Wind speed time sequence prediction method based on algorithm optimization and joint data denoising

Abstract

The invention discloses a wind speed time sequence prediction method based on algorithm optimization and combined data denoising, and belongs to the technical field of wind speed data processing. According to the method, wavelet threshold filtering and a deep learning model are combined, and the method comprises the steps that S1, two regulatory factors of wavelet threshold filtering WT are optimized through NOA, and filtering processing is conducted on wind speed data through an NOA-WT model; s2, performing phase-space reconstruction on the processed data, calculating a Lyapunov exponent and identifying the chaotic characteristic of the Lyapunov exponent; and S3, performing quantile regression (QR) interval prediction by using a deep learning model BiTCN-BiGRU optimized by the NOA. The accurate prediction of the wind speed plays a crucial role in wind power generation and directly influences the optimization of the power generation efficiency and energy management, the wind power plant can reasonably plan the operation of the wind generating set, the power generation amount is maximized, the influence of wind speed fluctuation on the stability of the power grid is reduced, and the operation and maintenance cost is effectively reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of wind speed data processing, and in particular to a wind speed time series prediction method based on algorithm optimization and combined data denoising. Background Art

[0002] Some scholars have proposed the concept of wavelet threshold filtering based on wavelet transform. Since this method can obtain the best estimate in Besov space, and any other linear estimate cannot achieve the same estimate result, the threshold filtering method has attracted widespread attention from scholars around the world. Wavelet threshold functions are divided into hard threshold functions and soft threshold functions. It is generally believed that wavelet coefficients less than the threshold are generated by noise, while wavelet coefficients greater than the threshold are generated by valid signals. In the prior art, there are methods that process wind speed data by applying wavelet threshold filtering and combine it with multivariate LSTM model for prediction, which significantly improves the prediction accuracy and significantly improves the accuracy of wind speed prediction. There are also methods that process wind power data by using wavelet denoising algorithm and determine the parameters of support vector machine by using improved slime mold optimization algorithm, which significantly improves the performance of prediction model. There are also scholars who proposed a short-term wind speed prediction model based on WT and CNN. Through decomposition, denoising and prediction reconstruction, it achieved the lowest error in the experiment, which is significantly better than other models. There are also methods that decompose the data into several subsequences, then use wavelet threshold filtering to process the highest frequency sequence, and finally use LSTM for prediction. This method has higher prediction accuracy. However, due to the discontinuity of the hard threshold function, the discontinuity of the derivative of the soft threshold function, and the constant deviation between the estimated wavelet coefficients and the wavelet coefficients of the processed signal, these defects have greatly limited the further application of these two methods.

[0003] In order to overcome the shortcomings of traditional soft and hard thresholds in signal denoising, a wind speed prediction model integrating wavelet soft threshold filtering and GRU is proposed in the prior art to improve the model accuracy by eliminating redundant information and optimizing GRU parameters. Specifically, the signal is first decomposed, and a continuous and differentiable wavelet threshold filter is used for the high-frequency components to delete the low-frequency components below the fixed threshold. Experiments have shown that the model has higher accuracy. In addition, two adjustment factors are introduced into the WT threshold function. By adjusting the parameters, the continuity of the function at the threshold point can be guaranteed, and the deviation problem of the wavelet coefficient can also be solved, which significantly improves the signal-to-noise ratio. This also generates a new problem. Improper setting of the adjustment factor will cause WT to over-smooth the data, resulting in the loss of nonlinear features in the original data. To solve this problem, some scholars have proposed an improved wavelet threshold function with adjustment parameters, and used the particle swarm optimization algorithm to find the optimal value of the improved threshold function in the background noise, which has a good filtering effect, as shown in Table 1-1. Therefore, the original information and nonlinear features of the signal can be retained to the greatest extent by combining algorithm optimization and data processing (phase space reconstruction technology).

[0004] Table 1-1WT model

[0005]

[0006] Although the point prediction method can provide results, it cannot reflect the random uncertainty of wind power generation. The information is limited, and it is difficult to evaluate the reliability and error range of the prediction results. The filtering process can effectively remove high-frequency noise and random fluctuations, so that the data presents a clearer trend and structure, which is particularly beneficial for interval prediction. At present, there are generally two types of interval prediction. The first type first makes a point prediction, and then further constructs a prediction interval based on the results of these point predictions. Some scholars use the random forest model to integrate three models, construct a combined prediction model, and expand the point prediction to an interval prediction through fuzzy information granulation. There is also a wind speed interval prediction system constructed using a multi-objective optimization algorithm and fuzzy information granulation, which improves the accuracy of point prediction and interval prediction at the same time. And based on the interval construction method, historical data is converted into interval data, and the bivariate empirical mode decomposition technology and the least squares support vector machine are used to predict the upper and lower limits of the interval respectively. However, this interval prediction method is overly dependent on the performance of the point prediction model and is easily affected by noise or outliers. The second type is to fit the prediction interval in the form of probability statistics. The parameterization method constructs a prediction interval by fitting a certain probability distribution function to generate the distribution probability of trajectory points. Some scholars use the t-location-scale function to describe the probability characteristics of wind power forecasting errors, and based on this, establish an error model for probability forecasting. Other scholars use normal exponential smoothing and sliding kernel density estimation to estimate the probability distribution of the forecast error, and then use the entropy weight method to weight it to obtain the final forecast interval. And use the empirical distribution model to fit the probability distribution of the error, and then perform Monte Carlo sampling to obtain the corresponding forecast interval. However, the parametric method relies on the pre-set data distribution, lacks flexibility when facing complex and irregular data, and is difficult to adapt to the multi-peak or asymmetric nature of the data. The non-parametric method can make interval predictions without making any assumptions about the distribution. Some scholars use the kernel density estimation method to expand the forecast interval, and use speed-constrained multi-objective particle swarm optimization to adjust the upper and lower bounds of the interval. Other scholars have proposed a method for constructing wind power forecast intervals based on the TCN conformal quantile regression (CQR) algorithm, which significantly improves the forecast accuracy. Although QR quantile regression is a flexible and efficient forecasting method, the forecast results depend on the selected regression model, which requires reasonable model settings and parameter adjustments. Therefore, some scholars have proposed an interval prediction model that combines deep learning and QR quantile regression. By optimizing parameters through algorithms, the coverage and accuracy of interval predictions are significantly improved, with higher robustness and narrower average bandwidth. Although the combined system model prediction has advantages, its parameter setting and nonlinear information loss are still two outstanding problems. Summary of the invention

[0007] The purpose of the present invention is to provide a wind speed time series prediction method based on algorithm optimization and joint data denoising, combining wavelet threshold filtering (WT) and a deep learning model (BiTCN-BiGRU) to solve the problems of parameter setting and nonlinear information loss in the combined system model prediction proposed in the above background technology.

[0008] To achieve the above object, the present invention provides the following technical solutions:

[0009] A wind speed time series prediction method based on algorithm optimization and joint data denoising includes the following steps:

[0010] S1: Use the Nutcracker Optimization Algorithm (NOA) to optimize the two adjustment factors of the wavelet threshold filter WT, and apply the NOA-WT model to filter the wind speed data;

[0011] S2: Reconstruct the phase space of the processed data, calculate the Lyapunov exponents and identify its chaotic characteristics;

[0012] S3: Quantile regression QR interval prediction using the NOA-optimized deep learning model BiTCN-BiGRU.

[0013] Furthermore, the wavelet threshold function in S1 is divided into a hard threshold function and a soft threshold function, where the wavelet coefficients less than the threshold are generated by noise, while the wavelet coefficients greater than the threshold are generated by valid signals. The calculation formula is as follows:

[0014] Hard threshold function:

[0015]

[0016] Soft threshold function:

[0017]

[0018] Among them, W j,k is the wavelet coefficient after threshold processing, w j,k is the wavelet decomposition coefficient,

[0019] Furthermore, the function expression of using NOA to optimize the WT filter model in S1 is as follows:

[0020]

[0021] Among them, α and β are adjustment factors. By adjusting the two parameters α and β, the deviation of the signal in the threshold function is reduced, thereby obtaining a better filtering effect.

[0022] Furthermore, the condition for phase space reconstruction in S2 is: d>2D+1, where d is the embedding dimension and D is the system correlation dimension. The time delay and embedding dimension are estimated using the correlation integral. Considering τ and d at the same time, the correlation integral of the embedded time series is used to analyze the correlation of the time series and obtain the statistic S cor (τ) and according to S cor (τ), and τ to obtain the optimal delay time τ d and the embedding window τ w , and finally find the embedding dimension d.

[0023] Furthermore, the bidirectional temporal convolutional network BiTCN in the deep learning model in S3 uses convolutional neural network CNN to efficiently process time series data. The specific methods include:

[0024] 1. Dilated convolution: By stacking diluted kernels with an expansion base d, a certain number of input data points are skipped in the convolution operation, so that the convolution kernel can expand the receptive field without increasing the computational cost;

[0025] 2.GELU activation function: Use Gaussian error linear unit instead of traditional ReLU activation function, so that the model returns some small negative values, thereby improving the learning ability of the model;

[0026] 3. Dropout layer: Prevent network overfitting by randomly discarding the output of some neurons and improve the generalization ability of the model.

[0027] Furthermore, the bidirectional gated recurrent unit BiGRU in the deep learning model in S3 is a recurrent neural network architecture based on the gated recurrent unit GRU for processing sequence data. The calculation process of the gated recurrent unit GRU is as follows:

[0028] 1. Update gate z t : Determines how much of the state of the current time step comes from past information and how much comes from the current input, allowing the network to selectively retain variable information:

[0029] z t =σ(W z ·[h t-1 ,x t ]+b z )

[0030] 2. Reset gate r t : Determines how the current input is combined with past information. If the value is close to 0, it means that the network will discard the past hidden state and only use the current input for update:

[0031] r t =σ(W r ·[h t-1 ,x t ]+b r )

[0032] 3. Hidden State Adjust the past state according to the reset gate and update the gate z t Under the control of , the new input is combined with the past hidden state to generate a new hidden state:

[0033]

[0034] In the formula, x t is the input data of the current time step, σ represents the sigmoid activation function, W represents the weight matrix of the update gate, and h t-1 represents the hidden state at the previous moment, and b represents the bias term;

[0035] In GRU, the hidden state h t Considering only information from previous time steps and the current input, BiGRU uses two independent GRU networks to process the time series forward and backward, respectively.

[0036] Furthermore, the method of using NOA to optimize the deep learning model BiTCN-BiGRU in S3 includes: using the NOA algorithm to optimize four parameters, namely the number of filters in the BiTCN model, the number of neurons in the BiGRU unit, and the learning rate and regularization parameter in the combined model, and find a suitable hyperparameter combination in the complex search space.

[0037] Furthermore, quantile regression QR in S3 is a statistical method used to estimate the relationship between the conditional quantile of the dependent variable and the independent variable. The goal of QR is to predict a specific quantile of the dependent variable and estimate the regression coefficients at different quantiles by minimizing the following asymmetric loss function:

[0038]

[0039] The above formula can be equivalent to:

[0040]

[0041] Among them, ρ τ (u) = u(τ-I(u<0)), I(Z) is an indicative function, which means that it returns 1 when u is less than zero, otherwise it returns 0; the two models optimized by NOA are combined with phase space reconstruction technology and QR quantile regression to form a complete prediction framework.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] 1. The wind speed time series prediction method based on algorithm optimization and joint data denoising of the present invention uses the NOA algorithm to optimize the parameters of the WT filtering model and the BiTCN-BiGRU deep learning model to ensure that the model can obtain the minimum error and better generalization ability in different data sets.

[0044] 2. The wind speed time series prediction method based on algorithm optimization and data denoising of the present invention combines QR quantile regression with BiTCN-BiGRU to provide multiple quantile predictions, avoiding the impact of the prediction interval due to poor model prediction performance. At the same time, the model can better capture the uncertainty and volatility in the data, further enhance the model's ability to capture complex time series nonlinear characteristics, and make the prediction results more accurate and robust.

[0045] 3. The accurate prediction of wind speed by the present invention plays a vital role in wind power generation, directly affecting the optimization of power generation efficiency and energy management. Wind farms can rationally plan the operation of wind turbines, maximize power generation, reduce the impact of wind speed fluctuations on grid stability, and effectively reduce operating and maintenance costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Flow chart of NOA optimization WT parameters of the present invention;

[0047] Figure 2 This is the framework diagram of the BiTCN model of the present invention;

[0048] Figure 3 This is the structural diagram of the GRU model of the present invention;

[0049] Figure 4 This is the BiGRU model structure diagram of the present invention;

[0050] Figure 5 Flowchart of BiTCN-BiGRU parameter optimization for NOA of the present invention;

[0051] Figure 6 It is a framework diagram of the prediction method of the present invention;

[0052] Figure 7 This is the wind speed time series diagram of data1 of the present invention;

[0053] Figure 8 This is the wind speed time series diagram of data2 of the present invention;

[0054] Fig. 9 This is the NOA optimization curve diagram of the present invention based on data1;

[0055] Fig.10This is the NOA-WT filtering result diagram based on data1 of the present invention;

[0056] Fig.11 This is a comparison chart of the interval prediction value and the actual value based on data1 of the present invention;

[0057] Fig.12 This is the NOA optimization curve diagram of the present invention based on data2;

[0058] Fig.13 This is the NOA-WT filtering result diagram based on data2 of the present invention;

[0059] Fig.14 This is a comparison chart of the predicted value and the actual value based on data2 of the present invention;

[0060] Fig.15 This is a one-way deep learning model prediction graph based on data1 of the present invention;

[0061] Fig.16 This is a prediction graph of the bidirectional deep learning model based on data1 of the present invention;

[0062] Fig.17 This is a comparison chart of ablation experiment prediction based on data1 of the present invention;

[0063] Fig.18 This is a comparison chart of the robustness prediction based on data1 of the present invention;

[0064] Fig.19 This is the SSA-WT filtering result diagram based on data1 of the present invention;

[0065] Fig. 20 This is a graph of NOA and SSA interval prediction results based on data1 of the present invention;

[0066] Fig.21 This is a one-way deep learning model prediction graph based on data2 of the present invention;

[0067] Fig. 22 This is a prediction graph of the bidirectional deep learning model based on data2 of the present invention;

[0068] Fig.23 This is a comparison chart of ablation experiment prediction based on data2 of the present invention;

[0069] Fig.24 This is a comparison chart of the robustness prediction based on data2 of the present invention;

[0070] Fig.25 This is the SSA-WT filtering result diagram based on data2 of the present invention;

[0071] Fig.26This is a graph of NOA and SSA interval prediction results based on data2 of the present invention. DETAILED DESCRIPTION

[0072] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0073] The embodiment of the present invention combines wavelet threshold filtering (WT) and a deep learning model (BiTCN-BiGRU) to propose a wind speed time series prediction method based on algorithm optimization and joint data denoising, comprising the following steps:

[0074] S1: The Nutcracker optimizer algorithm (NOA) is used to optimize the two adjustment factors of the wavelet threshold filter WT, and the NOA-WT model is applied to filter the wind speed data; among them, the Nutcracker optimizer algorithm (NOA) is evaluated through 23 classic Benchmark functions, CEC2014 test set, CEC2017 test set, CEC2020 test set and 5 engineering problems, and compared with the existing three types of optimization algorithms. The experimental results show that NOA has outstanding advantages among all methods and has the best comprehensive performance.

[0075] Among them, the wavelet threshold function in the wavelet threshold filter WT is divided into a hard threshold function and a soft threshold function. It is generally believed that the wavelet coefficients less than the threshold are generated by noise, while the wavelet coefficients greater than the threshold are generated by valid signals. The calculation formula is as follows:

[0076] Hard threshold function:

[0077]

[0078] Soft threshold function:

[0079]

[0080] Among them, W j,k is the wavelet coefficient after threshold processing, w j,k is the wavelet decomposition coefficient,

[0081] In the NOA optimized WT filtering model, in order to accurately reflect the uncertainty of wind speed and evaluate the reliability and error range of the prediction results, the present invention selects the improved WT model to filter the data, which can effectively remove high-frequency noise and random fluctuations, so that the data presents a clearer trend and structure, which is particularly beneficial for interval prediction. The functional expression of the improved wavelet threshold function proposed in the present invention for filtering time series data is as follows:

[0082]

[0083] Among them, α and β are adjustment factors. By adjusting these two parameters, the deviation of the signal in the threshold function can be effectively reduced; the function is continuous at the threshold point, which overcomes the defect that the hard threshold function is not differentiable at the threshold, and satisfies the odd function condition, which can keep the positive and negative parts of the processed signal symmetrical. In the actual filtering process, α and β can be dynamically adjusted according to the deviation size and actual conditions to obtain better filtering effect. Based on this, the present invention proposes a new model that uses the signal-to-noise ratio as the fitness function and uses the NOA algorithm to optimize the WT parameters. It can quickly and accurately process wind speed time series. The optimization process is as follows: Figure 1 shown.

[0084] S2: Reconstruct the phase space of the processed data, calculate the Lyapunov exponent and identify its chaotic characteristics; wherein, phase space reconstruction is a method of converting a one-dimensional time series into a multi-dimensional phase space trajectory by time delay embedding. The purpose of this method is to restore the attractor equivalent to the original system dynamics by embedding in a high-dimensional space, and analyze the system behavior. The reconstructed phase space retains the system's dynamic information, so that the nonlinear characteristics and chaotic behavior of the system can be studied through time series data. Takens' theorem provides theoretical support for phase space reconstruction, proving that it is feasible to reconstruct the complete dynamics of the system from a one-dimensional time series, and gives the conditions for reconstruction: d>2D+1 (d is the embedding dimension, D is the system correlation dimension); based on this, the present invention reconstructs the phase space of time series data, uses correlation integrals to estimate the time delay and embedding dimension, considers τ and d at the same time, and uses the correlation integral analysis of the embedded time series to obtain the correlation of the time series, and obtains the statistic S cor ( τ ) and according to S cor ( τ ) , The relationship between τ and time can be used to obtain the optimal delay time. τ d and embedded windows τ w, and finally find the embedding dimension d .

[0085] S3: Use the NOA optimized deep learning model BiTCN-BiGRU for quantile regression QR interval prediction; the bidirectional temporal convolutional network (BiTCN) uses convolutional neural network CNN to efficiently process time series data, and by combining past and future time information at the same time, it can better capture the long-term dependency between variables to improve prediction accuracy. The model structure is as follows: Figure 2 As shown, it includes:

[0086] 1. Dilated convolution: By stacking many diluted kernels with an expansion base d, a certain number of input data points are skipped in the convolution operation, so that the convolution kernel can expand the receptive field without increasing the computational cost;

[0087] 2.GELU activation function: Use Gaussian error linear unit instead of traditional ReLU activation function, so that the model can return some small negative values, avoid the problem of neuron "death", and thus improve the learning ability of the model;

[0088] 3. Dropout layer: Prevent network overfitting by randomly discarding the output of some neurons and improve the generalization ability of the model.

[0089] In addition, the Gated Recurrent Unit (GRU) is a recursive neural network architecture specifically designed for processing sequence data. It controls the flow of information and memory updates by introducing a gating mechanism. Unlike LSTM, GRU combines the forget gate and input gate into an update gate, simplifying the calculation and structure of the network. The model structure is as follows: Figure 3 As shown, the calculation process of the GRU unit is as follows:

[0090] 1. Update gate z t : Determines how much of the state of the current time step comes from past information and how much comes from the current input, allowing the network to selectively retain variable information;

[0091] z t =σ(W z ·[h t-1 ,x t ]+b z )

[0092] 2. Reset gate r t : Determines how the current input is combined with past information. If the value is close to 0, it means that the network will discard the past hidden state and only use the current input for update;

[0093] r t =σ(W r ·[h t-1 ,x t ]+b r )

[0094] 3. Hidden State Adjust the past state according to the reset gate and update the gate z t Under the control of , the new input is combined with the past hidden state to generate a new hidden state;

[0095]

[0096] In the formula, x t The input data of the current time step, σ represents the sigmoid activation function, W represents the weight matrix of the update gate, and h t-1 represents the hidden state at the previous moment, and b represents the bias term.

[0097] In GRU, the hidden state h t Only considering the information from the previous time step and the current input, BiGRU uses two independent GRU networks to process the time series forward and backward respectively. The hidden state of each time step is a combination of the two calculation results, so that the hidden state of each time step contains both the previous historical information and the future information. The model structure is as follows: Figure 4 shown.

[0098] Specifically, NOA optimizes the BiTCN-BiGRU interval prediction model: the embodiment of the present invention takes wind speed interval prediction as an example to construct a model to accurately predict the 95% confidence interval of the wind speed. Its main improvement is that on the basis of the BiTCN-BiGRU model, the NOA algorithm is used to optimize the four parameters of the number of filters in the BiTCN model, the number of neurons in the BiGRU unit, and the learning rate and regularization parameters in the combined model, and find a suitable hyperparameter combination in the complex search space; BiTCN can effectively process long time series data through convolution operations, capture long-distance time dependencies with fewer layers, and the gradient is more easily propagated in the deep network, and there is no gradient vanishing problem in RNN, which makes the model easier to train. Compared with LSTM, BiGRU has a smaller amount of computation and faster training speed due to the simplified gating mechanism. Without losing the ability to model long-term dependencies, the structure of LSTM is simplified and the amount of computation is reduced. The prediction process of the NOA-BiTCN-BiGRU model is as follows: Figure 5 shown.

[0099] In the above embodiment, QR quantile regression (Quantile Regression, QR) is a statistical method used to estimate the relationship between the conditional quantile of the dependent variable and the independent variable. Its goal is to predict a specific quantile of the dependent variable instead of predicting the mean or median. This method can provide more comprehensive information about the data distribution and is more robust to the regression prediction of skewed data.

[0100] QR estimates the regression coefficients at different quantiles by minimizing the following asymmetric loss function:

[0101]

[0102] The above formula can be equivalent to:

[0103]

[0104] Among them, ρ τ (u) = u(τ - I(u<0)), I(Z) is an indicative function, indicating that it returns 1 when u is less than zero, otherwise it returns 0.

[0105] The two models optimized using NOA mentioned above are combined with phase space reconstruction technology and QR quantile regression to form a complete system framework, such as Figure 6 shown.

[0106] In order to further better explain the above embodiment, the present invention uses two data sets for nonlinear time series analysis. The first data set (data1) comes from the public data set of the 2022 Baidu KDD CUP competition. The time resolution is 10 minutes, and a total of 1391 data points are selected. Figure 7 The second data set (data2) comes from the SotaventoGalicia wind farm in Spain (www.sotaventogalicia.com), with a time resolution of 10 minutes and a total of 3312 data points. Figure 8 As shown in the figure, the selected data has no missing values. The first 70% of the data set is used as training data, and the last 30% is used as test data, which are processed and analyzed using Matlab.

[0107] Example analysis based on data1:

[0108] Using the data1 dataset, when initializing the NOA algorithm, the population size is set to 30, the maximum number of iterations is set to 10, and the ranges of the adjustment factors α and β are [1,10] and [0.1,100]; when the number of iterations is the fifth, the fitness value is 29.57 and the curve tends to be flat, as shown in Fig. 9As shown. The optimal solution adjustment factors α = 10 and β = 0.1 are introduced into the WT model, the wavelet basis is set to db5, the wavelet decomposition level is set to 1, and the wind speed time series is filtered. The NCC value is 0.9994, indicating that the similarity between the two signals is very high. While filtering, useful information is retained as much as possible. The results are shown in Fig.10 As shown: The algorithm is used to calculate the time delay τ=32 and the embedding dimension d=3 of the wind speed time series. The Wolf method is used to determine whether the reconstructed wind speed time series has chaotic characteristics. Its Lyapunov index is 0.1671, and the time series is considered to be chaotic. The NOA-QR-BiTCN-BiGRU model is used for interval prediction.

[0109] The NOA algorithm is used to optimize the parameters of the BiTCN-BiGRU model to obtain reasonable parameter values. The optimized parameters are: the number of filters, the number of neurons, the initialization learning rate and the regularization parameter. The upper bound of the parameter range is [0.1, 18, 10, 0.01] and the lower bound is [0.001, 3, 1, 0.00001]. The remaining hyperparameters and network structure settings are shown in Table 2 below:

[0110] Table 2 Hyperparameters and network structure settings

[0111]

[0112]

[0113] In the optimization process, the minimum root mean square error is used as the objective function. When the number of iterations is completed, each parameter value corresponding to the minimum fitness value is saved as the optimized parameter value. The model proposed in the present invention is used to perform interval prediction on the filtered signal after phase space reconstruction. The predicted value is basically consistent with the actual value, such as Fig.11 As shown: NOA-QR-BiTCN-BiGRU has the smallest prediction error, with MSE, RMSE and MAE of only 0.2938, 0.5421 and 0.3799, and the highest prediction accuracy. PICP is 0.9607, indicating that the interval predicted by the model can cover about 96.07% of the true value. Its prediction interval coverage is the highest compared with other models, and it can better capture real data and has higher reliability. PIMW is 64.0593. The prediction interval of the model is narrow. The more accurate the model's prediction is, the less redundancy in the prediction range while the model provides accurate predictions. Therefore, the NOA-QR-BiTCN-BiGRU model not only has a strong prediction interval coverage capability, but also can achieve higher accuracy with a smaller prediction interval.

[0114] Example analysis based on data2:

[0115] Using the data2 dataset, when initializing the NOA algorithm, set the parameters exactly the same as those in Example Analysis 1. When the number of iterations is the third, the fitness value is -27.38092 and the curve tends to be flat, as shown in Fig.12 shown.

[0116] The optimal solution adjustment factors α = 10 and β = 100 are introduced into the WT model, the same parameters are set, and the wind speed time series is filtered. The NCC value is 0.9990, indicating that the similarity between the two signals is very high. While filtering, useful information is retained as much as possible. The results are as follows Fig.13 shown.

[0117] According to the algorithm, the time delay τ=35 and the embedding dimension d=4 of the wind speed time series are obtained. The Wolf method is used to determine whether the reconstructed wind speed time series has chaotic characteristics. Its Lyapunov index is 0.1862, which means that the time series has strong nonlinearity. The NOA-QR-BiTCN-BiGRU model is used for interval prediction.

[0118] The same hyperparameters and network structure are set, and the model proposed in the present invention is used to perform interval prediction on the filtered signal after phase space reconstruction. The predicted value is basically consistent with the actual value, such as Fig.14 shown.

[0119] From the above, we can see that NOA-QR-BiTCN-BiGRU has the smallest prediction error, with MSE, RMSE and MAE of only 0.6391, 0.7994 and 0.5665, indicating that the model has high prediction accuracy and can effectively capture trends and features in the data. PICP is 0.9719, indicating that the interval predicted by the model can cover about 97.19% of the true value, has high interval reliability, and can provide robust interval prediction results. PIMW is 93.0, and the prediction interval of this model is the narrowest among all the comparison models, indicating that while ensuring high coverage, the model can effectively narrow the prediction interval and improve the accuracy and efficiency of the prediction. Therefore, NOA-QR-BiTCN-BiGRU not only has excellent point prediction performance, but also shows good balance in interval prediction, and can achieve a good balance between coverage and interval width.

[0120] Result analysis based on data1:

[0121] In all single machine learning models and combined deep learning models, the same hyperparameters and network structures are set to study the effects of different model combinations on prediction accuracy. The results are shown in Table 3. Fig.15 and Fig.16 shown.

[0122] Table 3 Prediction evaluation indicators of different combination models

[0123]

[0124]

[0125] From the above, we can see that the error MSE, RMSE and MAE of the combined model (QRTCN-GRU and QRBiTCN-BiGRU) decreased by an average of 65.09%, 40.21% and 38.10% compared with the single machine learning models (QRTCN, QRGRU, QRBiTCN and QRBiGRU), indicating that the combined model can significantly reduce the prediction error. The PICP interval coverage increased by an average of 16.66%, indicating that the combined model is more reliable when predicting uncertainty and can better predict the possibility that the true value falls within the interval. The average width of the PIMW interval decreased by an average of 47.94%, indicating that while the combined model improves coverage, the prediction interval is also more compact and the accuracy is improved. Therefore, the combined model combines the advantages of multiple models, can better capture the complexity of the data, and improve the prediction performance.

[0126] Compared with the unidirectional deep learning model, the error MSE, RMSE and MAE of the bidirectional deep learning model decreased by 4.20%, 2.41% and 2.26% on average, indicating that the bidirectional model can learn from the forward and backward time information and still bring a certain error reduction. PICP increased by 22.951% on average, indicating that the bidirectional model is also slightly more reliable in the prediction interval and can better envelop the actual value. PIMW decreased by 27.57% on average, indicating that the bidirectional deep learning model can maintain the compactness of the prediction interval while increasing the coverage, reducing unnecessary interval width, and making the prediction more accurate.

[0127] Ablation experiment based on data1:

[0128] The purpose of the ablation experiment is to gradually remove components or modules in the model and observe the changes in model performance, so as to evaluate the contribution of each component to the overall model performance. In the system model proposed in this invention, the NOA algorithm, phase space reconstruction technology and WT filtering are removed respectively, and three comparative experiments are designed to understand the impact of each part on the prediction accuracy, as shown in Table 4 and Fig.17 shown.

[0129] Table 4 Comparison of evaluation indicators of ablation experiments

[0130]

[0131]

[0132] From the above, we can see that the NOA optimization algorithm has the greatest impact on the model, which can reduce the error MSE, RMSE and MAE by 80.57%, 55.91% and 62.40%, increase the PICP interval coverage by an average of 1.81%, and reduce the average width of the PIMW interval by an average of 250.78%, indicating that the prediction interval becomes narrower, thereby improving the prediction accuracy. Secondly, the phase space reconstruction technology can reduce the model's error MSE, RMSE and MAE by 43.92%, 25.11% and 31.37%, increase the PICP interval coverage by an average of 5.1%, and reduce the average width of the PIMW interval by an average of 167.89%, indicating that its effect on improving the coverage is more significant. The WT filtering technology has the smallest contribution to the model, with MSE, RMSE and MAE reduced by 27.52%, 14.86% and 17.09%, PICP interval coverage increased by an average of 3.8%, and PIMW interval average width reduced by an average of 70.90%, which can improve the model performance to a certain extent.

[0133] In order to further explore the improvement of the NOA algorithm on the model robustness, experiments were conducted on data sets with data processing (filtering + phase space reconstruction) and without any data processing. The experimental results are shown in Tables 5 and Fig.18 shown.

[0134] Table 5 Comparison of evaluation indicators

[0135]

[0136] From the above, we can see that the NOA optimization algorithm can reduce the model's error MSE, RMSE and MAE by an average of 23.89%, 32.40% and 39.71%, increase the PICP interval coverage by an average of 3.33%, and reduce the average width of the PIMW interval by 412.28%. In addition, the NOA optimization algorithm reduces the MSE, RMSE and MAE of the model with data processing by 20.97%, 14.90% and 18.05% compared with the model without data processing, increases the PICP interval coverage by 10.79%, and reduces the average width of the PIMW interval by 53.80%. Therefore, the NOA optimization algorithm further improves the robustness of the model on the model with data processing, not only significantly reducing the model's error, but also improving the coverage of the prediction interval and significantly reducing the width of the interval.

[0137] Algorithm comparison based on data1:

[0138] In order to prove that the NOA algorithm has higher prediction accuracy in optimizing deep learning models, this paper compares it with the most advanced SSA optimization algorithm. The SSA algorithm is widely used for its excellent performance and is one of the most widely used optimization algorithms today. In order to make a fair comparison, this paper designed experiments to optimize deep learning models using the NOA and SSA algorithms respectively, and ensured that the experiments were carried out under the same hyperparameters and network structure conditions to objectively evaluate the optimization effects of the two algorithms. First, the SSA algorithm was used to optimize the adjustment factor [α , β], and the same optimal parameter combination as NOA-WT [10,0.1] is obtained, and the corresponding fitness value is -29.57. The optimal adjustment factors α=10 and β=0.1 are introduced into the WT model to filter the wind speed time series. The filtering results are as follows Fig.19 shown.

[0139] Then, the phase space of the data after SSA-WT filtering is reconstructed. Its Lyapunov index is 0.1671, and the time series is considered to be chaotic. Therefore, after phase space reconstruction, the SSA-QR-BiTCN-BiGRU model is used for interval prediction. The final prediction results are as follows: Fig. 20 shown.

[0140] As shown in Table 6, compared with the SSA optimized model, the NOA optimization has a smaller prediction error with a reduction of 60.10%, 36.83% and 43.16% in MSE, RMSE and MAE. The PICP interval coverage rate increased by an average of 7.39%, indicating that the prediction interval covers a higher proportion of the true value and has a stronger credibility. The average width of the PIMW interval decreased by 67%, which means that the prediction interval is more accurate and concentrated, and closer to the actual situation.

[0141] Table 6 Comparison of NOA and SSA evaluation indicators

[0142]

[0143] Analysis of data2 results:

[0144] In all single machine learning models and combined deep learning models, the same hyperparameters and network structures are set to study the effects of different model combinations on prediction accuracy. The results are shown in Table 7. Fig.21 and Fig. 22 shown.

[0145] Table 7 Prediction evaluation indicators of different combination models

[0146]

[0147]

[0148] From the above, we can see that the error MSE, RMSE and MAE of the combined model (QRTCN-GRU and QRBiTCN-BiGRU) decreased by an average of 55.11%, 34.43% and 35.89% compared with the single machine learning model (QRTCN, QRGRU, QRBiTCN and QRBiGRU), indicating that the combined model has a significant improvement in prediction accuracy, can better fit the data and reduce prediction errors. The PICP interval coverage increased by an average of 9.99%, indicating that the combined model has higher reliability in interval prediction and can cover the true value more comprehensively. . The average width of the PIMW interval decreased by an average of 101.831%, indicating that the combined model successfully narrowed the prediction interval while maintaining a high coverage rate, improving the efficiency and accuracy of interval prediction.

[0149] Compared with the unidirectional deep learning model, the error MSE, RMSE and MAE of the bidirectional deep learning model decreased by 26.46%, 16.50% and 13.14% on average, indicating that the bidirectional model has a significant improvement in prediction accuracy and can capture data features and trends more comprehensively. PICP increased by an average of 15.27%, indicating that the bidirectional model is more reliable in interval prediction and can cover more true values. PIMW increased by an average of 71.68%, indicating that the interval width of the bidirectional deep learning model increased, the prediction interval was relatively wide, and there may be interval redundancy, indicating that there is still room for improvement in the optimization of interval width. Therefore, although the bidirectional model has improved in accuracy and coverage, while improving the accuracy of the prediction interval, the interval width needs to be further optimized to improve the overall efficiency.

[0150] Perform ablation experiment on data2:

[0151] In Example Analysis 2, an ablation experiment was also designed. The same parameter settings and network structure design were maintained. The NOA optimization algorithm, phase space reconstruction technology, and VMD data decomposition were removed respectively. Three comparative experiments were designed to understand the impact of each part on the prediction accuracy, as shown in Table 8 and Fig.23 shown.

[0152] Table 8 Comparison of evaluation indicators of ablation experiments

[0153]

[0154] From the above, we can see that the NOA optimization algorithm has the greatest impact on the model, which can reduce the error MSE, RMSE and MAE by 72.14%, 47.21% and 52.34%, increase the PICP interval coverage by an average of 6.05%, and reduce the average width of the PIMW interval by an average of 174.62%, indicating that the prediction interval is significantly narrowed and the coverage is improved, and the prediction accuracy of the model is greatly improved. Secondly, WT filtering can reduce the model's error MSE, RMSE and MAE by 40.99%, 23.18% and 27.52%, increase the PICP interval coverage by an average of 4.21%, and reduce the average width of the PIMW interval by an average of 135.02%, indicating that it is more significant in reducing errors and improving interval coverage, and the accuracy of the prediction interval has been enhanced. The phase space reconstruction technique contributes the least to the model, with MSE, RMSE and MAE reduced by 11.65%, 6.01% and 10.31%, respectively, the PICP interval coverage increased by an average of 2.59%, and the average width of the PIMW interval decreased by an average of 138.31%, indicating that the improvement is limited, but it can still optimize the prediction performance of the model to a certain extent.

[0155] In order to further explore the improvement of the NOA algorithm on the model robustness, experiments were conducted on data sets with data processing (filtering + phase space reconstruction) and without any data processing. The experimental results are shown in Tables 9 and Fig.24 shown.

[0156] Table 9 Comparison of evaluation indicators

[0157]

[0158] From the above, we can see that the NOA optimization algorithm can reduce the model's error MSE, RMSE and MAE by an average of 63.97%, 40.37% and 67.33%, increase the PICP interval coverage by an average of 6.73%, and reduce the average width of the PIMW interval by 126.50%. In addition, the NOA optimization algorithm reduces the MSE, RMSE and MAE of the model with data processing by 62.42%, 39.71% and 68.79, the PICP interval coverage increases by 6.73%, and the average width of the PIMW interval decreases by 126.5067% compared with the model without data processing. Therefore, the NOA optimization algorithm can significantly improve the prediction performance under different model conditions, reduce errors and improve interval coverage, while effectively narrowing the prediction interval width, making the model more accurate and robust under the processed data conditions.

[0159] Algorithm comparison based on data2:

[0160] First, the SSA algorithm is used to optimize the adjustment factor [α ,β], and the same optimal parameter combination as NOA-WT is obtained [10,100], and the corresponding fitness value is -27.38092. The optimal adjustment factors α=10 and β=100 are introduced into the WT model to filter the wind speed time series. The filtering results are as follows Fig.25 shown.

[0161] Then, the phase space of the data after SSA-WT filtering is reconstructed. Its Lyapunov index is also 0.1862. It is considered that the time series is chaotic. Therefore, after phase space reconstruction, the SSA-QR-BiTCN-BiGRU model is used for interval prediction. The final prediction results are as follows: Fig.26 shown.

[0162] As shown in Table 10, compared with the SSA optimized model, the NOA optimization has a smaller prediction error with a reduction of 10.39%, 5.34% and 7.07% in MSE, RMSE and MAE. The PICP interval coverage rate increased by 0.78%, indicating that the NOA optimized model has better prediction interval coverage and can more accurately cover the range of true values. The average width of the PIMW interval decreased by 81.78%, which means that the NOA optimization algorithm not only improves the accuracy of the prediction, but also narrows the prediction interval, making the prediction results more concentrated, thereby improving the credibility and reliability of the model.

[0163] Table 10 Comparison of NOA and SSA evaluation indicators

[0164]

[0165] In summary: the wind speed time series prediction method based on algorithm optimization and data denoising provided by the present invention has a better data fitting effect than the unidirectional machine learning model, and can more effectively fit the data, significantly reduce the prediction error (MSE, RMSE, MAE) and improve the interval coverage (PICP), indicating that the bidirectional model can more comprehensively capture the dependencies in the time series. Secondly, the NOA-WT filtering model of the present invention can effectively reduce the error of the deep learning model, and can effectively filter out noise while maintaining the signal characteristics, thereby improving the prediction accuracy of the model. Compared with the model without WT filtering, the NOA-WT model significantly reduces the prediction error by about 50%-80%, the PICP interval coverage rate increases by about 4.21%, and the average width of the PIMW interval is reduced by about 212%. Again, the phase space reconstruction technology of the present invention can better capture the chaotic characteristics in the time series by reconstructing the embedding dimension of the time series, significantly reducing the prediction error by about 25%-30%, making the prediction of the deep learning model on this basis more accurate, and further improving the prediction performance of the model. Moreover, the NOA optimization algorithm of the present invention can enhance the robustness of the deep learning model, significantly reduce the prediction error when processing data, and maintain high robustness under different data processing conditions, especially under various model conditions, it can improve the accuracy of the model and the prediction interval coverage ability. In addition, the NOA-QR-BiTCN-BiGRU model proposed in the present invention shows lower error, higher interval coverage and narrower prediction interval in various comparisons, which is significantly better than traditional optimization algorithms and other combined models, proving that it has better comprehensive prediction ability and application value in wind speed interval prediction.

[0166] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A wind speed time series prediction method based on algorithm optimization and joint data denoising, characterized in that: The following steps are involved: S1: Use the Nutcracker Optimization Algorithm (NOA) to optimize the two adjustment factors of the wavelet threshold filter WT, and apply the NOA-WT model to filter the wind speed data; S2: Reconstruct the phase space of the processed data, calculate the Lyapunov exponent and identify its chaotic characteristics; S3: Quantile regression QR interval prediction using the NOA-optimized deep learning model BiTCN-BiGRU.

2. A wind speed time series prediction method based on algorithm optimization and data denoising as claimed in claim 1, characterized in that: The wavelet threshold function in S1 is divided into hard threshold function and soft threshold function, where the wavelet coefficients less than the threshold are generated by noise, while the wavelet coefficients greater than the threshold are generated by valid signals. The calculation formula is as follows: Hard threshold function: Soft threshold function: Among them, W j,k is the wavelet coefficient after threshold processing, w j,k is the wavelet decomposition coefficient, 3. A wind speed time series prediction method based on algorithm optimization and data denoising as claimed in claim 2, characterized in that: The function expression of using NOA to optimize the WT filter model in S1 is as follows: Among them, α and β are adjustment factors. By adjusting the two parameters α and β, the deviation of the signal in the threshold function is reduced, thereby obtaining a better filtering effect.

4. The method for wind speed time series prediction based on algorithm optimization and data denoising as claimed in claim 1, characterized in that: The condition for phase space reconstruction in S2 is: d>2D+1, where d is the embedding dimension and D is the system correlation dimension. The time delay and embedding dimension are estimated using the correlation integral. Considering τ and d at the same time, the correlation integral of the embedded time series is used to analyze the correlation of the time series and obtain the statistic S cor (τ) and according to S cor (τ), and τ to obtain the optimal delay time τ d and the embedding window τ w , and finally find the embedding dimension d.

5. The method for wind speed time series prediction based on algorithm optimization and data denoising as claimed in claim 1, characterized in that: The bidirectional temporal convolutional network (BiTCN) in the deep learning model in S3 uses convolutional neural network (CNN) to efficiently process time series data. The specific methods include: (1) Dilated convolution: By stacking diluted kernels with an expansion base d, a certain number of input data points are skipped in the convolution operation, so that the convolution kernel can expand the receptive field without increasing the computational cost; (2) GELU activation function: Use Gaussian error linear unit instead of traditional ReLU activation function, so that the model returns some small negative values, thereby improving the learning ability of the model; (3) Dropout layer: By randomly discarding the outputs of some neurons, the network is prevented from overfitting and the generalization ability of the model is improved.

6. A wind speed time series prediction method based on algorithm optimization and data denoising as claimed in claim 5, characterized in that: The bidirectional gated recurrent unit BiGRU in the deep learning model in S3 is a recurrent neural network architecture based on the gated recurrent unit GRU for processing sequence data. The calculation process of the gated recurrent unit GRU is as follows: (1) Update gate z t : Determines how much of the state of the current time step comes from past information and how much comes from the current input, allowing the network to selectively retain variable information: z t =σ(W z ·[h t-1 ,x t ]+b z ) (2) Reset gate r t : Determines how the current input is combined with past information. If the value is close to 0, it means that the network will discard the past hidden state and only use the current input for update: r t =σ(W r ·[h t-1 ,x t ]+b r ) (3) Hidden state Adjust the past state according to the reset gate and update the gate z t Under the control of , the new input is combined with the past hidden state to generate a new hidden state: In the formula, x t is the input data of the current time step, σ represents the sigmoid activation function, W represents the weight matrix of the update gate, and h t-1 represents the hidden state at the previous moment, and b represents the bias term; In GRU, the hidden state h t Considering only information from previous time steps and the current input, BiGRU uses two independent GRU networks to process the time series forward and backward, respectively.

7. A wind speed time series prediction method based on algorithm optimization and data denoising as claimed in claim 6, characterized in that: The method of using NOA to optimize the deep learning model BiTCN-BiGRU in S3 includes: using the NOA algorithm to optimize the four parameters of the number of filters in the BiTCN model, the number of neurons in the BiGRU unit, and the learning rate and regularization parameters in the combined model, and finding a suitable hyperparameter combination in the complex search space.

8. The method for wind speed time series prediction based on algorithm optimization and data denoising as claimed in claim 7, characterized in that: Quantile regression QR in S3 is a statistical method used to estimate the relationship between the conditional quantile of the dependent variable and the independent variable. The goal of QR is to predict a specific quantile of the dependent variable and estimate the regression coefficients at different quantiles by minimizing the following asymmetric loss function: The above formula can be equivalent to: Among them, ρ τ (u) = u(τ-I(u<0)), I(Z) is an indicative function, which means that it returns 1 when u is less than zero, otherwise it returns 0; the two models optimized by NOA are combined with phase space reconstruction technology and QR quantile regression to form a complete prediction framework.

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