Clear sky bump probability prediction method based on gradient adaptive interpolation algorithm

Abstract

The invention discloses a clear sky bump probability prediction method based on a gradient adaptive interpolation algorithm, and aims to improve the interpolation precision and the turbulence level prediction effect through the advantage that the adaptive algorithm can capture local features. The method comprises the following steps: firstly, acquiring jolting data and meteorological data of a target area, and preprocessing the data; adaptively selecting an optimal interpolation mode based on the three-dimensional gradient change rate of the meteorological elements, and determining optimal gradient threshold division by using Bayesian optimization; thirdly, based on the interpolated meteorological elements and the actual jolting level labels, constructing a jolting feature set and training a random forest classification model; and finally, evaluating interpolation precision by using an ROC curve and an AUC value, quantifying model performance through a confusion matrix, and realizing hour-level prediction of moderate and above jolts. According to the invention, physical change characteristics and local characteristics of the meteorological element field can be fully considered, and the accuracy of clear sky bumping prediction is remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of aviation safety and intelligent weather forecasting, specifically involving a clear-sky turbulence probability prediction method based on gradient adaptive interpolation algorithm. Background Technology

[0002] Clear-air turbulence (CAT) is atmospheric turbulence occurring in cloudless airspace, typically at altitudes above 6000 meters, posing a serious threat to flight safety. Because CAT lacks obvious weather signs, traditional detection methods relying on clouds or radar are insufficient for effective early warning. Furthermore, existing numerical weather prediction (NWP) and turbulence index models suffer from low accuracy in predicting CAT due to resolution and real-time limitations. In recent years, with the rapid development of machine learning technology, especially in combining pilot reports (PIREP) with reanalysis meteorological data, machine learning has gradually become an important technology for CAT prediction due to its powerful capabilities in pattern recognition and nonlinear mapping. However, the predictive performance of machine learning models is highly dependent on data quality, particularly the accurate representation of meteorological elements at the location of turbulence points.

[0003] Current interpolation techniques (such as inverse distance weighting and kriging) typically employ a single strategy to process global data, neglecting the spatial heterogeneity of turbulence intensity. Specifically, traditional interpolation methods may generate redundant calculations in stable airflow regions, while lacking accuracy in complex turbulent regions. Significant differences also exist in the spatial correlation, covariance structure, and optimal interpolation methods among different meteorological elements. For example, research by Daly et al. shows that the optimal interpolation methods for different meteorological elements differ significantly, and existing methods fail to adequately consider these differences, leading to poor prediction results in turbulent regions with strong gradients. Meanwhile, the high dimensionality of meteorological data and the large-scale computational requirements further limit the application of real-time forecasting.

[0004] Meanwhile, PIREP data is typically unstructured or discretely distributed, requiring interpolation techniques to accurately map meteorological data to turbulence initiation points. However, traditional interpolation methods (such as linear interpolation, IDW, and Kriging) often employ fixed strategies, which cannot effectively address the spatial variability of meteorological fields and the locality of turbulence occurrence. This leads to decreased prediction accuracy in turbulent gradient regions and redundant computation in stable airflow regions. Therefore, existing interpolation methods struggle to balance local characteristics with overall efficiency, creating a trade-off between prediction accuracy and computational efficiency. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a clear-sky turbulence probability prediction method based on a gradient adaptive interpolation algorithm. This method fully considers the physical variation characteristics and local features of meteorological element fields, significantly improving the accuracy of clear-sky turbulence prediction.

[0006] Technical solution:

[0007] A method for predicting the probability of turbulence in clear skies based on a gradient adaptive interpolation algorithm includes the following steps:

[0008] Step 1: Obtain all turbulence data for the target area at altitudes above 6000 meters, as well as the corresponding meteorological data, and preprocess the data.

[0009] Step 2: Load ERA5 meteorological data. ERA5 meteorological data is four-dimensional gridded data including time, latitude, longitude, and altitude. Establish a gradient adaptive interpolation algorithm, and adaptively select the optimal interpolation method based on the three-dimensional gradient change rate of meteorological elements to interpolate the meteorological data. The root mean square error is used to evaluate the interpolation results. The four-dimensional interpolation process includes both time and space components. The reduction method is used to consider time as an independent dimension. First, time interpolation is performed to fill in the data gaps of the meteorological sample stations in the turbulence data, and then spatial interpolation is performed on this basis.

[0010] Step 3: Load the actual turbulence data, interpolate the meteorological environment of the turbulence point using the optimized adaptive interpolation algorithm, use it as input, and use the actual turbulence level as output, establish a random forest prediction model, and output the hourly prediction results of the flight route.

[0011] Preferably, in step 1, data preprocessing includes:

[0012] Step 1.1: First, obtain the turbulence data and process it to remove outliers and missing values, marking them as NAN (Not a number).

[0013] Step 1.2: Obtain meteorological data for the corresponding period and region based on the latitude and longitude range of the turbulence data. The original meteorological elements include five meteorological elements closely related to the formation of clear-sky turbulence: meridional wind, zonal wind, temperature, vertical wind speed, and geopotential height.

[0014] Step 1.3: Adjust the timestamps to align the two data time scales. Unify all data units to international standard units, including wind speed in m / s, temperature in ℃, geopotential height in m, meteorological data vertical height in hpa, horizontal resolution of 0.25°×0.25°, and time resolution in hours.

[0015] Preferably, the gradient adaptive interpolation algorithm in step 2 includes the following steps: First, linear interpolation is performed on the meteorological data in the time dimension to complete the data corresponding to the time of the bump point; then, the three-dimensional gradient change rate of the meteorological elements is calculated, and the gradient values ​​in the longitude, latitude, and altitude directions are fitted by the least squares method and standardized; the gradient values ​​are compared with a preset threshold to determine the region type; according to the region type, the corresponding interpolation algorithm is selected from the algorithm set consisting of linear interpolation, inverse distance weighted interpolation, and Kriging interpolation to perform the calculation; finally, the gradient threshold is dynamically optimized using the Bayesian optimization algorithm with the goal of minimizing the root mean square error, and the interpolation accuracy is evaluated by cross-validation, thereby achieving adaptive selection of the interpolation method.

[0016] Preferably, in step 2, linear interpolation is used over time based on the characteristics of meteorological elements:

[0017]

[0018] In the formula, t1 and t2 are the two time points in the meteorological data closest to the moment of turbulence, and the interval between the two time points is 1 hour.

[0019] As a preferred method, the least squares method is used to perform three-dimensional fitting of the meteorological variable values ​​around the interpolation point, and a linear function is established to estimate the gradient rate of change of these variables in the longitude, latitude, and altitude directions. And it undergoes standardization and normalization processing.

[0020]

[0021] Where G is the gradient rate of change, and G.min(axis=0) and G.max(axis=0) are the minimum and maximum values ​​of each meteorological variable on the corresponding gradient, respectively. The standardized data is then scaled to a specified range [0,1].

[0022]

[0023] in This is the scaled value.

[0024] Spatially, linear interpolation, inverse distance weighted interpolation, and kriging interpolation are used to interpolate the bump points. The method for determining the region type is as follows: setting an initial gradient threshold. When G < When the time is returned to the smooth region, linear interpolation is used. <G< When the transition region is defined, the inverse distance weighted interpolation algorithm is used, G> The time-varying region was identified using Kriging interpolation.

[0025] Preferably, a linear interpolation algorithm is used to weight the variable values ​​at the eight vertices of the small cube region where the target point is located according to spatial proportion, thereby determining the eight vertices of the cube where the target point is located. For each coordinate axis, the proportion of the target point in that interval is calculated (e.g., ...). Then, weight them using the following formula:

[0026]

[0027] ,ensure ;

[0028] As a preferred method, inverse distance weighted interpolation (IDW) is used to calculate the spatial distance between each candidate point and the target point. Set the exponent parameter Calculate the interpolation:

[0029] ;

[0030] In the initial selection, p=2 is commonly used, and adjustments are made to control the smoothness and local sensitivity of the interpolation;

[0031] As a preferred approach, the Kriging interpolation algorithm is used. A covariance matrix is ​​constructed based on spatial correlation, and the optimal unbiased interpolation is obtained through minimum variance estimation. First, the spatial distance matrix D between each pair of point-bump points is calculated. Then, a variogram γ(h) is constructed using a common spherical model, and a covariance matrix C is built. The covariance vector c0 between the target point and each candidate point is calculated. Finally, the following linear system is solved:

[0032]

[0033] The weight λ is obtained, and the interpolation variable is: .

[0034] As a preferred method, 5-fold cross-validation is employed. The ERA5 meteorological data is randomly divided into five equal subsets, with a training to validation set ratio of 8:2. Four subsets are used for model training, and one subset is used for model testing. This process is repeated five times, each time using one subset as the validation set and the remaining four as the training set. For each point in the validation set, interpolation predictions are performed using points from the training set. The root mean square error is calculated based on the actual and predicted values.

[0035] ,

[0036] In the formula, n is the number of grid points in the validation set. These are the actual value and the predicted value of the i-th sample point, respectively.

[0037] Preferably, a fitness function with a threshold of gradient rate of change as the variable is constructed using a Bayesian optimization algorithm. Search for thresholds, and in each candidate threshold... Next, interpolation is performed on the training set samples, and the interpolation error is calculated on the validation set. The minimum interpolation error is used as the optimization objective, and the values ​​are iteratively updated. It is determined whether the number of iterations has reached a target or whether the function has converged, ultimately obtaining the globally optimal gradient splitting threshold. 1, 2.

[0038] Preferably, step 3 includes: using the meteorological elements of the turbulence point calculated by the gradient adaptive interpolation algorithm as input features and the actual turbulence level as output label to construct a training sample set; subsequently, constructing a classification model based on the random forest algorithm, constructing multiple decision trees by performing bootstrap sampling on the training sample set, and randomly selecting a feature subset for optimal splitting based on the Gini index when dividing nodes; finally, performing majority voting on the input samples through the classification model to output the predicted turbulence level, and using ROC curves and AUC values ​​to quantitatively evaluate the model performance.

[0039] Preferably, step 3 includes: Step 3.1, using the bumpy location as a reference point, selecting the k nearest neighbor meteorological grid points within its spatial range to form a candidate data point set, and calculating the meteorological element values ​​at the bumpy location using the gradient adaptive interpolation algorithm, which are then used as input features for the random forest model. ;

[0040] Step 3.2: Convert the turbulence intensity level in the pilot's report from characters to numerical labels. With the input features and their corresponding numerical labels Constructing the training sample set ;

[0041] Step 3.3: Perform bootstrapping on the training sample set to construct... Each sub-training set is used; a CART decision tree is constructed for each sub-training set. When splitting at each node of the tree, a feature subset is randomly selected, and then the optimal split point is selected based on the Gini index; all decision trees are trained independently to form a complete random forest classifier.

[0042] Step 3.4, for the sample to be predicted In the random forest model, K decision trees make independent judgments and output the final predicted turbulence level through a majority voting mechanism. ;

[0043] Step 3.5: Based on the prediction results and the true labels, calculate the detection probability PODy for moderate to severe turbulence and the detection probability PODn for no turbulence, plot the receiver operating characteristic curve and calculate the area under the curve to quantitatively evaluate the predictive performance of the model.

[0044] Preferably, in step 3.4, for each input sample The model is passed The trees perform a majority vote and output the predicted turbulence level. The majority voting mechanism is as follows:

[0045]

[0046] in For indicator functions, For the first The predicted results for each tree;

[0047] Preferably, in step 3.5, the detection probability PODy of moderate or higher level turbulence and the turbulence threshold of detection probability PODn of no turbulence are calculated. A ROC curve is formed with PODn as the x-axis and PODy as the y-axis. The closer the curve is to 1, the better the prediction effect. The AUC value of the ROC curve is used as the performance skill score of the turbulence prediction model.

[0048] For each probability threshold, PODy and PODn are defined as follows:

[0049]

[0050] In the formula, TP is the number of samples where both the actual and predicted values ​​are positive, FP is the number of samples predicted as positive but actually negative, FN is the number of samples predicted as negative but actually positive, and TN is the number of samples where both the predicted and actual values ​​are negative.

[0051] Beneficial effects

[0052] (1) This invention dynamically selects the interpolation method based on the gradient rate of change of meteorological variables. By calculating the three-dimensional gradient rate of change of meteorological elements (such as temperature, wind speed, etc.), the optimal interpolation method is dynamically selected. Linear interpolation is used in the smooth region (low gradient) to improve efficiency, inverse distance weighted interpolation is used in the transition region (medium gradient) to balance accuracy and complexity, and Kriging interpolation is used in the drastic region (high gradient) to capture local features. This method takes into account the physical characteristics and computational resources of the turbulent region, and improves the interpolation accuracy and efficiency.

[0053] (2) The present invention inputs the interpolated meteorological elements into the random forest model to construct a turbulence level prediction model, and uses indicators such as ROC curve and AUC value to quantitatively evaluate the interpolated data, thereby improving the application effect of the model. Attached Figure Description

[0054] Figure 1 This is an overall flowchart of one embodiment of the present invention;

[0055] Figure 2 This is a horizontal gradient distribution map (250 hPa) with temperature as an example. The red dots in the map are the actual bump points that occurred during this time period, which are the points to be inserted.

[0056] Figure 3 It is a confusion matrix that uses data obtained through different interpolation methods for machine learning modeling.

[0057] Figure 4 These are ROC curves predicted using the same machine learning forest model but with different interpolation methods. Detailed Implementation

[0058] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. However, the present invention should not be limited to the following embodiments. All equivalent substitutions or modifications made within the spirit and protection scope of the present invention should be included within the protection scope of the present invention.

[0059] This invention discloses a clear-air turbulence probability prediction method based on a gradient adaptive interpolation algorithm, which is particularly suitable for high-precision prediction and real-time detection of clear-air turbulence (CAT). By combining meteorological data interpolation optimization with machine learning modeling techniques, this invention improves the accuracy and computational efficiency of turbulence prediction by dynamically selecting the optimal interpolation algorithm. This technology can be widely applied to flight safety early warning systems, intelligent route planning, and other fields involving clear-air turbulence risk assessment, providing reliable core technical support.

[0060] See Figure 1 The diagram illustrates a flowchart of a random forest algorithm based on an embodiment of the present invention, the method comprising the following steps:

[0061] Step 1: Data acquisition and preprocessing.

[0062] Pilot Turbulence Reports (PIREPs) and corresponding ERA5 reanalysis meteorological data for the target area were obtained from flight operation platforms and meteorological databases. PIREP data included report time, latitude and longitude, altitude (in hundreds of feet), aircraft type, and turbulence severity level (text or numerical labels). Meteorological data included multiple meteorological elements for the area within the corresponding time range (this paper selected five variables related to turbulence: temperature, latitude and longitude wind, vertical velocity, and geopotential height). This example uses pilot reports from the Washington, D.C. area, USA, from 2016 to 2020 as the research object.

[0063] Pilot reports were screened to remove missing or outlier values, and turbulence intensity was uniformly mapped to four levels: none, mild, moderate, and severe. Meteorological data were standardized in units (temperature in °C, wind speed in m / s, geopotential height in m, and altitude layer in hPa), and timestamps were adjusted to align with the turbulence data time, thus constructing a standardized dataset.

[0064] Step 2: Load ERA5 meteorological data. ERA5 meteorological data is four-dimensional gridded data in terms of time, latitude, longitude, and altitude. A gradient adaptive interpolation algorithm is established to interpolate the meteorological data, and the root mean square error is used to evaluate the interpolation results. The four-dimensional interpolation process includes both time and space components. The subtraction method treats time as an independent dimension. First, time interpolation is performed to fill in data gaps in the meteorological sample stations of the turbulence data. Then, spatial interpolation is performed based on this. Specifically...

[0065] Step 2.1: Since the timestamps of meteorological data and turbulence reports may not be perfectly aligned, we first align the data in the time dimension to prepare accurate time slice data for subsequent spatial interpolation.

[0066] Based on the characteristics of meteorological elements, linear interpolation is used over time to calculate the weighted average of meteorological data from the two most recent time points before and after the target time:

[0067]

[0068] In the formula, t1 and t2 are the two time points in the meteorological data closest to the moment of turbulence, and the interval between the two time points is 1 hour.

[0069] Step 2.2 involves calculating the meteorological element gradient to quantify the spatial drastic changes in the meteorological field around the interpolation point, providing a quantitative basis for subsequent judgments regarding whether the area belongs to a "smooth zone," "transition zone," or "drastic change zone." The least squares method is used to perform three-dimensional fitting of the meteorological variable values ​​around the interpolation point, establishing a linear function to estimate its gradient rate of change in the longitude, latitude, and altitude directions. And perform standardization and normalization:

[0070]

[0071] Where G is the gradient rate of change, and G.min(axis=0) and G.max(axis=0) are the minimum and maximum values ​​of each meteorological variable on the corresponding gradient, respectively. The standardized data is then scaled to a specified range [0,1].

[0072]

[0073] in This is the scaled value.

[0074] Step 2.3: Perform region determination and set the initial gradient threshold. When G < When the time is returned to the smooth region, linear interpolation is used. <G< When the transition region is defined, the inverse distance weighted interpolation algorithm is used, G> The time-varying region was identified using Kriging interpolation.

[0075] Linear interpolation algorithm: Using a linear interpolation algorithm, the variable values ​​at the 8 vertices of the small cube region where the target point is located are weighted according to spatial proportion to determine the 8 vertices of the cube where the target point is located. For each coordinate axis, the proportion of the target point in that interval is calculated (e.g., ...). Then, weight them using the following formula:

[0076]

[0077] ,ensure .

[0078] Inverse Distance Weighted Algorithm: This algorithm uses inverse distance weighted interpolation (IDW) to calculate the spatial distance between each candidate point and the target point. Set the exponent parameter Calculate the interpolation:

[0079] ;

[0080] In the initial selection, p=2 is commonly used, and adjustments are made to control the smoothness and local sensitivity of the interpolation.

[0081] Kriging interpolation algorithm: Based on spatial correlation, a covariance matrix is ​​constructed. The optimal unbiased interpolation is obtained through minimum variance estimation. First, the spatial distance matrix D between each pair of point bumps is calculated. Then, a variogram γ(h) is constructed using a common spherical model, and a covariance matrix C is constructed. The covariance vector c0 between the target point and each candidate point is calculated. Finally, the following linear system is solved:

[0082]

[0083] The weight λ is obtained, and the interpolation variable is: .

[0084] Step 2.4: Optimize the threshold from Step 2.3. Construct a fitness function using the threshold of the gradient rate of change as a variable through a Bayesian optimization algorithm. Search for thresholds, and in each candidate threshold... Next, interpolation is performed on the training set samples, and the interpolation error is calculated on the validation set. The minimum interpolation error is used as the optimization objective, and the values ​​are iteratively updated. It is determined whether the number of iterations has reached a target or whether the function has converged, ultimately obtaining the globally optimal gradient splitting threshold. 1, 2.

[0085] Step 2.5 employs 5-fold cross-validation, randomly dividing the ERA5 meteorological data into five equal subsets, setting the ratio of training to validation sets to 8:2. Four subsets are used for model training, and one subset is used for model testing. This process is repeated 5 times, each time using one subset as the validation set and the remaining four as the training set. For each point in the validation set, interpolation prediction is performed using points from the training set. Based on the actual and predicted values, the root mean square error is calculated.

[0086]

[0087] In the formula, n is the number of grid points in the validation set. Let be the actual value and the predicted value of the i-th sample point, respectively.

[0088] Table 1. Root mean square error of interpolation for various meteorological elements using different interpolation methods.

[0089] Meridional wind (m / s) Zonal wind (m / s) Temperature (°C) Vertical wind speed (m / s) Potential height (m) Linear 0.2051 0.2051 0.0832 0.0231 41.2554 IDW 0.2723 0.2318 0.1023 0.0199 32.0204 Kriging 0.0941 0.1286 0.0466 0.0178 19.2309 Gradient Adaptive 0.0775 0.0990 0.0376 0.0167 14.4861

[0090] As shown in Table 1, for various meteorological elements, gradient-based adaptive interpolation methods outperform single interpolation methods. Overall, Kriging interpolation is superior to linear interpolation and inverse distance weighted interpolation. However, in regions where the spatial variation of meteorological variables is relatively stable (i.e., smooth regions), the spatial covariance structure of meteorological variables is weak. Using covariance modeling introduced by Kriging interpolation may actually increase errors or fluctuations, leading to overfitting and a decrease in overall accuracy. Adaptive interpolation methods automatically select linear interpolation, inverse distance weighted interpolation, and Kriging interpolation based on gradients, reducing the global error caused by a single interpolation method and improving overall fitting accuracy. Although Kriging interpolation has higher accuracy than other interpolation methods, its computational efficiency is much lower than that of linear interpolation. Compared to using Kriging interpolation globally, the hybrid interpolation method improves overall speed by approximately 4.7 to 4.9 times while maintaining high accuracy, effectively balancing the real-time requirements and computational resource control in turbulence prediction tasks, and providing a better solution for practical aviation meteorological applications.

[0091] Step 3: Construct a stochastic forest aircraft turbulence prediction model based on interpolated meteorological data, including the following steps:

[0092] Step 3.1: Load the turbulence data and meteorological data. Using the turbulence location as the reference point, calculate the Euclidean distance between the reference point and each candidate grid point.

[0093]

[0094] in , , These are the longitude, latitude, and altitude of the location of the bumps. , , These are the grid points in the meteorological data. The spatial range is selected based on the calculation results. The nearest neighbor grid points are used as the candidate data points for interpolation. , For the corresponding grid points ( The data consists of meteorological variable values ​​obtained from observations or simulations, including u: meridional wind, v: zonal wind, t: temperature, w: vertical wind speed, and z: geopotential height. The dataset is centralized. These points constitute the local data environment around the target bump point.

[0095] The gradient adaptive interpolation algorithm from step 2 is invoked to calculate the bump points based on the candidate data point set. A complete set of meteorological element values ​​at precise locations serves as an input sample for the model. .

[0096] Figure 2 This displays a temperature gradient distribution map of the Washington area at 00:00 on January 1, 2016. Red dots represent actual turbulence records occurring one hour after that time. The gradient rate of change of the variable to be interpolated at that location is determined, and then a threshold is applied. 1, 2. Determine the interpolation method to be used for interpolation. Perform the same operation for each bump point and each meteorological variable to obtain the meteorological elements at the bump point location as input features. .

[0097] Step 3.2, Label Data Acquisition: Turbulence intensity is divided into seven levels: none, mild, mild to moderate, moderate, moderate to severe, severe, and extreme. Regular expressions are used to convert the turbulence levels from characters to numeric labels 0-6: Null'→0, 'LGT'→1, 'LGT-MOD'→2, 'MOD'→3, 'MOD-SEV'→4, 'SEV'→5, 'EXT'→6, where 'Null', 'LGT', 'MOD', 'SEV', and 'EXT' represent none, mild, moderate, severe, and extreme turbulence, respectively. The actual turbulence levels reported by the pilots are used as labels in supervised learning. To form a training sample set ;

[0098] Step 3.3: Construct a random forest classification model by performing bootstrap sampling on the training sample set. Each sub-training set is used; a CART decision tree is constructed for each sub-training set. In each node split, a feature subset is randomly selected for splitting, and the optimal split point is selected based on the Gini index; all decision trees are trained independently to form a complete random forest classifier.

[0099] Step 3.4, Model Training and Prediction: For each input sample The model is passed The trees perform a majority vote and output the predicted turbulence level. The majority voting mechanism is as follows:

[0100]

[0101] in For indicator functions, For the first The predicted results for each tree.

[0102] Step 3.5: Calculate the detection probability PODy for moderate or higher levels of turbulence and the turbulence threshold PODn for no turbulence. Construct an ROC curve with PODn as the x-axis and PODy as the y-axis. The closer the curve is to 1, the better the prediction performance. Use the AUC value of the ROC curve as the performance skill score for turbulence prediction. For each probability threshold, PODy and PODn are defined as follows:

[0103]

[0104] In the formula, TP is the number of samples where both the actual and predicted values ​​are positive, FP is the number of samples predicted as positive but actually negative, FN is the number of samples predicted as negative but actually positive, and TN is the number of samples where both the predicted and actual values ​​are negative.

[0105] This invention uses optimized interpolated data as input to train a random forest classification model for turbulence level prediction, and evaluates model performance quantitatively using ROC curves and AUC values. Existing machine learning methods often directly use raw interpolated data, neglecting the impact of data quality on the model. This invention improves data accuracy through the interpolation stage, indirectly enhancing the discriminative ability of the prediction model (e.g., ...). Figure 3 and Figure 4 As shown, the model with adaptive interpolation has the highest AUC value, reaching 0.931. This integrated "interpolation-modeling" design combines meteorological physical characteristics with a data-driven model.

[0106] The model was validated on a test set, and its accuracy was calculated using a confusion matrix. Furthermore, an ROC curve was plotted, and the AUC value was calculated. By comparing the AUC values ​​of the models under different interpolation methods, the effectiveness of the interpolation strategy proposed in this invention in improving the performance of downstream prediction models was indirectly evaluated, thus verifying its effectiveness.

[0107] Figure 3 shows the confusion matrix results obtained by building models based on different interpolation methods. As can be seen from the figure, the model trained using the adaptive interpolation method has an accuracy of 91.02%, which is better than linear interpolation (85.34%) and inverse distance weighted interpolation (85.11%), and slightly higher than Kriging interpolation (90.78%), showing the best performance in terms of classification accuracy.

[0108] Figure 4 shows the ROC curves and AUC values ​​of the models corresponding to each interpolation method. The Kriging interpolation model has an AUC of 0.899, which is significantly better than linear interpolation and inverse distance weighted interpolation; while the adaptive interpolation method has an AUC of 0.931, which is the strongest among all methods.

[0109] In summary, the adaptive interpolation method achieves significantly better model performance than single interpolation methods while balancing computational efficiency and prediction accuracy, demonstrating good applicability and potential for widespread application. The gradient-based adaptive interpolation method proposed in this invention provides more accurate and computationally efficient data support for turbulence prediction, offering a safety guarantee for coping with future intensification of clear-sky turbulence. It can provide pilots with practical reference before takeoff, thereby improving aviation safety and reducing economic costs. This has significant practical implications for ensuring the safety and efficiency of civil aviation transportation.

[0110] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details.

[0111] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A clear-air turbulence probability prediction method based on a gradient-adaptive interpolation algorithm, characterized in that, The method comprises the following steps: Step 1, obtaining all the bump data above a certain height of the target area and the corresponding area weather data, and preprocessing the data; Step 2, loading ERA5 weather data, ERA5 weather data is four-dimensional gridded data including time, latitude, longitude and height, establishing a gradient adaptive interpolation algorithm, based on the three-dimensional gradient change rate of meteorological elements, adaptively selecting the optimal interpolation method to interpolate the meteorological data, and using the root mean square error to evaluate the interpolation results; Step 3, loading the actual bump data, using the optimized adaptive interpolation algorithm to interpolate the meteorological environment of the bump point as input and the actual bump level as output, establishing a random forest prediction model, and outputting the hour-level prediction results of the route.

2. The prediction method of claim 1, wherein, Step 1 specifically comprises: Step 1.1, obtaining bump data and processing the bump data to remove outliers and missing values, and marking them as NAN; Step 1.2, based on the latitude and longitude range of the bump data, obtaining the weather data of the corresponding period and area, the original meteorological elements include zonal wind, meridional wind, temperature, vertical wind speed and potential height, which are closely related to clear air bump formation.

3. The prediction method of claim 1, wherein, The gradient adaptive interpolation algorithm in step 2 comprises the following steps: Firstly, linearly interpolating the meteorological data in the time dimension to complete the data of the bump point at the corresponding time; then, calculating the three-dimensional gradient change rate of meteorological elements, fitting the gradient values in the longitude, latitude and height directions by least squares method, and performing standardization processing; comparing the gradient values with the preset threshold to determine their belonging region type; according to the region type, selecting the corresponding interpolation algorithm from the algorithm set consisting of linear interpolation, inverse distance weighted interpolation and Kriging interpolation to perform calculation; finally, using Bayesian optimization algorithm to dynamically optimize the gradient threshold with the objective of minimizing the root mean square error, and evaluating the interpolation precision by cross-validation, so as to realize the adaptive selection of the interpolation method.

4. The prediction method of claim 3, wherein, The gradient change rate is expressed as , the standardization and normalization processing is: , where G is the rate of gradient change, G.min(axis=0) and G.max(axis=0) are the minimum and maximum values of each meteorological variable on the corresponding gradient, respectively, and the normalized data is scaled to the specified range [0, 1], , where is the scaled value.

5. The prediction method of claim 3, wherein, The method of determining the region type is to define a gradient threshold , When the gradient variation rate G is less than the gradient threshold, it is classified as a smooth region, and linear interpolation is used; When the gradient variation rate G is greater than the gradient threshold, it is classified as a transition region, and inverse distance weighted interpolation is used; and When the gradient variation rate G is greater than the gradient threshold, it is classified as a dramatic change region, and Kriging interpolation is used.

6. The prediction method of claim 5, wherein, The linear interpolation is: using a linear interpolation algorithm to determine the 8 vertices of the cube where the target point is located, weighting the variable values at the 8 vertices of the small cube region where the target point is located according to the space proportion, calculating the proportion of the target point in the interval for each coordinate axis, and then weighting using the following formula: , wherein is a three-axis linear weight, ensuring that ; The inverse distance weighted interpolation is: calculating the spatial distance between each candidate point and the target point using an inverse distance weighted interpolation algorithm , setting an index parameter , calculating the interpolation: , adjusting the index parameter to control the smoothness and local sensitivity of the interpolation; The Kriging interpolation is: based on the spatial correlation to construct the covariance matrix, through the minimum variance estimation to obtain the optimal unbiased interpolation, first calculate the spatial distance matrix D between each pair of points, through the use of common spherical model to construct the variogram γ(h) and construct the covariance matrix C, calculate the covariance vector c0 between the target point and each candidate point, then solve the following linear system: , get the weight λ, the interpolation variable is: .

7. The prediction method of claim 3, wherein, The threshold value is optimized based on a Bayesian optimization algorithm: a fitness function with the threshold value of the gradient change rate as a variable is constructed using the Bayesian optimization algorithm The threshold value is searched, and the gradient change rate of each candidate threshold value Next, the training set samples are interpolated, and the interpolation error is calculated on the validation set; the minimum interpolation error is taken as the optimization target, and the value is iteratively updated to determine whether the iteration number meets the standard or the function converges, and finally the global optimal gradient division threshold value is obtained 1, 2.

8. The prediction method according to any one of claims 1 to 7, characterized in that, Step 3 comprises: taking the meteorological elements of the bump point calculated by the gradient adaptive interpolation algorithm as input features, and taking the actual bump level as output label to construct a training sample set; then, based on the random forest algorithm, a classification model is constructed, a plurality of decision trees are constructed by self-sampling the training sample set, and a feature subset is randomly selected for optimal splitting according to the Gini index when node partitioning; finally, the classification model is used to perform majority voting on the input sample, output the predicted turbulence level, and use the ROC curve and AUC value to quantitatively evaluate the model performance.

9. The prediction method of claim 8, wherein, Step 3 specifically comprises: Step 3.1, taking the k nearest neighbor weather grid points in the spatial range of the bump position as the candidate data point set, calculating the weather element value of the bump position by the gradient adaptive interpolation algorithm as the input feature of the random forest model ; Step 3.

2. Convert the intensity level of the bump in the pilot's report from a character to a numerical label , the input features and their corresponding numerical labels form a training sample set ; Step 3.

3. Bootstrap sampling is performed on the training sample set to construct sub-training sets; for each sub-training set, a CART decision tree is constructed, and at each node of the tree, a subset of features is randomly selected, and then the optimal split point is selected according to the Gini index; all decision trees are independently trained to form a complete random forest classifier; Step 3.4, for the sample to be predicted K decision trees in the random forest model make independent judgments, and output the final prediction bump grade through the majority voting mechanism ; Step 3.5, based on the prediction results and the true labels, the detection probability PODy of moderate and above bumps and the detection probability PODn of no bumps are calculated, the receiver operating characteristic curve is drawn and the area under the curve is calculated, so as to quantitatively evaluate the prediction performance of the model.

10. The prediction method of claim 9, wherein, The predicted jerk level in step 3.4 is represented as: wherein is an indicator function, is the predicted result of the tree.

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