligence & Robotics (IAIR), Key Laboratory of Traffic Safety on Track of

Ministry of Education, School of Traffic and Transportation Engineering, Central South University,Changsha 410075, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2021

Abstract: Due to global energy depletion, solar energy technology has been widely used in the world. The output power of the solar energy systems is affected by solar radiation. Accurate short-term forecasting of solar radiation can ensure the safety of photovoltaic grids and improve the utilization efficiency of the solar energy systems. In the study, a new decomposition-boosting model using artificial intelligence is proposed to realize the solar radiation multi-step prediction. The proposed model includes four parts: signal decomposition (EWT), neural network (NARX), Adaboost and ARIMA. Three real solar radiation datasets from Changde, China were used to validate the efficiency of the proposed model. To verify the robustness of the multi-step prediction model, this experiment compared nine models and made 1, 3, and 5 steps ahead predictions for the time series. It is verified that the proposed model has the best performance among all models.

Key words: solar radiation forecasting; multi-step forecasting; smart hybrid model; signal decomposition

Cite this article as: HUANG Jia-hao, LIU Hui. A hybrid decomposition-boosting model for short-term multi-step solar radiation forecasting with NARX neural network [J]. Journal of Central South University, 2021, 28(2): 507-526. DOI: https://doi.org/10.1007/s11771-021-4618-9.

1 Introduction

As a safe and green renewable energy, solar energy has more potential than wind, hydro energy, and geothermal energy [1]. With the development of the world economy, the demand for energy continues to increase. Global warming and environmental pollution caused by fossil fuels are becoming increasingly serious. Compared with solar energy, fossil fuels are not likely to be the ultimate energy choice due to their non-renewable drawbacks. Although photovoltaic (PV) power generation has been widely used and developed in recent years, its output power is affected by factors such as solar irradiance, temperature, and climate. Its intermittent and non-stationarity are the main problems affecting the stability of photovoltaic power generation. High-precision radiation prediction can ensure the safety of photovoltaic grids and improve solar energy utilization efficiency [2, 3].

With the widespread application of solar power, substantial works have been done for solar radiation forecasting in recent years. The main prediction models can be summarized as follows [4]: physical models, image-based methods, artificial intelligence methods.

The physical models of solar prediction are usually based on numerical weather prediction (NWP), which simulates the physics of the atmosphere by using physical principle and terrain circumstances [5]. For predictions that exceed six hours and up to several days, models based on NWP perform well. The NWP is more suitable for mid-term and long-term predictions of solar radiation [6]. BAKKER et al [7] evaluated the improvement effect of 7 statistical post-processing methods on the NWP model. It was found that the non-parametric method performed better than the parametric method under sunny conditions. AGUIAR et al [8] integrated ground data and satellite data into the NWP model, which improved intra-day solar prediction accuracy. CERVONE et al [9] added artificial neural network (ANN) to the NWP model to predict the probability of photovoltaic power generation and found that the solar prediction accuracy of the ANN on the NWP model improved significantly. It can be found that the NWP model is mainly used as an external input combined with neural networks for solar radiation prediction.

The image-based methods fall into two categories: image based on satellite-derived data [10] and sky image based on ground monitoring [11]. A series of real-time cloud images are obtained by image technologies, which track the clouds from the ground or satellite perspective. Then, it combined the forecasting engine to make short-term (0-6 h) predictions of solar radiation [12]. Due to the need to process a large number of high- precision images, the computational complexity of image-based methods is high [13]. INAGE [14] proposed a solar prediction model based on ground- detection cloud image data [14]. The simulated solar motion was used to predict the radiation value of the photovoltaic system in an area. AYET and TANDEO [15] developed a global horizontal solar irradiance (GHI) probability prediction method based on geostationary satellite image simulation of dynamic cloud changes. This method does not require a numerical prediction model, and its accuracy is better than classical statistical methods. The trend in recent years is to add images to artificial intelligence algorithms for short-term solar radiation prediction. KAMADINATA et al [16] extracted color information from sky images, and used it as input as GHI data input for the ANN. It can predict GHI 1-5 min in advance. JANG et al [17] proposed a support vector machine (SVM) prediction model based on satellite imagery for a solar prediction method 15-300 min in advance. The minimum RMSE is 5.7 W/m², better than the prediction of the ANN model.

In recent years, artificial intelligence methods have been increasingly applied in the solar radiation field. Models like back propagation neural network, support vector machine (SVM), adaptive neuro- fuzzy inference system (ANFIS) and various hybrid systems are applied for solar radiation forecasting [18]. Artificial neural network adaptively solves complex problems by imitating biological neural processes in the brain, and its solar radiation prediction accuracy and calculation speed are superior to regression models and traditional empirical methods [19, 20]. ZHANG et al [21] compared the prediction performance of four models including radial basis function neural network (RBFNN), least square support vector machine (LSSVM), k-nearest neighbor (kNN), and weighted k-nearest neighbor (WkNN), and found that the kNN and the WkNN perform the best in 24 h ahead solar power prediction. ASRARI et al [22] used a heuristic shuffled frog leaping algorithm (SFLA) to optimize the short-term solar power prediction model of ANN, and found that SFLA significantly improves the prediction accuracy of ANN. The prediction result shows that multi-layer perceptron (MLP) model is the best model among them. QUEJ et al [23] evaluated the daily horizontal global solar radiation performance of ANFIS, ANN, and SVM models. The prediction accuracy of the SVM is the highest. It is believed that conventional methods can be effectively replaced by machine learning. BASER et al [24] utilized multiple kernel SVM model for solar time series prediction. They found that the SVM models based on Gaussian-kernel functions are the most suitable for solar time series prediction. ZOU et al [25] proposed an ANFIS model for daily global solar irradiance in three Chinese cities. The results show that the ANFIS is better than the improved empirical models.

Now, hybrid prediction models based on machine learning are the mainstream solar radiation prediction methods. The hybrid models get more accurate forecasting results by combining different types of models and integrating the merits of diverse models [26]. It normally consists of decomposition algorithms, optimization methods and forecasting engines [27]. Solar radiation data have typical non-linear and non-stationary characteristics [13]. Decomposition algorithms are widely used in the non-linear signal processing field. Some scholars began to add decomposition algorithms to the foundation of machine learning. SHANG and WEI proposed [28] an EEMD-ISVR model to forecast solar PV power. Experiments were conducted at four solar stations to verify the superiority of the proposed method. Improved support vector regression (ISVR) is the forecasting engine for IMFs. MAJUMDER et al [29] combined variational mode decomposition (VMD) and robust kernel-based extreme learning machine (RKELM) for the solar radiation forecasting. MONJOLY et al [30] compared the three decomposition algorithms, namely EMD, EEMD, and wavelet transform (WT). The conclusion is that the WT combined with other models has the best prediction effect for the prediction of solar radiation series at 1 h ahead. WANG et al [31] combined the EMD, local mean decomposition (LMD), the LSSVM and Volterra to build a new hybrid forecasting model. EMD and LMD algorithms were integrated to decompose historical solar radiation time series data into different frequency subsequences. Then, the high-frequency prediction model and low- frequency prediction model were established based on the LSSVM and Volterra model respectively. To achieve higher solar radiation prediction accuracy, many intelligent algorithms are used to optimize the forecasting engines. ESEYE et al [32] introduced a hybrid WT-PSO-SVM model. The WT was employed to decompose the PV solar power data. Particle swarm optimization (PSO) algorithm was used for SVM tuning. A hybrid model combining autoregressive moving average model (ARMA) and NAR was developed for hourly global horizontal solar radiation by BENMOUIZA et al [33]. The model is 23% more accurate than the single NAR model and 38% more accurate than the single ARMA model. The EEMD was used to decompose solar radiation time series into a series of subsequences by SUN et al [34]. K-means algorithm is performed to cluster the series of subsequences forecasting results, which are forecasted by the LSSVR model.

Based on the discussion of the three mainstream solar radiation forecasting methods mentioned above (NWP, satellite image or sky image, neural network), it can be found that the methods have the following characteristics:

1) NWP. NWP is a classic solar radiation prediction method, and many scholars have done a lot of research [12, 35]. The NWP-based method is suitable for long-term (6-48 h in advance) solar radiation prediction [3, 14, 15]. Moreover, the calculation amount of space-time prediction based on NWP is related to the number of weather stations, and the NWP needs to deal with many types of environmental parameters [21]. If there is no additional feature extractor or data reduction function, the computational cost of NWP-based space-time prediction will be prohibitive. Only adopting the NWP model for solar radiation forecasting encounters accuracy and spatial- temporal resolutions problems [36]. Recently, more scholars have mainly studied the research in the direction of NWP, which is to use NWP as a pre-processing [3, 7, 15], and then use data processing methods to make more accurate predictions.

2) Satellite image or sky image. The prediction time interval of the satellite image is suitable for the delivery time of 2-6 h [3], and it is more commonly used for longer prediction range and coarser resolution. Sky images taken on the ground are usually used for very short-term predictions within 30 min [12, 14]. Image-based methods can improve the accuracy of solar radiation predictions, but greatly increase the complexity of computer calculations [13]. High- precision short-term predictions have extremely high demands on computers and require a large number of cloud image data sets.

3) Neural network. As the mainstream method, the neural network has been widely used in the field of renewable energy prediction [37] (such as wind speed prediction [38], solar radiation prediction [39]). The prediction accuracy of a single neural network model is limited. At present, more strategies of mixed models are used to improve the prediction accuracy of neural network model. By combining different algorithms, a suitable hybrid prediction model is obtained [40, 41]. This is the main research direction of scholars and the focus of this paper.

The main contributions and innovations of this paper are given as follows: In this study, the data set uses real-time solar radiation data with non-linear characteristics, without the need to collect a large amount of spatial modeling data required by the NWP model. This is more conducive to the establishment of cross-regional prediction models and data collection. Using neural network can achieve 1-3 h advanced prediction, filling the gap of the short-term prediction of the classic NWP method. In terms of computational cost, image-based methods need to quickly process a large number of images to achieve accurate short-term forecasting, which requires extremely high computing power of the computer. The research object of this method is point data with time series characteristics, which significantly reduces the amount of calculation. The best model proposed can complete 1 h advance prediction of solar radiation in about 10 min based on ordinary workstations. Splitting the data into four datasets is based on the four seasons of the year. Different solar radiation prediction models can be obtained for the seasonal climate characteristics.

In the past solar radiation prediction research, data preprocessing techniques, such as clustering, regression analysis and time series analysis models, are rarely studied. The lack of data preprocessing results in the inability to filter out key parameters. Especially for the NWP method, the lack of data preprocessing will lead to an excessive amount of environmental data and cause computing disasters. This method uses the ARIMA model to perform autocorrelation and partial correlation tests on the data to obtain the internal correlation of non-linear solar radiation data, determining the critical data of neural network calculation input and output, saving computing resources. Due to the time series and non-stationarity of solar radiation data, the EWT method is used to perform time-frequency analysis on the data. EWT belongs to signal decomposition. It has good locality in the frequency and spatial domains. It can classify and extract multiple frequency characteristics of solar radiation. Using neural networks to fit stable multi-frequency signal sequences reduces the calculation difficulty and effectively improves the prediction accuracy. Moreover, the accuracy of single neural network is limited. The function of the Adaboost algorithm is to adjust the weights of multiple single predictors and integrate them into a strong predictor. It can universally improve the prediction accuracy of single model.

2 EWT-ARIMA-NARX-Adaboost hybrid model

2.1 Framework of proposed model

Figure 1 gives the framework of the hybrid EWT-ARIMA-NARX-Adaboost model. The modelling process is described in detail as follows:

1) Four original solar radiation datasets from Changde, China are adopted to train and test forecasting models. Training part and testing part include 600 samples and 200 samples, respectively. Each dataset contains two months of solar radiation time series data.

2) The solar radiation time series data are decomposed into a series of sub-layers by the EWT method adaptively. The WT, the VMD and fast ensemble empirical mode decomposition (FEEMD) are used as comparison models to verify the performance of the EWT method. The EWT and WT decomposition methods are introduced in Section 2.2 and Section 2.3, respectively.

3) The ARIMA algorithm can found the autocorrelation of time series data, so the two input delay of NARX network can be chosen. It can guarantee the maximum utilization of data to improve the prediction accuracy of NARX network. The optimization process is described in Section 2.4 and Section 2.5.

4) The Adaboost adjusts weights by training NARX-based weak classifiers to improve the prediction accuracy of strong classifiers. The details are shown in Section 2.6.

5) The NARX neural networks are employed to calculate sub-series from the EWT method to forecast future solar radiation. The structure and principle of the NARX network are given in Section 2.4.

2.2 Ensemble wavelet transform

The EWT is a new multi-resolution time- frequency transform, which combines the EMD and the WT. The EWT algorithm has the characteristics of adaptive division on the signal spectrum and high time-frequency resolution. The basic principles of the EWT algorithm are given as follows [42]:

Step 1: Calculate the Fourier spectrum.

Step 2: The Fourier support is segmented into N continuous segments, and N empirical wavelets are adaptively generated according to the Fourier spectrum segmentation.

Figure 1 Framework of proposed hybrid model

Step 3: Construct a low-pass filter and N-1 boundary-based band-pass filters.

Step 4: According to wavelet analysis theory, perform inner product operation. Reconstruct the solar radiation sequence.

The EWT decomposed results of solar radiation series No. 1 are given in Figure 2.

2.3 NARX neural networks

The NARX network is a nonlinear autoregressive model, which is composed of static neurons and network output feedback [43]. The definition of the NARX network is given in Eq. (1) [44].

                          (1)

where x(n) is the input of the NRAX network, while y(n) is the output at time n; d_y is the output delay and d_x is the input delay. Namely, y(n+1) depends on d_x past input values and d_y past output values.

Figure 2 Decomposition results of series No. 1 by EWT method

The architecture of NARX neural network is equivalent to a BP network with input delay and a delay feedback connection unit from output to input. The NARX neural network has a long-term memory function, which is more suitable for the solar prediction time series prediction. The convergence performance is robust.

2.4 ARIMA method

The ARIMA method was first proposed by BOX and JENKINS in 1970, which is a widely used time series analysis method [45]. The basic principle of ARIMA is to use the difference method to smooth the original time series. By calculating the autocorrelation and partial autocorrelation functions of the time series, (p, d, q) of the ARIMA model is determined. In the ARIMA (p, d, q) model, Autoregressive model (AR) is the autoregressive model, and p is the autoregressive term. Moving average model (MA) is a moving average model, and q is the number of moving average terms. d is the number of differences that the sequence made during the stabilization of the original time series data. Then the validity of the model is tested. Finally, the future time series is analyzed and predicted. The future value of the signal can be defined as [46]:

                (2)

where φ_iy_t-i represents the autoregressive process; θ_je_t-i represents the moving average process; ε_t is the random error. It can be obtained in Eq. (2): when q=0, it is the AR model. While p=0, it is the MA model.

2.5 Optimization of ARIMA model

In this study, the ARIMA model is not built for data prediction purpose, but the optimization of the built NARX network. By analyzing the autocorrelation function and partial autocorrelation function of the sequence, the inner connection of time series data can be discovered. It shows the number of time series data correlating. This characteristic is suitable for selecting the two-input delay. Parameters p and q of the ARIMA model are determined by the tailing and truncating properties of the solar radiation time series data after autocorrelation and partial correlation analysis.

For example, solar radiation series No. 1 was calculated by auto-correlation function (ACF) and partial autocorrelation function (PACF), the ACF and the PACF results in Figure 3.

Figure 3 Solar radiation autocorrelation test (ACF) result (a) and solar radiation partial autocorrelation test (PACF) result (b) of series No. 1

As shown in Figure 3, the ACF result is tailing, and the PACF is 17-stage truncation. So, the two input delays of NARX neural networks are 17.

2.6 NARX neural networks improved by Adaboost algorithm

Adaboost algorithm is developed based on boosting algorithm proposed by FREUND and SCHAPIRE [47]. With the rise of machine learning, Adaboost algorithm can be combined with almost all artificial intelligence algorithms to improve prediction accuracy. Adaboost algorithm to optimize artificial intelligence algorithm is an iterative process. This process weights multiple weak classifiers in the same training set to form a strong classifier. The weight of each weak classifier is adjusted by the training error [48]. In this study, the NARX neural network acts as the weak classifier. The steps of the Adaboost algorithm to optimize the NARX neural network are given as follows [49]:

Step 1: Input training sample set A={(X_i, y_i)}, the number of iterations T, weak classifier C(X);

Step 2: Initialize training sample weights:

                                 (3)

where t is the current number of iterations, t=1;

Step 3: Train the weak classifier C_t(x) based on the NARX neural network using weighted sample data to get error coefficient e_t. Calculate weak classifier weights d_t:

                            (4)

Step 4: Update training sample weights:

               (5)

where Z_t is the normalization factor so that the probability distribution of the sample sums to 1.

Step 5: While the number of iterations t=T, outputting the final strong classifier F(x). Otherwise, repeating Step 3 and Step 4.

                           (6)

3 Solar radiation forecasting computation

3.1 Original solar radiation series

To verify the prediction effectiveness of solar radiation forecasting models, four sets of solar radiation time series data are selected for comparison experiments. The historical solar radiation data are obtained from Changde (29°N 111°E) weather station in Hunan, China. Before making predictions on the datasets, the points where the solar radiation value is zero (in the night) have already been removed. The four datasets, time series No. 1-No. 4, are divided by various seasons of 2005. The solar radiation time series data are sampled one point per hour and each series lasts for 60 d. The data are predicted in 1-step (1 h), 3-step (3 h), and 5-step (5 h) ahead. Each dataset contains 800 samples and is divided into a training set and a testing set. The training set includes 600 samples, and the testing set contains the rest 200 samples. In Figures A1-A4 in Appendix section, the four datasets of the original solar radiation time series are demonstrated briefly.

3.2 Error criteria for proposed models

To assess forecasting accuracy of the comparison models, the MAE, the MAPE and the R index are adopted in the study. The equations of these indexes are denoted as follows:

                (7)

         (8)

         (9)

where X(t) is the solar radiation series;is the forecasted values; N is the number of the sample in the X(t).

3.3 Solar radiation forecasting experiments (case 1)

3.3.1 Solar radiation forecasting results

In this section, eight models are compared with the EWT-ARIMA-NARX-Adaboost model to evaluate the performance. The forecasting results of all models in different steps (1, 3, 5) are recorded respectively. Figure 4 shows the solar radiation forecasting results of series No. 1 for 1-step (1 h), 3-step (3 h), 5-step (5 h). Figure 5 shows the solar radiation forecasting results of series No. 2, No. 3 and No. 4 for 1-step (1 h). The forecasting errors of each model are evaluated by three indexes, the MAE, the MAPE and the R, as shown in Table 1.

Figure 4 Results of 1-step (a), 3-step (b), 5-step (c) ahead prediction of solar radiation series No. 1

The best prediction performance of each series is marked in bold. Figure 6 shows the MAE indexes of nine forecasting models in multi-step forecasting.

3.3.2 Error estimated analysis

From the whole trend of forecasting results, it can be summarized that:

1) It can be found from Figures 4 and 6 that with the prediction steps increasing, the MAE, the MAPE, and the R values of the prediction model decrease. It is because the prediction difficulty increases when the prediction time range increases. Generally, models with lower prediction accuracy in the 1 step correspond to lower errors in the 3 and 5 steps. However, in the experiment, the multi-step prediction error of VMD-ARIMA-NARX model increases significantly, indicating that VMD decomposition is not suitable for multi-step ahead prediction. This is because of the limits of VMD decomposition in boundary effects and abrupt signals. Multi-step ahead prediction may miss information of some intermediate key points; however, VMD decomposition cannot adapt to this problem. Changde in Hunan Province, from which the data are obtained, is subtropical monsoon climate. It has variable weathers in spring and summer, while relatively stable weather in autumn and winter, like continuous sunny days or consecutive rainy days. Rainy days significantly reduce solar radiation, so the prediction accuracy of the autumn and winter datasets is better than that of the spring and summer datasets.

Figure 5 Results of 1-step ahead prediction of solar radiation series No. 2 (a), series No. 3 (b), series No. 4 (c)

2) Table 1 demonstrates that all the hybrid models have lower estimated errors than the single NARX model in multi-step forecasting experiments. It shows that the integration of these optimizing methods with NARX neural networks are effective. Moreover, the more complex the model, the higher the prediction accuracy.

3) As shown in Table 1, the best results (the MAE is 2.6542, the RMSE is 0.0919, the R is 99.98%) appear in the one-step ahead prediction by the WT-ARIMA-NARX-Adaboost model for data series No. 3. However, the proposed model EWT- ARIMA-NARX-Adaboost performed best in the data sets of the other three seasons and the 1-step and 3-step errors are all satisfying. In addition, it is worth noting that when the forecasting step is up to 5, the R indexes of the proposed model still remained above 0.99 in four datasets. Besides, the WT algorithm has a larger error improvement in the 3-step and 5-step lead prediction, due to its multiple resolutions resulting from the scalability of the scale window. However, in the multi-step prediction, it cannot select the wavelet base adaptively for the lack of EWT decomposition.

4) In the one-step ahead forecasting simulation, the EWT-ARIMA-NARX-Adaboost model presents high forecasting accuracy in both four sets of solar radiation series. The EWT-ARIMA-NARX model, EWT-ARIMA-NARX-Adaboost model,WT-ARIMA-NARX model and WT-ARIMA- NARX-Adaboost model have similar excellent and robust performance for all the datasets. In the error index of series No. 2, the R indexes of the four models are 99.97%, 99.97%, 99.98%, 99.84%, respectively. It shows that the four models have good performance and robust in 1-step ahead forecasting, and are suitable for different solar radiation datasets.

Table 1 Prediction errors indexes of solar radiation (case 1)

Figure 6 MAE indexes of nine forecasting models for multistep forecasting

5) In 3-step ahead forecasting simulation, the EWT-ARIMA-NARX-Adaboost model shows the best forecasting performance with R index values of 99.93%, 99.85%, 99.95% and 99.97% in four series, respectively. Besides, the errors of the other forecasting models increase to varying degrees compared with the one-step ahead forecasting.

6) In 5-step ahead forecasting simulation, the EWT-ARIMA-NARX model still outperforms the other eight models. But its error has inevitably increased as the expansion of the prediction range to 5 h.

3.3.3 Comparison and analysis of percent changes in accuracy indexes

In this section, the improvement effects of the four decomposition methods (EWT, VMD, FEEMD, and WT) are compared. The improvement effects of the Adaboost algorithm and the ARIMA algorithm in promoting prediction accuracy are analyzed and compared. To compare the optimization performance of the above models, the promoting percentage of estimated error is used, which is defined in Eq. (21):

              (10)

where MAE₁ is MAE of the VMD-ARIMA-NARX model, and MAE₂ is the MAE of the EWT- ARIMA-NARX. The MAE promoted percentages of developed models are presented in Table 2 and Figure 7.

As given in Figure 7 and Table 2, it can be found that:

1) From results of No. 1 comparison models in 1-step ahead forecasting, the EWT-ARIMA- NARX has the highest accuracy in three solar radiation datasets. In the comparison of the VMD- ARIMA-NARX model, the reduction percentages of MAE are 73.10%, 83.13%, 85.07% and 78.16%, respectively. Besides, compared to the FEEMD- ARIMA-NARX model, the accuracy improvement is about 86%. In series No. 2, the performance of the WT-ARIMA-NARX model is almost the same as the EWT-ARIMA-NARX model. But in other series, the promotion of accuracy is all above 36%. The performance of four models can be concluded in the following sequence as: EWT-ARIMA-NARX, WT-ARIMA-NARX, VMD-ARIMA-NARX and FEEMD-ARIMA-NARX.

2) From results of No. 2 comparison models in three-step ahead forecasting, the EWT-ARIMA- NARX model is more accurate than the other three models, the average of promotion percentage of VMD, FEEMD and WT are 85.63%, 89.48% and 77.28%, respectively. Compared with the results of one-step forecasting, the EWT method improves the forecasting model more. The FEEMD method can adaptively decompose a non-stationary signal into several Eigen mode components according to its own characteristics. However, this method also has many obvious shortcomings, such as common under-envelope, end effect and mode, state aliasing. Moreover, EWT and FEEMD have the ability to adaptively decompose and process noise better and are more suitable for non-linear solar radiation prediction. Besides, the biggest limitation of the VMD method is the boundary effect and the inability to handle burst signals and the WT method lacks adaptive decomposition capability. So EWT is the best way to decompose now.

Table 2 Comparison of forecasting models by P_MAE index

3) From results of No. 3 comparison models in 5-step ahead forecasting, the EWT-ARIMA- NARX model is still robust. With the number of steps increasing, the accuracy promotion percentage of the EWT-ARIMA-NARX model compared to other models has dramatically decreased, mainly due to the increased MAE indexes of the model. The averages of promotion percentage of VMD, FEEMD and WT are 83.14%, 80.12% and 74.35%. Thus, the forecasting performance in this step can be concluded in the following sequence as: EWT- ARIMA-NARX, WT-ARIMA-NARX, FEEMD- ARIMA-NARX and VMD-ARIMA-NARX. The EWT decomposition method has such a high decomposition effect because it is a self-adaptive decomposition method. It is a combination of EMD and WT, so it has the adaptive decomposition characteristics of EMD and the AM-FM mode of WT.

4) According to results of No. 5, No. 6 and No. 7 comparison models, in 1-step ahead forecasting simulation, the Adaboost algorithm has a weak effect on the EWT-ARIMA-Adaboost model. In the multi-step ahead forecasting, the promotion effect is more obvious. The average promotion percentages of three-step forecasting are 18.32%, 24.71% and 15.99% for the EWT- ARIMA-NARX model, the ARIMA-NARX model and the WT-ARIMA-NARX model. The average promotion percentages of 5-step forecasting are 24.93%, 24.11% and 21.21%, respectively. Under the same model, the Adaboost algorithm improves the prediction accuracy of winter data the most. The Adaboost algorithm adjusts the weight of the weak classifier through the variation of the training error during the training of the weak classifier of the neural network. Finally, a strong classifier is formed according to the weights. Adaboost’s ability to improve data is universal and can be adapted to almost all machine learning. It can be found from the results that Adaboost has a very limited improvement on the model when the original model has high prediction accuracy. But for the case where the prediction accuracy is not high, Adaboost can improve the accuracy by about 20%.

Figure 7 Promoting percentages of comparison models by P_MAE index

5) The No. 8 comparison model shows the effect of the ARIMA method to enhance the NARX. The averages of promotion percentages are 17.14%, 11.63%, 13.52% in 1-step, 3-step and 5-step ahead, respectively. ARIMA performs time series analysis on solar radiation data to determine the internal correlation of the data through stationarity. Thus, the connection between the prediction point and the data is obtained to improve the accuracy of the subsequent NARX neural network.

3.4 Case 2

In this section, to verify the robustness of the proposed model, the historical solar radiation data from Beijing (39°N116°E) was selected. The climate characteristics of the Beijing area are obviously different from Changde.

Before making predictions on the datasets, the points with the solar radiation value of 0 (in the night) are removed. Two datasets are divided according to the spring (Figure A5 in Appendix), summer (Figure A6 in Appendix) of 2005. The ratio of training data to prediction data was changed. Each dataset contains 1200 samples, which is composed of a training set and a testing set. The data interval is 1 h. The training set includes 700 samples, and the testing set contains the rest 500 samples. The EWT-ARIMA-NARX, the WT- ARIMA-NARX, the ARIMA-NARX and the NARX are selected for comparison experiments. The results of one-step ahead prediction of the solar radiation series No. 5 and No. 6 are shown in Figure 8, Which include details. The prediction errors indexes of the solar radiation are shown in Table 3.

Analysis from Figure 8 and Table 3: Because the decomposition accuracy of the EWT is very high, the universal Adaboost has less lifting effect. EWT-ARIMA-NARX-Adaboost and EWT- ARIMA-NARX have a high degree of coincidence. As a whole, the error in spring and summer is lower than that in Changde. Due to the subtropical monsoon climate in Hunan, the rainfall in spring and summer is greater. Beijing has a continental monsoon climate with rainy summers, so the forecast errors in summer are even greater. Despite the vast differences in climate between the two places, the accuracy of solar radiation prediction of the proposed model is still very high, proving the robustness of EWT-ARIMA-NARX-Adaboost. The results predicted in multiple steps 3-5 are also excellent. The other models are still stable, and the WT decomposition performs the same as EWT in 1-step prediction, but in multi-step prediction, the error increases dramatically.

Figure 8 Results of 1-step ahead prediction of solar radiation series No. 5 (a) and solar radiation series No. 6 (b)

Table 3 Prediction errors indexes of solar radiation (case 2)

3.5 Operation time

In this section, the calculation cost of different models is given. All the simulations were run on the one workstation.The parameters of the workstation are given in Table 4. The operation times are given in Table 5.

Table 4 Parameters of workstation

Table 5 Operation time of proposed model

4 Conclusions

In this study, a new solar radiation forecasting hybrid model EWT-ARIMA-NARX-Adaboost is proposed. The proposed model uses the EWT model for signal decomposition, the ARIMA algorithm for NARX network parameter optimization and Adaboost algorithm for reinforcement learning. For further verification, solar radiation prediction experiments datasets are obtained from two regions with different climates. Experiments prove that the proposed model has robust and the best performance among all datasets in two regions. It can be concluded as follows:

1) Among the EWT, WT, VMD, FEEMD decomposing methods, the performance of the EWT decomposing method keeps the highest accuracy in all datasets for different steps. As the number of advance prediction steps increases, the error improvement of EWT decreases. EWT’s improvement of the NARX neural network reached an average of 92%.

2) Adaboost’s ability to improve the prediction engine is reflected in the model with poor accuracy. Because Adaboost’s reinforcement learning is generalized. The higher the original prediction accuracy of the model, the worse the Adaboost algorithm’s ability in prediction improvement. The improvement of EWT is minimal, but the improvement of other decomposition algorithm models has reached 20%.

3) The ARIMA algorithm can improve the prediction accuracy of the NARX network by 14.10% on average.

4) The EWT-ARIMA-NARX-Adaboost hybrid model shows the best performance in solar radiation forecasting among all models. It is robust and suiting for multi-step prediction. The proposed model performs well in all four seasons. The best result is in autumn (case 1) that MSE is 3.0872, RMSE is 4.19%, R is 99.96%. The worst result is in summer (case 1) that MSE is 11.1204, RMSE is 21.13%, R is 99.86%. It is mainly because of the rapid climate change in summer and the stable climate in autumn.

Besides, some factors affecting the change of solar radiation are not taken into consideration except for solar radiation time-series data. If temperature, humidity, wind speed, cloud cover, PM2.5 and other factors are included in the proposed model for calculation, the result may become better. Besides solar radiation forecasting, the proposed model can be employed in other forecasting fields, such as wind speed forecasting, hydrological forecasting, financial forecasting.

Appendix: Solar radiation original series

Figure A1 Spring original solar radiation series No. 1 in Changde

Figure A2 Summer original solar radiation series No. 2 in Changde

Figure A3 Autumn original solar radiation series No. 3 in Changde

Figure A4 Winter original solar radiation series No. 4 in Changde

Figure A5 Spring original solar radiation series No. 5 in Beijing

Figure A6 Summer original solar radiation series No. 6 in Beijing

Contributors

HUANG Jia-hao performed writing original draft, review, editing and experimental validation. LIU Hui performed proposing forecasting ideas, writing original draft and, review and experimental validation.

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References

[1] GUERMOUI M, MELGANI F, DANILO C. Multi-step ahead forecasting of daily global and direct solar radiation: A review and case study of Ghardaia region [J]. Journal of Cleaner Production, 2018, 201: 716-734. DOI: 10.1016/ j.jclepro.2018.08. 006.

[2] FATEMI S A, KUH A, FRIPP M. Parametric methods for probabilistic forecasting of solar irradiance [J]. Renewable Energy, 2018, 129: 666-676. DOI: 10. 1016/j.renene. 2018.06.022.

[3] DAVID M, LUIS M A, LAURET P. Comparison of intraday probabilistic forecasting of solar irradiance using only endogenous data [J]. International Journal of Forecasting, 2018, 34(3): 529-547. DOI: 10.1016/j.ijforecast.2018.02. 003.

[4] MOHANTY S, PATRA P K, MOHANTY A, VISWAVANDYA M, RAY P K. Artificial intelligence based forecasting & optimization of solar cell model [J]. Optik, 2019, 181: 842-852. DOI: 10.1016/j.ijleo.2018.12.176.

[5] ZHENG Wei-qin, PENG Xian-gang, LU Di, ZHANG Dan, LIU Yi, LIN Zhe-hao, LIN Li-xiang. Composite quantile regression extreme learning machine with feature selection for short-term wind speed forecasting: A new approach [J]. Energy Conversion and Management, 2017, 151: 737-752. DOI: 10.1016/j.enconman.2017.09.029.

[6] KUSHWAHA V, PINDORIYA N M. A SARIMA-RVFL hybrid model assisted by wavelet decomposition for very short-term solar PV power generation forecast [J]. Renewable Energy, 2019, 140: 124-139. DOI: 10.1016/ j.renene.2019.03.020.

[7] BAKKER K, WHAN K, KNAP W, SCHMEITS M. Comparison of statistical post-processing methods for probabilistic NWP forecasts of solar radiation [J]. Solar Energy, 2019, 191: 138-150. DOI: 10.1016/j.solener.2019. 08.044.

[8] AGUIAR L M, PEREIRA B, LAURET P, DIAZ F, DAVID M. Combining solar irradiance measurements, satellite-derived data and a numerical weather prediction model to improve intra-day solar forecasting [J]. Renewable Energy, 2016, 97: 599-610. DOI: 10.1016/j.renene.2016. 06.018.

[9] CERVONE G, CLEMENTE-HARDING L, ALESSANDRINI S, DELLE MONACHE L. Short-term photovoltaic power forecasting using artificial neural networks and an analog ensemble [J]. Renewable Energy, 2017, 108: 274-286. DOI: 10.1016/j.renene.2017.02.052.

[10] INAGE S I. Development of an advection model for solar forecasting based on ground data first report: Development and verification of a fundamental model [J]. Solar Energy, 2017, 153: 414-434.

[11] SUN Yu-chi, VENUGOPAL V, BRANDT A R. Short-term solar power forecast with deep learning: Exploring optimal input and output configuration [J]. Solar Energy, 2019, 188: 730-741. DOI: 10.1016/j.solener. 2017.05.019.

[12] YAGLI G M, YANG D Z, SRINIVASAN D. Automatic hourly solar forecasting using machine learning models [J]. Renewable and Sustainable Energy Reviews, 2019, 105: 487-498. DOI: 10.1016/j.rser.2019.02.006.

[13] LAN Hai, ZHANG Chi, HONG Ying-yi, HE Yin, WEN Shu-li. Day-ahead spatiotemporal solar irradiation forecasting using frequency-based hybrid principal component analysis and neural network [J]. Applied Energy, 2019, 247: 389-402. DOI: 10.1016/j.apenergy.2019.04.056.

[14] INAGE S I. Development of an advection model for solar forecasting based on ground data. Part II: Verification of the forecasting model over a wide geographical area [J]. Solar Energy, 2019, 180: 257-276. DOI: 10.1016/j.solener. 2018.12.068.

[15] AYET A, TANDEO P. Nowcasting solar irradiance using an analog method and geostationary satellite images [J]. Solar Energy, 2018, 164: 301-315. DOI: 10.1016/j.solener.2018.02. 068

[16] KAMADINATA J O, KEN T L, SUWA T. Sky image-based solar irradiance prediction methodologies using artificial neural networks [J]. Renewable Energy, 2019, 134: 837-845. DOI: 10.1016/j.renene.2018.11. 056

[17] JANG H S, BAE K Y, PARK H S, SUNG D K. Solar power prediction based on satellite images and support vector machine [J]. IEEE Transactions on Sustainable Energy, 2016, 7(3): 1255-1263. DOI: 10.1109/TSTE.2016. 2535466.

[18] YADAV A K, CHANDEL S S. Solar radiation prediction using artificial neural network techniques: A review [J]. Renewable and Sustainable Energy Reviews, 2014, 33: 772-781. DOI: 10.1016/j.rser.2013. 08.055.

[19] CITAKOGLU H. Comparison of artificial intelligence techniques via empirical equations for prediction of solar radiation [J]. Computers and Electronics in Agriculture, 2015, 118: 28-37. DOI: 10.1016/j. compag.2015.08.020.

[20] SHARIFI S S, REZAVERDINEJAD V, NOURANI V. Estimation of daily global solar radiation using wavelet regression, ANN, GEP and empirical models: A comparative study of selected temperature-based approaches [J]. Journal of Atmospheric and Solar-Terrestrial Physics, 2016, 149: 131-145. DOI: 10.1016/j.jastp.2016.10.008.

[21] ZHANG Y, BEAUDIN M, TAHERI R, ZAREIPOUR H, WOOD D. Day-ahead power output forecasting for small- scale solar photovoltaic electricity generators [J]. IEEE Transactions on Smart Grid, 2015, 6(5): 2253-2262. DOI: 10.1109/TSG.2015.2397003.

[22] ASRARI A, WU T X, RAMOS B. A hybrid algorithm for short-term solar power prediction: Sunshine state case study [J]. IEEE Transactions on Sustainable Energy, 2017, 8(2): 582-591. DOI: 10.1109/TSTE.2016. 2613962.

[23] QUEJ V H, ALMOROX J, ARNALDO J A, SAITO L. ANFIS, SVM and ANN soft-computing techniques to estimate daily global solar radiation in a warm sub-humid environment [J]. Journal of Atmospheric and Solar- Terrestrial Physics, 2017, 155: 62-70. DOI: 10.1016/ j.jastp.2017.02.002.

[24] BASER F, DEMIRHAN H. A fuzzy regression with support vector machine approach to the estimation of horizontal global solar radiation [J]. Energy, 2017, 123: 229-240. DOI: 10.1016/j.energy.2017.02. 008.

[25] ZOU Ling, WANG Lun-che, XIA Li, LIN Ai-wen, HU Bo, ZHU Hong-ji. Prediction and comparison of solar radiation using improved empirical models and adaptive neuro-fuzzy inference systems [J]. Renewable Energy, 2017, 106: 343-353. DOI: 10.1016/j.renene.2017.01. 042

[26] OZOEGWU C G. Artificial neural network forecast of monthly mean daily global solar radiation of selected locations based on time series and month number [J]. Journal of Cleaner Production, 2019, 216: 1-13. DOI: 10.1016/ j.jclepro.2019.01.096.

[27] LIU Hui, JIN Kai-rong, DUAN Zhu. Air PM_2.5 concentration multi-step forecasting using a new hybrid modeling method: Comparing cases for four cities in China [J]. Atmospheric Pollution Research, 2019, 10(5): 1588-1600. DOI: 10.1016/ j.apr.2019.05.007.

[28] SHANG Chuan-fu, WEI Peng-cheng. Enhanced support vector regression based forecast engine to predict solar power output [J]. Renewable Energy, 2018, 127: 269-283. DOI: 10.1016/j.renene.2018.04.067.

[29] MAJUMDER I, DASH P K, BISOI R. Variational mode decomposition based low rank robust kernel extreme learning machine for solar irradiation forecasting [J]. Energy Conversion and Management, 2018, 171: 787-806. DOI: 10.1016/j.enconman.2018. 06.021.

[30] MONJOLY S, ANDRE M, CALIF R, SOUBDHAN T. Hourly forecasting of global solar radiation based on multiscale decomposition methods: A hybrid approach [J]. Energy, 2017, 119: 288-298. DOI: 10.1016/j.energy.2016. 11.061.

[31] WANG Z, TIAN C, ZHU Q, HUANG M. Hourly solar radiation forecasting using a Volterra-least squares support vector machine model combined with signal decomposition [J]. Energies, 2018, 11(1): 68. DOI: 10.3390/en11010068.

[32] ESEYE A T, ZHANG Jian-hua, ZHENG De-hua. Short-term photovoltaic solar power forecasting using a hybrid wavelet-PSO-SVM model based on SCADA and meteorological information [J]. Renewable Energy, 2018, 118: 357-367. DOI: 10.1016/j.renene.2017.11.011.

[33] BENMOUIZA K, CHEKNANE A. Small-scale solar radiation forecasting using ARMA and nonlinear autoregressive neural network models [J]. Theoretical and Applied Climatology, 2016, 124(3, 4): 945-958. DOI: 10.1007/s00704-015-1469-z.

[34] SUN Shao-long, WANG Shou-yang, ZHANG Guo-wei, ZHENG Jia-li. A decomposition-clustering-ensemble learning approach for solar radiation forecasting [J]. Solar Energy, 2018, 163: 189-199. DOI: 10.1016/j.solener.2018. 02.006.

[35] YANG Da-zhi. On post-processing day-ahead NWP forecasts using Kalman filtering [J]. Solar Energy, 2019, 182: 179-181. DOI: 10.1016/j.solener.2019. 02.044.

[36] FENG C, CUI M J, HODGE B M, ZHANG J. A data-driven multi-model methodology with deep feature selection for short-term wind forecasting [J]. Applied Energy, 2017, 190: 1245-1257. DOI: 10.1016/j. apenergy.2017.01.043.

[37] ALFADDA A, RAHMAN S, PIPATTANASOMPORN M. Solar irradiance forecast using aerosols measurements: A data driven approach [J]. Solar Energy, 2018, 170: 924-939. DOI: 10.1016/j.solener.2018.05. 089.

[38] LIU Hui, MI Xi-wei, LI Yan-fei. Wind speed forecasting method based on deep learning strategy using empirical wavelet transform, long short term memory neural network and Elman neural network [J]. Energy Conversion and Management, 2018, 156: 498-514. DOI: 10.1016/ j.enconman.2017. 11.053.

[39] BENALI L, NOTTON G, FOUILLOY A, VOYANT C, DIZENE R. Solar radiation forecasting using artificial neural network and random forest methods: Application to normal beam, horizontal diffuse and global components [J]. Renewable Energy, 2019, 132: 871-884. DOI: 10.1016/ j.renene.2018.08.044.

[40] EL MGHOUCHI Y, CHHAM E, ZEMMOURI E M, EL BOUARDI A. Assessment of different combinations of meteorological parameters for predicting daily global solar radiation using artificial neural networks [J]. Building and Environment, 2019, 149: 607-622. DOI: 10.1016/j.buildenv. 2018. 12.055.

[41] SALISU S, MUSTAFA M W, MUSTAPHA M, MOHAMMED O O. Solar radiation forecasting in Nigeria based on hybrid PSO-ANFIS and WT-ANFIS approach [J]. International Journal of Electrical and Computer Engineering (IJECE), 2019, 9(5): 3916. DOI: 10.11591/ijece.v9i5. pp3916-3926.

[42] GILLES J. Empirical wavelet transform [J]. IEEE Transactions on Signal Processing, 2013, 61(16): 3999-4010. DOI: 10.1109/TSP.2013. 2265222.

[43] MARCJASZ G, UNIEJEWSKI B, WERON R. On the importance of the long-term seasonal component in day-ahead electricity price forecasting with NARX neural networks [J]. International Journal of Forecasting, 2019, 35(4): 1520-1532. DOI: 10.1016/j. ijforecast.2017.11.009.

[44] JAMIL M, ZEESHAN M. A comparative analysis of ANN and chaotic approach-based wind speed prediction in India [J]. Neural Computing and Applications, 2019, 31(10): 6807-6819. DOI: 10.1007/ s00521-018-3513-2.

[45] WANG Yu, WANG Chun-heng, SHI Cun-zhao, XIAO Bai-hua. Short-term cloud coverage prediction using the ARIMA time series model [J]. Remote Sensing Letters, 2018, 9(3): 274-283. DOI: 10.1080/2150704X.2017.1418992.

[46] ZHANG G P. Time series forecasting using a hybrid ARIMA and neural network model [J]. Neurocomputing, 2003, 50: 159-175. DOI: 10.1016/ S0925-2312(01)00702-0.

[47] FREUND Y, SCHAPIRE R E. A decision-theoretic generalization of on-line learning and an application to boosting [J]. Journal of Computer and System Sciences, 1997, 55(1): 119-139. DOI: 10.1006/ jcss.1997.1504.

[48] XING H J, LIU W T. Robust AdaBoost based ensemble of one-class support vector machines[J]. Information Fusion, 2020, 55: 45-58. DOI: 10.1016/ j.inffus.2019.08.002.

[49] LI Lin, HUANG Yi-xiang, TAO Jian-feng, LIU Cheng-liang, LI Kai. Featured temporal segmentation method and AdaBoost-BP detector for internal leakage evaluation of a hydraulic cylinder [J]. Measurement, 2018, 130: 279-289. DOI: 10.1016/j.measurement.2018.08.029.

(Edited by YANG Hua)

中文导读

基于NARX神经网络的短期多步太阳辐射预测的混合分解强化模型

摘要：由于全球能源枯竭，太阳能技术已在世界范围内广泛使用，而太阳能系统的输出功率受太阳辐射影响。准确的太阳辐射短期预测可以保证光伏电网的安全，提高太阳能系统的利用效率。在本研究中，提出了一种新的利用人工智能的分解促进模型，以实现太阳辐射多步预测。所提出的模型包括四个部分：信号分解(EWT)，神经网络(NARX)，强化学习(Adaboost)和ARIMA算法。基于湖南常德的三个太阳辐射数据集用于检验所提出模型的预测效果。为了验证多步预测模型的鲁棒性，本实验对比了9个模型，并对太阳辐射时间序列数据进行了1、3和5步的超前预测。验证了所提模型在所有模型中具有最佳的预测性能。

关键词：太阳辐射预测；多步超前预测；智能混合模型；信号分解

Foundation item: Project(2020TJ-Q06) supported by Hunan Provincial Science & Technology Talent Support, China; Project(KQ1707017) supported by the Changsha Science & Technology, China; Project(2019CX005) supported by the Innovation Driven Project of the Central South University, China

Received date: 2020-02-24; Accepted date: 2020-10-15

Corresponding author: LIU Hui, PhD, Professor; Tel: +86-13637487240; E-mail: csuliuhui@csu.edu.cn; ORCID: https://orcid.org/0000- 0001-6654-4965