Application of functional deep belief network for estimating daily global solar radiation: A case study in China
Introduction
Due to the rising consciousness of fossil fuel substitution and environment protection, it is of more necessity to develop and promote renewable energy sources. Among those, solar energy is a significant resource and its exploration development grows rapidly, as it is abundant, stable and widely distributed [1,2]. For the sake of urban planning, photovoltaic array sizing and solar thermal system designing [3,4], a proper knowledge of daily global solar radiation is required at various regions [[5], [6], [7]]. However, daily solar radiation data are usually missing and even unavailable at many meteorological stations, due to complex equipment and high maintenance cost of measurements [8,9]. Therefore, numerous research focusing on solar radiation estimation has been carried out recently.
Three major methods are commonly applied in estimating daily global solar radiation, i.e. satellite-derived, stochastic and relationship methods [10]. Satellite-derived method can analyze earth-atmospheric reflectivity of irradiation [11], gather daily radiation values accurately [12], and estimate solar radiation within a large range of regions [13,14]. Nevertheless, equipment cost of satellite is also quite high, which is unacceptable at some meteorological stations. In stochastic algorithms, daily global solar radiation data are generated based on the mean values of historical weather observations [15]. Apparently, the method is infeasible if a station possesses no recent historical solar radiation records. Relationship methods are aimed to establish relations between solar radiation and other meteorological elements [16]. In the methods, empirical equations or soft-computing models are commonly utilized. Those methods have been most broadly studied as they can easily achieve high estimation precision with correct weather inputs. Besides, another advantage is that the historical solar radiation data involved for training those models are sometimes not needed as model inputs at the forecasting phase.
Relationship models that apply empirical equations are also named empirical models. They use dissimilar weather elements, e.g. temperature, sunshine duration, cloud cover, to form different empirical models [17]. Temperature-based (TB) models are the most commonly-used ones, as ambient temperature records are more accessible than any other meteorological data [18]. The difference between the daily maximum and minimum temperature values is usually considered in TB models. Because the temperature difference is able to indicate the fluctuation of daily global solar radiation [19,20]. In Ref. [21], the new TB model also involves daily mean temperature and demonstrates great estimation performance. Similarly, sunshine duration is an important factor that influences the level of radiation. Hence, sunshine-duration-based (SDB) models are proposed to analyze the factor [[22], [23], [24]]. It remains a problem that sunshine duration data are unavailable at some stations. In this case, cloud-based models can be adopted instead of SDB models [25,26], as cloud cover is able to be calculated according to daily sunshine duration. However, sometimes cloud-based models are not appropriate in regions with heavy haze due to the poor air condition [27]. Moreover, day-of-the-year-based (DYB) model is another kind of empirical model, also called independent model [28]. It holds a concise formula without using meteorological inputs [[29], [30], [31], [32]], whereas its precision is usually worse than TB and SDB models.
In contrary to empirical models, soft-computing methods utilize historical datasets to train a machine learning model, where the relations between solar radiation and meteorological elements can be modeled. They are able to merge various weather inputs efficiently and adapt to different climatic regions, receiving more attention from researchers than conventional empirical equations. In Refs. [[33], [34], [35]], artificial neural network (ANN) has been validated for estimating and predicting solar radiation. It possesses a great potential of self-learning, while often suffering from local optimum problems. Support vector regression (SVR) and adaptive neuro-fuzzy inference system (ANFIS) are two machine learning models suitable for high-dimensional inputs, which are frequently applied and studied in the field of solar radiation estimation [36,37]. Nevertheless, they can hardly deal with big datasets. Besides, as parameters in Gaussian process regression (GPR) and extreme learning machine (ELM) can be optimized under adaptive searching approaches, hybrid models based on the two methods are proposed in Refs. [38,39]. Among those, GPR model is a method that is usually able to acquire promising results with less computational cost [40,41]. It is noted that their accuracy may decrease when a great deal of inputs raise the difficulty of optimization.
The above machine learning models have all been proven feasible and practicable in the field of solar radiation estimation. However, they share a common weakness that they often perform with low training efficiency on a large number of samples. For example, the computation complexity of kernel functions in SVR and GPR will rise sharply, causing it hardly to complete the training process. Hence, those models are normally site-dependent, which means that they are trained and applied at different sites individually. On the contrary, deep neural networks utilize mini-batch gradient decent training strategy, which is suitable for huge samples. Additionally, the estimation accuracy can be further improved under deep models, as they usually possess better nonlinear representation abilities than conventional machine learning models. Thus, deep-learning-based models haven been proposed and applied recently in the field of renewable energy assessment. In Ref. [42], long short-term memory (LSTM) network is proposed to forecast global solar radiation. Owing to the recurrent use of hidden layer units, LSTM network is suitable for processing series inputs. Comparatively, another common kind of deep models is built by stacking massive hidden layers. They can adapt to point inputs of multiple elements, which are established for solar radiation prediction and estimation [43,44]. However, a deep model with a great number of layers may also face gradient vanishing problems [45], leading to non-convergence issues. Motivated by this, a deep learning model named deep belief network (DBN) is introduced to estimate daily global solar radiation in this study. It contains a pre-training operation when stacking hidden layers, which alleviates the non-convergence problem [46]. A sole DBN model contains a great number of parameters and can be directly utilized at different stations. The knowledge of empirical equations is also merged in the proposed DBN using functional network (FN). As there are few researches of solar radiation estimation focusing on deep learning methods nowadays [43], the functional DBN is thus proposed and will be validated based on the case study in China. The main contributions of this study can be summarized as follows:
- (1)
Deep learning method is introduced to solar radiation estimation. Owing to its strong capabilities of nonlinear representation and big data analysis, it is avoidable to model solar radiation at different meteorological stations separately.
- (2)
The DBN model is utilized instead of ordinary deep neural network. Its parameters can be pre-trained under restricted Boltzmann machine (RBM), which reduces the training difficulty of deep networks.
- (3)
The knowledge from empirical equations is involved in the estimation model by means of FN. Thus, reliability of the proposed model is guaranteed and its training difficulty can be further decreased.
- (4)
A novel clustering method called embedding clustering (EC) is proposed to divide meteorological stations. It consists of auto-encoder (AE) and k-means. The method can overcome the weakness of conventional k-means that the clustering result is easily affected by the initial clusters.
The rest of this paper is organized as follows. The case study, along with training and testing datasets, is introduced in Section 2. The framework and algorithms of the utilized method are described in Section 3. In Section 4, results and discussions based on the case study are presented. The conclusion is drawn in Section 5.
Section snippets
Study area and datasets
A total of 30 meteorological stations in China that hold vast climatic differences are studied in this paper. Their geographical locations and annual average weather values are shown in Table 1. According to the positions, those stations cover wide ranges of latitudes from 18.04°N in Sanya to 46.14°N in Jiamusi, longitudes from 75.16°E in Kashgar to 130.05°E in Jiamusi and altitudes from 2.5 m in Tianjin to 4507.0 m in Nagqu, which are presented in Fig. 1. Their daily global solar radiation
Estimation framework for daily global solar radiation
From Fig. 2, solar radiation estimation is to build and train a model with inputs of meteorological elements and the output of daily global solar radiation. As there are commonly a small number of trainable parameters in empirical or machine learning methods, one model is suitable for merely one station. In order to avoid building estimation models separately for different stations, enhancing the convenience and efficiency of practical applications, deep learning models, i.e. functional DBNs,
Results and discussions
In order to validate the reliability and accuracy of the proposed methods, a case study including 30 meteorological stations in China is adopted. In this study, DBN model without functional neurons, the proposed functional DBN and functional DBN with EC method are established to estimate daily global solar radiation. Three machine learning models, namely SVR, GPR and ANFIS, are built for comparisons. As they demonstrate low efficiency when trained on a large number of samples, they are modeled
Conclusion
Daily global solar radiation estimation is an essential step for solar energy utilization. Various meteorological elements, e.g. sunshine duration, wind speed, temperature and humidity, can be beneficial to the improvement of estimation accuracy, where it remains unsolved on how to efficiently merge them into an estimation model. Empirical models and machine learning models are commonly used in this field, but very often they appear poor adaptability and must be re-calculated in order to be
Acknowledgments
The research is supported by National Natural Science Foundation of China (Program No. 51507052) and the Fundamental Research Funds for the Central Universities (Program No. 2018B15414). The authors would also like to extend the gratitude to the China Meteorological Administration.
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