Laser wind finding radar missing measurement data filling method based on DFA scale index

Abstract

The invention discloses a laser wind-finding radar missing measurement data filling method based on a DFA scale index, and the method comprises the following steps: (1) carrying out the standardization processing and quality control of the original data of a laser wind-finding radar, and obtaining the wind speed standardization data; step (2), performing detrending fluctuation analysis on the wind speed standardized data and calculating a DFA scale index; combining the wind speed standardized data with the DFA scale index to construct wind speed data containing the DFA index; (3) dividing the wind speed data containing the DFA index into a training set and a test set; performing machine learning model training by using the training set to generate a missing data filling model; and step (4), filling the missing measurement data of the laser wind finding radar by using the evaluated missing measurement data filling model. The method can solve the problem that the existing laser wind-finding radar missing measurement data filling method depends on artificial experience and cannot fully utilize the internal physical mechanism of the wind speed, so that the data restoration precision is not ideal.

Description

Technical Field

[0001] This invention relates to the field of meteorological data processing technology. Specifically, it is a method for filling in missing data from laser wind radar based on the DFA scaling index. Background Technology

[0002] As a core device for wind energy resource assessment and meteorological monitoring, the continuity of data from laser wind radar directly impacts the accuracy of wind farm site selection, weather forecasting, and extreme weather warnings. However, during equipment operation, environmental interference such as power outages, low clouds, and precipitation often leads to missing data. Traditional interpolation methods (such as linear interpolation and mean fill) struggle to capture the nonlinear temporal characteristics and long-term persistence of wind speed, resulting in significant reconstruction errors. In recent years, machine learning models (such as random forests and neural networks) have been introduced into the field of data restoration, but problems remain, including reliance on human experience in feature construction and insufficient utilization of the inherent physical mechanisms of wind speed.

[0003] Existing research has explored various methods to impute missing data in different scenarios. Traditional statistical methods such as Multiple Linear Regression (MLR) have shown outstanding performance in meteorological data restoration. Experiments by Sun Yue et al. on temperature data in Hubei Province demonstrated that MLR's error was significantly lower than that of Inverse Distance Weighted (IDW) and Ordinary Kriging (OK), with a more uniform error distribution and less influence from altitude and season. Regarding machine learning models, Generative Adversarial Networks (GANs), combining autoencoders and attention mechanisms, effectively restore missing values ​​in multidimensional time series. Zhao Jingqi et al. verified its superiority in complex time series on the PhysioNet dataset. Yang et al. used Self-Associative LSTM (AALSTM) to handle multidimensional time series missing data through the synergy of historical and current information, validating its effectiveness on multiple datasets. Li Yan et al. utilized a spatiotemporal hybrid interpolation method, integrating time series and spatial characteristics, to significantly improve the accuracy of real-time missing data restoration in Chongqing meteorological data, validating the necessity of spatiotemporal joint modeling.

[0004] Detrended volatility analysis (DFA) can quantify the long-range persistence characteristics of time series, and its scaling exponent α can effectively characterize the long-term memory of wind speed, and also plays a role in data imputation. Existing studies mostly use DFA for wind speed mechanism analysis, and rarely introduce it as a feature into data imputation models. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to provide a method for filling in missing data of laser wind radar based on the DFA scaling index, so as to solve the problem that the existing methods for filling in missing data of laser wind radar rely on human experience and cannot make full use of the inherent physical mechanism of wind speed, resulting in unsatisfactory data repair accuracy.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] A method for filling in missing data from a laser wind radar based on the DFA scaling index includes the following steps:

[0008] Step (1): Standardize and quality control the raw data of the laser wind radar to obtain standardized wind speed data;

[0009] Step (2): Perform detrended fluctuation analysis on the wind speed standardized data and calculate the DFA scaling index; combine the wind speed standardized data with the DFA scaling index to construct wind speed data containing the DFA index;

[0010] Step (3): Divide the wind speed data containing the DFA index into a training set and a test set; use the training set to train a machine learning model and generate a missing data imputation model; use the test set to evaluate the performance of the generated missing data imputation model.

[0011] Step (4): Use the evaluated missing data to fill in the missing data of the laser wind radar.

[0012] This invention presents a method for incomplete data restoration from laser wind-measuring radar based on the Detrended Fluctuation Analysis (DFA) scaling exponent. The method standardizes and performs quality control on the raw laser wind-measuring radar data; extracts a feature set containing wind speed time series and related physical quantities; and introduces a scaling exponent from Detrended Fluctuation Analysis (DFA) as a new feature. Based on the optimized feature set, random forest, K-nearest neighbor, and artificial neural network models are trained respectively to generate incomplete models. The effectiveness is verified by comparing the model performance before and after introducing the DFA exponent. This method provides a new approach for the efficient restoration of laser wind-measuring radar data and has significant application value in fields such as wind energy resource assessment and meteorological forecasting.

[0013] In the above-mentioned method for filling missing data of laser wind radar based on DFA scaling index, in step (1), the original data of laser wind radar is the radial data and wind field data of each height layer observed by the radar station at a certain time; the data file after standardization contains the wind speed time series of all times at each height layer; the quality control includes boundary value check, missing value check, duplicate value check and spatiotemporal consistency check.

[0014] The above-mentioned method for filling in missing data in laser wind radar based on the DFA scaling index includes the following steps in step (2):

[0015] Step (2-1): Accumulate the anomaly sequences of the original wind speed standardized data to obtain the profile sequence;

[0016] Step (2-2): First, decompose the profile sequence into windows of equal time length that do not overlap. Then, divide the windows again from the tail of the profile sequence in the opposite direction to obtain non-overlapping windows.

[0017] Steps (2-3): Within each window, fit the profile sequence using a k-order polynomial to obtain the fitted trend sequence; then subtract the fitted trend sequence from the profile sequence in all windows to obtain the detrended sequence.

[0018] Steps (2-4): Calculate the variance function of the detrended sequence in each window, and use the variance function to calculate the volatility function; finally, use the volatility function to calculate the DFA scaling index.

[0019] In the above-mentioned method for filling in missing data from laser wind radar based on the DFA scaling index, the calculation method for the profile sequence in step (2-1) is as follows:

[0020]

[0021] In equations (1) to (3), {x i} represents the original sequence. The average value of the original sequence, {x} i ′} is the anomaly sequence, {Y(j)} is the profile sequence, and N is a positive integer greater than or equal to 1;

[0022] In step (2-2), the method for dividing the windows into non-overlapping sections is as follows: N s = N / s; N s Let be the number of unidirectional partitioning windows, and s be the equal time length; step (2-2) yields a total of 2N. s One window;

[0023] In steps (2-3), the detrended sequence is calculated as follows:

[0024]

[0025] In equation (4), {Y s (j)} is a detrended sequence, The fitted trend sequence; k = 2;

[0026] In steps (2-4), the variance function The method for calculating the wave function F(s) is as follows:

[0027]

[0028] In equation (5), Here, v is the variance function, and v is the window number.

[0029]

[0030] The above-mentioned method for filling in missing data in laser wind radar based on the DFA scaling index, and the calculation method of the DFA scaling index: original sequence {x i The function F(s) and the window s are long-range dependent, and a power-law scaling relationship should be satisfied between them: F(s) ~ s. α Taking the logarithm of F(s) and s, we obtain lg(F(s)) and lg(s) respectively. We then perform a linear fit between lg(F(s)) and the window size lg(s) to obtain the scaling exponent α.

[0031] In the above-mentioned method for filling missing data of laser wind radar based on DFA scaling index, in step (3), the machine learning model is a random forest model, a K-nearest neighbor model, or an artificial neural network model.

[0032] In the above-mentioned method for filling missing data of laser wind radar based on DFA scaling index, the machine learning model in step (3) is a random forest model.

[0033] The aforementioned method for imputing missing data in laser wind radar based on the DFA scaling index utilizes a random forest model to generate the imputation model. The method involves: randomly selecting N samples with replacement from the training set to form a training subset for each decision tree; and randomly selecting m candidate features from all features when splitting nodes in each tree. p represents the total number of features. The optimal split point is selected only on this training subset to introduce randomness and reduce the risk of overfitting. The data is recursively divided based on the CART (Classification and Regression Tree) algorithm until the preset termination condition is reached, thereby generating a decision tree. The prediction results of each tree are averaged as the final output.

[0034] The method for generating missing data to fill in the model using the K-nearest neighbor model is as follows: For the sample to be predicted, calculate its Euclidean distance with all samples in the training set; sort by distance and select the K nearest samples as "neighbors"; take the mean or weighted mean of the target values ​​of the K "neighbors" as the predicted value.

[0035] The method for generating missing data to impute models using artificial neural network models is as follows: The artificial neural network model is structured into an input layer, hidden layers, and an output layer. The number of nodes in the input layer equals the feature dimension, and it is responsible for receiving the raw data. The hidden layers consist of 1-3 layers, with parameter tuning for the number of nodes in each layer, introducing non-linearity through activation functions. The output layer uses a linear activation function to output the results. Data is passed from the input layer to the output layer layer by layer, and each layer is calculated as: z l =W l a l-1 +b l a l =g(z) l); where W l and b l Here, g represents the weights and biases of the l-th layer, and g is the activation function; the loss function uses mean squared error. The backpropagation algorithm is used to calculate the gradient during the calculation process, and the weights are updated in combination with the optimizer to minimize the loss function.

[0036] In the above-mentioned laser wind radar missing data imputation method based on DFA scaling index, step (3) includes the coefficient of determination R as the performance evaluation index of the missing data imputation model. 2 Root mean square error (RMSE) and bias;

[0037]

[0038] In equations (7) to (9), y i It is the actual value. It is a predicted value. is the mean of the true values, and n is the sample size.

[0039] The technical solution of the present invention achieves the following beneficial technical effects:

[0040] 1. The present invention provides a method for filling in missing data of laser wind radar based on the DFA scaling index. By combining the DFA scaling index with a machine learning model, the DFA scaling index is introduced as a feature to enhance the machine learning model's ability to represent the long-term persistence of wind speed, thereby significantly improving the filling accuracy.

[0041] 2. In the laser wind radar missing data filling method based on DFA scaling index of the present invention, the introduced DFA index of wind speed sequence can better capture the trend of wind speed change over time. By introducing the DFA index of wind speed at each height level, the machine learning model can contain more information on the physical dynamic law of wind speed, making the prediction results closer to the actual wind speed, thereby making the reliability of the wind speed filling model higher, which is helpful for the research of wind field data interpolation methods and the acquisition of more complete wind speed change data. Attached Figure Description

[0042] Figure 1 A flowchart of a method for filling missing data in laser wind radar based on the DFA scaling index in an embodiment of the present invention;

[0043] Figure 2 In the embodiments of the present invention, the R-values ​​of each wind speed prediction model before and after introducing the DFA exponent are as follows: 2 Statistical chart;

[0044] Figure 3 RMSE statistics of each wind speed prediction model before and after introducing the DFA index in the embodiments of the present invention;

[0045] Figure 4 Bias statistics of each wind speed prediction model before and after introducing the DFA index in the embodiments of the present invention. Detailed Implementation

[0046] This embodiment takes the minute-by-minute wind speed data of Guangzhou laser wind radar from January 2023 to March 2025 as an example to further illustrate the missing data filling method of laser wind radar based on DFA scaling index of the present invention.

[0047] I. Research Data

[0048] This embodiment utilizes the Wind Print S4000 coherent Doppler lidar manufactured by Qingdao Huahang Environmental Technology Co., Ltd. in Shandong Province, located in Guangzhou. It obtains atmospheric wind field information by measuring the movement of aerosol particles, with a detection range from 50m to 6000m. The data used in this embodiment is minute-by-minute wind speed, covering the period from January 2023 to March 2025. All data underwent quality control according to previous research methods, including checks for duplicate values, outliers, missing values, and spatial consistency.

[0049] II. Data Filling Method for Laser Wind Measurement Radar Based on DFA Scale Index

[0050] The research process of this embodiment is as follows: Figure 1 As shown, the detailed steps are explained below:

[0051] 1. Data standardization and quality control

[0052] 1.1 The raw data files of the laser wind radar are generally named according to the observation time. Therefore, a data file usually contains various data of a certain radar station A at a certain observation time T, including radial data and wind field data at each height level. After the collected raw data is standardized, a new data file is obtained after re-extraction and organization. The new file contains the wind speed time series of all times at each height level of the laser wind radar at radar station A.

[0053] 1.2 Perform basic quality control on the standardized data to remove erroneous data to avoid affecting the final result; quality control includes: boundary value checking, missing value checking, duplicate value checking, and spatiotemporal consistency checking; retain the quality-controlled data for subsequent processing.

[0054] 2. Calculate the DFA scaling exponent

[0055] 2.1 Given an original sequence {x} i}; i = 1, 2, ..., N, the anomaly sequence of the original sequence By accumulating the data, we obtain the profile sequence: Where: {x i} represents the original sequence; The average value of the original sequence; {x i ′} represents the anomaly sequence; {Y(j)} represents the profile sequence; N is a positive integer greater than or equal to 1;

[0056] 2.2 Decompose the profile sequence {Y(j)} into N segments of equal time length s that do not overlap. s =N / s windows; then, starting from the end of the sequence, perform another window division in the reverse direction, similarly obtaining N non-overlapping windows. s 1 window; get 2N s There are 10 windows, and each window is numbered v.

[0057] 2.3 Within each window v, the profile sequence {Y(j)} is fitted using a k-th order polynomial to obtain the fitted trend sequence. Then, subtract the fitted trend sequence from the profile sequence {Y(j)} in all windows. This yields the detrended sequence {Y}. s (j)}: Where k = 2;

[0058] 2.4 For detrended series, calculate the variance function in each window.

[0059] 2.5 will 2N s The square root of the summation of the variance functions calculated in each window yields the fluctuation function F(s) to be calculated.

[0060] 2.6 Original sequence {x i The function F(s) and the window s are long-range dependent, and a power-law scaling relationship should be satisfied between them: F(s) ~ s. α Taking the logarithm of F(s) and s, we obtain lg(F(s)) and lg(s) respectively. We then perform a linear fit between lg(F(s)) and the window size lg(s) to obtain the scaling exponent α.

[0061] 3. Train the machine learning model

[0062] 3.1 Prepare wind speed sequence datasets with DFA exponent and datasets containing only wind speed, and divide them into training set and test set. The test set is reserved for performance evaluation, and the training set is used for model training. Train the model with DFA exponent and the model without DFA exponent respectively.

[0063] 3.2 Random Forest is a supervised algorithm based on ensemble learning. It improves model performance by constructing multiple decision trees and integrating their prediction results. The core steps include: randomly selecting N samples (N being the dataset size) with replacement from the original dataset to form the training subset for each decision tree; and randomly selecting m candidate features (usually 1000 m) from all features when splitting at a node of each tree. p is the total number of features. The optimal split point is selected only on this subset to introduce randomness and reduce the risk of overfitting. The data is recursively divided based on the CART (Classification and Regression Tree) algorithm until the preset termination condition is reached (such as the number of node samples is less than the threshold or the purity no longer increases), thereby generating a decision tree. The prediction results of each tree are averaged as the final output.

[0064] 3.3 K-Nearest Neighbors (KNN) is an instance-based lazy learning algorithm whose predictions directly depend on the spatial distribution of the training samples. The specific process is as follows: For the sample to be predicted, calculate its Euclidean distance to all samples in the training set; sort by distance and select the K nearest samples as "neighbors"; take the mean or weighted mean of the target values ​​of the K neighbors (weights are inversely proportional to the distance) as the predicted value.

[0065] 3.4 Artificial Neural Networks (ANNs) achieve complex nonlinear mappings by simulating the structure of biological neurons. Taking a Multilayer Perceptron (MLP) as an example, its core method is as follows: The network structure consists of an input layer, hidden layers, and an output layer. The number of nodes in the input layer equals the feature dimension, and it is responsible for receiving the raw data. The hidden layers typically have 1-3 layers, and the number of nodes in each layer needs to be tuned (e.g., 64, 128, etc.). Nonlinearity is introduced through activation functions (e.g., ReLU, Sigmoid). The output layer uses a linear activation function to output the result. Data is passed from the input layer to the output layer layer by layer, and each layer calculates: z l =W l a l-1 +b l ,a l =g(z) l ); where W l and b l Here, g represents the weights and biases of the l-th layer, and g is the activation function; the loss function uses mean squared error. The backpropagation algorithm is used to calculate the gradient during the calculation process, and the weights are updated in combination with optimizers (such as Adam and SGD) to minimize the loss function.

[0066] 4. Evaluate model performance

[0067] Using the model's predicted values ​​and the corresponding test set, calculate the model performance metrics before and after introducing DFA. Performance evaluation metrics include Ra. 2 RMSE and Bias; among which: Where: y i It is the actual value. It is a predicted value. is the mean of the true values, and n is the sample size.

[0068] III. Results and Analysis

[0069] Figures 2 to 4 The paper presents the R-values ​​of three models—Random Forest (RF), K-Nearest Neighbors (KNN), and Artificial Neural Network (ANN)—for predicting wind speed on the corresponding test sets before and after incorporating the DFA exponent as a feature. 2 Values ​​of performance metrics such as RMSE and Bias.

[0070] As can be seen from the figure, the three models already achieved good performance before the introduction of the DFA exponent, with R... 2 All three models showed R values ​​above 0.95. Introducing the DFA exponent as a feature variable improved the predictive performance of all three models. Specifically, the Random Forest model showed the highest R value. 2 It improved by 0.4% and reduced RMSE by 5.0%; the R-squared value of the K-nearest neighbor model... 2 It improved by 0.17% and reduced RMSE by 1.7%; the R of artificial neural networks 2 The improvement was 0.3%, and the RMSE decreased by 3.0%. The results show that introducing the DFA index significantly improves the model's RMSE, with the random forest model showing the best improvement. Therefore, introducing the DFA index of wind speed sequences at various altitudes as feature variables into the existing wind speed data can further improve the performance of machine learning models in wind speed data imputation.

[0071] IV. Conclusion

[0072] This embodiment uses minute-by-minute wind speed data from a Guangzhou laser wind radar from January 2023 to March 2025. It employs machine learning methods such as random forest, K-nearest neighbors, and artificial neural networks, and introduces a scaling index calculated using detrended fluctuation analysis (DFA). By comparing the differences in model prediction performance before and after adding the DFA scaling index, the influence of the DFA scaling index on the filling effect of missing wind speed data from the laser wind radar is explored. The results show that the R² of the random forest model... 2 It improved by 0.4% and reduced RMSE by 5.0%; the R-squared value of the K-nearest neighbor model... 2It improved by 0.17% and reduced RMSE by 1.7%; the R of artificial neural networks 2 It increased by 0.3%, while RMSE decreased by 3.0%.

[0073] Wind speed is a crucial variable in atmospheric science, and the accuracy and completeness of its data are essential for atmospheric research. LiDAR (LiDAR wind radar) is a vital tool for measuring wind speed, capable of acquiring wind field data at various vertical altitudes. This embodiment utilizes machine learning methods to impute missing data from lidar wind radar and compares the performance changes of models before and after introducing the DFA (Digital Facing Amplifier) ​​scaling index. The results show that, based on wind speed as a feature variable, introducing the DFA index of wind speed at each altitude as an additional feature variable effectively improves the predictive performance of various machine learning models. This method yields more complete and accurate wind speed data, providing more reliable data support for wind energy resource assessment and meteorological forecasting.

[0074] Wind speed is influenced by a variety of meteorological factors, and its prediction methods are also diverse. Future research can further incorporate more types of environmental and meteorological variables as features, as well as introduce more novel prediction models to evaluate the impact of different variables and models on wind speed prediction, thereby providing more complete wind speed data.

[0075] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of the claims of this patent application.

Claims

1. A method for filling in missing data in laser wind radar based on the DFA scaling index, characterized in that, Includes the following steps: Step (1): Standardize and quality control the raw data of the laser wind radar to obtain standardized wind speed data; Step (2): Perform detrended fluctuation analysis on the standardized wind speed data and calculate the DFA scaling index; By combining standardized wind speed data with the DFA scaling index, wind speed data containing the DFA index is constructed. Step (3): Divide the wind speed data containing the DFA index into a training set and a test set; use the training set to train a machine learning model and generate a missing data imputation model; use the test set to evaluate the performance of the generated missing data imputation model. Step (4): Use the evaluated missing data to fill in the missing data of the laser wind radar.

2. The method for filling in missing data in laser wind radar based on the DFA scaling index according to claim 1, characterized in that, In step (1), the original data of the laser wind radar is the radial data and wind field data of each height layer observed by the radar station at a certain time. The data file after standardization contains the wind speed time series of all times at each height layer. Quality control includes boundary value checking, missing value checking, duplicate value checking and spatiotemporal consistency checking.

3. The method for filling in missing data in laser wind radar based on the DFA scaling index according to claim 1, characterized in that, The method for constructing wind speed data containing the DFA index in step (2) includes the following steps: Step (2-1): Accumulate the anomaly sequences of the original wind speed standardized data to obtain the profile sequence; Step (2-2): First, decompose the profile sequence into windows of equal time length that do not overlap. Then, divide the windows again from the tail of the profile sequence in the opposite direction to obtain non-overlapping windows. Steps (2-3): Within each window, fit the profile sequence using a k-order polynomial to obtain the fitted trend sequence; then subtract the fitted trend sequence from the profile sequence in all windows to obtain the detrended sequence. Steps (2-4): Calculate the variance function of the detrended sequence in each window, and use the variance function to calculate the volatility function; finally, use the volatility function to calculate the DFA scaling index.

4. The method for filling in missing data in laser wind radar based on the DFA scaling index according to claim 3, characterized in that, In step (2-1), the method for calculating the profile sequence is as follows: In equations (1) to (3), {x i + represents the original sequence. The average value of the original sequence, {x} i ′ + represents the anomaly sequence, {Y(j)+ represents the profile sequence, and N is a positive integer greater than or equal to 1; In step (2-2), the method for dividing the windows into non-overlapping sections is as follows: N s = N / s; N s Let be the number of unidirectional partitioning windows, and s be the equal time length; step (2-2) yields a total of 2N. s One window; In steps (2-3), the detrended sequence is calculated as follows: In equation (4), {Y s (j)+ represents the detrended sequence. The fitted trend sequence; k = 2; In steps (2-4), the variance function The method for calculating the wave function F(s) is as follows: In equation (5), Here, v is the variance function, and v is the window number.

5. The method for filling in missing data in laser wind radar based on the DFA scaling index according to claim 4, characterized in that, The calculation method of DFA scaling exponent: Original sequence {x i The + sign indicates long-range dependence; the function F(s) and the window s should satisfy a power-law scaling relationship: F(s) ~ s. α Taking the logarithm of F(s) and s, we obtain lg(F(s)) and lg(s) respectively. We then perform a linear fit between lg(F(s)) and the window size lg(s) to obtain the scaling exponent α.

6. The method for filling in missing data in laser wind radar based on the DFA scaling index according to claim 1, characterized in that, In step (3), the machine learning model is a random forest model, a K-nearest neighbor model, or an artificial neural network model.

7. The method for filling in missing data in laser wind radar based on the DFA scaling index according to claim 6, characterized in that, In step (3), the machine learning model is a random forest model.

8. The method for filling in missing data in laser wind radar based on the DFA scaling index according to claim 6, characterized in that, The method for generating missing data to impute the model using a random forest model is as follows: N samples are randomly drawn with replacement from the training set to form the training subset of each decision tree; when splitting at a node of each tree, m candidate features are randomly selected from all features. p represents the total number of features. The optimal split point is selected only on this training subset to introduce randomness and reduce the risk of overfitting. The data is recursively divided based on the CART (Classification and Regression Tree) algorithm until the preset termination condition is reached, thereby generating a decision tree. The prediction results of each tree are averaged as the final output. The method for generating missing data to fill in the model using the K-nearest neighbor model is as follows: For the sample to be predicted, calculate its Euclidean distance with all samples in the training set; sort by distance and select the K nearest samples as "neighbors"; take the mean or weighted mean of the target values ​​of the K "neighbors" as the predicted value. The method of using artificial neural network models to generate missing data to fill in the model is as follows: The structure of the artificial neural network model is divided into an input layer, a hidden layer, and an output layer. The number of nodes in the input layer is equal to the feature dimension, and it is responsible for receiving the raw data; the hidden layer consists of 1-3 layers, and the number of nodes in each layer is tuned by adjusting the parameters, and non-linearity is introduced through activation functions; the output layer uses a linear activation function to achieve the output result. Data is passed from the input layer to the output layer, and each layer is calculated as: z l =W l a l-1 +b l a l =g(z) l ); where W l and b l Let g be the weights and biases of the l-th layer, and g be the activation function; The loss function uses mean squared error: The backpropagation algorithm is used to calculate the gradient during the calculation process, and the weights are updated in combination with the optimizer to minimize the loss function.

9. The method for filling in missing data of laser wind radar based on the DFA scaling index according to any one of claims 1-8, characterized in that, In step (3), the performance evaluation index of the missing data imputation model includes the coefficient of determination R. 2 Root mean square error (RMSE) and bias; In equations (7) to (9), y i It is the actual value. It is a predicted value. is the mean of the true values, and n is the sample size.

Images