Short-term wind speed prediction of wind farm based on TSO-VMD-BiLSTM

Acquisition and processing of short-term wind speed data

Wind speed data acquisition

This article takes the open-source wind speed data of a certain wind farm in 2022 as the research object, and draws the line chart of monthly average wind speed distribution, as shown in Fig. 1. As can be seen from Fig. 1, the average monthly wind speed in January is the lowest, the average monthly wind speed in May is the highest, and the average wind speed tends to stabilize in other months. To ensure the representativeness of SWSP, this article selects specific months to conduct example studies. Specifically, January, characterized by its lowest average monthly wind speed, is chosen as an example of a valley month. On the other hand, May, known for its highest average monthly wind speed, is selected as an example of a peak month. This approach takes into account the randomness, variability, and periodicity of wind speed in order to provide a comprehensive analysis of SWSP. The data for Example 1 is from January 1 to January 31, 2022, and the data for Example 2 is from May 1 to May 31, 2022. The input variables of both data sets are wind speed, direction, pressure and temperature, and the output variable is wind speed.

Due to various factors such as natural and human factors that may affect the collection of meteorological data (Dong et al., 2022), occasional incomplete data may occur in the collected meteorological data. For a small amount of individual missing data, this article supplements it by using the mean of adjacent dates to ensure data continuity.

Figures 2 and 3 show the wind speed distribution series of the wind farm in January and May, respectively. It is apparent that the randomness and fluctuation of wind speed are more obvious in these two wind speed series, which directly leads to an increase in the difficulty of prediction. Both datasets consist of 2,976 sample sequences, and the training and testing sets are partitioned in an 8:2 ratio.

Wind speed data processing

Wind speed data collected by wind tower in wind farm is usually affected by external environment or other uncontrollable factors, which may bring noise information into the data. Therefore, it is necessary to process the collected historical data in advance to improve the characteristics of the data.

VMD can decompose wind speed data of the same category and time period, further obtaining wind speed sub sequences with different frequencies but stronger regularity, thereby reducing the complexity of wind speed sequences (Wang, Wei & Teng, 2023). Each component decomposed by VMD has an independent center frequency, thus multiple sub sequences with different frequencies and corresponding features can be obtained. In addition, VMD can handle both stationary and non-stationary sequences (Ye, Che & Wang, 2022). The process of VMD processing for wind speed data is shown in Fig. 4.

The VMD processing results of Example 1 and Example 2 are shown in Figs. 5 and 6, respectively. The original wind speed is decomposed into five components (intrinsic mode function (IMF) 1, IMF2, IMF3, IMF4, IMF5), each component represents a sub sequence of wind speeds with different frequencies but relatively stable.

In this article, the range standardization method is employed to normalize the original wind speed data. This method involves converting the sample data values into a range between 0 and 1. By applying this normalization technique, the wind speed data is standardized, enabling easier comparison and analysis across different scales or datasets (Liu et al., 2018). The specific calculation method is shown in Eq. (1): (1)${\displaystyle X_{nor}=\frac{x-x_{\min }}{x_{\max }-x_{\min }}}$

where x represents the true value of the data; x_max depicts the maximum value of the data; x_min denotes the minimum value of the data; X_nor stands for the normalized value obtained after applying the range standardization method.

In order to better compare the predicted value of wind speed with the real value, it is necessary to perform inverse normalization on the predicted value, and the equation is as follows: (2)${\displaystyle x=X_{nor}\left(x_{\max }-x_{\min }\right)+x_{\min }.}$

Basic principles of LSTM, BiLSTM and TSO

Basic principles of LSTM

On the basis of recurrent neural networks (RNN), LSTM introduces several components such as forget gate, input gate, memory unit update and output gate to enhance the performance of the repetitive hidden layer neuron structure. These additions enable LSTM to effectively store and remain historical messages and control the convergence of gradients during training (Fukuoka et al., 2018). The issue of gradient vanishing and gradient exploding during RNN training is effectively addressed and resolved (Germánico & Pablo, 2022). The basic structure of LSTM hidden layer neurons is shown in Fig. 7, where x_t refers to the input data, h_t represents the output of the recurrent layer, c_t denotes the output of the memory unit, h_t−1 signifies the output of the previous recurrent layer, and c_t−1 represents the output of the previous memory unit.

The function of the forget gate is to determine whether to forget information, usually with a certain probability to control whether to forget the corresponding information. Use the sigmoid function to process h_t−1 and x_t, in order to obtain the output f_t. Since the value range of f_t is [0, 1], f_t also represents the probability of forgetting, and its expression is: (3)${\displaystyle f_t=\sigma \left(W_f{h}_{t-1}+U_f{x}_t+b_f\right)}$

where, σ refers to the activation function, W_f and U_f represent the coefficients of the linear relationship, b_f is the bias coefficient.

The input gate is mainly accountable for dealing with the input of the current sequence position, consisting of two components: the output of the first part i_t with the matching activation function σ, and the output of the second part a_t with the activation function tanh. The expression for the input gate can be represented as follows:

(4)${\displaystyle i_t=\sigma \left(W_i{h}_{t-1}+U_i{x}_t+b_i\right)}$ (5)${\displaystyle a_t=tanh\left(W_a{h}_{t-1}+U_a{x}_t+b_a\right).}$

W_i, U_i, W_a and U_a represent the coefficients of linear relationship; b_i and b_a stand for the bias coefficients of the linear relationship.

The cell state c_t is affected by the outputs of the forget gate and the input gate. As a result, c_t can be separated into two components: the first component refers to the multiplication of c_t−1 and f_t, and the second component involves the product of i_t and a_t. c_t can be obtained by adding the two products. For the specific calculation process, see Eq. (6): (6)${\displaystyle c_t=c_{t-1}\otimes f_t+i_t\otimes a_t.}$

The output gate is accountable for determining the final output information, and the update of h_t is also divided into two components. The first component is o_t, which is composed of h_t−1, x_t and activation function σ. The second component consists of the hidden state c_t and the activation function tanh.

(7)${\displaystyle o_t=\sigma \left(W_o{h}_{t-1}+U_o{x}_t+b_o\right)}$ (8)${\displaystyle h_t=o_t\otimes tanh\left(c_t\right)}$

where W_o and U_o are also the coefficients of linear relationship, and b_o is the bias coefficient.

Through these four mechanisms, LSTM can selectively control the flow of information, giving memory cells the ability to preserve long-term information dependencies, while also preventing internal gradients from being disturbed by external factors during the training process (Wang et al., 2023).

Basic principles of BiLSTM

BiLSTM is based on classical LSTM by using two layers of independent cell units, namely forward cell unit and reverse cell unit (He et al., 2023). The model structure is shown in Fig. 8. In Fig. 8, x_t−1, x_t and x_t+1 represent the inputs at t-1, t and t+1, respectively. h_t−1, h_t and h_t+1 denote the outputs at t-1, t and t+1 in forward and reverse states, respectively. y_t−1, y_t and y_t+1 stand for the final outputs at t-1, t and t+1. In the forward state, input x_t−1, x_t and x_t+1 to get the forward outputs h_t−1, h_t and h_t+1; In the reverse state, input x_t+1, x_t and x_t−1 to obtain the reverse outputs h_t+1, h_t and h_t−1. Finally, the two sets of outputs are combined, and finally the outputs y_t−1, y_t and y_t+1 corresponding to the inputs x_t−1, x_t and x_t+1 are obtained (Gao & Hao, 2023).

The processing method of BiLSTM is the same as that of classical LSTM, but BiLSTM traverses the input data twice in forward and reverse ways, increasing the training times, thus improving the wind speed prediction accuracy under micrometeorological parameters (Liu et al., 2022), and the final prediction result is more accurate than that of a single LSTM (Zheng, Zhou & Nan, 2023).

Basic principles of TSO

TSO is a new type of intelligent optimization algorithm, which mimics the foraging behavior of tuna populations to solve the optimization problems. It has simple structure, few adjustment parameters, fast convergence speed, strong optimization capability and easy implementation (Guo et al., 2022)

Similar to other intelligent optimization algorithms, tuna populations are typically randomly initialized within the search space, and the initialization process can be represented as: (9)${\displaystyle X_i^{\mathrm{int}}=rand\cdot \left(ub-lb\right)+lb,i=1,2,\cdot \cdot \cdot ,np}$

$X_i^{\mathrm{int}}$ represents the initial position of the i-th individual, ub and lb denote the upper and lower bounds of the search space, respectively. np stands for the number of tuna populations, and rand represents a random vector uniformly distributed within the range [0, 1].

Tuna populations usually choose a spiral foraging method. During foraging, tuna individuals exchange prey information with each other. Due to each individual following the previous individual to forage, tuna populations can share hunting information in real-time (Liu, Fan & Li, 2023). Equations (10) and (11) represent the mathematical model of the spiral foraging strategy.

(10)${\displaystyle X_i^{t+1}=\left\{\begin{array}{c}{\alpha }_1\cdot \left(X_{best}^t+\beta \cdot \left|X_{best}^t-X_i^t\right|\right)+{\alpha }_2\cdot X_i^t,i=1\hfill \\ {\alpha }_1\cdot \left(X_{best}^t+\beta \cdot \left|X_{best}^t-X_i^t\right|\right)+{\alpha }_2\cdot X_{i-1}^t,i=2,3,\cdot \cdot \cdot ,np\hfill \end{array}\right.}$ (11)${\displaystyle \beta =e^{bl}\cdot cos\left(2\pi b\right)}$ (12)${\displaystyle l=e^{3cos\left(\left(\left(t_{\max }+1/t\right)-1\right)\pi \right)}}$

$X_i^{t+1}$ represents the i-th individual at the t+1 iteration, $X_i^t$ represents the i-th individual at the t iteration, $X_{best}^t$ stands for the current best individual, α1 and α2 indicate the weight coefficients that control the movement trend of an individual towards to the best individual and the previous individual, respectively. t represents the number of current iterations, t_max stands for the maximum iteration number, and b represents a random number evenly distributed between 0 and 1.

When the optimal individual of tuna populations is unable to find food, blindly following it is not conducive to group foraging. Thus, it becomes necessary to generate a random coordinate within the search space as a reference for the search of tuna populations. This enables each individual to explore in a broader area and gives TSO the capability to explore globally (Xue, Liu & Wang, 2022). The specific mathematical model description can be found in Eq. (13): (13)${\displaystyle X_i^{t+1}=\left\{\begin{array}{c}{\alpha }_1\cdot \left(X_{rand}^t+\beta \cdot \left|X_{rand}^t-X_i^t\right|\right)+{\alpha }_2\cdot X_i^t,i=1\hfill \\ {\alpha }_1\cdot \left(X_{rand}^t+\beta \cdot \left|X_{rand}^t-X_i^t\right|\right)+{\alpha }_2\cdot X_{i-1}^t,i=2,3,\cdot \cdot \cdot ,np\hfill \end{array}\right.}$

where $X_{rand}^t$ indicates a randomly generated reference point within the search space. Such heuristic algorithm conducts extensive global exploration in the early stage, and gradually transitions to more precise local development. Therefore, with the increasing number of iterations of the algorithm, the reference object of the tuna populations is transformed from random coordinates to the optimal individual.

Apart from the spiral foraging strategy, tuna populations also adopt another foraging strategy, called parabolic foraging strategy, which is to form a parabolic shape with prey as a reference point, and then gradually narrow the search area (Xie, Han & Zhou, 2021). The probability of the tuna population choosing the two foraging strategies is basically the same, both are 50%. The mathematical model description of parabolic foraging strategy is shown by Eqs. (14) and (15): (14)${\displaystyle X_i^{t+1}=\left\{\begin{array}{c}{X}_{best}^t+rand\cdot \left(X_{best}^t-X_i^t\right)+TF\cdot p^2\cdot \left(X_{best}^t-X_i^t\right),rand<0.5\hfill \\ TF\cdot p^2\cdot X_i^t,rand\ge 0.5\hfill \end{array}\right.}$ (15)${\displaystyle p={\left(1-\frac{t}{t_{\max }}\right)}^{\frac{t}{t_{\max }}}}$

TF represents a random number within a value range of [−1, 1].

Example 1

The results of the four SWSP models are shown in Fig. 10. Obviously, the predicted value curve of the TSO-VMD-BILSTM model exhibits a tendency to closely align with the true value curve, especially in the high wind speed range, that is, the sample sequence 310–480, and its prediction effect is significantly better than that of the other three models.

Take the true value of wind speed as the horizontal axis and the predicted value of the four models as the vertical axis, and observe the linearity of the curve (Liu, Yu & Cang, 2015). The linearity is directly proportional to the prediction accuracy, that is, the better linearity, the higher prediction accuracy. The linearity curves of the four models in Example 1 are shown in Fig. 11, from which two pieces of information can be obtained. (1) Because of the randomness and intermittency of wind speed, the linearity curves show an unordered state; (2) In the unordered state, the more concentrated the linearity curve distribution of the prediction model, the higher the accuracy. Obviously, compared to the other three models, the predictive curve of the TSO-VMD-BiLSTM model has a more concentrated and compact linear distribution, which means that the model has the best predictive performance.

Figure 12 shows the AE values of the four prediction models in Example 1. The fluctuation range of AE values of TSO-VMD-BiLSTM is about [0, 2.52]. Except for the high wind speed range, the AE values of the vast majority of test samples are less than 1 m/s, and the AE values of each test sample are lower than the other three models in the high wind speed range. Compared to the TSO-VMD-LSTM model, the overall fluctuation range of TSO-VMD-BiLSTM has been reduced, and the prediction results are more accurate than unidirectional LSTM. This indicates that the introduction of BiLSTM effectively captures micro meteorological parameters.

The other evaluation indicators of the four prediction models in Example 1 are shown in Table 2. The RMSE value of TSO-VMD-BiLSTM is only 0.81, which is 0.88, 0.61 and 0.28 lower than that of LSTM, VMD-LSTM and TSO-VMD-LSTM, respectively. MAE is only 0.54, which is 0.61 less than LSTM, 0.44 less than VMD-LSTM, and 0.16 less than TSO-VMD-LSTM. MAPE is only 6.89%, which is 8.38%, 5.64% and 2.61% lower than LSTM, VMD-LSTM and TSO-VMD-LSTM, respectively. Therefore, by integrating various evaluation indicators, it can be found that the SWSP model based on TSO-VMD-BiLSTM has the best performance and the highest accuracy.

Example 2

The SWSP results of the four prediction models in Example 2 are shown in Fig. 13. It is not difficult to see that TSO-VMD-BiLSTM exhibits good tracking performance, and its predicted value curve demonstrates a closer resemblance to the true value curve compared to the other three prediction models. In addition, the predicted values closely track and reflect the changes observed in the true values.

The linearity curves of the four prediction models in Example 2 are shown in Fig. 14, and we can get the same conclusion as in Example 1. The linearity curve of TSO-VMD-BiLSTM is the most concentrated and tight distribution, followed by TSO-VMD-LSTM and VMD-LSTM, and finally LSTM. Therefore, the TSO-VMD-BiLSTM model has the highest prediction accuracy.

Figure 15 shows the AE graph of the TSO-VMD-BiLSTM prediction model. By comparing the AE values of each model, it is noticeable that the TSO-VMD-BiLSTM model has the best prediction performance, the smallest AE value, and the error value is controlled within 2 m/s. Moreover, the AE values of most test samples are less than 1 m/s. Similarly, compared with TSO-VMD-LSTM, the overall error fluctuation range has been decreased, especially at sample sequence 240, BiLSTM still shows good ability to capture micro meteorological parameters.

Table 3 illustrates the results of other evaluation indicators of the four prediction models in Example 2. The RMSE of TSO-VMD-BiLSTM is only 0.48, which is 1.07, 0.47 and 0.05 lower than LSTM, VMD-LSTM and TSO-VMD-LSTM, respectively. The MAE is only 0.38, which is 0.79 less than LSTM, 0.36 less than VMD-LSTM, and 0.03 less than TSO-VMD-LSTM, respectively. MAPE is only 5.98%, which is 5.37%, 2.81% and 0.17% better than LSTM, VMD-LSTM and TSO-VMD-LSTM, respectively. All in all, TSO-VMD-BiLSTM prediction model has the highest accuracy and the best performance.