Significant wave height forecasting via an extreme learning machine model integrated with improved complete ensemble empirical mode decomposition
Introduction
Rising carbon dioxide levels with a subsequent increase in global mean temperatures compounded by rapidly depleting non-renewable energy sources have pushed for advancements in environmental-friendly and renewable energy technologies. The technologies for hydro-electricity, solar and wind energy are well established and reasonably economical, yet the developments in ocean renewable energy have been lagging behind [1]. Australia, the ‘island-continent’ is surrounded by a vast ocean with enormous wave energy potential. The key advantage of Australia is that huge wave energy resources are within viable proximity to household and prospective industries [2] that can allow for the cost-effective transmission of electricity. In addition, the wave energy is found to have a higher degree of certainty and consistency in comparison to wind energy [2]. However, wave is a variable source of energy controlled by nature's chaotic behavior. Therefore, this intermittency component must carefully be studied through appropriate forecasting approaches in order to gauge the availability and reliability of wave energy for sustainable electricity generation.
One key ocean wave parameter that needs to be forecasted is the significant wave height (Hs). Since Hs describes the ocean wave conditions, very short-term Hs forecasts are imperative for electricity generation [3], oceanic engineering purposes, improvement of safety and efficiency in maritime activities [4] and coastal disaster risk management. The wave power level is directly associated with Hs, and it is the key parameter in wave energy generation [5]. Hence, scholars have developed a number of forecasting models using data-intelligent approaches in order to emulate Hs, yet these studies are still in their nascent stages. The algorithms that have been explored in prediction of ocean wave parameters includes classification and regression tree type C5 algorithm [6], M5’ tree models [7], artificial neural networks (ANN) [6], [8], [9], support vector machine (SVM) [8], [9], Adaptive-Network-Based Fuzzy Inference System (ANFIS) [9], [10]. In a review on computational intelligence in wave energy applications, Cuadra, Salcedo-Sanz [11] found that ANN was a widely used model with better performance in comparison to regression models. However, these are classical standalone models, which may not be able to sufficiently capture the non-linear dynamics of the stochastic ocean waves.
The natural stochastic nature of the ocean waves that induces non-stationarity and non-linearity within the time series is one of the most important challenges in coastal and maritime engineering applications [6] and forecasting. The non-stationarity features bring about non-normality, bimodality, asymmetric cycles and non-linearities embedded within the series. In order to handle non-stationarity features, the inputs for respective data-driven models need to be properly pre-processed [12], [13], [14], [15]. Therefore, a multi-resolution analysis (MRA) [16], [17] tool is utilized to unveil the embedded features overcoming the non-stationarity issue.
Conventionally, the Fourier transformation was used, yet it only performs transformation at frequency resolutions and loses the more important time stamp. The discrete wavelet transformation (DWT) which is an alternative MRA utility has been widely used in many forecasting applications [18], [19], [20], [21]. Similarly, few studies with discrete wavelet hybrid models have been applied in Hs forecasting whereby the widely used ANN has been hybridized with DWT called W-ANN [22], [23], [24], [25]. In another study, Özger [26] performed a study with wavelet fuzzy logic approach. The DWT, however, has a critical weakness called the decimation effect. During frequency resolution conversions of DWT, only half the wavelet coefficients are generated and the other half is recursively transformed at a coarser resolution leading to a loss of vital information [27]. As a result, a non-decimated wavelet tool called the maximum-overlap discrete wavelet transformation (MODWT) ideally overcomes the decimation issue [27], [28], [29], [30], [31]. Yet, MODWT has not been explored in Hs forecasting purposes. The other issue with wavelets (including DWT and MODWT) is that they require the defining of a well-suited mother wavelet a priori [32]. This is still an unresolved issue and generally requires a lengthy trial and error process [28]. On the other hand, the empirical mode decomposition (EMD) multiresolution utility developed by Huang et al., [33] offers self-adaptability by avoiding the need for any basis function and/or mother wavelets. EMD is completely data-adaptive that uses temporal local decomposition method in extracting the salient features. Then EMD isolates these significant features into sub-series that represents the physical structure of the time series [34]. Consequently, EMD based models have been adopted in forecasting Hs including EMD-Autoregressive (AR) model [4] and EMD-support vector regression (SVR) [35]. However, the performance of EMD is compromised by the inherent ‘mode mixing’ shortcoming. The ensemble-EMD (EEMD) solves this issue by addition of a Gaussian white noise to the original (undecomposed) time series and then extracts the embedded periodic and trend information [36]. However, the reconstruction of EEMD decomposed data is not completely noise-free as a different number of IMFs can be obtained [37]. Hence, to create a completely noise-free reconstruction of data, a complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) was proposed [37]. CEEMDAN requires a Gaussian white noise to be added sequentially at each decomposition stage, yet has limitations on parallel computing resulting in slower performance than EEMD [38]. The newer, improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) was developed in response to address the shortcomings of the predecessor EMD-based algorithms [38].
The ICEEMDAN has successfully been explored for multi-resolution signal processing, particularly in vibrational fault diagnosis [39], [40]. ICEEMDAN has also been successfully applied in the estimation of decay ratio in boiling water reactors [41] and to reconstruct spectral data for removing noise form near-infrared spectra signals [42]. Studies pertaining to modeling showed improved performance of ICEEMDAN integrated with particle swarm optimization (PSO) of SVR (ICEEMDAN-PSO-SVR) in the modeling of near-infrared non-invasive glucose detection [43]. In a recent study, Al-Musaylh et al., [44] applied ICEEMDAN-PSO-SVR in long-term electrical energy demand predictions. These studies found that ICEEMDAN hybridized models performed better in emulating the respective variables capturing the non-stationarity features well [43], [44]. To the best of the authors’ knowledge, the application of ICEEMDAN multi-resolution technique is yet to be explored in forecasting of Hs.
The aim of the paper is to address non-stationarity issues in Hs forecasting at a very short-time i.e., half-hourly forecast horizons using a non-decimated, self-adaptive, fast and computationally efficient data pre-processing utility (ICEEMDAN). Subsequently, the ICEEMDAN is integrated with a fast and efficient extreme learning algorithm (ELM) to develop the novel ICEEMDAN-ELM models in Hs forecasting. Two sites at the eastern coast of Australia that have great wave energy generation potential have been selected to validate the models. The ICEEMDAN-ELM is benchmarked against a comparative online sequential ELM (ICEEMDAN-OSELM) and random forest (ICEEMDAN-RF) and the respective standalone models. The application of ELM and their variants are very uncommon in Hs forecasting studies as only two studies have been noted that used ensemble-ELM [45] and grouping genetic algorithm-ELM [46]. Also, no such studies with random forest have been performed so far which is substantiated here.
Section snippets
Theoretical framework
The basic theory involved in the construction of the proposed collaborative ICEEMDAN-ELM model for Hs forecasting is presented in this section.
Study region and wave height dataset
In this paper, we have utilized the Hs data (in meters) obtained from the Environment and Science, Queensland Government, Coastal Data System, Queensland, Australia from January-2000 to March-2018 [62] for the two selected coastal regions, Gold Coast and Mooloolaba, as shown in Fig. 1. At respective sites, the Hs data is acquired at half-hourly intervals using Datawell Waverider wave-monitoring buoys.
To evaluate the versatility of the proposed ICEEMDAN-ELM model for Hs forecasting in
Results
The proposed ICEEMDAN-ELM is appraised in comparison with ICEEMDAN-OSELM, ICEEMDAN-RF, standalone ELM, standalone OSELM, and standalone RF models, using statistical metrics, diagnostic plots and error distributions (Eqs. (5), (6), (7), (8), (9), (10), (11), (12)) between the forecasted and observed Hs.
In Table 5, the preciseness of the ICEEMDAN-ELM is evaluated in relation to the respective models i.e., ICEEMDAN-OSELM, ICEEMDAN-RF, standalone ELM, OSELM and RF models where the results for each
Discussions: merits, limitation, and further scope
The empirical mode decomposition is the lesser-explored data decomposition techniques used in Hs forecasting studies. In this pilot study, an advanced version of EMD i.e., the ICEEMDAN [38] is explored. The half-hourly Hs data series were aptly decomposed via ICEEMDAN into respective IMFs and a residual component revealing the embedded features. The ICEEMDAN has proven to be a vital multi-resolution data pre-processing tool.
Integration of ICEEMDAN with the fast and efficient ELM [48] model, led
Conclusion
In this study, an ICEEMDAN-ELM model is developed using the Hs data for training purposes as the predictors for the model forecasting of future Hs at Gold Coast and Mooloolaba stations. The Hs data from January-2000 to March-2018 at 30-min intervals were used to decompose into IMFs and residuals through ICEEMDAN algorithm. The PACF of the corresponding IMFs and residuals were computed where the significant lags were inserted into the ELM model to develop the ICEEMDAN-ELM model in order to
Acknowledgements
The significant wave height data was acquired from Environment and Science, Queensland Government, Coastal Data System, Queensland, Australia and the authors are thankful for that. We also duly acknowledge that this research project has been sponsored by The University of Southern Queensland's Postgraduate Research Scholarship (2017–2019) awarded to both the authors, managed by the Office of Research and Graduate Studies Division. The authors are also grateful to both the reviewers in providing
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