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A fuzzy series‐parallel preprocessing (FSPP) based hybrid model for wind forecasting

2021; Institution of Engineering and Technology; Volume: 16; Issue: 3 Linguagem: Inglês

10.1049/gtd2.12291

1751-8695

Mehrnaz Ahmadi, Mehdi Khashei,

Solar Radiation and Photovoltaics

IET Generation, Transmission & DistributionVolume 16, Issue 3 p. 430-452 ORIGINAL RESEARCH PAPEROpen Access A fuzzy series-parallel preprocessing (FSPP) based hybrid model for wind forecasting Mehrnaz Ahmadi, Mehrnaz Ahmadi Department of Industrial and Systems Engineering, Isfahan University of Technology (IUT), Isfahan, IranSearch for more papers by this authorMehdi Khashei, Corresponding Author Mehdi Khashei Khashei@cc.iut.ac.ir orcid.org/0000-0002-2607-2665 Department of Industrial and Systems Engineering, Isfahan University of Technology (IUT), Isfahan, Iran Correspondence Mehdi Khashei, Department of Industrial and Systems Engineering, Isfahan University of Technology (IUT), Isfahan 84156-83111, Iran. Email: Khashei@cc.iut.ac.irSearch for more papers by this author Mehrnaz Ahmadi, Mehrnaz Ahmadi Department of Industrial and Systems Engineering, Isfahan University of Technology (IUT), Isfahan, IranSearch for more papers by this authorMehdi Khashei, Corresponding Author Mehdi Khashei Khashei@cc.iut.ac.ir orcid.org/0000-0002-2607-2665 Department of Industrial and Systems Engineering, Isfahan University of Technology (IUT), Isfahan, Iran Correspondence Mehdi Khashei, Department of Industrial and Systems Engineering, Isfahan University of Technology (IUT), Isfahan 84156-83111, Iran. Email: Khashei@cc.iut.ac.irSearch for more papers by this author First published: 10 September 2021 https://doi.org/10.1049/gtd2.12291AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract Wind power is one of the most important renewable energy sources that is widely used in many developed and developing countries. However, it is generally stated in the literature that providing accurate forecasts for large-scale planning purposes is not a simple task, especially by single models. It is the main reason for this fact that why researchers in recent years have sought to propose hybrid models for increasing the accuracy of predictions. In general, choosing the appropriate type and the number of components, as well as the proper type of hybridization methodology, are the most effective factors in the performance of the developed hybrid models. Although in the literature, numerous attempts have been made in order to answer these questions, there is no general consensus on this matter. For this reason, the main idea of this paper is to concurrently combine different hybrid methodologies as well as different single models in order to benefit from the advantages of these models and methodologies, simultaneously. In this way, three well-known and widely used hybrid methodologies, including the preprocessing, the series, and the parallel methodologies, are combined together by incorporating the linear/nonlinear and certain/uncertain components. In addition, in the proposed model, a new process is proposed based on the complex/uncertain modelling to model the preprocessing phase residuals, which have been ignored in the modelling procedures. In this way, in the first stage of the proposed model, the data is preprocessed by the Kalman filter as a preprocessing approach in order to divide data into two groups of trend and residual patterns. The trend data provided in the previous step, with the original data, are simultaneously considered input data of an autoregressive integrated moving average as the certain linear model and a multilayer perceptron as the certain nonlinear model for certain linear and nonlinear modeling of patterns. This step is repeated for the residual data by the series hybridization of models in the previous stage by the fuzzy models for the uncertain linear and nonlinear modelIng of patterns. Finally, each component's weight is optimally calculated by the least square algorithm, and then the results are combined together in a parallel process. Empirical results of two benchmarks of wind domain indicate that the proposed method has averagely improved the performance of its component used separately, parallel-based hybrid models, and series-based hybrid models 46%, 22%, and 19%, respectively, for predicting wind power time series. 1 INTRODUCTION Wind energy is an appropriate alternative to fossil fuels, which are currently widely used in electricity generation due to reduced air pollution and environmental hazards. However, wind energy is highly dependent on climate change, which intermittently characterizes wind power and disturbs the dispatching system. For this reason, researchers have expanded single models into complex and efficient hybrid models for the economical use of this renewable energy source to increase the accuracy of wind power and speed. In general, wind power and speed forecasting methodologies are divided into two groups of single and hybrid models, that single model divided into three main subscripts. (1) physical methods (such as the Numerical Weather Prediction (NWP) and the Weather Research and Forecasting Model (WRFM)), (2) statistical methods (such as Time series models, Grey models, Quantile regression, Stochastic differential equations, and Markov regime-switching model), and (3) intelligent methods (such as Artificial Neural Networks, Fuzzy Sets and Systems, and Support Vector Machines). Cheng et al. [1] have introduced the numerical weather prediction (NWP) model for ultra short-term wind speed forecasting. In this study, wind speed and direction data sets are used to test the proposed model. Numerical results show that the designed model improves the mean absolute error by 30–40%. Bivona et al. [2] have provided a seasonal autoregressive integrated moving average (SARIMA) model for short-term wind speed forecasting. The proposed approach is applied to the time series recorded for 4 years in two sites of Sicily, a region of Italy. Numerical results display that the proposed model can obtain valuable results in terms of modeling and forecasting. Bessa et al. [3] have introduced a Quantile regression model, QR, for 6–48 h wind power forecasting. In this study, two datasets from NREL's Eastern Wind Integration and a real wind farm located in the United States Midwest region are used. Their results indicate that the proposed model can achieve more reliable results in wind power forecasting. Xydas et al. [4] have provided a stochastic differential equation model, KDE, for short-term probabilistic wind power forecasting. The forecasting model is applied to real wind power data sets. They claim that their predictions' accuracy improves by frequent updating of the predictions taking into value the last measured wind power. Carpinone et al. [5] have proposed a Markov regime-switching model for ultra-short-term wind power forecasting. The dataset utilized in the paper is obtained from data reported over 10 min measurements of wind power for 28 months. Numerical results show the effectiveness of the proposed method in predicting wind power data. Filik et al. [6] have introduced an artificial neural network, the MLP model, for ultra-short-term wind speed forecasting. In this study, three configurations are used, including (1) only the wind speed data, (2) both wind speed and temperature data, and (3) the wind speed, the weather temperature, and the weather pressure data. According to their results, the lowest RMSE and MAE values are obtained from the third structure. Dong et al. [7] have used Fuzzy Sets and Systems (FSS), Local linear fuzzy neural network (LLNF) model for short-term wind power forecasting. The numerical results from the two data sets demonstrate that the proposed hybrid model is a practical approach to predict wind power with high accuracy compared to another hybrid model. Hua et al. [8] have introduced a support vector machine, the NSVR model for ultra-short-term wind speed forecasting. In this study, a real-world sample set of wind speed in Heilongjiang Province is applied. The results show the effectiveness of the proposed technique. Although single models have many advantages, such as low computational cost, low complexity, low running time, easy implementation, hybrid models can generally achieve more accurate and reliable results. One of the most important reasons for the widely used hybrid methodologies is the advantages of single models and the reduction of their limitations simultaneously. Hybrid methods can be divided into four subscripts: (1) data preprocessing-based approaches, (2) parameter optimization-based approaches, (3) postprocessing-based approaches, and (4) component-based approaches in the series or the parallel forms. Jiang et al. [9] have proposed a new data preprocessing-based hybrid technique, incorporating the variational mode decomposition-multi objective slap swarm algorithm and least square support square machine (LSSVM) model for wind power forecasting. In this study, wind speed data in China for 10 min, 30 min, and 60 min time horizons are used. Numerical results demonstrate that the multi-objective optimization models show superior performance than single-objective optimization methods and others. Rahmani et al. [10] have used a new hybrid swarm technique (HAP), which consists of ant colony optimization (ACO) and particle swarm optimization (PSO), for short-term wind power forecasting. The empirical hourly wind power output of the Binaloud wind farm for 364 days is used to train and test the developed model. Liang et al. [11] have proposed the ELM and least-squares support models to predict wind power. The SVM model is used to predict wind power, and the ELM model is used as a postprocessing model to predict the remaining errors in wind power. The numerical results show that the hybrid models can significantly improve the short-term wind power forecasting accuracy. Guo et al. [12] have developed the series component-based hybrid model for ultra-short-term wind speed forecasting. In this study, the monthly data from January 2001 to December 2006 in Mazong Mountain and Jiuquan is used for model testing. In the proposed model, the seasonal autoregression integrated moving average method is combined with the least square support vector machine (LSSVM). The proposed model is compared with the single autoregression integrated moving average (ARIMA), SARIMA, LSSVM models. The simulation results indicate that the accuracy of the developed method is higher than the others. Okumus et al. [13] have used a parallel component-based hybrid model, ANFIS and ANN, for ultra-short-term wind power forecasting. In this article, wind power, wind speed, wind direction, and air temperature from the National Renewable Energy Laboratory (NREL) website are used. The numerical results show the mean absolute percentage errors of the proposed model are significantly better than other models. Some other hybrid methods for wind power and speed forecasting are reported in Table 1. TABLE 1. Some recently developed hybrid models for wind power and speed forecasting [Ref.] Year Applied Model(s) Description [14] 2019 OSORELM-C, HMD Developing a novel data preprocessing-based hybrid method based on the online sequential outlier robust extreme learning machine and hybrid mode decomposition method for ultra wind speed forecasting. [15] 2019 CNNSVM, SSA, EMD Designing a data preprocessing-based hybrid method for ultra-short-term wind speed forecasting, using singular spectrum analysis, empirical mode decomposition, and convolutional support vector machine. [16] 2019 LSSVM, QPSO Proposing a parameter optimization-based hybrid method based on the least square support square machine and quantum-behaved particle swarm optimization for ultra-short-term wind speed forecasting. [17] 2018 RELM, GWO Presenting a new parameter optimization-based hybrid method, using the Grey Wolf Optimizer algorithm and regularized extreme learning machine network for ultra-short-term wind speed forecasting. [18] 2018 LSSVM, MOALO Using a parameter optimization-based hybrid method based on the least square support square machine and Multi-Objective Ant Lion Algorithm to forecast the ultra-short-term wind speed. [19] 2018 BFGS, WF Presenting a new postprocessing-based hybrid method, using Broyden–Fletcher–Goldfarb–Shanno and the Wavelet Filter as a postprocessing technique for ultra-short-term wind speed forecasting. [20] 2018 ELM, ARIMA Proposing a postprocessing-based hybrid method, incorporating the extreme learning machine and the autoregressive integrated moving average, as a postprocessing technique, for ultra-short-term wind speed forecasting. [21] 2018 LSTM, RELM Presenting a postprocessing-based hybrid method, using the long short-term memory network and regularized extreme learning machine network, as a postprocessing technique, for ultra-short-term wind speed forecasting. [22] 2018 NWP, GPR Using a series component-based hybrid technique based on numerical weather prediction and the Gaussian process regression method to forecast the medium-term wind speed. [23] 2018 LSSVM, GARCH Presenting a new series component-based hybrid technique based on the least square support square machine and generalized autoregressive conditional heteroskedasticity for ultra-short-term wind speed forecasting. [24] 2018 ARIMA, ANN Presenting a new series component-based hybrid technique, incorporating autoregressive integrated moving average and artificial neural networks for ultra-short-term wind speed forecasting. [25] 2018 ARIMAX, Polynomial regression, Kriging Designing a parallel component-based hybrid method, integrating an ARIMA with explanatory variable and polynomial regression, as prediction models, and Kriging algorithm, as weighting approach, for short-term wind power forecasting. [26] 2018 LSTMDE, HELM, LSTM Presenting a parallel component-based hybrid method, combining long short term memory neural network with differential evolution (DE) algorithm and hysteretic extreme learning machine models, as forecasting models, and long short-term memory neural network for weighting the models. [27] 2018 RNN, SVM, LSTM, SA Designing a parallel component-based hybrid method, merging regression neural network, support vector machine, and long short-term memory neural network, as forecasting models, and simulated annealing, as weighting approach. [28] 2018 BPNN, ENN, GRNN, PLS Presenting a parallel component-based hybrid method, using backpropagation neural network, Elman neural network, and generalized regression neural network, as forecasting models, and partial least square as weighting method. As mentioned, hybrid methodologies have been widely used in recent researches due to the use of the benefits of single models as well as reducing their structural risk. The structure of hybrid models should maximize predictions' accuracy by the proper selection of type and the number of components and structures. For this reason, in this paper, the idea of combining different structures and different components to expand hybrid structures is proposed. For this purpose, three of the more widely used hybrid methodologies, including data preprocessing-based, series component-based, and parallel component-based approaches, are combined for modeling linear/nonlinear and certain/uncertain patterns. On the other hand, the proposed model's main idea is that if the combination of different prediction methods together can reduce the limitations of single models and use their benefits simultaneously, the combination of different structures may also lead to such results. Therefore, various structures can be combined to provide a more comprehensive hybrid model with less risk, and consequently, more accurate predictions. In general, hybrid methodologies, such as preprocessing data methods that improve the raw data before entering the prediction models, increase predictions' accuracy more than other hybrid models. Although the data preprocessing techniques generally increase predictions' performance, often in this process, by ignoring the residual data as noise data, the accuracy of the predictions is not maximized by removing the critical data. Therefore, in this paper, preprocessed data using the Kalman filter is divided into two groups of trend and residual patterns. The original data are simultaneously considered input data of linear and nonlinear models. Component-based in series or parallel models are other hybrid methodologies used extensively in the subject literature. Based on the above mentioned and the benefits of hybrid methodologies in improving the prediction accuracy by using a combination of different prediction models, in this paper, in addition to using the data preprocessing technique, a fuzzy series-parallel structure is presented by linear and nonlinear models to model complex linear/nonlinear and certain/uncertain patterns. For this purpose, two popular approximators including, the Multi-Layer Perceptrons (MLPs) and Autoregressive Integrated Moving Average with Explanatory Variable (ARIMAX), have been used to model the linear and nonlinear patterns with a high degree of accuracy. In general, the main differences between our proposed model with other existing hybrid models in the literature that cause the proposed model to become more comprehensive can be overall summarized as follows: In the classical hybrid structures in the data preprocessing field, only the data preprocessing technique's trend data is considered for the prediction. While, in the proposed method, the trend data and residual data are simultaneously included in the prediction model. Accordingly, if the data obtained from the studied system involves dynamic multiple-trend structures, the proposed model will generally have a higher ability to model them. In the classical hybrid approaches, only one type model or one type class of models, such as linear/nonlinear and certain/uncertain, is considered for the prediction. While, in the proposed method, four categories of models, for example, certain linear, certain nonlinear, uncertain linear, and uncertain nonlinear models are simultaneously included in the prediction model. Accordingly, if the data obtained from the studied system involves multiple and/or mixed patterns, the proposed model will generally have a higher ability to model them. In the classical hybrid approaches, only one type or two types of hybridization methodologies, such as preprocessing, postprocessing, series component hybridization, and parallel component hybridization, are considered for the prediction. While, in the proposed method, three classes of hybridization methodologies, for example, preprocessing, series component hybridization, and parallel component hybridization, are simultaneously included in the prediction model. Accordingly, if the data obtained from the studied system involves multiple and/or mixed structures, the proposed model will generally have a higher ability to model them. In the classical parallel hybrid approaches, only simple or iterative suboptimal algorithms, such as simple average metaheuristic, are considered for obtaining the weights of combination. While in the proposed method, an exact and optimal algorithm, for example, the ordinary least square (OLS), is used in the prediction model. Accordingly, the proposed model will generally have higher accuracy and lower computational cost to obtain each component's weight. The rest of this paper is organized as follows: In the next section, the methodology and the applied models as components of the proposed model are briefly introduced. In Section 3, the explanation and formulation of the proposed model are introduced. In Section 4, the used data sets and evaluation metrics are reviewed. In Section 5, the proposed model's empirical results for wind power forecasting are represented, and the proposed model is compared with other models in accuracy and improvement. In the last section, the conclusions are discussed. 2 METHODOLOGY AND MODELS In this section, the models and structures used in the proposed method, such as Kalman filter, linear and nonlinear prediction models, fuzzy systems, and series and parallel structures, are described. 2.1 Kalman filtering The Kalman filter is a robust linear quadratic estimator with two steps of prediction and measurement that are widely used to track system status based on the system dynamics and measurements. This approach minimizes the variance of the estimation error, so it effectively reduces the undesirable fluctuations of measured data [29]. The Kalman filter also could be described as an approach consisting of a state equation and a measurement equation. The system state equation obtained by Equation (1): X t = A t X t − 1 + W t . (1) The measurement equation obtained by Equation (2): Y t = X t H t + V t , (2)where X t denotes n-dimensional system states, A t denotes n × n the state transition matrix, Y t denotes m-dimensional measurement vector, H t denotes m × n output matrix, W t denotes n-dimensional system error, and V t denotes m-dimensional measurement error. The noise vectors W t and V t are white noise. Known covariance matrices E W t W t T = Q , E V t V t T = R , (3)where Q and R are positive definite and positive semi-definite matrices, correspondingly. The basic Kalman filter algorithm could be suggested by the following equations. The time update equation is given by Equations (4) and (5). x ̂ t t t − 1 t − 1 = A t x ̂ t − 1 , (4) P t t t − 1 t − 1 = A t P t − 1 A t T + Q . (5) The state update equation is obtained from Equations (6)–(8). K t = p t t t − 1 t − 1 H t T + R H t p t t t − 1 t − 1 H t T + R − 1 , (6) x ̂ t = x ̂ t t t − 1 t − 1 + K t Y t − H t x ̂ t t t − 1 t − 1 , (7) P t = I − K t H t P t t t − 1 t − 1 . (8) Before the Kalman filter is used to determine an optimal estimation, a system process model should design with a minimal set of information. 2.2 Autoregressive Integrated Moving Average with Explanatory Variable models (ARIMAX) The A R I M A X model is a combination of the A R I M A and the linear regression model. The A R I M A X model can be explained as the combination of the Auto-Regressive A R ( P ) , Integrated ( d ) , Moving Average M A ( q ) and the Exogenous X ( r ) models, thus demonstrated by A R I M A X ( p , d , Q , r ) . A simplified form to represent this model is described in Equation (9): Z t = β + ∑ i = 1 p ϕ i z t − i + ∑ j = 1 q θ j ε t − j + ∑ j = 1 m ξ j φ j t = 1 , 2 , … , m (9)where, Z t is a dependent variable at the time t, β is a constant; Z t − i is a dependent variable (lagged by the time steps, i; ϕ i is a coefficient of Z t − i ; p is the maximum number of time intervals; φ j represents the exogenous variables (in this case, trend data, wind power data); ξ j represents the coefficients of the exogenous variables; q is the maximum number of exogenous variables; θ j is the coefficient of the term ε t − j , which represents the error in time t lagged from j. Finally, ε t is the error component of the model with ε t ∼ N ( 0 , σ 2 ) . The coefficients of the models are estimated by regression [30]. 2.3 Artificial neural networks Multilayer perceptrons (MLPs) are the most popular types of artificial neural networks that were first presented in 1943 by the neurophysiologist McCulloch and by the mathematician Walter Pitts [31]. MLPs are used as one of the computational intelligence techniques in trying to predict time series in recent years. Multilayer perceptrons are often applied to supervised learning problems. They train on a set of input-output pairs and learn to model the correlation (or dependencies) between those inputs and outputs. Training involves adjusting the parameters, or the weights and biases, of the model in order to minimize error. Backpropagation is used to make these weights and biases adjustments relative to the error, and the error itself can measure in a variety of ways, including by root mean squared error (RMSE). A multilayer perceptron (MLP) is used in order to model the nonlinear, trend, and residual correlation structures in the underlying data sets as follows: Y i , t = ∑ j = 0 P W j · g ∑ k = 0 q W k j Y i , t − k + ε t i = 1 , 2 , … , N , t = 1 , 2 , … , T , (10)where W j and W k j called connection weights, q is the number of input nodes and p is the number of hidden nodes. 2.4 Series hybrid models In series methodologies, components are sequentially used on the original data. In this form of combination, each component's input data is the output (residual) of the previous component. In this way, the input of the first component is the original data, and the residual of the final component will be the residual of the series hybrid model. On the other hand, the final prediction of these models is obtained by summing up the predictions of components. In the series hybrid model with n components, the final forecast of the series hybrid model can be obtained as follows: y ̂ t = ∑ k = 1 n C ̂ k , t , (11)where C ̂ k , t denotes the prediction of the kth component and n is the number of components. 2.5 Parallel hybrid models In parallel methodologies, in contrast to the series hybrid models, each component's input data is the raw data, and the final prediction is obtained from a linear or nonlinear combination of components predictions. This stage of parallel hybrid models is often called the weighting process. The linear weighting-based parallel hybrid approaches are the most widely-used parallel hybrid models in the literature. In these hybrid models, the final forecasts are obtained as follows: f ̂ C , t = W 1 f ̂ 1 , t W 2 f ̂ 2 , t + W n f ̂ n − 1 , t + W n f ̂ n , t ∑ i = 1 n W i f ̂ i , t i = 1 , 2 , … , n t = 1 , 2 , … , m , (12)where f ̂ c , t ( t = 1 , 2 , … , m ) is the forecasted value of the hybrid model at the time t, W i ( i = 1 , 2 , … , n ) is the weight of the ith component, f ̂ i , t ( i = 1 , 2 , … , n ) ( t = 1 , 2 , … , m ) is the forecasted value of the ith component at time t, n is the number of components used in constructing the hybrid model, and m is the number of the dataset. 3 THE PROPOSED FUZZY SERIES-PARALLEL PREPROCESSING-BASED (FSPP) HYBRID MODEL Despite the advantages of single models, hybrid methodologies have a special place in modelling scientific problems due to the reduction of the single models' risks and limitations. In hybrid models, the proper selection of components, the combination structure's methodology to increase predictive performance are of great importance. In order to select proper components in a parallel hybridization, two main rules should be considered simultaneously. In general, the output performance of a parallel hybrid model has a direct relationship to the performance of each component as well as their differences. On the other hand, by increasing the accuracy of each used component, the performance of parallel hybridization of them will be increased. At the same time, by decreasing the correlation of each pair used component, the performance will be increased. In the proposed model, components are selected in such a way that these rules have been satisfied. First, all used components (e.g. ARIMAX, FARIMAX, MLP, and FMLP) in the proposed model have desired performance in its particular domain. Second, the first component, as an example, can only model crisp linear patterns and consequently cannot model other patterns (e.g. non-crisp linear, crisp nonlinear, and non-crisp nonlinear) and vice versa. Therefore, these selected components are in different categories and model different patterns, so have a low correlation. For the second purpose, in this paper, three well-known hybrid methodologies of data preprocessing, series, and parallel are used to achieve a comprehensive structure. Therefore, in the first stage of the proposed model, the raw data is preprocessed by the Kalman filter preprocessor. In this step, in addition to considering the trend patterns, the residual patterns along with the raw data are also used as input data of single linear/nonlinear, certain/uncertain series hybrid models to use all basic patterns. In this way, the trend patterns that frequently contain low complexity and uncertainty are entered into certain linear (e.g. ARIMAX) and certain nonlinear (e.g. MLP) models. However, the residual patterns that frequently include a higher complexity and uncertainty cannot be directly entered into certain linear and nonlinear models. Thus, these patterns are modelled by a series of combinations of the aforementioned linear and nonlinear models with fuzzy techniques to better model the data's existing uncertainty. In the last step of the proposed model, all the single and series hybrid models' predicted values are combined in a parallel process. There