CN111126655A - Toll station vehicle emission prediction method based on vehicle specific power and model tree regression - Google Patents

Toll station vehicle emission prediction method based on vehicle specific power and model tree regression Download PDF

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CN111126655A
CN111126655A CN201910164037.0A CN201910164037A CN111126655A CN 111126655 A CN111126655 A CN 111126655A CN 201910164037 A CN201910164037 A CN 201910164037A CN 111126655 A CN111126655 A CN 111126655A
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叶智锐
孙卓群
王超
于泳波
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Abstract

The invention discloses a toll station vehicle emission prediction method based on vehicle specific power and model tree regression. The method comprises the steps of basic data acquisition, basic data preprocessing, data modeling and application analysis; the basic data acquisition comprises the acquisition of volume concentration, vehicle speed, acceleration and vehicle dead weight data of various gases in the vehicle exhaust gas; the basic data preprocessing comprises the steps of converting the mass emission rate of various types of pollution gases and calculating the specific power of the vehicle, and performing time synchronization on the mass emission rate and the specific power of the vehicle by using an interpolation method; the data modeling is to build a toll station vehicle emission model based on vehicle specific power and model tree regression on the processed data; the method is based on a model tree and a Vehicle Specific Power (VSP) regression model, and can give accurate prediction to the emission of gasoline vehicles and diesel vehicles at toll stations.

Description

Toll station vehicle emission prediction method based on vehicle specific power and model tree regression
Technical Field
The invention relates to a traffic energy-saving and emission-reducing technology, in particular to a toll station vehicle emission prediction method based on vehicle specific power and model tree regression.
Background
Climate change and air quality issues have become a worldwide issue in recent years. Among them, the exhaust gas emissions generated by traffic, especially inter-city traffic, is one of the important sources of air pollution. The exhaust gases such as particles, carbon monoxide, carbon dioxide, hydrocarbons, nitrogen oxides and the like discharged by vehicles in the process of transportation can cause great harm to the air quality and the human health. The highway toll station is a high-occurrence section with intercity traffic jam, and the main reason is that the traffic capacity of the road section at the toll station is more easily limited by the service capacity of the toll station besides the restriction of the inherent traffic capacity of the road. The vehicle must be decelerated and driven into the station to be parked for payment, and then accelerated and driven out of the toll station, so that the subsequent vehicles are always queued. More remarkably, the generation of the crowded road conditions leads to the start and stop of vehicles and insufficient fuel combustion, and causes the emission pollutants such as hydrocarbon, carbon monoxide and nitrogen oxide to be increased sharply. Due to the special dynamic characteristics of vehicles passing through toll stations, the common emission prediction model is poor in applicability, and relevant research is urgently needed to fill the blank of the section.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects of the prior art, the invention provides a toll station vehicle emission prediction method based on vehicle specific power and model tree regression.
The technical scheme is as follows: a toll station vehicle emission prediction method based on vehicle specific power and model tree regression comprises the following steps:
s1, acquiring basic data, wherein the basic data acquisition comprises the steps of testing the volume concentration of tail gas discharged by gasoline vehicles and diesel vehicles by using vehicle tail gas discharge detection equipment, and measuring the data of vehicle speed, acceleration and delay time by using GPS equipment and vehicle dead weight parameter data;
s2, preprocessing basic data, calculating the mass emission rate conversion of the tail gas based on the volume concentration of various gases in the vehicle exhaust gas in S1, and calculating the vehicle specific power based on the acquired vehicle speed, acceleration and dead weight parameters; after obtaining the exhaust gas mass emission rate and the vehicle specific power, performing time synchronization by using a linear interpolation method;
and S3, modeling data, and constructing an emission model of the gasoline vehicle and the diesel vehicle passing through the artificial toll lane and the ETC lane based on the vehicle specific power and a model tree regression method.
The volume concentration of the exhaust gas measured by the vehicle exhaust emission detection device in the steps S1 and S2 is the volume concentration of O2, CO2, HC and NOx gases in the exhaust gas;
and the speed data in the steps S1 and S2 are the real-time vehicle speed of the test vehicle during emission measurement, the acceleration data are calculated according to the speed data, and meanwhile the dead weight parameter data of the test vehicle are recorded.
In the step S2, the mass emission rate of the exhaust gas is converted, specifically, the volume concentrations of the CO, HC, NOx, and CO2 pollution gases obtained in the data acquisition process are converted into the corresponding emission mass of the pollution gases in unit time.
For gasoline fueled vehicles, the formula for calculating the mass exhaust rate of the exhaust gas is as follows:
COg/s＝(mair+mfuel)×MCO/Mexhaust×CO％×10-2
HCg/s＝(mair+mfuel)×MHC/Mexhaust×HCppm×10-2
Figure RE-GDA0002358142580000021
Figure RE-GDA0002358142580000022
wherein M isCOIs the molecular weight of CO; mHCMolecular weight of incompletely combusted HC in the exhaust gas, HC being hydrocarbon;
Figure RE-GDA0002358142580000023
is NOxThe molecular weight of (a);
Figure RE-GDA0002358142580000024
is CO2The molecular weight of (a); CO2g/s、HCg/s、NOxg/sAnd CO2g/sMass emission rates of CO, HC, NOx, and CO2, respectively; HCppmIs the gas volume concentration of hydrocarbons in the exhaust gas; CO2％Is the volume percentage of carbon monoxide in the exhaust gas; NOxppmIs the volume concentration of nitrogen oxide in the exhaust gas; CO22％Is the volume percentage of carbon dioxide in the exhaust gas; m isairAnd mfuelThe consumption quality of air and fuel per unit time, respectively;
Mexhaustthe molecular weight of the tail gas is calculated by the following formula:
Mexhaust＝(13.88×HCppm×10-6)+(28.01×CO％×10-2)+(44.01×CO2％×10-2)
+(31.46×NOxppm×10-6)+(32.00×O2％×10-2)+(2.016×H2％×10-2)+18.01×(1-K)
+(100-HCppm/104-CO％-CO2％-NOxppm/104-O2％-H2％-100×(1-K))×28.01/102
wherein K is represented by the formula K ═ 1+0.005 × (CO)％+CO2％)×y-0.01×H2％]-1To calculate, H2％By the formula H2％＝[0.5×y×CO％×(CO％+CO2％)]/[CO％+3×CO2％]To calculate;
wherein O2% is the volume percentage of oxygen in the exhaust gas, and H2% is the volume percentage of hydrogen in the exhaust gas.
The test Vehicle Specific Power (VSP) is the ratio of the maximum power of an automobile engine to the total mass of the automobile, and the calculation formula is as follows:
VSP＝v×(a×(1+ε)+g×grade+g×CR)+0.5×ρa×CD×A×v3/m
wherein m is the mass of the test vehicle, v is the real-time speed of the test vehicle, a is the real-time acceleration of the test vehicle, and epsilon is a quality factor; grade is the length ratio of the vertical height to the slope, g is the gravity acceleration, CR is the rolling friction coefficient (dimensionless), and CD is the resistance coefficient; a is the maximum cross-sectional area of the vehicle, ρaThe density of the ambient air.
The data modeling in step S3 includes modeling model tree regression models of CO, HC, NOx, and CO2 pollutants generated by gasoline-powered and diesel-powered vehicles passing through an artificial toll lane and an ETC lane, respectively.
The model tree regression is an extension of a decision tree regression model, the central idea of the model tree regression method is to combine with the algorithm of the decision tree regression, divide the data with high overall modeling difficulty into a plurality of pieces of data easy to model, then model respectively, and also can approximately regard the model tree regression algorithm as the combination of several piecewise functions, the main difference is that the model tree algorithm regresses from the angle of overall error minimization, and the piecewise function obtained by direct observation may not be the optimal regression curve of the system. Because of these characteristics of the model tree regression model, each model can be visualized in the form of FIG. 2.
The most representative model tree regression is M5' model tree, which mainly comprises three parts of initial tree construction, tree pruning and serialization. For a model tree, the leaf nodes of the tree are all linear equations. If too many states of nodes occur, this indicates a situation where the model may "overfit" the data. The process of avoiding overfitting by reducing the complexity of the decision tree is called Pruning (Pruning). The three processes for building the model tree can be summarized as follows:
(1) constructing an initial tree: for the M5' model tree algorithm, the nodes of the tree model are divided by taking the standard deviation of the values in the nodes as the measure of the error of the nodes and taking the error reduction value after the nodes are divided into the maximum values as the standard. The standard deviation reduction values before and after dividing the nodes can be expressed as follows:
Figure RE-GDA0002358142580000031
in the formula, SDR is a standard deviation reduction value before and after dividing the node, sd is a standard deviation, T is a data set before dividing the node, and Ti is a set generated by dividing the node according to the selected attribute.
(2) Pruning the tree: after the initial model tree is constructed, a linear multiple regression model may be computed for each internal node. If the error of the estimated value after the child node is modeled is lower than the expected error, the node is deleted according to the error sequence of the estimated value. The expected error is calculated by averaging the absolute values of the predicted and actual values for each training sample, however, the average will underestimate the expected error for the unseen case. Thus, the expected error is multiplied by a factor ((n + v))/((n-v)), where n represents the number of training example nodes; v represents the number of parameters representing the value of the node in the model.
(3) And (3) continuous operation: after pruning, the linear regression models of neighboring leaf nodes will not be continuous at the boundaries, especially for some models constructed with a small amount of training data. Smoothing is often required to form the final model based on the pruned model. In the process, during the smoothing process, the actual prediction value of the linear regression model of each leaf node is adjusted in combination with the estimation of the root node:
Figure RE-GDA0002358142580000041
always, p' is the actual predicted value of the model tree regression model, p is the predicted value transmitted to the node, q is the predicted value of the linear regression model of the node, and k is a preset constant.
The data modeling method is based on a model tree regression model of the specific power of the vehicle. The model tree is an extension of the decision tree regression model by combining leaf nodes in the decision tree model with the multiple linear regression model. The model tree regression model is a piecewise linear regression that provides a structural representation of the data and individual leaf nodes, i.e., the model consists of a vehicle specific power polynomial linear regression model in a number of different intervals.
Has the advantages that: the toll station vehicle emission prediction method based on vehicle specific power and model tree regression has the following advantages:
1. the method is simple and feasible in the measurement process of vehicle dynamics characteristics and vehicle exhaust emission characteristics, the prediction method using the model tree linear regression model is more accurate compared with other real-time emission prediction models, and the structure of the decision tree enables the model to be more visual and convenient to use.
2. The method provides theoretical guidance for exploring the emission rule and formulating the energy-saving and emission-reducing policy, provides guidance suggestions for optimizing the construction of the toll lane, enables managers and designers to better manage, adjust and optimize system operation and system design, and further reduces the greenhouse gas emission amount of vehicles at the highway toll station.
Drawings
FIG. 1 is a flow chart of a toll station vehicle emissions prediction method using vehicle specific power and model tree regression;
FIG. 2 is a diagram of an exemplary structure of a model tree regression method;
FIG. 3 is a CO emission model of a gasoline passenger car based on vehicle specific power and model tree regression in an embodiment.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
A flow chart of a toll station vehicle emission prediction method based on vehicle specific power and model tree regression is shown in fig. 1, the method comprising the steps of:
s1, basic data acquisition
The basic data acquisition comprises testing O in the exhaust gas of gasoline vehicles and diesel vehicles by using vehicle exhaust emission detection equipment2、CO、HC、NOx、CO2Measuring the speed and the acceleration of the vehicle by using GPS equipment, and simultaneously recording the dead weight parameters of the experimental vehicle;
s2 preprocessing basic data
The basic data preprocessing process includes calculating CO, HC, NOx, CO based on the volume concentrations of the various types of gases in the exhaust gas of the test vehicle2Converting mass emission rate of the polluted gas, and calculating Vehicle Specific Power (VSP) based on the acquired vehicle speed, acceleration and self-weight parameters. After the mass emission rate of the polluted gas and the specific power of the vehicle are obtained, a linear interpolation method is used for carrying out time synchronization;
s3, modeling data
The data modeling comprises the steps of constructing an emission model of gasoline vehicles and diesel vehicles passing through an artificial toll lane and an ETC lane based on a vehicle specific power and model tree regression method;
the following further describes the aspects with reference to the drawings and the embodiments. It should be understood that the description is intended to be exemplary only, and is not intended to limit the scope of the present invention.
Example (b):
taking ETC lane and artificial toll lane on Schrocheba toll station on G42 national road as examples, CO, HC, NOx and CO of gasoline-powered and diesel-powered vehicles passing through two types of toll lanes2And (3) establishing a real-time mass emission rate model based on vehicle specific power and model tree regression. Firstly, acquiring basic data of a toll station, acquiring the volume concentration of CO, HC, NOx and CO2 in vehicle exhaust gas in real time by using an AUTOplus automobile exhaust analyzer on-board, acquiring the speed of a test vehicle in emission measurement in real time by using a GPS 16-HVS instrument, and adjusting two data as much as possible when acquiring the two dataThe seed instrument time is consistent; in the embodiment, 1352 experimental samples are collected, wherein 1092 samples are used as a training data set to establish a model, and 260 experimental samples are used as a testing data set to evaluate and compare the quality of the model.
Table 1 shows the sample size collected in the example and the descriptive statistical index of each parameter of each vehicle type
Figure RE-GDA0002358142580000051
Figure RE-GDA0002358142580000061
Secondly, basic data preprocessing work is carried out, wherein the basic data preprocessing work comprises two parts of mass emission rate conversion of various types of pollution gases and vehicle real-time specific power (VSP) calculation. The conversion of the mass emission rate of various polluted gases refers to the conversion of CO, HC and NO obtained in the data acquisition processxAnd CO2The volume concentration of the polluted gas is converted into the corresponding emission quality of the polluted gas in unit time, and for the vehicle taking gasoline as fuel, the calculation formula of the mass emission rate of various polluted gases is as follows:
COg/s＝(mair+mfuel)×MCO/Mexhaust×CO％×10-2
HCg/s＝(mair+mfuel)×MHC/Mexhaust×HCppm×10-2
Figure RE-GDA0002358142580000062
Figure RE-GDA0002358142580000063
wherein M isCOIs the molecular weight of CO; mHCMolecular weight of incompletely combusted HC in the exhaust gas, HC being hydrocarbon;
Figure RE-GDA0002358142580000064
is NOxThe molecular weight of (a);
Figure RE-GDA0002358142580000065
is CO2The molecular weight of (a); CO2g/s、HCg/s、NOxg/sAnd CO2g/sRespectively being CO, HC and NOxAnd CO2Gas mass emission rate; HCppmIs the gas volume concentration of hydrocarbons in the exhaust gas; CO2％Is the volume percentage of carbon monoxide in the exhaust gas; NOxppmIs the volume concentration of nitrogen oxide in the exhaust gas; CO22％Is the volume percentage of carbon dioxide in the exhaust gas; m isairAnd mfuelThe consumption quality of air and fuel per unit time, respectively;
the vehicle specific power is an index used for representing dynamic characteristics in the vehicle running process, and for the situation in the embodiment, the calculation formula of the VSP can be simplified as follows:
Figure RE-GDA0002358142580000071
in the embodiment, the mass m of the gasoline motor coach is 1570kg, the mass m of the diesel motor coach is 14200kg, v is the real-time speed of the test vehicle, a is the real-time acceleration of the test vehicle, the mass factor epsilon is 0.1, g is the acceleration of gravity, CRTaking 0.0135 as rolling friction coefficient (dimensionless), and C as resistance coefficientDTaking 0.6; a is the maximum cross-sectional area of the vehicle, and 1.9m is taken for a gasoline passenger car28.3m for diesel motor coach2，ρaIs the density of ambient air. By specifying the coefficients, the VSP equations for gasoline and diesel buses can be simplified to the following form:
VSPpetrol＝v(1.1a+0.132)+4.38×10-4v3
VSPdiesel＝v(1.1a+0.132)+2.12×10-4v3
before modeling, the dynamic characteristics and the emission characteristics of ETC lanes, gasoline motor cars and diesel buses under artificial toll lanes are subjected to t test in the embodiment. the formula and principle of the t-test are as follows:
H0：μ1-μ2＝0
H0：μ1-μ2≠0
suppose H0Can reject when:
Figure RE-GDA0002358142580000072
the resulting p-values for each t-test are given in the table, all p-values being less than 0.05. the t test result shows that the indexes of the two types of vehicles are obviously different under the conditions of an ETC lane and an artificial toll lane. It is necessary to model the behavior of two types of vehicles on different toll lanes separately.
TABLE 2 various indexes t test results of two types of vehicles under ETC lane and artificial toll lane conditions
Figure RE-GDA0002358142580000081
After calculating the vehicle real-time VSP and mass emission rates, data modeling work follows. In the embodiment, model tree regression modeling based on M5' algorithm is carried out on four types of pollution gas of two types of passenger cars passing through toll stations. The training process of the model is completed by three steps of initial tree construction, pruning and serialization on the selected training data set. In the embodiment, model tree models are respectively established for various exhaust gases of each vehicle type, and each model tree model can be displayed in a tree form. Taking fig. 3 as an example, the model tree shown in fig. 3 has the following four rules: (1) when VSP is less than or equal to 4, the CO emission of the gasoline passenger car is 0.0170 VSP + 0.2177; (2) 4< VSP is less than or equal to-1, and the CO emission of the gasoline passenger car is-0.0355 VSP + 0.0077; (3) when the VSP is more than or equal to 1 and less than or equal to 2, the CO emission of the gasoline passenger car is 0.0181 times VSP + 0.0613; (4) when VSP >2, the CO emission of the gasoline passenger car is 0.0158 VSP + 0.0660.
CO, HC, NOx, CO established for gasoline passenger car and diesel bus passing through toll lane2The model is as follows:
(1) CO emission model Tree prediction model:
Figure RE-GDA0002358142580000082
Figure RE-GDA0002358142580000083
(2) HC emission model Tree prediction model:
Figure RE-GDA0002358142580000091
Figure RE-GDA0002358142580000092
(3) NOx emission prediction model:
Figure RE-GDA0002358142580000093
Figure RE-GDA0002358142580000094
(4)CO2an emission prediction model:
Figure RE-GDA0002358142580000095
Figure RE-GDA0002358142580000096
after the model is built, the prediction accuracy of the model can be evaluated from a number of aspects. In the examples, goodness of fit (R) is introduced2) Mean Absolute Percent Error (MAPE), Root Mean Square Error (RMSE), and Normalized Root Mean Square Error (NRMSE) as model predictorsAnd measuring accuracy evaluation indexes, wherein the calculation formula is as follows:
Figure RE-GDA0002358142580000097
Figure RE-GDA0002358142580000098
Figure RE-GDA0002358142580000099
the results in table 3 are numerical averages of the prediction accuracy indexes in the respective cases. Compared with other existing methods, the goodness-of-fit index of the proposed model is improved fundamentally, and various error indexes are reduced remarkably.
Table 4 calculation of RMSE and NRMSE in examples
Figure RE-GDA0002358142580000101
The embodiments of the present invention have been described in detail with reference to the drawings and examples, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention.

Claims (7)

1. A toll station vehicle emission prediction method based on vehicle specific power and model tree regression is characterized in that: the method comprises the following steps:
s1, acquiring basic data, wherein the basic data acquisition comprises the steps of testing the volume concentration of tail gas discharged by gasoline vehicles and diesel vehicles by using vehicle tail gas discharge detection equipment, and measuring the data of vehicle speed, acceleration and delay time by using GPS equipment and vehicle dead weight parameter data;
s2, preprocessing basic data, calculating the mass emission rate conversion of the tail gas based on the volume concentration of various gases in the vehicle exhaust gas in S1, and calculating the vehicle specific power based on the acquired vehicle speed, acceleration and dead weight parameters; after obtaining the exhaust gas mass emission rate and the vehicle specific power, performing time synchronization by using a linear interpolation method;
and S3, modeling data, and constructing an emission model of the gasoline vehicle and the diesel vehicle passing through the artificial toll lane and the ETC lane based on the vehicle specific power and a model tree regression method.
2. The toll station vehicle emission prediction method based on vehicle specific power and model tree regression as claimed in claim 1 wherein: the volume concentration of the exhaust gas measured by the vehicle exhaust emission detection device in the steps S1 and S2 is O in the exhaust gas2、CO、CO2HC and NOxThe volume concentration of the gas.
3. The toll station vehicle emission prediction method based on vehicle specific power and model tree regression as claimed in claim 1 wherein: and the speed data in the steps S1 and S2 are the real-time vehicle speed of the test vehicle during emission measurement, the acceleration data are calculated according to the speed data, and meanwhile the dead weight parameter data of the test vehicle are recorded.
4. A toll station vehicle emission prediction method based on vehicle specific power and model tree regression as claimed in claim 1 or 2 wherein: converting the mass emission rate of the exhaust gas in the step S2, specifically, converting CO, HC and NO obtained in the data acquisition processxAnd CO2The volume concentration of the polluted gas is converted into the corresponding emission quality of the polluted gas in unit time.
5. The toll station vehicle emission prediction method based on vehicle specific power and model tree regression of claim 4 wherein: for gasoline fueled vehicles, the formula for calculating the mass exhaust rate of the exhaust gas is as follows:
COg/s＝(mair+mfuel)×MCO/Mexhaust×CO％×10-2
HCg/s＝(mair+mfuel)×MHC/Mexhaust×HCppm×10-2
NOxg/s＝(mair+mfuel)×MNOx/Mexhaust×NOxppm×10-2
Figure FDA0001985678210000011
wherein M isCOIs the molecular weight of CO; mHCMolecular weight of incompletely combusted HC in the exhaust gas, HC being hydrocarbon;
Figure FDA0001985678210000012
is NOxThe molecular weight of (a);
Figure FDA0001985678210000013
is CO2The molecular weight of (a); CO2g/s、HCg/s、NOxg/sAnd CO2g/sRespectively being CO, HC and NOxAnd CO2Gas mass emission rate; HCppmIs the gas volume concentration of hydrocarbons in the exhaust gas; CO2％Is the volume percentage of carbon monoxide in the exhaust gas; NOxppmIs the volume concentration of nitrogen oxide in the exhaust gas; CO22％Is the volume percentage of carbon dioxide in the exhaust gas; m isairAnd mfuelThe consumption quality of air and fuel per unit time, respectively;
Mexhaustthe molecular weight of the tail gas is calculated by the following formula:
Mexhaust＝(13.88×HCppm×10-6)+(28.01×CO％×10-2)+(44.01×CO2％×10-2)+(31.46×NOxppm×10-6)+(32.00×O2％×10-2)+(2.016×H2％×10-2)+18.01×(1-K)+(100-HCppm/104-CO％-CO2％-NOxppm/104-O2％-H2％-100×(1-K))×28.01/102
wherein K is represented by the formula K ═ 1+0.005 × (CO)％+CO2％)×y-0.01×H2％]-1To calculate, H2％By the formula H2％＝[0.5×y×CO％×(CO％+CO2％)]/[CO％+3×CO2％]To calculate;
wherein, O2％Is the volume percentage of oxygen in the exhaust gas, H2％Is the volume percentage of hydrogen in the exhaust gas.
6. A toll station vehicle emission prediction method based on vehicle specific power and model tree regression according to claim 1 or 3, characterized by: the test Vehicle Specific Power (VSP) is the ratio of the maximum power of an automobile engine to the total mass of the automobile, and the calculation formula is as follows:
VSP＝v×(a×(1+ε)+g×grade+g×CR)+0.5×ρa×CD×A×v3/m
wherein m is the mass of the test vehicle, v is the real-time speed of the test vehicle, a is the real-time acceleration of the test vehicle, and epsilon is a quality factor; grade is the ratio of the vertical height to the length of the slope, g is the acceleration of gravity, CRIs rolling friction coefficient (dimensionless), CDIs a coefficient of resistance; a is the maximum cross-sectional area of the vehicle, ρaThe density of the ambient air.
7. A toll station vehicle emission prediction method based on vehicle specific power and model tree regression as claimed in claim 1 wherein: the step S3 of modeling data includes generating CO, HC, NOx and CO for gasoline-powered and diesel-powered vehicles passing through an artificial toll lane and an ETC lane, respectively2The polluted gas carries out modeling of a model tree regression model,
the process of building the model tree comprises the following steps:
(1) constructing an initial tree: for the M5' model tree algorithm, the nodes of the tree model are divided by taking the standard deviation of the numerical values in the nodes as the measurement of the error of the nodes and taking the error reduction value after the nodes are divided into the maximum values as the standard; the standard deviation reduction values before and after dividing the nodes can be expressed as follows:
Figure FDA0001985678210000031
in the formula, SDR is a standard deviation reduction value before and after dividing nodes, sd is a standard deviation, T is a data set before dividing the nodes, and Ti is a set generated by dividing the nodes according to selected attributes;
(2) pruning the tree: after the initial model tree is constructed, a linear multiple regression model can be calculated for each internal node; if the error of the estimated value after the child node is modeled is lower than the expected error, deleting the node according to the error sequence of the estimated value;
the expected error is obtained by averaging the absolute values of the predicted value and the actual value of each training sample, and the expected error is multiplied by a coefficient ((n + v))/((n-v)), wherein n represents the number of training example nodes; v represents the number of parameters representing the value of the node in the model.
(3) And (3) continuous operation: forming a final model by smoothing treatment on the basis of the pruned model; in the smoothing process, the actual predicted values of the linear regression models of the leaf nodes are adjusted in combination with the estimation of the root node:
Figure FDA0001985678210000032
wherein p' is the actual predicted value of the model tree regression model, p is the predicted value transmitted to the node, q is the predicted value of the linear regression model of the node, and k is a predetermined constant.
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