A wind speed prediction method based on a CART-based multi-mode integrated model

Abstract

The application relates to a wind speed prediction method based on a CART-based multi-mode integrated model, which comprises the following steps: 1) obtaining data information, and interpolating the obtained data information to a fine grid with a resolution of 0.1 DEG x 0.1 DEG by using bicubic interpolation; 2) pre-processing the data information, screening sample information, and dividing the sample information into training period data and prediction period data; 3) comparing the errors of each prediction mode in the prediction period with observation, and analyzing the prediction accuracy of each mode; 4) establishing a CART-based multi-mode integrated model according to the training period data, and establishing a prediction model of mode integration based on a bias-eliminating ensemble average method as comparison; 5) inputting the prediction period data into the CART-based multi-mode integrated model for prediction, obtaining a prediction result, and comparing and analyzing the prediction errors by using root mean square errors. Compared with the prior art, the application has the advantages of being suitable for modeling complex data of multi-feature variables and having good prediction effect.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wind speed prediction, in particular to a wind speed prediction method based on a CART multi-mode integrated model. BACKGROUND

[0002] Numerical weather prediction technology plays an extremely important role in the prediction and early warning of new energy power generation such as wind power generation, photovoltaic power generation, and major meteorological disasters (cold wave, icing, flood, etc.). Therefore, developing fine prediction is an important strategic goal of weather prediction development. However, due to the systematic errors of the single mode itself and the uncertainty of the initial field of the prediction results provided by various international weather prediction research organizations, numerical prediction of different meteorological elements still has different degrees of error, and each prediction research institution needs to improve its prediction skill to reduce the prediction bias. In recent years, fine prediction technology has developed rapidly, and has realized the transition from single deterministic prediction to multi-mode integrated numerical prediction, that is, two independent prediction results are combined. Studies have found that compared with single mode prediction output, the output of multi-mode integrated prediction has the characteristics of stability, better prediction skill, and smaller prediction bias. Therefore, it has been widely applied and researched at home and abroad.

[0003] At present, the multi-mode integrated method has certain effect on improving the prediction accuracy, but also has disadvantages. Neural networks can well deal with nonlinear models, but require a large amount of training data. Ordinary linear regression method does not require a large amount of data, but the prediction accuracy still has a lot of room for improvement. The basic linear regression model belongs to a global model, and in the linear regression model, the premise is to assume that the data between the global data is linear, and the final model is trained by fitting all sample points. However, many problems in actual meteorological prediction are nonlinear, and the relationship between variables is complex. When dealing with such complex regression problems of data, the relationship between features is not a simple linear relationship, at this time, it is impossible to use a global linear regression model to fit such data, and thus accurate prediction effect cannot be achieved. SUMMARY

[0004] The purpose of the present application is to overcome the defects of the prior art and provide a wind speed prediction method based on a CART multi-mode integrated model.

[0005] The purpose of the present application can be achieved by the following technical solutions:

[0006] A wind speed prediction method based on a CART multi-mode integrated model, the method comprising the following steps:

[0007] 1) Obtain data information, and interpolate the obtained data information to a fine grid with a resolution of 0.1°x0.1° by using bicubic interpolation.

[0008] 2) Preprocess the data, screen the sample data, and divide the sample data into training period data and forecast period data.

[0009] 3) Compare the errors of each forecast mode and observation in the forecast period, and analyze the forecast accuracy of each mode.

[0010] 4) Establish a CART-based multi-mode integrated model based on the training period data, and establish a forecast model for mode integration based on the bias-eliminating ensemble average method as a comparison.

[0011] 5) Input the forecast period data into the CART-based multi-mode integrated model for prediction, obtain the prediction results, and compare and analyze the prediction errors using the root mean square error.

[0012] Further, the data includes wind speed forecast mode data and observation data.

[0013] The wind speed forecast mode data is taken from the average of the 10m wind speed of each ensemble member of the global ensemble forecast mode of the European Medium-Range Weather Forecast Center and the National Environmental Prediction Center in the TIGGE data set, which is reported at 00:00 every day; and the observation data uses the initial field of the control forecast of the ERA5 reanalysis data, which is reported at 00:00 every day.

[0014] Further, the specific steps of preprocessing the data include:

[0015] 201) Increase the resolution of the forecast data of ECMWF with a resolution of 0.5°x0.5°, the forecast data of NCEP with a resolution of 0.5°x0.5°, and the observation data of ERA5 with a resolution of 0.25°x0.25° to 0.1°x0.1° by bicubic interpolation;

[0016] 202) Select wind speed forecast mode data and observation data with consistent latitude and longitude, preprocess the data, select reasonable data, and select the final total sample data length and training period data.

[0017] Further, the specific steps of establishing a CART-based multi-mode integrated model based on the training period data include:

[0018] 401) A regression tree corresponds to a division of the input space, i.e., a feature space, and an output value on the divided unit. Assuming that the input space has been divided into M units R1, R2, …, RM, and there is a fixed output value c on each unit R m , the regression model can be represented as: m m ​​

[0019]

[0020] Then, the error between the model output value and the actual value is calculated:

[0021]

[0022] Let c on each unit m To minimize the squared error, when c m The optimal output value is obtained when the average of all actual values ​​of the corresponding unit is taken.

[0023]

[0024] Suppose X and Y are the input and output variables, respectively, and Y is a continuous variable. Given a training set:

[0025] D = (x1, y1), (x2, y2), ..., (x n ,y n )

[0026] Where D represents the entire dataset, y n This is the output value of the nth sample;

[0027] 402) Assume we choose variable x (j) Let 's' be the splitting variable, and its value 's' be the splitting point. Values ​​less than or equal to 's' are assigned to the left subtree, and otherwise to the right subtree, thus obtaining two regions:

[0028] R1(j,s)={x|x (j) ≤s},R2(j,s)={x|x (j) >s}

[0029] at this time:

[0030]

[0031] In the formula, N m Given the number of samples in each region, solve for:

[0032]

[0033] Iterate through variable j, scan the split point s, and select the pair (j, s) that minimizes m(s), where R m For the partitioned input space, c m For space R m The corresponding output value;

[0034] 403) Divide the region using the selected pair (j,s) and determine the corresponding output value;

[0035] 404) continue to call steps 402), 403) on two sub-regions until the stop condition is met;

[0036] 405) divide the input space into M regions R1, R2,..., RM; m , generate a decision tree:

[0037]

[0038] 406) for multi-feature input, on the basis of generating a decision tree and deriving a residual error for the previous feature input, use the next feature input to establish a decision tree to fit the residual error, and integrate the regression tree:

[0039] f = f(X1) + f(X2) +....

[0040] After integrating the regression tree, the pruning operation of the regression tree is also included, and the specific steps include:

[0041] (1) when any one of the sub-trees T t , without pruning, its loss function is:

[0042] C α (T t ) = C(T t ) + a |T t |

[0043] In the formula, a is a regularization parameter, C(T t ) is the error of the training data, and |T t | is the number of leaf nodes;

[0044] When pruning to the root node, i.e. only the root node is retained, its loss function is:

[0045] C α (T) = C(T t ) + a

[0046] When a = 0 or close to 0, then: C α (T t ) < C α (T); when a increases to a certain extent: C α (T t ) = C α (T); therefore when T and T t satisfy C α (T t ) = C α (T), i.e.: Prune T t , cut off all the child nodes, leaving one leaf node T;

[0047] (2) When all nodes are calculated whether to prune alpha, the optimal subtree corresponding to alpha is cross-validated on the training set, and the optimal subtree is found as the final result.

[0048] Further, the expression of the prediction model of the pattern integration based on the bias elimination set average method is:

[0049]

[0050] In the formula, F BREM is the bias elimination set average prediction value, is the average value of the measured value in the training period, N is the total number of patterns participating in the set, F i is the prediction value of the i-th pattern, is the average of the prediction value of the i-th pattern in the training period.

[0051] Further, the formula for comparing and analyzing the prediction error by using the root mean square error is:

[0052]

[0053] In the formula, f i represents the pattern prediction value of the i-th sample; o i is the corresponding observation value, and n is the sample number.

[0054] The wind speed prediction method of the multi-pattern integrated model based on CART provided by the application at least includes the following beneficial effects compared with the prior art:

[0055] 1) The application considers that many problems in actual meteorological prediction are nonlinear, and the relationship between variables is complex. When processing the regression problem of such complex data, the relationship between features is not a simple linear relationship. At this time, it is impossible to use a global linear regression model to fit such data. The application proposes to use the CART algorithm to solve the problem, divide the global data set into multiple data sets that are easy to model, and perform local regression modeling on each local data set. Better fitting of nonlinear data can be achieved, and it is suitable for modeling complex data with multiple feature variables. Through comparative analysis, the regression tree model proposed by the application shows better integration effect.

[0056] 2) In the generation of the regression tree mentioned in the application, in order to prevent overfitting and improve the generalization ability, the minimum number of samples contained in the leaf node is limited, and the optimized regression tree is pruned to obtain the best prediction effect.

[0057] 3) The present application adopts tree regression algorithm to establish multi-mode integrated model for complex wind speed data, and improves the modeling of the algorithm and the optimization performance of the algorithm by applying CART algorithm to regression problems. Similar to the traditional linear regression, only a small amount of training data is needed during training, and compared with linear regression, tree regression is more suitable for processing complex nonlinear problems.

[0058] 4) Regarding the problem of matching low-resolution wind speed data of weather forecast mode with observed high-resolution data, the present application adopts interpolation method to interpolate low-resolution forecast mode data to fine grid, and selects consistent longitude and latitude of forecast and observation information, and pre-processes the data, selects reasonable data, and then is used for subsequent simulation modeling, which is more accurate in data processing and can further improve the accuracy of wind speed forecast. BRIEF DESCRIPTION OF DRAWINGS

[0059] Figure 1 The main flowchart of the wind speed prediction method based on CART multi-mode integrated model in the embodiment;

[0060] Figure 2 The flowchart of the CART algorithm in the embodiment;

[0061] Figure 3 The flowchart of the regression tree model generation in the embodiment;

[0062] Figure 4 The flowchart of the pruning mentioned in the embodiment;

[0063] Figure 5 The comparison chart of the ground wind speed prediction data and observation data of ECMWF and NCEP modes in the embodiment;

[0064] Figure 6 The relationship chart of the minimum sample number and error contained in the leaf node in the regression tree modeling in the embodiment;

[0065] Figure 7 The regression tree model after pruning in the embodiment;

[0066] Figure 8 The comparison chart of the ground wind speed prediction by CART and observation in the embodiment;

[0067] Figure 9 The comparison chart of the ground wind speed prediction by BREM and observation in the embodiment;

[0068] Figure 10 The root mean square error comparison of the ground wind speed prediction of ECMWF, NCEP and BREM, CART and observation value in the embodiment. DETAILED DESCRIPTION

[0069] The application will be described in detail below with reference to the drawings and specific embodiments. Obviously, the described embodiments are part of the embodiments of the application, rather than all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those of ordinary skill in the art without creative labor shall fall within the scope of protection of the application.

[0070] Embodiments

[0071] The application aims at the defect of inaccurate prediction caused by large training amount and complex data of the current multi-mode integration method, and proposes a technical solution of using CART algorithm (Classification And Regression Tree algorithm) to solve it, and proposes a method which can improve the prediction performance. The method of the application divides the global data set into multiple data sets which are easy to model for complex wind speed data, and performs local regression modeling on each local data set. Similar to the traditional linear regression, the tree regression algorithm only needs a small amount of training data during training. Compared with linear regression, tree regression is more suitable for processing complex nonlinear problems.

[0072] Specifically, Figure 1 The main process of the wind speed prediction method based on the CART multi-mode integrated model is shown, as shown in the figure, the method specifically includes the following steps: Figure 1

[0073] Step one, obtain data, including wind speed prediction mode data and observation data; use bicubic interpolation to interpolate the obtained wind speed prediction mode data and observation data to a fine grid with a resolution of 0.1°x0.1°.

[0074] The source of the data is as follows:

[0075] The wind speed prediction mode data is taken from the average of the 10m wind speed of each ensemble member of the global ensemble prediction mode of the European Center for Medium-Range Weather Forecasts (ECMWF) and the National Environmental Prediction Center (NCEP) in the TIGGE data set, which is reported at 00 (world time) every day. The observation data uses the control prediction initial field of the ERA5 reanalysis data reported at 00 every day.

[0076] Step two, pre-process the data in step one and select reasonable data as sample data. Select a certain length of data in the sample data as training period data (training set), and the rest as prediction period data (prediction set).

[0077] The pre-processing of the mode data and the observation data includes the following steps:

[0078] ​(201) The forecast data of ECMWF with a resolution of 0.5°x0.5° in the mode forecast, the forecast data of NCEP with a resolution of 0.5°x0.5°, and the observation data of ERA5 with a resolution of 0.25°x0.25° are interpolated to a resolution of 0.1°x0.1° by bicubic interpolation.

[0079] (202) Select the consistent longitude and latitude of the forecast and observation information. After pre-processing the data and screening the reasonable data, select the final total sample data length and the training period data.

[0080] Step three, compare the errors of each forecast mode and observation in the forecast period, and analyze the forecast accuracy of each mode.

[0081] Step four, establish a multi-mode integrated model based on CART according to the training period data, and compare it by using the method of eliminating bias ensemble average.

[0082] As shown in Figure 2 , the specific steps of establishing a multi-mode integrated model based on CART according to the training period data include:

[0083] (1) A regression tree corresponds to a division of the input space (i.e. feature space) and the output value on the unit of the division. Suppose the input space has been divided into M units R1, R2, …, R m , and there is a fixed output value c m on each unit R m , so the regression model can be represented as:

[0084]

[0085] In this way, the error between the model output value and the actual value can be calculated:

[0086]

[0087] We hope that c m on each unit can minimize the square error, and when c m is the mean of all actual values of the corresponding unit, the optimal value can be obtained:

[0088]

[0089] In order to generate these unit divisions, it can be assumed that X and Y are input and output variables respectively, and Y is a continuous variable, and a training set is given:

[0090] D=(x1,y1),(x2,y2),…,(x n ,y n )

[0091] Where D represents the entire dataset, y n This is the output value of the nth sample.

[0092] (2) Assume that variable x is chosen. (j) Let 's' be the splitting variable, and its value 's' be the splitting point. Values ​​less than or equal to 's' are assigned to the left subtree; otherwise, they are assigned to the right subtree. This will result in two regions:

[0093] R1(j,s)={x|x (j) ≤s},R2(j,s)={x|x (j) >s}

[0094] at this time:

[0095]

[0096] In the formula, N m Given the number of samples in each region, solve for:

[0097]

[0098] Iterate through variable j, scan the split point s, and select the pair (j, s) that minimizes m(s), where R m It is the partitioned input space, c m It is space R m The corresponding output value.

[0099] (3) Divide the region using the selected pair (j,s) and determine the corresponding output value.

[0100] (4) Continue calling steps (2) and (3) on the two sub-regions until the stopping condition is met.

[0101] (5) Divide the input space into M regions R1, R2, ..., R m Generate a decision tree:

[0102]

[0103] (6) For multi-feature inputs, based on the decision tree generated from the previous feature input and the residual obtained, a decision tree is built using the next feature input to fit the residual, and then the regression tree is integrated:

[0104] f = f(X1) + f(X2) + ...

[0105] The main steps in using the CART algorithm to process regression problems also include pruning the regression tree, such as... Figure 4 As shown, its principle is as follows:

[0106] Decision tree algorithms are prone to overfitting. To improve the model's generalization ability and reduce overfitting, CART provides pruning methods. Pruning methods include pre-pruning and post-pruning. Pre-pruning typically involves adding an early termination condition when selecting nodes. This method has some limitations, being sensitive to the order of magnitude of the error. Post-pruning, on the other hand, is a more ideal method. It primarily uses the training set to split leaf nodes and the test set to determine whether merging leaf nodes reduces the error. CART uses the post-pruning method. The pruning process generates many pruned trees. This embodiment uses cross-validation to evaluate the effectiveness of each pruning method and selects the best-performing tree as the final model.

[0107] The pruning process for regression trees uses mean squared error as the loss function. The process is as follows:

[0108] (1) When located in any subtree T of node t t Without pruning, its loss function is:

[0109] C α (T t )=C(T t )+α|T t |

[0110] Where α is the regularization parameter, C(T) t ) represents the error of the training data, |T t | represents the number of leaf nodes.

[0111] When pruning reaches the root node, i.e., only the root node is retained, the loss function is:

[0112] C α (T)=C(T t )+α

[0113] When α = 0 or is very small, then: C α (T t ) < C α (T); When α increases to a certain extent: C α (T t ) = C α (T). Therefore, when T and T t Satisfy C α (T t ) = C α (T), that is: You can then target T t Prune the tree by removing all child nodes, leaving only one leaf node T.

[0114] (2) When the α of whether all nodes are pruned is calculated, the optimal subtree corresponding to α is cross-validated on the training set to find the optimal subtree as the final result.

[0115] In the process of evaluating the regression tree model, the trained regression tree model is used to predict each sample. In the prediction process, the following cases are mainly divided:

[0116] (1) If there is only a root node at this time, directly return its value as the final prediction result;

[0117] (2) If there are left and right child trees at this time, compare the value at the index in the sample with the value at the division in the regression tree model: ① If the value at the index in the sample is greater than the value in the regression tree model, select the right child tree; ② If the value at the index in the sample is less than or equal to the value in the regression tree model, select the left child tree.

[0118] After the prediction is completed, the residual error is calculated using the predicted value and the original sample label.

[0119] In this embodiment, the prediction model based on the debiased ensemble average method is established according to the obtained training period data as a comparison, including the following formula:

[0120] The calculation formula of the debiased ensemble average is:

[0121]

[0122] Wherein, F BREM is the debiased ensemble average prediction value, is the average value of the measured value in the training period, N is the total number of patterns participating in the set, F i is the prediction value of the i-th pattern, is the average of the prediction value of the i-th pattern in the training period.

[0123] Step five, the effectiveness of the prediction model is verified by using the prediction period data, and the root mean square error (RMSE) is used to compare and analyze the prediction error in detail.

[0124] In this embodiment, the root mean square error (RMSE) is used to compare and analyze the prediction error in detail, including the following formula:

[0125]

[0126] Wherein, f i represents the prediction value of the i-th sample; o i is the corresponding observation value; n is the sample number. The smaller the RMSE, the smaller the error between the prediction value and the observation value, and the better the prediction effect.

[0127] Step six, analyze the limitations of the debiased ensemble average method, and use the proposed tree regression model as the prediction model of pattern integration to reduce the error between prediction and observation.

[0128] Based on the above process, the specific implementation steps of the method in the embodiment of the application include:

[0129] S1: In this embodiment, the data set contains a total of 150 sampling points, and the time interval is 1d, wherein the first 130 sample points are used as the training sample set, and the last 20 sampling points are used as the test sample set. Because the wind speed data is divided into 0.5°x0.5° forecast mode data and 0.25°x0.25° observation data, the resolutions are not uniform, therefore, the cubic method in Matlab is used to interpolate the forecast and observation data to a fine grid with a resolution of 0.1°x0.1°, and the forecast and observation information with consistent longitude and latitude is selected, so that the dimension of the input information is consistent. The selected area range is 120°52'-122°12'E, 30°40'-31°53'N, the selected time length is from January 1, 2018 to May 31, 2018, and the selected forecast point is 121.45°E, 31.4°N.

[0130] S2: The fitrtree function in Matlab is used to perform regression tree modeling on the obtained training period data, and the minimum number of samples contained in the leaf node is set to 30, so as to generate an optimized decision tree.

[0131] S3: The cross-validation error under different pruning is calculated, and the prune function is used to select the minimum error to prune the regression tree.

[0132] S4: In the process of evaluating the regression tree model, the trained regression tree model is used, and the predict function is used to predict each forecast period sample.

[0133] S5: In order to verify the effectiveness of the CART-based multi-mode integrated method of the application in improving the wind speed prediction effect, the bias-corrected ensemble average method is used for comparison, the training sample set is used to train the model, and the prediction effects of the two methods are analyzed and compared, and the root mean square error (RMSE) is used to compare and analyze the prediction error in detail.

[0134] In S1, the mode data is obtained from the average of the respective ensemble members of the 10m wind speed of the global ensemble prediction mode of the European Center for Medium-Range Weather Forecasts (ECMWF) and the National Environmental Prediction Center (NCEP) in the TIGGE data set, which is reported every day at 00 (world time). The observation data uses the control prediction initial field of the ERA5 reanalysis data reported every day at 00.

[0135] In S2, the fitrtree function in Matlab is used to perform regression tree modeling on the obtained training period data, and the minimum number of samples contained in the leaf node is set to 30, so as to generate an optimized decision tree, combined with Figure 3As shown, the steps to build a regression tree model are:

[0136] (1) A regression tree corresponds to a partition of the input space (i.e. feature space) and output values on the partitioned cells. Suppose the input space has been partitioned into M cells R1, R2,..., RM, and there is a fixed output value c m on each cell R m , then the regression model can be represented as: m

[0137]

[0138] Thus, the error between the model output value and the actual value can be calculated:

[0139]

[0140] We want to minimize the error square error on each cell c m , and the optimal value can be obtained when c m is the mean of all actual values of the corresponding cell:

[0141]

[0142] To generate these cell partitions, we can assume that X and Y are input and output variables, respectively, and Y is a continuous variable, given a training set:

[0143] D = (x1, y1), (x2, y2),..., (x n , y n )

[0144] where D represents the entire data set, and y n is the output value of the nth sample.

[0145] (2) Suppose we choose variable x (j) as the split variable, and its value s as the split point, and less than or equal to s is divided into the left subtree, otherwise into the right subtree, then we get two regions:

[0146] R1(j, s) = {x | x (j) ≤ s}, R2(j, s) = {x | x (j) > s}

[0147] At this time:

[0148]

[0149] N m is the number of samples in each region, and solve:

[0150] ​

[0151] Traverse variable j, scan the split point s, select the pair (j, s) that makes m(s) minimum, where R m is the divided input space, c m is the space R m corresponding output value.

[0152] (3) Divide the region with the selected pair (j, s) and determine the corresponding output value.

[0153] (4) Continue to call steps (2) (3) on the two sub-regions until the stop condition is met.

[0154] (5) Divide the input space into M regions R1, R2, …, R m , generate the decision tree:

[0155]

[0156] (6) For multi-feature input, on the basis of generating a decision tree and deriving the residual error for the previous feature input, use the next feature input to establish a decision tree to fit the residual error, and integrate the regression tree:

[0157] f = f(X1) + f(X2) + …

[0158] In step S3, the cross-validation error under different pruning is calculated, and the prune function is used to select the minimum error to prune the regression tree, including the following steps:

[0159] (1) When any one of the sub-trees T t located at node t is not pruned, its loss function is:

[0160] C α (T t ) = C(T t ) + α |T t |

[0161] Where, α is a regularization parameter, C(T t ) is the error of the training data, and |T t | is the number of leaf nodes.

[0162] When pruning to the root node, i.e. only the root node is retained, its loss function is:

[0163] C α (T) = C(T t ) + α

[0164] When α = 0 or very small, then: C α (T t ) < Cα (T) ; when a increases to a certain extent: C α (T t ) = C α (T). So when T and T t satisfy C α (T t ) = C α (T), namely: T t can be pruned, and all child nodes are pruned, leaving a leaf node T.

[0165] (2) When all nodes are calculated whether to prune a, the optimal subtree corresponding to a is cross-validated on the training set to find the optimal subtree as the final result.

[0166] In step S4, in the process of evaluating the regression tree model, the trained regression tree model is used to predict each forecast sample by using the predict function. In the prediction process, the following cases are mainly divided:

[0167] (1) If there is only a root node at this time, the value is directly returned as the final prediction result;

[0168] (2) If there are left and right child trees at this time, compare the value at the index in the sample with the value at the division in the regression tree model: ① If the value at the index in the sample is greater than the value in the regression tree model, select the right child tree; ② If the value at the index in the sample is less than or equal to the value in the regression tree model, select the left child tree.

[0169] After the prediction is completed, the residual error is calculated using the predicted value and the original sample label.

[0170] In step S5, in order to verify the effectiveness of the method of the present application for improving the prediction effect of wind speed, the bias-corrected ensemble average method is used for comparison, the model is trained using the training sample set, and the prediction effects of the two methods are analyzed and compared. The root mean square error (RMSE) is used for detailed comparative analysis of the prediction error, including the following formula:

[0171] The calculation formula of the bias-corrected ensemble average is:

[0172]

[0173] Where F BREM is the bias-corrected ensemble average prediction value, is the average value of the training period measured value, N is the total number of patterns participating in the set, F i is the forecast value of the i-th pattern, is the average of the forecast value of the i-th pattern in the training period.

[0174] The root mean square error (RMSE) detailedly compares and analyzes the prediction error, including the following formula:

[0175]

[0176] Wherein, f i represents the mode prediction value of the i-th sample; o i is the observation value corresponding thereto. The smaller the RMSE is, the smaller the error between the prediction value and the observation value is, and the better the prediction effect is.

[0177] The scheme of the present application is further illustrated below with a specific embodiment:

[0178] Step 1: Based on the wind speed data of Shanghai, the mode data is obtained from the TIGGE data set, and the average of the 10m wind speed of each ensemble member of the global ensemble prediction mode of the European Center for Medium-Range Weather Forecasts (ECMWF) and the National Environmental Prediction Center (NCEP) is reported at 00 (world time) every day. The horizontal resolution of the mode is 0.5°x0.5°, and the prediction time is 24h. The observation data is the control prediction initial field reported at 00 every day by ERA5 reanalysis data. The data length is selected from January 1, 2018 to May 31, 2018, and the selected area range is 120°52'-122°12'E, 30°40'-31°53'N. The data set contains a total of 150 sampling points, and the time interval is 1d, wherein the first 130 sample points are used as the training sample set, and the last 20 sample points are used as the test sample set.

[0179] Because the resolution of the prediction mode data and the observation data is different, the bicubic interpolation method is used to interpolate the prediction and observation data to the 0.1°x0.1° resolution fine grid, and the longitude and latitude consistent prediction and observation information is selected, so that the input information dimension is consistent.

[0180] In order to better compare the simulation results, one of the grid points (121.45°E, 31.4°N) in Shanghai area is selected for simulation experiment.

[0181] Figure 5 The comparison chart of the wind speed prediction data of each mode at the prediction point and the observation data in the prediction period with a prediction time of 24h. In the figure, observation value represents the observation value, which is calculated by Figure 5 It can be clearly seen that the prediction errors of the two modes are different, and the wind speed prediction effect of ECMWF is better than that of NCEP. However, the time-averaged root mean square error of the prediction and observation value is greater than 1m / s. Obviously, the prediction results of the two modes have a large difference from the expected prediction value.

[0182] Step 2: Regression tree modeling is performed on the obtained training data using the fitrtree function in Matlab, and the minimum amount of data contained in each leaf node is limited. If no limitation is imposed, the minimum amount of data contained in each leaf node is 1, and excessive leaf nodes will inevitably reduce the generalization ability of the decision tree. Therefore, a Leaf(min) should be obtained to minimize the cross-validation error. Figure 6 As a result, the minimum number of samples contained in the leaf node is set to 30 to generate an optimized decision tree.

[0183] Step 3: The cross-validation error under different pruning is calculated, and the prune function is used to select the minimum error to prune the regression tree. The pruned tree model is shown in Figure 7

[0184] Step 4: In the process of evaluating the regression tree model, the trained regression tree model is used to predict each forecast period sample using the predict function. Figure 8 The comparison chart of the sample data after tree regression and the observed value is shown. As can be seen, the error between the predicted value after tree regression and the observed value is reduced.

[0185] Step 5: To verify the effectiveness of the CART-based multi-mode integration method proposed in the present application in improving the wind speed prediction effect, the bias elimination ensemble average (BREM) method is used for comparison. The model is trained using the training sample set, and the prediction effects of the two methods are analyzed and compared. The bias elimination ensemble average is based on the sliding training period method, and the training period of fixed length is slid day by day, and only the day close to the training period is predicted each time. Figure 9 The comparison chart of the sample data after tree regression and the observed value is shown. As can be seen, the error between the predicted value after tree regression and the observed value is reduced.

[0186] The root mean square error (RMSE) is used to compare and analyze the prediction error in detail. Figure 10 The root mean square error comparison chart of the wind speed prediction of each mode and the observed value after the two integration methods is shown in Figure 10 ​As shown, the root mean square error of the forecast by the tree regression is greatly reduced compared with the bias-corrected ensemble average method. The root mean square error of the ensemble forecast by the bias-corrected ensemble average method is reduced by nearly 12.91% compared with the best single-mode ECMWF and by nearly 45.67% compared with NCEP. The forecast effect of the ECMWF itself is better than that of NCEP, so the improvement is also correspondingly smaller than that of NCEP, which also shows that the improvement effect of the multi-mode ensemble on the forecast ultimately depends on the forecast effect of the mode itself. The root mean square error of the ensemble forecast by the tree regression is reduced by nearly 52.88% compared with the ECMWF and by nearly 70.6% compared with NCEP. According to the calculation, the root mean square error is reduced by 45.9% compared with the bias-corrected ensemble average method, which is further improved. It can be seen that the multi-mode ensemble method based on CART reduces the forecast error and has a very good improvement effect compared with the single mode, and from the root mean square error, the CART is better than the bias-corrected ensemble average method.

[0187] The above merely illustrates the specific implementation of the present application, but the protection scope of the present application is not limited to this. Any person skilled in the art can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present application, and these modifications or replacements should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A wind speed forecasting method based on a CART-based multi-modal ensemble model, characterized in that, The method comprises the following steps: 1) Obtain data, and use bicubic interpolation to interpolate the obtained data to a fine grid of resolution R. resolution R. 2) pre-processing the data, screening the sample data, and dividing the sample data into training period data and prediction period data; 3) comparing the errors of each prediction mode and observation in the prediction period, and analyzing the prediction accuracy of each mode; 4) establishing a CART-based multi-mode integrated model according to the training period data, and establishing a prediction model of mode integration based on the bias-corrected ensemble average method as a comparison; 5) inputting the prediction period data into the CART-based multi-mode integrated model for prediction, obtaining the prediction results, and comparing and analyzing the prediction errors by using the root mean square error, The data includes wind speed prediction mode data and observation data, The wind speed prediction mode data is obtained from the average of the 10m wind speed of each ensemble member of the global ensemble prediction mode of the European Medium-Range Weather Forecast Center and the National Environmental Prediction Center in the TIGGE data set, and the observation data is obtained from the control prediction initial field of the ERA5 reanalysis data, The specific steps of pre-processing the data include: 201) The ECMWF forecast data with resolution of 0.125°*0.125°, the NCEP forecast data with resolution of 0.5°*0.5° and the ERA5 observation data with resolution of 0.25°*0.25° in the wind speed forecast model data are interpolated to 0.01°*0.01° by bi-cubic interpolation. ;​​​ 202) selecting wind speed prediction mode data and observation data with consistent latitude and longitude, pre-processing the data, selecting reasonable data, and selecting the final total sample data length and training period data, The specific steps of establishing a CART-based multi-mode integrated model according to the training period data include: 401) A regression tree corresponds to a partition of the input space, i.e. a feature space, and output values on the cells of the partition. Assume that the input space has been partitioned into cells , and there is a fixed output value on each cell , then the regression model can be represented as: Y = f(X) = f (x1, x2,..., xn) = f (x1) = f (x2) =... = f (xn) Then, the error between the model output value and the actual value is calculated: Let the output value of each cell be the average of all the actual values of the corresponding cell Minimize this error squared error when The optimal output value is obtained when the average of all the actual values of the corresponding cell : Assume with are input and output variables, respectively, and are continuous variables, given a training set: wherein, represents the entire data set, is the output value for the th sample; 402) Hypothesis selection variable is the cut variable, which takes values is the cut point, and values less than or equal to are partitioned into the left child and otherwise into the right child, two regions are obtained: At this time: wherein is the number of samples for each region, and solving for: traversing variable , scan split points , select pairs of that attain a minimum , where is the input space being partitioned, is the space corresponding output values; 403) using the selected pair divides the region and determines the corresponding output value; 404) continue to call steps 402 and 403 for the two sub-regions until the stop condition is met; 405) dividing the input space into regions , generating a decision tree: 406) for multiple feature inputs, based on the generation of the decision tree and the residual error obtained by the previous feature input, a decision tree is established using the subsequent feature input to fit the residual error, and the regression tree is integrated: ， After integrating the regression tree, the pruning operation of the regression tree is also included, The specific steps of the pruning operation of the regression tree include: (1) When located in any one sub-tree of the node , without pruning, its loss function is: ​ wherein is a regularization parameter, is an error of the training data, is a number of leaf nodes; When pruning to the root node, i.e., only the root node is retained, the loss function is: When or close to 0, then: ; when increases to a certain extent: ; therefore when and satisfy , i.e.: , the pruning, all the child nodes are cut off, leaving a leaf node ; (2) When all nodes are calculated whether to be pruned After that The corresponding optimal subtree is cross-validated on the training set to find the optimal subtree as the final result. 2.The wind speed forecasting method of the CART-based multi-model ensemble model according to claim 1, wherein, In step 5), the trained regression tree model is used to predict each sample, and the prediction process includes two cases: (1) if there is only a root node at this time, the value of the root node is directly returned as the final prediction result; (2) if the node at this time has left and right child trees, the value of the sample at the index is compared with the value of the regression tree model at the division: ① if the value of the sample at the index is greater than the value of the regression tree model, the right child tree is selected; ② if the value of the sample at the index is less than or equal to the value of the regression tree model, the left child tree is selected. 3.The wind speed forecasting method of the CART-based multi-mode integrated model according to claim 1, wherein, The expression of the prediction model of mode integration based on the bias-corrected ensemble average method is: wherein is the ensemble average prediction, is the average of the measured values during the training period, is the total number of patterns in the ensemble, is the predicted value for the th pattern, is the average of the predicted values for the th pattern during the training period. 4.The wind speed forecasting method of the CART-based multi-model ensemble model according to claim 1, wherein, The formula for comparing and analyzing the prediction error by using the root mean square error is: wherein represents the mode forecast value of the n is the number of samples.​​

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