A double decomposition-based modelling approach to forecast weekly solar radiation
Introduction
Under the Sustainable Development Goal 7 (SDG 7), the world is committed to increase electricity generations from renewable sources and to meet a country-driven target by the year 2030. Consequently, Australia is also committed to this global challenge, and the Australian energy market is changing with the key focus to increase the electricity generation via renewable sources. However, in ensuring affordability, reliability and modern energy facilities (SDG 7.1) from renewable sources, the world including Australia is falling short of meeting the targets [1]. With high economic pressures from businesses and industries, Australia has committed to developing the smart grid-smart city display project costing up to $AUD100 million, in association with the energy companies and firms [2]. Such initiatives require accurate short-term (such as weekly) monitoring and conjectures of solar radiation (Rdn) for integrated photovoltaic (PV) grid systems and concentrated solar power technologies to maintain an optimal generation mix for stable grid supply. Hence, for effective and optimized generation mix forecasting tools become essential to bring the supply on par with the demand in implementation of smart-grid systems.
The use of regression-based autoregressive models are the common forecasting technique on solar radiation forecasting, yet the autoregressive models are disadvantages as it does not consider the past disturbances in determining the current output. In addition, the empirical models have the advantage of simplicity; however, they lack generalizations [3]. Furthermore, the physical radiative transfer models do offer better generalization and accuracy, yet, such models are very complex and require a large amount of input data, which are not always available [3]. On the other hand, machine learning models have low computational complexity and are point-based that could be developed for specific sites, which complements the generation of renewable electricity that essentially are site-specific. Fundamentally, the machine learning algorithms are capable of ‘learning’ many of the entrenched features within the historical data in emulating future Rdn values, and could aptly be applied in smart grid technologies [4]. A solar irradiation data processing via estimator matrices (SIMS) was developed in Portugal [5]. Weather and Research Forecasting (WRF) model was integrated with Data Assimilation (DA) technique to forecast solar radiation in Singapore [6]. Yet, the stochastic nature of Rdn time series due to the natural variability of solar irradiance compounded by environmental factors (such as cloud cover), atmospheric conditions (such as particulate matter and dust), latitude and season makes the ‘learning’ more challenging. Hence, to increase the forecast precision of machine learning modelling approaches, data pre-processing via multi-resolution analysis (MRA) needs to be incorporated. To ameliorate this issue, a data-dependent demarcation technique is more suited in comparison to the conventional wavelet techniques [7] which is known as Empirical Mode Decomposition (EMD) pioneered by Huang, Shen [8]. The variants of EMD including, Ensemble EMD (EEMD) [9], complete ensemble EMD with adaptive noise (CEEMDAN) [10] and improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) [11] has been progressively developed to address the shortcomings of their respective predecessors. The EMD and its variants have been preferred due to their self-adaptability making it completely data-dependent in extracting salient predictive information without loss of underpinning features [7,12]. Further, the EMD based decomposition preserves the physical configurations of the temporal input data [13].
Despite such progressive evolution of the remarkable MRA tool, the EMD based decomposition techniques can only be applied to decompose a single input data series at a time [7,[9], [10], [11],14]. For instance, only the significant historical lags of weekly Rdn could be used to forecast the prospective weekly Rdn values, which a major issue with EMD, since as aforementioned, Rdn is contingent upon a number of key predictors. In such a multiple inputs case, a sequential decomposition needs to be adopted following Prasad, Deo [15], which though is a promising approach, yet, in sequential decomposition approach, some pertinent information may not be lucid since each EMD demarcation is carried out in isolation. To overcome this challenge and incorporate multiple predictor inputs with simultaneous decomposition an advanced and versatile version of EMD viz., multivariate empirical mode decomposition (MEMD) is being applied to resolve the entrenched sub-frequency components of respective inputs. The MEMD is a direct multichannel data analysis that performs concurrent time-frequency analysis to address non-linearity and non-stationarity of input signals [16]. In addition to performing an accurate investigation of composite and non-linear processes, the MEMD overcomes the mode alignment issues that are realized in the joint analysis of multidimensional data [17]. A few studies pertaining to MEMD has been detailed in literature with forecasting of the water content of soil [18], price of crude oil [19], evapotranspiration [20], and more recently standardized precipitation index [21]. So far only one study in the forecasting of solar radiation at monthly timescale has been noted [22]. These studies ascertain the suitability of MEMD as a multichannel MRA utility, yet the application of the algorithm in the short-term such as weekly Rdn forecasting has not been piloted so far.
Furthermore, this study also utilizes a robust feature optimization procedure via singular valued decomposition (SVD) [23]. The SVD is able to aptly decompose the input data series into a matrix whilst reducing its dimensionality [24]. Through this technique, the SVD conveniently extracts the characteristics more closely [25,26]. The successful studies of SVD include diagnostic analysis of meteorological fields [27], reversing engineered gene networks [28] and partitioning in the bi-plot analysis of multi-environment scenarios [29]. However, the SVD has not been applied for dimensionality reduction in Rdn forecasting studies in Australia. Additionally, the powerful random forest (RF) forecasting model which is a bootstrapped-aggregated regression tree approach has proven to have good forecasting accuracy in forecasting of energy-related variables including, wind energy [30], solar radiation [22,31], temperature variations [32] together with environmental variables like soil moisture [7,33] and standardized precipitation index [34]. However, RF has not been extensively studied for Rdn forecasting and thus has been adopted in this study. Moreover, to avoid the common issues identified by Quilty and Adamowski [35] in previous decomposition-based modelling approaches, this study partitions the data before advancing to the development of the MEMD-SVD-RF model for weekly Rdn forecasts.
This paper develops a novel hybrid model that addresses non-stationarity issues in multiple predictor inputs using self-adaptive approach whilst generating accurate forecasts of short-term, i.e., weekly solar radiation, which can have better potential of practical applications. To achieve this goal, the multichannel multiresolution analysis method, MEMD was utilized to concurrently transform the weekly time series of 8 meteorological predictor inputs into respective IMFs and residual components. Then the hybrid MEMD-SVD-RF model was developed and evaluated at three sites within sunshine-state, Queensland, Australia. Finally, the hybrid MEMD-SVD-RF model was benchmarked against multivariate adaptive regression splines (MARS) model (i.e., MEMD-SVD-MARS) and multiple linear regressions (MLR) (i.e., MEMD-SVD-MLR) equivalent models. The following section presents the theories of the machine learning algorithms, followed by MEMD decomposition technique, methods and data description, and the results. Then, the challenges and prospects of short-time to real-time Rdn forecasting using this novel MEMD-SVD-RF approach is presented and the paper is closed with concluding remarks.
Section snippets
Multivariate empirical mode decomposition (MEMD)
The MEMD technique is an advanced version of the conventional EMD. MEMD is a self-adaptive method capable of handling the hurdles of mode alignment and the mathematical structure of MEMD is defined as:
In Eq. (1) , and are the input variables, the kth IMF and residual respectively. The MEMD [16] demarcates the multiple inputs into IMFs using White Gaussian noise [11]. The mean can be computed as:
The term is called the envelop
Study locations
Australia has a very conducive environment for electricity production through solar radiation [54]. Being a rich solar radiation continent, in this paper, the study sites are located in Queensland (QLD) State, which receives a profusion of solar radiation with a small number of overcast days. Following SDG7, the QLD state government has warranted that by the year 2030, there would an increase in the energy generation mix by up to 50% from renewable sources [55]. Fig. 1 demonstrates these
Results
The double-decomposition MEMD-SVD-RF model is utilized to forecast Rdn at four highly rich solar radiation regions in Queensland, Australia. The performance of MEMD-SVD-RF accuracy is evaluated with respect to the benchmark models on the basis of R, RMSE, MAE, EWI, ENS, ELM, RMSPE, and MAPE.
The MEMD-SVD-RF model in forecasting Rdn for Sunshine Coast, produced the highest magnitudes of R and lowest RMSE and MAE values (R ≈ 0.977, RMSE ≈ 1.30 MJm−2, MAE ≈ 1.00 MJm−2) benchmarked with MEMD-SVD-MLR
Further discussion
The aptness of the MEMD-SVD-RF model (against MEMD-SVD-MARS, MEMD-SVD-MLR, standalone RF, MARS and MLR models) to predict weekly Rdn has been explored in this paper. The accuracy of MEMD-SVD-RF was significantly higher than the other benchmark counterpart models (Table 4, Table 5, Table 6, Table 7) for all locations illustrating that the MEMD-SVD-RF was a well-designed algorithm to extract pertinent features for weekly Rdn estimation. The precision of MEMD-SVD-RF model has revealed that the
Conclusions
A reliable machine learning model based on double decomposition approaches (i.e., MEMD and SVD) for Rdn solar radiation modelling is designed in this paper. The newly constructed MEMD-SVD-RF model concurrently splits the input predictors into suitable IMFs and residual components via MEMD and later incorporating decomposed features (i.e., IMFs) into the SVD approach for dimensionality reduction. Here, the demarcated datasets were based on the antecedent values (i.e., one week ahead) of eight
CRediT authorship contribution statement
Ramendra Prasad: Writing - original draft, Conceptualization, Methodology, Software. Mumtaz Ali: Visualization, Conceptualization, Writing - review & editing, Investigation. Yong Xiang: Writing - review & editing, Supervision. Huma Khan: Writing - review & editing.
Declaration of competing 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.
Acknowledgements
There are no conflicts of interest in this research article. The authors are thankful to Scientific Information for Landowners (SILO) to provide the relevant meteorological and solar radiation data. The authors are also indebted to the anonymous reviewers for their valuable feedback in improving the overall quality of the paper.
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