A method for preprocessing data in mines based on improved bagging

By applying Bagging improved methods and BP neural networks in the in-mile data preprocessing to identify and process abnormal data, the problem of low prediction accuracy of mine settlement value in the existing technology is solved, data credibility and prediction accuracy are improved, and the risk of mine settlement is reduced.

CN114862612BActive Publication Date: 2025-03-18HANGZHOU DIANZI UNIV
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Patent Information

Application Number
CN202210494493.3
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-05-07
Publication Date
2025-03-18
Estimated Expiration
2042-05-07

AI Technical Summary

Technical Problem

The existing mine settlement value prediction model fails to effectively identify abnormal data when processing mining data, resulting in low prediction accuracy and increasing the risk of mine settlement.

Method used

Using Bagging-improved in-mine data preprocessing method, the mining parameters and mine settlement values ​​are measured through sensors, and randomly divided into training sets and test sets. Sub-models are constructed using BP neural network, abnormal data are identified and marked, and data type weights are updated to build the final prediction model.

Benefits of technology

It improves data credibility, effectively identifies and handles abnormal data, improves the accuracy of the mine settlement value prediction model, and reduces the mine settlement risk.

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Abstract

The present invention discloses a method for preprocessing data in a mine based on improved bagging. The method collects multiple groups of mining parameters and mine settlement values ​​through multiple sensors, extracts multiple training subsets through training sets, and respectively establishes multiple sub-models; records the extraction weights of all data in the training set in multiple sub-models, and calculates the errors in the multiple sub-models; based on the errors, calculates the average error of each group of data in all sub-models; arranges the average errors in descending order, and takes the larger groups of data as abnormal data; uses the test set data to test the model built by the training set before and after the weight update; if the test set error is lower than before the weight update, the new training set is used to return and start the cycle, otherwise the abnormal data is returned. The present invention identifies abnormalities in the collected data on the basis of integrated learning bagging, and effectively preprocesses the data in the mine.
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Description

Technical Field

[0001] The invention relates to a method for preprocessing data in a mine based on bagging improvement, belonging to the technical field of preprocessing data in a coal mine. Background Art

[0002] Coal is the main energy source in my country, accounting for more than 50% of the primary energy production and consumption structure for a long time, and is the "ballast stone" of my country's safe and stable energy supply. Coal mining is divided into two methods: open-pit mining and underground mining. At present, the proportion of underground mining in my country is as high as 85%, making it the country with the highest proportion of underground coal mining in the world. In the process of underground coal mining, a large number of mines need to be excavated in order to meet the needs of coal mining and transportation. In the process of underground engineering operations, there is often the risk of mine subsidence. Once an accident occurs, it will directly threaten the life safety of underground workers. Therefore, it is very important to ensure that underground engineering avoids the risk of mine subsidence.

[0003] At present, the traditional prediction of mine settlement value requires the deployment of a large number of sensors at multiple key points for real-time monitoring, and then the modeling is carried out using the collected historical data of various mining parameters to obtain a prediction model with multiple mining parameters as input and mine settlement value as output. Mining parameters mainly include three parts: mining engineering geological parameters, mining equipment construction parameters and mining engineering working surface parameters. However, due to the harsh conditions of underground mining engineering, the credibility of mining data is often low or even distorted. Most mining engineering practices do not process mining data, but directly model based on mining data; a few mining projects use multiple sensors to obtain the average value as the final parameter. However, these processing methods cannot accurately identify abnormal data in the mine data.

[0004] In order to improve the accuracy of the mine settlement prediction model and thus achieve the purpose of reducing the risk of underground engineering, it is necessary to preprocess the data of mining parameters. A method of preprocessing data in the mine based on improved bagging is proposed. The bagging algorithm is a parallel ensemble learning method. Its main idea is to use the independence between different base learners to combine independent base classifiers, thereby significantly reducing the error. The bagging algorithm automatically samples multiple sets of data training models, so it has strong generalization ability and plays a great role in reducing the variance of the model. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention proposes an improved mine data preprocessing method based on Bagging.

[0006] First, the present invention measures multiple sets of mining parameters and mine settlement values using sensors, and randomly divides them into a training set and a test set according to a certain ratio; then, identifies the training set data as normal data and abnormal data, assigns different weights to the normal data and abnormal data respectively, and establishes a settlement value prediction model; afterwards, uses the test set for verification to determine whether all the abnormal data in the training set are completely identified, and returns the identified normal data and abnormal data; finally, establishes prediction models using the unprocessed data and the processed normal data respectively to verify the effectiveness of the method.

[0007] The method of the present invention includes the following:

[0008] (1) Using sensors, collect multiple sets of data in the mine. Each set of data in the mine includes mining parameters and mine settlement values. Among them, the mining parameters are used as the input of this set of data, and a total of 8 factors are included, x1: cohesive force, x2: compression modulus, x3: internal friction angle, x4: advancing footage of the shearer, x5: cutting speed of the shearer, x6: average thickness of the coal seam, x7: dip length of the working face, x8: strike length of the working face. The mine settlement value is used as the output of this set of data, y: mine settlement value.

[0009] (2) Randomly divide the multiple sets of collected data into a training set and a test set according to the set ratio. Denote the training set as T m and the test set as S. Denote the type weight of each set of data in the training set as where m represents the m-th cycle, and l represents the l-th set of data in the training set. When m = 1, that is, in the first cycle, the type weight of each set of data in the training set is denoted as 1.

[0010] (3) Randomly select P% (0 < P < 100) sets of data from the training set T m as training subsets, and conduct N extractions. Each extraction is performed on the complete training set T m to obtain N training set subsets Among them, represents the n-th subset of data in the m-th cycle.

[0011] (4) Using a BP neural network, take the product of the input of each set of data in the training subset and the corresponding data type weight as the training data, and the product of the output and the corresponding data type weight as the prediction data to construct a BP neural network model. Use N subsets of data to construct N sub-models Among them represents the model established using the n-th subset of data in the m-th cycle.

[0012] (5) Record that each set of data in the training set T m is respectively covered by N subsets of data The extracted weight And in N sub-models Error in in, Represents the training set T m The lth group of data in the training subset The extraction weight of Represents the training set T m The first group of data in the model The error in .

[0013] (6) Based on the training set T obtained in (5) m The extraction weights of each group of data for all training subsets and the errors in all sub-models are calculated for the training set T m The average error of all data in N sub-models

[0014] (7) The training set T obtained in step (6) m The average error of all data in Arrange in descending order and take the training set T m The first 1% of the data with the largest error are marked as abnormal data, and the other groups of data are marked as normal data.

[0015] (8) Based on the training set T identified in (7) m The normal data and abnormal data in the training set T m Update the data type weights of all the data in to get a new training set T m+1 , the data type weight of normal data does not change, and the data type weight of abnormal data is recorded as 0.

[0016] (9) Use training set T respectively m With the training set T m+1 Using BP neural network, the product of the input of each group of data in the training set and the corresponding data type weight is used as the training data, and the product of the output and the corresponding data type weight is used as the prediction data. Two BP neural network models R are constructed. m With R m+1 .

[0017] (10) Calculate the mean absolute error of all data in the test set S in the two models if It is considered that the abnormal data is effectively identified, and the training set T is used m+1 Continue with step (3) to the next cycle; otherwise, the training set T m All abnormal data in are successfully identified and the training set T is returned mThe data with a data type weight of 0 is abnormal data, and the data with a data type weight of 1 is normal data.

[0018] (11) Two settlement value prediction models were constructed using the unprocessed training set data and the normal data obtained after preprocessing, respectively, combined with the traditional prediction model modeling method. The average error of the test set data in the two models was calculated to verify the effectiveness of this method.

[0019] Beneficial effects of the present invention:

[0020] First, most traditional mine settlement prediction models do not consider whether the data required for modeling is abnormal, but directly use the data monitored by sensors for modeling. Such directly constructed prediction models are often not accurate and easily increase the risk of mine settlement. In view of this shortcoming, the present invention proposes an effective data preprocessing method in mines to improve data credibility.

[0021] Second, although a small number of mine settlement prediction models pre-process the collected data, they often only use simple numerical processing methods such as averaging, which does not meet the data requirements of model construction. In view of the fact that the model needs to reflect the relationship between input and output, the present invention uses data to build a model during the identification process, which can more effectively identify normal data and abnormal data. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a flowchart of the method of the present invention.

[0023] Figure 2 It is the experimental result of verifying the effectiveness of the method in the embodiment of the present invention. DETAILED DESCRIPTION

[0024] The present invention relates to a method for preprocessing data in a mine based on improved bagging. Multiple groups of data in the mine are obtained through sensors, and are divided into training sets and test sets; the improved bagging method is used to identify normal data and abnormal data in the training set; different processing methods are used for normal data and abnormal data, and different weights are assigned to each data and a model is established; the test set is used to verify whether the abnormal data is successfully identified, until the abnormal data in the training set is completely identified; finally, the unprocessed data and the preprocessed normal data are used to build a prediction model to verify the effectiveness of the method. The present invention specifically includes the following steps:

[0025] (1) Using sensors, multiple groups of mine data are collected. Each group of mine data includes mining parameters and mine settlement values. Among them, the mining parameters are used as the input of this group of data, which include a total of 8 factors: x1: cohesion, x2: compression modulus, x3: internal friction angle, x4: advancing footage of the shearer, x5: cutting speed of the shearer, x6: average coal seam thickness, x7: dip length of the working face, x8: strike length of the working face. The mine settlement value is used as the output of this group of data, y: mine settlement value.

[0026] (2) According to a ratio of 4:1, the multiple groups of collected data are randomly divided into a training set and a test set. Denote the training set as T m , the test set as S, and the type weight of each group of data in the training set is denoted as where m represents the m-th cycle, and l represents the l-th group of data in the training set. When m = 1, that is, in the first cycle, the type weight of each group of data in the training set is denoted as 1, and there is

[0027] (3) Randomly select P% (0 < P < 100) groups of data from the training set T m as a training subset. A total of N extractions are performed, and each extraction is carried out in the complete training set T m to obtain N training set subsets Among them, represents the n-th subset of data in the m-th cycle.

[0028] (4) Using a BP neural network, the product of the input of each group of data in the training subset and the corresponding data type weight is used as the training data, and the product of the output and the corresponding data type weight is used as the prediction data to construct a BP neural network model. Use N subsets of data to construct N sub-models Among them represents the model established using the n-th subset of data in the m-th cycle.

[0029] (5) Record the weights m that each group of data in the training set T is extracted by the N subsets of data and the errors in the N sub-models Among them, represents the extraction weight of the l-th group of data in the training set T m for the training subset , represents the error of the l-th group of data in the training set T m in the model .

[0030] (6) According to (5), the training set T m The extraction weights of each group of data for all training subsets and the errors in all sub-models are calculated for the training set T m The average error of all data in N sub-models

[0031] (7) The training set T obtained in step (6) m The average error of all data in Arrange in descending order and take the training set T m The first 1% of the data with the largest error are marked as abnormal data, and the other groups of data are marked as normal data.

[0032] (8) Based on the training set T identified in (7) m The normal data and abnormal data in the training set T m Update the data type weights of all the data in to get a new training set T m+1 , the data type weight of normal data does not change, and the data type weight of abnormal data is recorded as 0.

[0033] (9) Use training set T respectively m With the training set T m+1 Using BP neural network, the product of the input of each group of data in the training set and the corresponding data type weight is used as the training data, and the product of the output and the corresponding data type weight is used as the prediction data. Two BP neural network models R are constructed. m With R m+1 .

[0034] (10) Calculate the mean absolute error of all data in the test set S in the two models if It is considered that the abnormal data is effectively identified, and the training set T is used m+1 Continue with step (3) to the next cycle; otherwise, the training set T m All abnormal data in are successfully identified and the training set T is returned m The data with a data type weight of 0 is abnormal data, and the data with a data type weight of 1 is normal data.

[0035] (11) Two settlement value prediction models were constructed using the unprocessed training set data and the normal data obtained after preprocessing, respectively, combined with the traditional prediction model modeling method. The average error of the test set data in the two models was calculated to verify the effectiveness of this method.

[0036] Furthermore, in step (3), P takes the same value in each cycle, that is, the training subset satisfies Where φ represents the amount of data contained in the set, such as φ(T m )=500 means training set T m Contains 500 sets of data.

[0037] In order to deepen the understanding of extracting training subsets, an example is given here. Assume that the training set T m The size of φ(T m )=500, the fixed ratio coefficient is P=80, and the number of training subsets is N=30, then we have

[0038] Furthermore, in the step (4), when all sub-models are constructed using the BP neural network, the BP neural network uses the same settings and is implemented in Matlab using the fitnet function; the number of hidden layers in the function is set to 5, and the function is implemented as hiddenLayerSize=5; the network training algorithm uses the Levenberg-Marquardt algorithm, and the function is implemented as trainFcn='trainlm'.

[0039] Furthermore, in step (5) The calculation method is shown in formula (1):

[0040]

[0041] in, Represents the training set T m The first group of data in Represents the training set T m Data in For the training subset The extraction weight of Represents the training set T m Data in In the model The error in Represents the training set T m Data in In the model The predicted output in Representation data The true output of m Data in Included in the training subset In the middle of the day, The error is calculated by the model's predicted value and the true value; otherwise, the data extraction weight and error are both recorded as 0.

[0042] In order to deepen the Here is an example to illustrate the understanding of the calculation formula. Take l = 1, that is, take the training set T m The first set of data, the number of training subsets is N = 30, assuming that the first set of data in the 30 training subsets is as shown in Table 1:

[0043] Table 1 The relationship between the first set of data and the 30 training subsets

[0044]

[0045]

[0046] According to the inclusion relationship between the first set of data and the 30 training subsets shown in Table 1 and formula (1), the extraction weights of the first set of data for the 30 training subsets can be obtained: As shown in Table 2:

[0047] Table 2 Extraction weights of the first set of data for 30 training subsets

[0048]

[0049] Assume that the product of the input of the first set of data and the corresponding data type weight is input into the sub-model And get the predicted value of each sub-model According to Table 2 and formula (1), the error of the first set of data for 30 sub-models is obtained: As shown in Table 3:

[0050] Table 3 Errors of the first set of data for 30 sub-models

[0051]

[0052]

[0053] Furthermore, the average error in step (6) is The calculation formula is shown in formula (2):

[0054]

[0055] Among them, l=1,…l,…L calculate the training set T in turn m The average error of each set of data in N training subsets.

[0056] In order to deepen the average error Here is an example to illustrate the understanding of the calculation. For the training set T m The first set of data, assuming that its error for each training subset and the extraction weights are shown in Table 2 and Table 3, the average error of the first set of data is calculated as follows:

[0057]

[0058] Furthermore, when the data type weight is updated in step (8), its calculation formula is as shown in formula (3):

[0059]

[0060] When the data is identified as abnormal data, μ=0; when the data is identified as normal data, μ=1.

[0061] Furthermore, the test set error in step (10) is The calculation formula is as follows:

[0062]

[0063] Among them, I is the size of the test set S, y i is the actual output of the i-th group of data in the test set S, The i-th group of data in the test set S is in the training set T m The established model R m The predicted output in .

[0064] In order to deepen the test set error Here is an example to illustrate the understanding of . Assume that m = 10, that is, in the 10th cycle, the training set T at the beginning of the 10th cycle is used 10 Establish a model and use formula (4) to calculate the error of the test set S on this model After the 10th cycle, the training set T with the changed data type weight is used. 11 Build a model and calculate the error of the test set S on this model

[0065] Assumptions exist At this time, the training set T with the data type weight changed after the 10th cycle is used 11 Return to step (3) to start the next cycle and continue to identify abnormal data.

[0066] The following is a detailed description of the embodiments of the method of the present invention with reference to the accompanying drawings:

[0067] The flowchart of the method of the present invention is as follows Figure 1As shown in the figure, the core parts are: extract multiple training subsets from the training set and build corresponding sub-models; calculate the extraction weight and sub-model error of each group of data in the training set; calculate the average error of each group of data in the training set for all sub-models; identify abnormal data and normal data according to the average error of each group of data in the training set; update the type weights of abnormal data and normal data; use the training set data before and after each cycle to build different models, and use the average error of the test set data in different models to determine whether to end the cycle; determine all abnormal data and return the normal data and abnormal data identified in the training set; finally, use the unprocessed data and the preprocessed normal data to build models respectively to verify the effectiveness of this method.

[0068] The following is a best embodiment of the method of the present invention, which is described in detail based on the changes in mine settlement values ​​along with mining engineering geological parameters, mining equipment construction parameters and mining engineering working surface parameters during the internal construction of the mine.

[0069] 1. Collection and preprocessing of experimental data

[0070] Using sensors, 500 sets of data were collected. Each set of mine data used mining parameters as the input of the data set, including 8 factors, x1: bonding force, x2: compression modulus, x3: internal friction angle, x4: coal mining machine pushing and mining footage, x5: coal mining machine coal cutting speed, x6: average thickness of coal seam, x7: working face inclination length, x8: working face strike length, and mine settlement value as the output of the data set, y: mine settlement value. Among them, 400 sets were randomly selected as training set T 1 , 100 groups as the test set S, that is, φ(T 1 )=400,φ(S)=100,T 1 The data type weights of all data in are equal, both

[0071] 2. Extraction of training subsets and construction of sub-models

[0072] Take P = 80, from the training set T 1 80% (320 groups) of data were randomly selected as training subsets, and 30 extractions were performed, each time in the complete training set T 1 , and 30 training set subsets were obtained. Use 30 sub-datasets respectively Build 30 sub-models using neural networks The specific parameters of the neural network are set as follows: the function fitnet is used in Matlab; the number of hidden layers in the function is set to 5, and the function is implemented as hiddenLayerSize=5; the network training algorithm uses the Levenberg-Marquardt algorithm, and the function is implemented as trainFcn='trainlm'.

[0073] 3. Calculate the extraction weight and sub-model error of each group of data in the training set

[0074] According to the training set T 1 Are the 400 data sets included in the sub-datasets? Calculate the extraction weights of 400 sets of data for 30 sub-data sets Where n=1,…,30, l=1,…,400; T 1 400 sets of data are input into 30 sub-models Combine the extraction weights of 400 sets of data for 30 sub-datasets and formula (1) to calculate the sub-model errors of 400 sets of data for 30 sub-models. Where n=1,…,30, l=1,…,400.

[0075] 4. Calculate the average error of each group of data in the training set for all sub-models

[0076] According to the requirements of step (6) and formula (2), combined with the data obtained in step (5), the training set T is calculated 1 400 sets of data for 30 sub-models The average error Where l=1,…,400.

[0077] 5. Identify abnormal data and normal data based on the average error of each group of data in the training set; update the type weights of abnormal data and normal data

[0078] The training set T obtained in step (5) 1 The average error of 400 sets of data Arrange in descending order and take the training set T corresponding to the first 1% (4 groups) 1 The data in is marked as abnormal data, and the other data is marked as normal data. For the type weight update of normal data, μ=1, then Where l represents the data number identified as normal data; for the type weight update of abnormal data, μ=0, then Where l represents the data number identified as abnormal data.

[0079] 6. Use the training set data before and after each cycle to build different models, and use the average error of the test set data in different models to determine whether to end the cycle.

[0080] According to the training set T 1 The training set T obtained after updating the data weight 2 , using neural networks to build two different models R 1 With R 2 , calculate the mean absolute error of the test set S under different models if It is considered that the abnormal data is effectively identified, and the training set T is used 2 Continue with step (3) to the next cycle; otherwise, the training set T 2 All abnormal data in the dataset are successfully identified, and the abnormal data and normal data in the dataset are returned.

[0081] 7. Use the unprocessed training set data and the normal data obtained after preprocessing to verify the effectiveness of this preprocessing method.

[0082] Using the training set T 1 The 400 sets of data and the normal data obtained after preprocessing were combined with the traditional prediction modeling method to build two different models. The average error of the test set data in the two models was calculated respectively, and the average error of the test set data in the model built by the unprocessed data was 0.00228, and the average error in the model built by the normal data after preprocessing was 0.00164, which reduced the error by 28%, proving the effectiveness of this method.

Claims

1. A mine data preprocessing method based on improved bagging, characterized in that The method comprises the following steps: (1) Using sensors, multiple groups of mine data are collected. Each group of mine data includes mining parameters and mine settlement values. The mining parameters are used as the input of this group of data, including 8 factors in total, x1: cohesive force, x2: compression modulus, x3: internal friction angle, x4: coal mining machine pushing and mining footage, x5: coal mining machine coal cutting speed, x6: average thickness of coal seam, x7: working face inclination length, x8: working face strike length. The mine settlement value is used as the output of this group of data, y: mine settlement value; (2) According to the set ratio, the collected data sets are randomly divided into training sets and test sets; the training set is denoted as T m , the test set is S, and the type weight of each group of data in the training set is recorded as Where m represents the mth cycle, and l represents the lth group of data in the training set; when m=1, i.e. the first cycle, the type weight of each group of data in the training set is recorded as 1; (3) From the training set T m P% of the data are randomly selected as training subsets, and a total of N extractions are performed, each time in the complete training set T m To obtain N training set subsets in, Represents the nth sub-dataset in the mth cycle; (4) Using the BP neural network, the product of the input of each group of data in the training subset and the corresponding data type weight is used as the training data, and the product of the output and the corresponding data type weight is used as the prediction data to construct a BP neural network model; Use N sub-datasets respectively Construct N sub-models in Indicates that in the mth cycle, the model is established using the nth sub-dataset; (5) Record the training set T m Each set of data in is divided into N sub-datasets The extracted weight And in N sub-models Error in in, Represents the training set T m The first group of data in the training subset The extraction weight of Represents the training set T m The first group of data in the model Error in (6) Based on the training set T obtained in (5) m The extraction weights of each group of data for all training subsets and the errors in all sub-models are calculated for the training set T m The average error of all data in N sub-models (7) The training set T obtained in step (6) m The average error of all data in Arrange in descending order and take the training set T m The first 1% of the data with the largest error are marked as abnormal data, and the other groups of data are marked as normal data; (8) Based on the training set T identified in (7) m The normal data and abnormal data in the training set T m Update the data type weights of all the data in to get a new training set T m+1 , the data type weight of normal data does not change, and the data type weight of abnormal data is recorded as 0; (9) Use training set T respectively m With the new training set T m+1 Using BP neural network, the product of the input of each group of data in the training set and the corresponding data type weight is used as the training data, and the product of the output and the corresponding data type weight is used as the prediction data. Two BP neural network models R are constructed. m With R m+1 ; (10) Calculate the mean absolute error of all data in the test set S in the two models if It is considered that the abnormal data is effectively identified, and the new training set T is used m+1 Continue with step (3) to the next cycle; otherwise, the training set T m All abnormal data in are successfully identified and the training set T is returned m The data with a data type weight of 0 is abnormal data, and the data with a data type weight of 1 is normal data; (11) Using the unprocessed training set data and the normal data obtained after preprocessing, combined with the prediction model modeling method, two sedimentation value prediction models were constructed; the average error of the test set data in the two models was calculated to verify the effectiveness of the method; In step (3), P takes the same value in each cycle, that is, the training subset satisfies φ(T1 m )=φ(T m )*P% Where φ represents the amount of data contained in the set.

2. The improved mine data preprocessing method based on bagging according to claim 1 is characterized in that: In step (4), when all sub-models are constructed using the BP neural network, the BP neural network uses the same settings and is implemented in Matlab using the fitnet function; the number of hidden layers in the function is set to 5, and the function is implemented as hiddenLayerSize = 5; the network training algorithm uses the Levenberg-Marquardt algorithm, and the function is implemented as trainFcn = 'trainlm'.

3. The improved mine data preprocessing method based on bagging according to claim 1 is characterized in that: In step (5) The calculation of is as follows: in, Represents the training set T m The first group of data in Represents the training set T m Data in For the training subset The extraction weight of Represents the training set T m Data in In the model The error in Represents the training set T m Data in In the model The predicted output in Representation data The true output; when the training set T m Data in Included in the training subset In the middle of the day, The error is calculated by the model's predicted value and the true value; otherwise, the data extraction weight and error are both recorded as 0.

4. The improved mine data preprocessing method based on bagging according to claim 1 is characterized in that: The average error in step (6) The calculation of is as follows: Among them, l=1,…l,…L calculate the training set T in turn m The average error of each set of data in N training subsets.

5. The improved mine data preprocessing method based on bagging according to claim 1 is characterized in that: When the data type weight is updated in step (8), it is calculated as follows: When the data is identified as abnormal data, μ=0; when the data is identified as normal data, μ=1.

6. The improved mine data preprocessing method based on bagging according to claim 1 is characterized in that: The mean absolute error of the test set in step (10) The calculation of is as follows: Among them, I is the size of the test set S, y i is the actual output of the i-th group of data in the test set S, The i-th group of data in the test set S is in the training set T m The established model R m The predicted output in .

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