CN110555552B - Terminal area take-off and landing capacity prediction method based on weather risk index - Google Patents
Terminal area take-off and landing capacity prediction method based on weather risk index Download PDFInfo
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Abstract
The invention relates to a terminal area take-off and landing capacity prediction method based on a weather risk index. The terminal area take-off and landing capacity prediction method based on the weather risk index comprises the following steps: control operation experience abstraction influencing the take-off and landing capacity of the terminal area; according to the control operation experience abstraction, the terminal area airspace structure is divided again; acquiring a terminal area rising and falling peak period and an initial sample; calculating the characteristics of the initial sample and establishing a model training set; establishing a random forest regression model according to the training set; and verifying and predicting the random forest regression model. According to actual operation experience abstraction, the relevant airspace structure of the terminal area is divided again for modeling and relevant characteristics are extracted, the influence of convection weather is related to the time period capacity, regression analysis is carried out by using flight historical data, a terminal area take-off and landing capacity prediction model is obtained through training, and then a weather prediction product is input, and capacity prediction under the corresponding weather can be output.
Description
Technical Field
The invention relates to the field of capacity prediction of airport terminal areas, in particular to a terminal area take-off and landing capacity prediction method based on a weather risk index.
Background
The international civil aviation organization proposes Aviation System Block Upgrading (ASBU) in the global air navigation plan (ICAO DOC9750), and China correspondingly proposes the development and implementation strategy of the aviation system block upgrading of China. Airspace capacity is one of 11 key performance areas published by the global air navigation system performance manual (ICAO DOC9883), which reflects the capacity of the air traffic supply side. In addition, the airspace capacity is used as a chunk in the ASBU performance improvement field 3, and the effective improvement of the airspace capacity is the basis for realizing the capacity-flow balance and the cooperative decision.
In DOC9883, it is specified that in calculating a general capacity index (e.g. annual average capacity of an airport, etc.), basic measures and calculation methods for capacity under specific conditions (e.g. convection weather, etc.) must be considered. The national civil aviation industry development statistics bulletin shows that in aviation abnormal cause classification statistics, weather causes are high in percentage of 51.28%. Therefore, the prediction of the airspace capacity under the influence of the convection weather is not only a basic work for supporting performance evaluation, but also a basis for implementing an air traffic flow management strategy under the influence of the convection weather so as to reduce flight irregularity.
The terminal area is an area where the navigation data of the aircraft change most frequently in the flight process, the mutual crossing of the take-off and landing aircrafts, the sequencing of the approach aircrafts, the preparation before landing and the like are all completed in the terminal area, and particularly under the influence of severe weather, the airport runway and the terminal area are combined to form a bottleneck limiting the normal operation of air traffic. At present, capacity evaluation technology under the normal state (namely, without any external influence) of China tends to be mature, but a capacity prediction technology under the abnormal state (such as severe weather) is still in a preliminary stage, a capacity reduction method of multiplying a single index by a nominal capacity is too rough, cannot reflect the actual change of the air domain capacity in the operation process, has larger difference with the actual and lower applicability, and cannot meet the requirement of fine management of a civil aviation operation management department, an evaluation method based on a computer simulation technology is suitable for capacity evaluation work under a specific scene, and because a radar basic reflectivity diagram and the like reflecting weather are updated once in six minutes, the method cannot keep consistent with the updating frequency of meteorological elements, so that the influence of actual operation influence factors on the air domain capacity change, including weather change and the like, the evaluation method based on the workload of a controller generally depends on a controller simulator to reproduce a control scene, and then extracting influence factors (such as call frequency and the like) influencing the workload of a controller, and carrying out quantitative analysis to obtain the airspace capacity, but the control scene under the influence of weather is difficult to reproduce and operate, and the method can only be applied to the evaluation under a specific scene (such as a scene with only some thermodynamic weather).
How to solve the above problems is a need to be solved.
Disclosure of Invention
The invention aims to provide a terminal area take-off and landing capacity prediction method based on a weather risk index.
In order to solve the technical problem, the invention provides a terminal area take-off and landing capacity prediction method based on a weather risk index, which comprises the following steps: control operation experience abstraction influencing the take-off and landing capacity of the terminal area;
according to the control operation experience abstraction, the terminal area airspace structure is divided again;
acquiring a terminal area rising and falling peak period and an initial sample;
calculating the characteristics of the initial sample and establishing a model training set;
establishing a random forest regression model according to the training set;
and verifying and predicting the random forest regression model.
The method has the beneficial effects that the invention provides a terminal area take-off and landing capacity prediction method based on the weather risk index. The terminal area take-off and landing capacity prediction method based on the weather risk index comprises the following steps: control operation experience abstraction influencing the take-off and landing capacity of the terminal area; according to the control operation experience abstraction, the terminal area airspace structure is divided again; acquiring a terminal area rising and falling peak period and an initial sample; calculating the characteristics of the initial sample and establishing a model training set; establishing a random forest regression model according to the training set; and verifying and predicting the random forest regression model. According to the practical operation experience abstraction, the airspace structure related to the terminal area (including the terminal area airspace and the area sector adjacent to the terminal area corridor) is divided again for modeling, the related characteristics are extracted, the influence of convection weather is related to the time interval capacity, regression analysis is carried out by using flight historical data, a terminal area take-off and landing capacity prediction model is obtained through training, then the capacity prediction under the corresponding weather can be output by inputting a weather prediction product, and a dynamic capacity data basis is provided for the strategy and pre-tactical stages of deep analysis of system efficiency and air traffic flow management.
Drawings
The invention is further illustrated with reference to the following figures and examples.
FIG. 1 is a core flow diagram of the present invention;
FIGS. 2 and 3 are schematic diagrams of the relevant spatial domain structure repartitioning of the terminal region;
FIG. 4 is a histogram of the take-off and landing traffic for the Guangzhou terminal area;
FIG. 5 is a schematic view of a weather avoidance zone image product;
FIG. 6 is a schematic diagram of the relationship between WSI and airspace traffic;
FIGS. 7 and 8 are schematic diagrams of a relationship between a model performance metric and a model scale;
fig. 9 and 10 are schematic diagrams of model stability and accuracy.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic views illustrating only the basic structure of the present invention in a schematic manner, and thus show only the constitution related to the present invention.
Example 1
As shown in fig. 1, this embodiment 1 provides a method for predicting the landing capacity of a terminal area based on a weather risk index. According to the practical operation experience abstraction, the airspace structure related to the terminal area (including the terminal area airspace and the area sector adjacent to the terminal area corridor) is divided again for modeling, the related characteristics are extracted, the influence of convection weather is related to the time interval capacity, regression analysis is carried out by using flight historical data, a terminal area take-off and landing capacity prediction model is obtained through training, then the capacity prediction under the corresponding weather can be output by inputting a weather prediction product, and a dynamic capacity data basis is provided for the strategy and pre-tactical stages of deep analysis of system efficiency and air traffic flow management.
Specifically, the method comprises the following steps:
s110: control operation experience abstraction influencing the take-off and landing capacity of the terminal area;
s120: according to the control operation experience abstraction, the terminal area airspace structure is divided again;
s130: acquiring a terminal area rising and falling peak period and an initial sample;
s140: calculating the characteristics of the initial sample and establishing a model training set;
s150: establishing a random forest regression model according to the training set;
s160: and verifying and predicting the random forest regression model.
Wherein, step S110 includes:
when weather covers the vicinity of a runway, severe influence is caused on the take-off and landing of the runway, particularly, low clouds cover the vicinity of five sides (even a downslide), and the take-off and landing of flights almost completely depend on the judgment of a unit to carry out trial take-off and landing; when the terminal area controller sequences the flight in the approach, according to the control experience accumulated all the year round, a program similar to a landing and landing route is established near the airport and the flights are guided to join, so that the reference standard of flight sequencing is established. When weather covers the two sides of the airport runway, the experience rule formed by a controller is destroyed, the control load is increased, and the flight taking-off and landing of a terminal area are influenced; the bad weather of the area control sectors adjacent to the terminal area departure point can indirectly influence the terminal area taking off and landing times, because the terminal area departure times can be limited when the passing capacity of the area control sectors is blocked, so that the terminal area control load is increased in a short time, and a terminal area manager can limit the taking off and landing of an airport according to the actual running condition of the sectors if necessary.
Referring to fig. 2 and 3, in step S120, according to the control experience abstraction, the airspace structural division focuses on a circular airspace with a radius of 350KM and centered on an airport tower, and the specific structural division is as follows:
an airspace within a radius of 30km with the tower as a center is called an "inner circle" (hereinafter, referred to as an inner circle ") of a terminal area, and includes an airspace near an airport runway, and dangerous weather in the airspace has a large influence on the take-off and landing of the airport. Further, a rectangular area (the long side of which is parallel to the center line direction of the runway) with the width of 10KM and the length of 40KM is arranged by taking the tower as the center, and the rectangular area is divided into A, B, C, D parts along the center line direction of the runway and the direction vertical to the center line direction of the runway, and the inner ring of the terminal area is divided into E, F, G, H parts. Taking the Guangzhou airport as an example, assuming that the airport is operating in the north, when the area A is covered by dangerous weather, the takeoff flights of the 01/19 runway will be greatly affected; when the area B is covered by weather, takeoff flights of 02L/20R and 02R/20L runways are greatly influenced; when the area C is covered by dangerous weather, the landing flight of the 01/19 runway will be greatly influenced; when the area D is covered by weather, the landing flights of 02L/20R and 02R/20L runways will be greatly influenced (the influence is opposite when the airport runs to the south, namely the landing flights of 01/19 runway are influenced by the area A); when E, F, G and the H area are covered by weather, the trilateral sequencing work of the controllers on incoming flights (such as the inability to extend trilateral) is affected.
In addition, 4 annular zones are provided centered on the tower: an I region with a radius of 30-110 KM; a J region with a radius of 110KM-190 KM; a K region with the radius of 190-270 KM; the radius is 270KM-350KM L area. The I area is used for monitoring the weather in the terminal area, and the J, K, L area is used for monitoring the weather in the area sectors at different distances from the terminal area.
In this embodiment, step S130 includes:
s131: acquiring an hourly take-off and landing flow sample set of a terminal area based on historical data;
s132: acquiring a high peak hour set of the terminal area based on quantiles through a terminal area hourly take-off and landing flow sample set;
s133: initial samples based on peak hours are taken through the terminal area take-off and landing peak hours sets.
In this embodiment, referring to fig. 4, in step S131, a day is divided into 24-hour time periods, which are respectively 0:00-1:00, 1:00-2:00, 1.. and 23:00-24:00, and are numbered from 1 to 24, where the i-th time period 1, theThe end time isThe Airport code number in the terminal area is Airport, and the taking-off and landing Flight set of the terminal area in one year is Flight _ set ═ f1,...,fN1, F-th flight, and Dep, F flight departure airportfLanding airport is ArrfActual takeoff time is ADTfThe actual landing time is AATf;
Is provided withThenThe f-th flight belongs to the takeoff flight in the t-th time period of the Airport, and the same principle is setThenIndicating that the f-th flight belongs to a landing flight in the t-th time period of the Airport;
the flight take-off and landing flow of the terminal area of the Airport in the ith time period isThereby obtaining the hourly take-off and landing Flow sample set Flow _ set ═ Flow of the terminal areai,t|i=1,...,365;t=1,...,24}。
In this embodiment, step S132 is:
obtaining the Flow sample set Flow _ set of the t-th time period from the hourly take-off and landing Flow sample set Flow _ set of the terminal areat={flowi,t1, the 365}, and generating a sequence statistic { flow } after sorting 365 flow samples of the t-th time period from small to larget(1),flowt(2),...,flowt(365)In which flow is lowt(1)≤flowt(2)≤...≤flowt(365)Setting the flow rate in the t-th period as a random variable XtSuppose XtObedience probability density of f (x)t) If P is greater than 0 and less than 1, the distribution of (A) satisfies the equation P (X)t<mt,p)≤p,P(Xt≤mt,p) Unique m of not less than pt,pReferred to as the p quantile of traffic during period t.
Flow is arrangedt(j)J 1.. 365 represents a sequence statistic { flow }t(1),flowt(2),...,flowt(365)J is flowt(j)At the index in the order statistic, then the p quantile of flow at the t-th time hour is estimated as
Assuming the nominal hourly capacity for the terminal region to take off and land is C, the peak hourly set for the terminal region isWherein m ist,95%Representing the 0.95 quantile of flow during period t.
In the present embodiment, referring to fig. 5, fig. 5 is a schematic view of a WAF image product, and S133, a method for obtaining an initial sample based on peak hours through a terminal area rising and falling peak hour set includes:
let WAF be the sample set of weather avoidance zone products, and record the w-th WAF sample as WAFwThe observation time is waftimewSelecting a product in a weather avoidance area in a peak period as an initial sample of a subsequent study, namely, selected WAF _ set ═ WAFw|waftimew∈peakhour_set};
Wherein, the WAF is a sample set of Weather Avoidance area (Weather airspace Field) products, the Weather Avoidance area products reflect the intensity of convective Weather in the airspace, and the corresponding airspace with the value of 3 is a suggested Avoidance airspace.
In the present embodiment, referring to fig. 6, step S140 includes: the method for calculating the characteristics of the initial sample and establishing the model training set comprises the following steps: the area of a research airspace is S, and the area of an area covered by dangerous weather is SwxIn the space domain
For each Weather avoidance area product sample in the selectedWAF _ set, respectively calculating a WSI (Weather Severity Index) value from A to L airspaces, and recording the WSI value as WSI _ A, WSI _ B,. and WSI _ L, wherein the WSI (Weather Severity Index) is a Weather risk Index, and the WSI value refers to the proportion of coverage of the airspace by dangerous Weather, namely when the Weather avoidance area product sample value is equal to 3;
let M peak _ set denote the total number of peak hours, M1End time isThen, the sample set of the weather avoidance area belonging to the M peak hours is 1
Since the observation time interval of the weather avoidance area product is 6 minutes, 10 weather avoidance area product samples, namely | wf _ set, are contained in one hourmSequencing the 10 weather avoidance area product samples according to observation time, and taking the WSI values of an A-L airspace corresponding to the sequenced weather avoidance area product samples as the features of a final model training set, and recording the features as WSI _ A _1, WSI _ B _1,.
The training set D has a size M, that is, M peak _ set sample data are shared in the set D, 120 features are listed, and the target column is the M1mEstablishing space domain characteristics under the influence of weather on a training set through a machine learning methodCapacity to take off and land in hours CmIs mapped toNamely, it is
In the present embodiment, step S150: the method for establishing the random forest regression model according to the training set comprises the following steps:
s151: establishing a regression model on a training set by adopting a random forest model;
s152: performing performance measurement on random forest models of different scales through a performance measurement index and an evaluation method;
s153: and obtaining a final random forest regression model.
Fig. 7 and 8 respectively show the relationship between the mean square error and the decision coefficient and the model scale, and in the method for performing performance measurement on random forest models of different scales through the performance measurement index and the evaluation method:
the performance metric comprises a mean square error and a decision coefficient;
let the test set T contain N, yiFor testing samplesData flag of fDFor the model learned on the training set D, the mean square error of the model on the test set T is:
is provided withMeans for labeling T data of test setThat is, the decision coefficient of the model on the test set is:
the evaluation method is a K-fold cross validation and self-help method;
recording Data set formed by training set and test set as Data _ set, dividing Data set Data _ set into training set D and test set T before machine learning, whereinThe K-fold cross-validation method is to divide the Data set Data _ set into K mutually exclusive subsets with equal sizeIn each training, using K-1 subsets as training set, using the rest one as test set, repeating the training and testing K times, and finally returning the average value of the performance of the K training metrics as final model performance metric, wherein in K-fold cross validation, the number of training samples per time is always less than the total number N of samplesThe self-help method generates a training set with the same scale as the original sample set on the basis of the disposable sampling, the total number of Data set Data _ set samples is set to be N, the disposable sampling is carried out on the Data set Data _ set for N times, and the sampled Data is used as the training set for model training.
In the present embodiment, step S153: prediction mean square error for random forest of scale alphaAnd the coefficient of determination is MSEαAnd R2 αThe final random forest has a size ofWherein the content of the first and second substances,the expression takes the value of alpha that minimizes the mean square error,this indicates that the value of α is set so that the coefficient of determination is maximized.
In the present embodiment, please refer to fig. 9 and fig. 10, which respectively show the stability and accuracy of the forest model. Set to a scale offinalThe random forest prediction model isGeneration of 1000 training sets and D by the self-service method1,...,D1000And corresponding test set T1,...,T1000Test modelIs determined by taking the coefficient of determination between the predicted value and the true value of R as the coefficient of determination generated by 1000 tests2 1,...,R2 1000If there is R for any one test2 i1., 1000, where δ is the threshold for correlation, 0.85 being taken, has higher stability, i.e. the scale adopted is αfinalThe random forest of (1) is used as a final prediction model;
when a measured hour is set, the abstract characteristics of the WAF product contained in the measured hour are as follows:then its corresponding hourly predicted capacity is
In summary, the invention provides a terminal area take-off and landing capacity prediction method based on a weather risk index. The terminal area take-off and landing capacity prediction method based on the weather risk index comprises the following steps: control operation experience abstraction influencing the take-off and landing capacity of the terminal area; according to the control operation experience abstraction, the terminal area airspace structure is divided again; acquiring a terminal area rising and falling peak period and an initial sample; calculating the characteristics of the initial sample and establishing a model training set; establishing a random forest regression model according to the training set; and verifying and predicting the random forest regression model. According to the practical operation experience abstraction, the airspace structure related to the terminal area (including the terminal area airspace and the area sector adjacent to the terminal area corridor) is divided again for modeling, the related characteristics are extracted, the influence of convection weather is related to the time interval capacity, regression analysis is carried out by using flight historical data, a terminal area take-off and landing capacity prediction model is obtained through training, then the capacity prediction under the corresponding weather can be output by inputting a weather prediction product, and a dynamic capacity data basis is provided for the strategy and pre-tactical stages of deep analysis of system efficiency and air traffic flow management.
In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.
Claims (5)
1. A terminal area take-off and landing capacity prediction method based on a weather risk index is characterized by comprising the following steps:
acquiring control operation experience abstraction influencing the take-off and landing capacity of a terminal area;
according to the control operation experience abstraction, the terminal area airspace structure is divided again;
acquiring a terminal area rising and falling peak period and an initial sample;
calculating the characteristics of the initial sample and establishing a model training set;
establishing a random forest regression model according to the training set;
verifying and predicting the random forest regression model;
the method for establishing the random forest regression model according to the training set comprises the following steps:
establishing a regression model on a training set by adopting a random forest model;
performing performance measurement on random forest models of different scales through a performance measurement index and an evaluation method;
obtaining a final random forest regression model;
the method for calculating the characteristics of the initial sample and establishing the model training set comprises the following steps: the area of a research airspace is S, and the area of an area covered by dangerous weather is SwxIn the space domain
Respectively calculating WSI values of an airspace from A to L and recording the WSI values as WSI _ A, WSI _ B, WSI and WSI _ L for each weather avoidance area product sample in the selectedWAF _ set, wherein the WSI is a weather risk index and refers to the proportion of the airspace covered by dangerous weather;
let M peak _ set denote the total number of peak hours, M1End time isThe product sample set of the M weather avoidance areas with peak hours is 1
Since the observation time interval of products in the weather avoidance area is 6 minutes, 10 weathers are contained in one hourAvoidance zone product samples, | wf _ setmSequencing the 10 weather avoidance area product samples according to observation time, and taking the WSI values of an A-L airspace corresponding to the sequenced weather avoidance area product samples as the features of a final model training set, and recording the features as WSI _ A _1, WSI _ B _1,.
The training set D has a size M, that is, M peak _ set sample data are shared in the set D, 120 features are listed, and the target column is the M1mEstablishing space domain characteristics under the influence of weather on a training set through a machine learning methodCapacity to take off and land in hours CmThe mapping f of (c):namely, it is
The method for measuring the performance of the random forest models with different scales through the performance measurement indexes and the evaluation method comprises the following steps:
the performance metric comprises a mean square error and a decision coefficient;
let the test set T contain N, yiFor testing samplesData flag of fDFor the model learned on the training set D, the mean square error of the model on the test set T is:
is provided withMeans for labeling T data of test setThat is, the decision coefficient of the model on the test set is:
the evaluation method is a K-fold cross validation and self-help method;
recording Data set formed by training set and test set as Data _ set, dividing Data set Data _ set into training set D and test set T before machine learning, whereinThe K-fold cross-validation method is to divide the Data set Data _ set into K mutually exclusive subsets with equal size In each training, using K-1 subsets as training set, using the rest one as test set, repeating the training and testing K times, and finally returning the average value of the performance of the K training metrics as final model performance metric, wherein in K-fold cross validation, the number of training samples per time is always less than the total number M of samplesThe final model generates deviation due to the scale of training samples, a self-help method generates a training set with the same scale as an original sample set on the basis of sample putting back, the total number of Data set Data _ set samples is set to be M, the Data set Data _ set is subjected to M times of sample putting back, and the sampled Data is used as the training set for model training;
the method for obtaining the final random forest regression model comprises the following steps: setting the prediction mean square error and the decision coefficient of the random forest with the scale of alpha as MSE respectivelyαAnd R2 αThe final random forest has a size ofWherein the content of the first and second substances,the expression takes the value of alpha that minimizes the mean square error,the expression takes the value of α such that the coefficient of determination is maximized;
the method for acquiring initial samples based on peak hours through the terminal area start-and-landing peak hour set comprises the following steps:
let WAF be the sample set of weather avoidance zone products, and record the w-th WAF sample as WAFwThe observation time is waftimewSelecting weather avoidance area data in peak time period as weather data samples for subsequent feature extraction, namely, selected WAF _ set { (WAF) }w|waftimew∈peakhour_set}。
2. The method for terminal region takeoff and landing capacity prediction based on weather hazard index as claimed in claim 1, wherein the method for obtaining terminal region takeoff and landing peak periods and initial samples comprises:
acquiring an hourly take-off and landing flow sample set of a terminal area based on historical data;
acquiring a high peak hour set of the terminal area based on quantiles through a terminal area hourly take-off and landing flow sample set;
initial samples based on peak hours are taken through the terminal area take-off and landing peak hours sets.
3. The method for predicting the terminal area take-off and landing capacity based on the weather risk index as claimed in claim 2, wherein the obtaining of the terminal area take-off and landing hourly traffic sample set based on the historical data is:
the day is divided into 24 hours, which are respectively 0:00-1:00, 1:00-2:00,. eta.23: 00-24:00 and are numbered from 1 to 24, and the starting time of the ith 1,. eta.365 day 1,. eta.24 time periods in the year is set asThe end time isThe Airport code number in the terminal area is Airport, the terminal area take-off and landing Flight set in one year is Flight _ set { F1fLanding airport is ArrfActual takeoff time is ADTfThe actual landing time is AATf;
Is provided withThenThe f-th flight belongs to the takeoff flight in the t-th time period of the Airport, and the same principle is setThenIndicating that the f-th flight belongs to a landing flight in the t-th time period of the Airport;
4. The method for terminal region takeoff and landing capacity prediction based on weather hazard index as claimed in claim 3, wherein the method for obtaining the quantile-based terminal region peak hour set through the terminal region hour takeoff and landing traffic sample set is that:
obtaining a Flow sample set Flow _ set of the t-th period from the hourly rise-and-fall Flow sample set Flow _ set of the terminal area as Flow _ sett ═ Flowi,t1, the 365}, and generating a sequence statistic { flow } after sorting 365 flow samples of the t-th time period from small to larget(1),flowt(2),...,flowt(365)In which flow is lowt(1)≤flowt(2)≤...≤flowt(365)Setting the flow rate in the t-th period as a random variable XtSuppose XtObedience probability density of f (x)t) If P is more than 0 and less than 1, the inequality P (X) is satisfiedt<mt,p)≤p,P(Xt≤mt,p) Unique m of not less than pt,pP quantile called t time period flow;
flow is arrangedt(j)J 1.. 365 represents a sequence statistic { flow }t(1),flowt(2),...,flowt(365)J is flowt(j)At the index in the order statistic, then the p quantile of flow at the t-th time hour is estimated as
5. The method for terminal region takeoff and landing capacity prediction based on weather hazard index as claimed in claim 4, wherein the method for verifying and predicting the random forest regression model comprises:
set to a scale offinalThe random forest prediction model isGeneration of 1000 training sets D by the self-service method1,...,D1000And corresponding test set T1,...,T1000Testing random forest prediction modelIs determined by taking the coefficient of determination between the predicted value and the true value of R as the coefficient of determination generated by 1000 tests2 1,...,R2 1000If there is R for any one test2 i1., 1000, where δ is the threshold for correlation, 0.85 is taken, i.e. the scale employed is αfinalThe random forest of (1) is used as a final prediction model;
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