A composite framework coupling multiple feature selection, compound prediction models and novel hybrid swarm optimizer-based synchronization optimization strategy for multi-step ahead short-term wind speed forecasting

https://doi.org/10.1016/j.enconman.2019.112461Get rights and content

Highlights

  • Adaptive aggregation for decomposed series is achieved by TVF-EMD and FE theory.

  • SSA is used to extract dominant and residuary ingredients of the aggregated series.

  • Mutation and hierarchy-based hybridization strategy for HHO and GWO is proposed.

  • Parameters optimization and FS are implemented by MHHOGWO synchronously.

  • Two predictors are employed for subseries forecasting considering inherent traits.

Abstract

Accurate wind speed prediction plays a vital role in power system in terms of rational dispatching and safe operation. For this purpose, a novel composite framework integrating time varying filter-based empirical mode decomposition (TVF-EMD), fuzzy entropy (FE) theory, singular spectrum analysis (SSA), phase space reconstruction (PSR), compound prediction models adopting kernel-based extreme learning machine (KELM) and convolutional long short-term memory network (ConvLSTM) as well as mutation and hierarchy-based hybrid optimization algorithm, is proposed in this paper. Among the supplementary strategies, TVF-EMD, FE and SSA are employed to achieve non-stationary raw series attenuation, aggregation for approximate IMFs as well as separation of dominant and residuary ingredients from the aggregated IMFs, respectively. Besides, parameters of PSR and KELM as well as wrapper method-based feature selection (FS) for input combination are synchronously optimized by the newly developed swarm optimizer integrating Harris hawks optimization (HHO) and grey wolf optimizer (GWO) with mutation operator and hierarchy strategy. Meanwhile, such hybrid structure is adopted to predict the preprocessed high-frequency components, while the remaining component is predicted by ConvLSTM cells-based deep learning network. Subsequently, the ultimate forecasting results of the raw wind speed are calculated by superimposing the predicted values of all components. Four datasets collected from various sites with two different time intervals and nine relevant contrastive models are carried out to evaluate the proposed approach, where the corresponding results demonstrate that: (1) data preprocessing strategy applying TVF-EMD and FE theory can significantly reduce the time consumption of the entire model without decreasing forecasting performance; (2) SSA-based dominant ingredients extraction can further improve the forecasting capability of combined model; (3) the proposed MHHOGWO can synchronously accomplish parameters optimization and FS effectively, thus improving the forecasting effectiveness of the entire model significantly; (4) the proposed compound prediction models based on KELM and ConvLSTM can exert the capabilities of each model adequately as well as ulteriorly reducing computational requirements.

Introduction

To ameliorate the conditions of environmental pollution caused by fossil resources and the corresponding limited storage, wind energy has been received wide attention and rapid development as one of the most reliable and efficient renewable energy. Following the statistics reported by world wind energy association (WWEA) in February 2019, global installed wind capability by the end of 2018 achieved 597 Gigawatt, of which the total installed wind power capacity accomplished in China firstly exceeded 200 Gigawatt [1]. However, some potential problems will arise as the installed wind turbines capacity increases, such as more unreliable power system caused by integrating a series of wind energy resources containing the inherent natures of intermittent, stochastic and fluctuation. Consequently, the stability and economic operation of power system will meet unprecedented challenges. Therefore, it is necessary to construct an accurate short-term wind speed forecasting framework for both facilitating power system scheduling and economical operation of wind farms [2], [3].

Over the past decade, wind speed forecasting considered as time series prediction problem has been widely investigated, where the forecasting approaches can be roughly divided into four categories [4]: (1) physical models, (2) conventional statistical models, (3) spatial correlation models and (4) artificial intelligence (AI) models. Among them, wind speed prediction implemented by physical models usually take into account many meteorological information, such as ambient humidity, atmospheric pressure, temperature, wind speed and direction, etc. [5], which can also be contributed to being auxiliary inputs for other prediction methods. However, drawbacks of such models can be summarized as: they are not suitable for short-term forecasting as well as requiring huge computation resources and time. The conventional statistical models including autoregressive (AR) [6], auto regressive moving average (ARMA) [7], auto regressive integrated moving average (ARIMA) [8], autoregressive fractionally integrated moving average (ARFIMA) [9], generalized autoregressive conditional heteroscedasticity (GARCH) [10] and so on can achieve wind speed forecasting effectively by mining implicit information of historical data adequately. Nevertheless, the capabilities of such models will be significantly restricted by nonlinearity and non-stationarity within wind speed data. Considering that forecasting results would be affected by spatial relationship of various sites, various spatial correlation models have been investigated accordingly [11], [12], with which potential wind energy of the sites without wind measurements can be evaluated reliably [13]. In contrast, AI models including artificial neural networks (ANN) [14], least squares support vector machine (LSSVM) [15], extreme learning machine (ELM) [16] and long short-term memory (LSTM) network [17], [18], have been rapidly developed for short-term wind speed forecasting due to the well-performed extensiveness and adaptability to various nonlinear and non-stationary data. The previous references demonstrated that all of the mentioned AI models can perform admirable effectiveness on short-term wind speed prediction, while the network structures of ANNs are difficult to be determined appropriately as well as the increasing computation cost of SVM with the growing of data scale significantly. By contrast, ELM possessing remarkable computation speed and fewer parameters to be set has been widely implemented for wind speed forecasting [16], [19], while the forecasting results possess strong randomness due to the randomly generated weights and bias within ELM. To the end, a modified ELM combining regularization coefficient and kernel functions is proposed by Huang et al. [20], of which two improved strategies are employed to enhance the solution phase and replace hidden layer in ELM, respectively. Fu et al. [21], [22] developed two compound wind speed forecasting models integrating KELM and synchronous optimization strategy applying newly proposed swarm-based optimizer, where the results illustrated that competitive performance can be obtained by KELM-based combined model. Compared with the above machine learning methods, deep learning networks possessing excellent performance on nonlinear series have been widely regarded recently. Liu et al. [23], [24] constructed two various composite deep learning models based on LSTM for multi-step short-term wind speed forecasting, where the satisfactory results could be obtained by LSTM-based hybrid structure. In addition, to improve the data processing capability of the normal LSTM, Shi et al. [25] investigated a novel structure of LSTM for precipitation nowcasting, where convolutional structures are appended in LSTM for both input-to-state and state-to-state transitions, thus achieving superior forecasting results to LSTM.

To our knowledge, the difficulty in forecasting for wind speed series is attributed to the nonlinearity and non-stationarity of the raw series accurately. Recently, feature selection (FS) techniques classified into two categories, i.e., filter and wrapper methods have been developed to improve the forecasting performance and efficiency [26], [27]. The filter methods including singular spectrum analysis (SSA) [24], wavelet transform (WT) [28], empirical mode decomposition (EMD) [29] as well as the corresponding the modified version, such as ensemble empirical mode decomposition (EEMD) [30], complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) [31] and time varying filter based EMD (TVF-EMD) [19], can directly weaken the prediction difficulty by decomposing the raw non-stationary series into several subseries with various frequency-scales [32]. Among the aforementioned decomposition methods, EMD is one of the data preprocessing approaches possessing adaptive capability for nonlinear series compared with WT, while the existing drawbacks namely end effect and mode mixing will restrict the corresponding decomposition efficiency and effectiveness to some extent. To this end, EEMD and CEEMDAN are developed in sequence, of which the latter one solves the mode mixing problem while achieving better reconstruction than EEMD. Nevertheless, parameters of EEMD and CEEMDAN that affect the decomposition effectiveness are difficult to determine, which may result in unsatisfactory prediction performance. Compared with above EMD-based decomposition methods, mode mixing problem can be effectively worked out by TVF-EMD applying time varying filter, which can contribute to dealing with the mode mixing as well as implementing robustness against noise interference [19]. However, the computation cost of the filter methods-based models will be increased significantly due to the increased number of the components to be predicted. To balance the forecasting efficiency and effectiveness effectively, entropies developed to measure the chaotic degree of the series have been investigated to aggregate the decomposed subseries, of which sample entropy (SE) is one of the most investigated one [14], [33]. Nevertheless, the measuring capability of SE will be restricted by ambiguous boundaries of various series, which may result in inapposite aggregation. Hence, an improved entropy based on SE namely fuzzy entropy (FE) is proposed by Chen et al. [34] for better measuring complexity and irregularity of series, which will be employed in this study for effective subseries aggregation. On the other hand, considering that irrelevant features may be contained in the constructed input matrix, wrapper methods are integrated with some advanced predictors to implement the extraction of effective features [16], [35], of which various binary-based swarm intelligence algorithms have been developed to handle such issue effectively [36], [37].

Generally, the forecasting effectiveness of the aforementioned AI-based prediction models is significantly affected by the corresponding inherent structure and parameters. For this purpose, various swarm intelligence algorithms have been rapidly developed for various optimization requirements over the past few decades, such as particle swarm optimization (PSO) [38], sine cosine algorithm (SCA) [39], [40], grey wolf optimizer (GWO) [41], Harris hawks optimization (HHO) [42] and so on. Among the optimizers, a unique leadership mechanism following the pack hierarchy for organizing the various roles in the wolves pack is proposed in GWO creatively, which achieves excellent performance on different benchmark functions. In addition, three best solutions are preserved in GWO, which can contribute to better performance than the optimizers that save the best solution for each agent as well as merely obtaining the global best solution so far by all individuals. For the newly developed HHO, there exist four chasing patterns based on the dynamic nature of scenarios and escaping patterns of the prey, where the corresponding investigation have illustrated that the proposed novel nature-inspired optimization technique can achieve better global optimization. Additionally, numerous supplementary strategies including mutation operation and hybridization of two or more developed algorithms have been drawn extensive attention. For instance, Pehlivanoglu [43] introduced a new mutation application strategy based on ideal of population variety into PSO, with which the efficiency and speed of PSO can be enhanced by the mutation operator. Besides, hybridization of two or more developed algorithms have been investigated in [44], [45], where SCA is integrated with PSO and GWO with two various composite strategies, i.e., hierarchy- and updating approach-based, respectively. Inspired by the previous investigations, an innovative algorithm compositing GWO and HHO on the basis of mutation operation and hierarchical strategy namely MHHOGWO is proposed in this study, which will be employed to achieve the parameters optimization and aforementioned wrapper methods-based FS synchronously.

Summarily, to achieve accurate multi-step short-term wind speed forecasting, a novel composite framework combining multiple FS, compound prediction models adopting KELM and ConvLSTM as well as synchronous optimization strategy based on the proposed MHHOGWO is proposed in this study. Among the FS strategies, TVF-EMD is adopted to decompose the raw wind speed into a set of intrinsic mode functions (IMFs), after which the aggregation for all the IMFs is accomplished according to the FE values of each IMF. Meanwhile, SSA is employed to further separate the dominant and residuary ingredients from the aggregated IMFs, where all of residuary ingredients are integrated into an additional component. Subsequently, synchronous optimization strategy-based hybrid prediction model and ConvLSTM cells-based model are implemented to forecast the high-frequency components and low-frequency one, respectively. Furthermore, the ultimate forecasting results of various prediction horizons are deduced by linear summation of the predicted results of all components. What’s more, four datasets collected from different sites with 10 min and 1 h intervals and nine relevant prediction models are employed to testify the effectiveness and superiority of the proposed approach. In conclusion, the main contributions of this study can be expressed as follows: (a) the FE theory-based aggregation strategy integrated with TVF-EMD can significantly decrease the computation cost of the whole model without descending the forecasting performance; (b) SSA-based separation of dominant and residuary ingredients as well as reconstruction of all residuary ones can contribute to further enhancing the capability of the compound model; (c) synchronous optimization strategy accomplishing parameters optimization and FS can be implemented by the proposed MHHOGWO algorithm effectively, with which the satisfactory prediction performance for high-frequency components can be obtained; (d) the proposed composite prediction approaches containing KELM and ConvLSTM in the light of the frequency-scale of each component can exert the advantage of each model adequately, which can contribute to achieving accurate predictions while diminishing optimization consumption.

The remainder of this paper is organized as follows: Section 2 presents the base knowledge of TVF-EMD, FE, SSA, PSR, KELM and ConvLSTM. Section 3 minutely introduces the proposed auxiliary modules including aggregation for the IMFs decomposed by TVF-EMD applying FE theory, SSA-based dominant ingredients extraction, the proposed hybrid optimization algorithm and the composite prediction strategy. Section 4 demonstrates the main procedures of the proposed composite framework. Section 5 describes the effectiveness and superiority of the proposed model with the detailed experimental results and analyses in various levels. The conclusions are summarized in Section 6.

Section snippets

Time varying filter based empirical mode decomposition

Empirical mode decomposition (EMD) decomposing the nonlinear and non-stationary series into several intrinsic mode functions (IMFs) with various frequencies adaptively has been frequently adopted technique for time-frequency analysis [46]. Nevertheless, drawbacks of separation and intermittence contributing to infirm performance of separating the similar frequency components as well as being susceptible to noise result in to mode mixing. To this end, an improved EMD based on time varying filter

Aggregation for subseries decomposed by TVF-EMD based on fuzzy entropy

Following our previous work [51], forecasting methods combining decomposition techniques can achieve significant improvement in terms of various evaluation indicators compared with single models. However, computation complexity and time consumption of such combined models increase observably as the number of decomposed series increases. To strike a balance between prediction accuracy and time consumption, aggregation strategy based on FE is proposed to recombine the initially decomposed IMFs,

Multi-step wind speed forecasting model based on TVF-EMD, FE, SSA, PSR, KELM, ConvLSTM and MHHOGWO

In this section, the major procedures of the proposed composite multi-step wind speed forecasting framework combining TVF-EMD, FE, SSA, PSR, KELM, ConvLSTM and simultaneous realization of parameters optimization and FS adopting the proposed MHHOGWO algorithm are illustrated as follows:

  • Step 1: Decompose the collected wind speed series into a set of IMFs {mi | i = 1, …, K} adopting TVF-EMD with preset parameters n and ξ.

  • Step 2: Calculate FE values for all IMFs and achieve the corresponding

Data collection

Considering various demand of power system managers bearing on the intervals of wind speed series, two different time horizons (10 min and 1 h) wind speed data are selected for further investigation. Besides, to verify the effectiveness of the proposed method performing on wind speed datasets from various regions, two datasets containing 1008 samples with 10 min interval are collected from Sotavento Galicia (SG) and Beresford (BF) respectively, while the 1 h interval wind speed series

Comparison of the proposed composite framework with relevant literature

In this section, the comparison of the proposed composite framework with relevant literature will be discussed. To begin with, compared with relevant decomposition technique-based combined models [29], [30], [31], [51], TVF-EMD possessing superior decomposition efficiency and effectiveness as well as robustness for parameters is employed to preliminarily weaken the non-stationarity of the original data. However, such decomposition-based models generally possess a large amount of computation,

Conclusions

To construct an accurate multi-step short-term wind speed forecasting model, a novel composite framework combining TVF-EMD, FE, SSA, PSR, KELM, ConvLSTM and the proposed MHHOGWO-based simultaneous realization of parameters optimization and FS is developed in this paper. To begin with, the collected wind speed time series is decomposed into several IMFs applying TVF-EMD, after which the aggregation for the decomposed subseries is effectively implemented with FE theory. Then SSA is employed to

CRediT authorship contribution statement

Wenlong Fu: Funding acquisition, Project administration, Writing - review & editing. Kai Wang: Writing - original draft, Visualization, Validation, Writing - review & editing. Jiawen Tan: Methodology, Resources. Kai Zhang: Software.

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

This work described in this paper is supported by the National Natural Science Foundation of China (NSFC) (51741907), The Open Fund of Hubei Provincial Key Laboratory for Operation and Control of Cascaded Hydropower Station (2017KJX06), Hubei Provincial Major Project for Technical Innovation (2017AAA132).

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