CN106202635B - A kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models - Google Patents
A kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models Download PDFInfo
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Abstract
The bullet train dynamic shaft temperature prediction technique based on multivariate regression models that the invention discloses a kind of, be specifically implemented according to the following steps: step 1 classifies to the initial data of train；Step 2: sorted data being carried out to step 1 and carry out multidomain treat-ment；Step 3: the data after the multidomain treat-ment obtained to step 2 establish the flow model of axis temperature analysis；Step 4: testing to the flow model that step 3 obtains, the present invention solves the problems, such as that the axis temperature change mechanism existing in the prior art that can be based on realizes axle temperature prediction.
Description
Technical field
The invention belongs to bullet train technical field of data prediction, and in particular to a kind of high speed based on multivariate regression models
Train Dynamic axis temperature prediction technique.
Background technique
In recent years, as railway four indulges being becoming better and approaching perfection day by day for four cross lines, train becomes the first choice of most people trip,
And high-speed rail is because its is convenient, fast, safe, the favor of the advantages more by trip personage such as on schedule.By the end of 2015 end of the year China
High-speed rail operating mileage reach 1.9 ten thousand kilometers, rank first in the world, account for 60% or more of world's high-speed rail total kilometrage.With China's height
The fast development of fast train, operating mileage are continuously increased, and the safety problem of bullet train is concerned, wherein the safety of axle
It is particularly important.Train often causes locomotive breakage, locomotive failure because train axle temperature is excessively high in the process of moving, or even causes great
Train derailment accident, thus axis temperature become axle failures detection core index.Since the factor for influencing axle is complicated, such as
The main reason for bearing generation hot axis has: bearing inner race or retainer burst apart, and quality of lubrication oil does not meet standard requirements, lubricating oil
Consistency is excessively high, and tension, load excessive etc., so that the axle temperature prediction based on mechanism there is no solution are assembled by mechanism.For
This problem, the thinking based on big data and data mining turn causality analysis as correlativity analysis, pre-process to data
During, discovery train axle temperature and speed v, the primitive axis temperature value T0 in start-stop stage, environment temperature C, runing time t with
And load-carrying L has apparent relationship.
Summary of the invention
The bullet train dynamic shaft temperature prediction technique based on multivariate regression models that the object of the present invention is to provide a kind of solves
The problem of capable of realizing axle temperature prediction based on axis temperature change mechanism existing in the prior art.
The technical scheme adopted by the invention is that a kind of bullet train dynamic shaft temperature prediction side based on multivariate regression models
Method is specifically implemented according to the following steps:
Step 1 classifies to the initial data of train；
Step 2: sorted data being carried out to step 1 and carry out multidomain treat-ment；
Step 3: the data after the multidomain treat-ment obtained to step 2 establish the flow model of axis temperature analysis；
Step 4: testing to the flow model that step 3 obtains.
The features of the present invention also characterized in that
Step 1 is specifically implemented according to the following steps:
Step (1.1), acquisition train original axis temperature data, are put into set " Num.1 ", train original axis temperature data packet
It includes: train speed v, axis temperature T, the primitive axis temperature T in each start-stop stage0, environment temperature C, runing time t and load-carrying L；
Step (1.2), by train original axis temperature data acquisition system " Num.1 " collected in the step (1.1) according to speed
Degree is divided into n start-stop stage, and each start-stop stage includes n boost phase, n even running stage and n deceleration rank
Section；
The data of n boost phase in step (1.2) are put into the table sheet1 in set " Num.2 " by step (1.3)
In, then by table sheet1 renamed as " boost phase ", the data in n even running stage are put into set " Num.2 "
Table sheet2 in, then by sheet2 renamed as " even running stage ", the data in n decelerating phase are put into set
In table sheet3 in " Num.2 ", then by table sheet3 renamed as " decelerating phase ".
N=9 in step (1.1).
Step 2 is specifically implemented according to the following steps:
For the runing time point t of three operation phase in " Num.2 " in step 1, t=random (10) are enabled, at random
It generates one 0~10 random number and is assigned to variable t, be "true" if t > 3, be otherwise "false", and export corresponding comprising t > 3
Variable is used as " training sample " data set, and export does not include the corresponding variable of t > 3 and is used as " test sample " data set, with this side
Method will respectively obtain " accelerating training sample .xls ", " steady training sample .xls ", and " deceleration training sample .xls " " accelerates
Test sample .xls ", " steady test sample .xls ", " deceleration test sample .xls ".
Step 3 is specifically implemented according to the following steps:
Step (3.1), the correlation of predictive variable:
To by the step 2, treated " accelerating training sample .xls ", " steady training sample .xls " and " instruction of slowing down
The predictive variable practiced in sample .xls " carries out correlation analysis, i.e. speed v, the primitive axis temperature T in each start-stop stage0, environment temperature
The relative coefficient between C, runing time t and load-carrying L and axis temperature T is spent, based on the following:
Wherein, N is the number of variable, xiFor independent variable, yiFor dependent variable --- axis temperature T, r are Pearson came Pearson related
Coefficient, when
When (1) 0.8≤r≤1, variable is extremely strong correlation；
When (2) 0.6≤r < 0.8, variable is strong correlation；
When (3) 0.4≤r < 0.6, variable is moderate correlation；
When (4) 0.2≤r < 0.4, variable is weak correlation；
When (5) 0.0≤r < 0.2, variable is extremely weak related or without correlation,
Because the factor for influencing axis temperature is more, therefore extremely weak related or unrelated shadow can be weeded out according to correlation coefficient r
The factor of sound；
The calculating of step (3.2), regression coefficient:
Regression analysis, regression mould are carried out to the training sample data in the three obtained stage after step 2 processing
The matrix of type is expressed asWherein, e be dependent variable measured value and estimated value difference,For partial regression coefficient, table
Show when other independent variable values are fixed, independent variable xiY when one unit of every changeiVariable quantity, will be in three operation phase
Variable speed v (x1i), the primitive axis temperature T in each start-stop stage0(x2i), environment temperature C (x3i), runing time t (x4i) and carry
Weight L (x5i) as the independent variable x in regression modelki, and it is as follows to generate independent variable matrix X:
In above formula, k is the number of independent variable, and i is first prime number that each independent variable includes,
By axis temperature T (yi) as the dependent variable y in regression modeli, and generate the k dimensional vector Y comprising all object sets such as
Under:
WithFormula obtains each regression coefficientAnd then obtain dependent variable yiEstimated value Wherein, X' is the transposition of the matrix X of independent variable composition；
Step (3.3) establishes flow model in Data Mining Tools SPSS Modeler:
In SPSS Modeler, " excel " node is selected inside " source " tabs first, by " training sample .xls "
It imports in this node, then selection " filtering " the node filter and " type " node type inside " Field Options " tabs,
It can filter out " moment " item of train operation with this " filtering " node, role of " type " node each variable is arranged, so
Selection " feature selecting " feature selection and " recurrence " regression node inside " modeling " tabs afterwards, connect
Get off and select " export " node export in " field " tabs, the axis temperature value and original axis temperature obtained to reduced model is right
The table and block diagram of ratio.
Step 4 is specifically implemented according to the following steps:
Step (4.1), model summarize inspection:
The quality of model entirety is measured with following formula, wherein coefficient of multiple correlation R, coefficient of determination R2, the decision system of correction
Number Radj 2:
Wherein, coefficient of multiple correlation R indicates the level of intimate of independent variable and dependent variable linear relationship in model.Wherein yiFor because
Variable shaft temperature T,For y obtained in the step (3.2)iEstimator, actually it is yiWith the simple linear of its estimator
Related coefficient, value range are (0,1), and without negative value, R value is bigger, illustrates that linear regression relation is closer, coefficient of determination R2
Indicate the ratio as shared by the part of independent variable explanation in regression model, the explanation strengths one of regression equation in total variation of dependent variable
As be by coefficient of determination R2Come what is measured, therefore R under normal circumstances2It is the bigger the better, wherein SSR is regression sum of square, SStotalFor
Total quadratic sum,For the mean value of dependent variable axis temperature T, the coefficient of determination R of correctionadj 2It is the important finger for measuring model built quality
One of mark, wherein what n was indicated is the content of sample, and that p is indicated is the number of independent variable, Radj 2Bigger, the effect of model is got over
It is good；
The relative error histogram of step (4.2), training sample:
To training sample obtained in step 2, respectively to the training sample of three operation phase, obtained with step (3.2)
Regression equation calculation go out estimated valueThen relative error is
Then its histogram is drawn, its distribution situation is observed；
Step (4.3) tests to test sample:
To test sample obtained in step 2, respectively to the test sample of three operation phase, obtained with step (3.2)
Regression equation calculation go out estimated valueThen relative error is
Then respectively to the test sample of three operation phase, dependent variable axis temperature T is drawn in one drawing, axis temperature T estimates
EvaluationThe line chart of relative error (relative error), and using double coordinate forms, relative error figure is able to reflect out
The case where models fitting effect, can be clearly seen that models fitting by the line chart of predicted value and true value in this figure
Effect, and pass through relative error line chart it can be seen that prediction effect quality, if over time, relative error
Value becomes increasing, then illustrate model to later period prediction effect not as good as early stage because prediction error is in acceptable always
Range, therefore this method can effectively predict axis temperature, so as to which train hot box trouble is regarded in the abnormal heating of axis temperature
One discrimination standard of detection, with the expansion for avoiding accident of maximum possible.
The invention has the advantages that a kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models, right
High-speed rail train axle temperature data sectional is analyzed, and the bullet train axis temperature prediction technique based on data is realized, and is divided with returning
Analysis method effectively can carry out approximation to axis temperature data, and the error of prediction is within the scope of acceptable always.It will be real
The prediction axis temperature that border detection axis Wen Yuben regression model obtains is compared, and analyzing its difference degree can establish based on axis temperature
Axle failures discrimination model avoids the accident of train operation to the greatest extent.
Detailed description of the invention
Fig. 1 is a kind of overall procedure of the bullet train dynamic shaft temperature prediction technique based on multivariate regression models of the present invention
Figure；
Fig. 2 is to establish subregion stream in a kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models of the present invention
Cheng Tu；
Fig. 3 is to establish to return mould in a kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models of the present invention
Type flow chart；
Fig. 4 is in a kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models of the present invention to test sample
The flow chart tested；
Fig. 5 is in a kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models of the present invention to boost phase
The relative error histogram that training sample is tested；
Fig. 6 is in a kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models of the present invention to even running
The relative error histogram that stage-training sample is tested；
Fig. 7 is in a kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models of the present invention to the decelerating phase
The relative error histogram that training sample is tested；
Fig. 8 is in a kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models of the present invention to boost phase
The curve graph tested of test sample；
Fig. 9 is in a kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models of the present invention to even running
The curve graph that stage test sample is tested；
Figure 10 is in a kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models of the present invention to deceleration rank
The curve graph that section test sample is tested.
Specific embodiment
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
A kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models of the present invention, detailed process such as Fig. 1 institute
Show, be specifically implemented according to the following steps:
Step 1 classifies to the initial data of train；
Step 2: sorted data being carried out to step 1 and carry out multidomain treat-ment；
Step 3: the data after the multidomain treat-ment obtained to step 2 establish the flow model of axis temperature analysis；
Step 4: testing to the flow model that step 3 obtains.
Wherein, step 1 is specifically implemented according to the following steps:
Step (1.1), acquisition train original axis temperature data, are put into set " Num.1 ", train original axis temperature data packet
It includes: train speed v, axis temperature T, the primitive axis temperature T in each start-stop stage0, environment temperature C, runing time t and load-carrying L；
Step (1.2), by train original axis temperature data acquisition system " Num.1 " collected in the step (1.1) according to speed
Degree is divided into n start-stop stage, n=9, and each start-stop stage includes that n boost phase, n even running stage and n subtract
The fast stage；
The data of n boost phase in step (1.2) are put into the table sheet1 in set " Num.2 " by step (1.3)
In, then by table sheet1 renamed as " boost phase ", the data in n even running stage are put into set " Num.2 "
Table sheet2 in, then by sheet2 renamed as " even running stage ", the data in n decelerating phase are put into set
In table sheet3 in " Num.2 ", then by table sheet3 renamed as " decelerating phase ".
Step 2 detailed process is as shown in Fig. 2, follow the steps below to implement:
For the runing time point t of three operation phase in " Num.2 " in step 1, t=random (10) are enabled, at random
It generates one 0~10 random number and is assigned to variable t, be "true" if t > 3, be otherwise "false", and export corresponding comprising t > 3
Variable is used as " training sample " data set, and export does not include the corresponding variable of t > 3 and is used as " test sample " data set, with this side
Method will respectively obtain " accelerating training sample .xls ", " steady training sample .xls ", and " deceleration training sample .xls " " accelerates
Test sample .xls ", " steady test sample .xls ", " deceleration test sample .xls ".
Step 3 is specifically implemented according to the following steps:
Step (3.1), the correlation of predictive variable:
To by the step 2, treated " accelerating training sample .xls ", " steady training sample .xls " and " instruction of slowing down
The predictive variable practiced in sample .xls " carries out correlation analysis, i.e. speed v, the primitive axis temperature T in each start-stop stage0, environment temperature
The relative coefficient between C, runing time t and load-carrying L and axis temperature T is spent, based on the following:
Wherein, N is the number of variable, xiFor independent variable, yiFor dependent variable --- axis temperature T, r are Pearson came Pearson related
Coefficient, when
When (1) 0.8≤r≤1, variable is extremely strong correlation；
When (2) 0.6≤r < 0.8, variable is strong correlation；
When (3) 0.4≤r < 0.6, variable is moderate correlation；
When (4) 0.2≤r < 0.4, variable is weak correlation；
When (5) 0.0≤r < 0.2, variable is extremely weak related or without correlation,
Because the factor for influencing axis temperature is more, therefore extremely weak related or unrelated shadow can be weeded out according to correlation coefficient r
The factor of sound；
The calculating of step (3.2), regression coefficient, detailed process are as shown in Figure 3:
Regression analysis, regression mould are carried out to the training sample data in the three obtained stage after step 2 processing
The matrix of type is expressed asWherein, e be dependent variable measured value and estimated value difference,For partial regression coefficient, table
Show when other independent variable values are fixed, independent variable xiY when one unit of every changeiVariable quantity, will be in three operation phase
Variable speed v (x1i), the primitive axis temperature T in each start-stop stage0(x2i), environment temperature C (x3i), runing time t (x4i) and carry
Weight L (x5i) as the independent variable x in regression modelki, and it is as follows to generate independent variable matrix X:
In above formula, k is the number of independent variable, and i is first prime number that each independent variable includes,
By axis temperature T (yi) as the dependent variable y in regression modeli, and generate the k dimensional vector Y comprising all object sets such as
Under:
WithFormula obtains each regression coefficientAnd then obtain dependent variable yiEstimated value Wherein, X' is the transposition of the matrix X of independent variable composition；
In the present invention, the regression equation for respectively obtaining three phases is as follows:
Boost phase: Axle temperature=t*0.00077+v*0.001162+C* (- 0.01033)+T0*
0.9732+L*(-0.05983)+14.31
The even running stage: Axle temperature=t*0.007062+v*0.02243+C*0.1834+T0*1.139
+L*(-1.129)+241.6
Decelerating phase: Axle temperature=t* (- 0.01343)+v* (- 0.01225)+C*0.2036+T0*
0.9274+L*0.04744+(-6.442)
Step (3.3) establishes flow model in Data Mining Tools SPSS Modeler:
In SPSS Modeler, " excel " node is selected inside " source " tabs first, by " training sample .xls "
It imports in this node, then selection " filtering " the node filter and " type " node type inside " Field Options " tabs,
It can filter out " moment " item of train operation with this " filtering " node, role of " type " node each variable is arranged, so
Selection " feature selecting " feature selection and " recurrence " regression node inside " modeling " tabs afterwards, connect
Get off and select " export " node export in " field " tabs, the axis temperature value and original axis temperature obtained to reduced model is right
The table and block diagram of ratio.
Step 4 is specifically implemented according to the following steps:
Step (4.1), model summarize inspection:
The quality of model entirety is measured with following formula, wherein coefficient of multiple correlation R, coefficient of determination R2, the decision system of correction
Number Radj 2:
Wherein, coefficient of multiple correlation R indicates the level of intimate of independent variable and dependent variable linear relationship in model.Wherein yiFor because
Variable shaft temperature T,For y obtained in the step (3.2)iEstimator, actually it is yiWith the simple linear of its estimator
Related coefficient, value range are (0,1), and without negative value, R value is bigger, illustrates that linear regression relation is closer, coefficient of determination R2
Indicate the ratio as shared by the part of independent variable explanation in regression model, the explanation strengths one of regression equation in total variation of dependent variable
As be by coefficient of determination R2Come what is measured, therefore R under normal circumstances2It is the bigger the better, wherein SSR is regression sum of square, SStotalFor
Total quadratic sum,For the mean value of dependent variable axis temperature T, the coefficient of determination R of correctionadj 2It is the important finger for measuring model built quality
One of mark, wherein what n was indicated is the content of sample, and that p is indicated is the number of independent variable, Radj 2Bigger, the effect of model is got over
It is good；
The relative error histogram of step (4.2), training sample:
To training sample obtained in step 2, respectively to the training sample of three operation phase, obtained with step (3.2)
Regression equation calculation go out estimated valueThen relative error is
Then its histogram is drawn, obtained graphic result observes its distribution situation, by scheming as shown in Fig. 5, Fig. 6, Fig. 7
5, Fig. 6, Fig. 7 be it will be seen that more relative error is in a smaller range, therefore the figure by exporting can be with
Find out that the model has reached certain precision；
Step (4.3) tests to test sample, and specific flow chart is as shown in Figure 4:
To test sample obtained in step 2, respectively to the test sample of three operation phase, obtained with step (3.2)
Regression equation calculation go out estimated valueThen relative error is
Then respectively to the test sample of three operation phase, dependent variable axis temperature T is drawn in one drawing, axis temperature T estimates
EvaluationThe line chart of relative error (relative error), and using double coordinate forms, relative error figure is able to reflect out
The case where models fitting effect.Obtained graphic result is as shown in Fig. 8, Fig. 9, Figure 10, in this figure, by predicted value and really
The line chart of value can be clearly seen that the effect of models fitting, and pass through relative error line chart it can be seen that prediction effect
Quality then illustrates model to later period prediction effect not as good as early if over time, relative error magnitudes become increasing
Phase, because prediction error is in tolerance interval always, therefore this method can effectively be predicted axis temperature, so as to by axis
A discrimination standard of train hot box trouble detection is regarded in the abnormal heating of temperature, with the expansion for avoiding accident of maximum possible.
Claims (5)
1. a kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models, which is characterized in that specifically according to following
Step is implemented:
Step 1 classifies to the initial data of train；
Step 2: sorted data being carried out to the step 1 and carry out multidomain treat-ment；
Step 3: the data after the multidomain treat-ment obtained to the step 2 establish the flow model of axis temperature analysis, specifically according to following
Step is implemented:
Step (3.1), the correlation of predictive variable:
To by the step 2, treated " accelerating training sample .xls ", " steady training sample .xls " and " slow down training sample
Predictive variable in this .xls " carries out correlation analysis, i.e. speed v, the primitive axis temperature T in each start-stop stage0, environment temperature C,
Relative coefficient between runing time t and load-carrying L and axis temperature T, based on the following:
Wherein, N is the number of variable, xiFor independent variable, yiFor dependent variable --- axis temperature T, r are Pearson came Pearson phase relation
Number, when
When (1) 0.8≤r≤1, variable is extremely strong correlation；
When (2) 0.6≤r < 0.8, variable is strong correlation；
When (3) 0.4≤r < 0.6, variable is moderate correlation；
When (4) 0.2≤r < 0.4, variable is weak correlation；
When (5) 0.0≤r < 0.2, variable is extremely weak related or without correlation,
Because the factor for influencing axis temperature is more, thus can be weeded out according to correlation coefficient r extremely weak correlation or unrelated influence because
Element；
The calculating of step (3.2), regression coefficient:
Regression analysis, regression mould are carried out to the training sample data in the three obtained stage after the step 2 processing
The matrix of type is expressed asWherein, e be dependent variable measured value and estimated value difference,For partial regression coefficient, table
Show when other independent variable values are fixed, independent variable xiY when one unit of every changeiVariable quantity, will be in three operation phase
Variable speed v (x1i), the primitive axis temperature T in each start-stop stage0(x2i), environment temperature C (x3i), runing time t (x4i) and carry
Weight L (x5i) as the independent variable x in regression modelki, and it is as follows to generate independent variable matrix X:
In above formula, k is the number of independent variable, and i is first prime number that each independent variable includes,
By axis temperature T (yi) as the dependent variable y in regression modeli, and it is as follows to generate the k dimensional vector Y comprising all object sets:
WithFormula obtains each regression coefficientAnd then obtain dependent variable yiEstimated value Wherein, X' is the transposition of the matrix X of independent variable composition；
Step (3.3) establishes flow model in Data Mining Tools SPSS Modeler:
In SPSS Modeler, " excel " node is selected inside " source " tabs first, " training sample .xls " is imported
In this node, then selection " filtering " the node filter and " type " node type inside " Field Options " tabs, uses this
" filtering " node can filter out " moment " item of train operation, then role of " type " node each variable is arranged exists
Selection " feature selecting " feature selection and " recurrence " regression node inside " modeling " tabs, next
" export " node export is selected in " field " tabs, axis temperature value and original axis the temperature comparison obtained to reduced model
Table and block diagram；
Step 4: the flow model obtained to the step 3 is tested.
2. a kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models according to claim 1, special
Sign is that the step 1 is specifically implemented according to the following steps:
Step (1.1), acquisition train original axis temperature data, are put into set " Num.1 ", and train original axis temperature data include: column
Vehicle speed v, axis temperature T, the primitive axis temperature T in each start-stop stage0, environment temperature C, runing time t and load-carrying L；
Step (1.2) divides train original axis temperature data acquisition system " Num.1 " collected in the step (1.1) according to speed
It is segmented into n start-stop stage, each start-stop stage includes n boost phase, n even running stage and n decelerating phase；
The data of n boost phase in the step (1.2) are put into the table sheet1 in set " Num.2 " by step (1.3)
In, then by table sheet1 renamed as " boost phase ", the data in n even running stage are put into set " Num.2 "
Table sheet2 in, then by sheet2 renamed as " even running stage ", the data in n decelerating phase are put into set
In table sheet3 in " Num.2 ", then by table sheet3 renamed as " decelerating phase ".
3. a kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models according to claim 2, special
Sign is, n=9 in the step (1.2).
4. a kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models according to claim 1, special
Sign is that the step 2 is specifically implemented according to the following steps:
For the runing time point t of three operation phase in " Num.2 " in the step 1, t=random (10) are enabled, at random
It generates one 0~10 random number and is assigned to variable t, be "true" if t > 3, be otherwise "false", and export corresponding comprising t > 3
Variable is used as " training sample " data set, and export does not include the corresponding variable of t > 3 and is used as " test sample " data set, with this side
Method will respectively obtain " accelerating training sample .xls ", " steady training sample .xls ", and " deceleration training sample .xls " " accelerates
Test sample .xls ", " steady test sample .xls ", " deceleration test sample .xls ".
5. a kind of bullet train dynamic shaft temperature prediction technique based on multivariate regression models according to claim 1, special
Sign is that the step 4 is specifically implemented according to the following steps:
Step (4.1), model summarize inspection:
The quality of model entirety is measured with following formula, wherein coefficient of multiple correlation R, coefficient of determination R2, the coefficient of determination of correction
Radj 2:
Wherein, coefficient of multiple correlation R indicates the level of intimate of independent variable and dependent variable linear relationship in model, wherein yiFor dependent variable
Axis temperature T,For y obtained in the step (3.2)iEstimator, actually it is yiIt is related to the simple linear of its estimator
Coefficient, value range are (0,1), and without negative value, R value is bigger, illustrates that linear regression relation is closer, coefficient of determination R2It indicates
The ratio as shared by the part of independent variable explanation in regression model in total variation of dependent variable, the explanation strengths of regression equation are usually
By coefficient of determination R2Come what is measured, therefore R under normal circumstances2It is the bigger the better, wherein SSR is regression sum of square, SStotalIt is total
Quadratic sum,For the mean value of dependent variable axis temperature T, the coefficient of determination R of correctionadj 2Be measure model built quality important indicator it
One, wherein what n was indicated is the content of sample, and that p is indicated is the number of independent variable, Radj 2Bigger, the effect of model is better；
The relative error histogram of step (4.2), training sample:
To training sample obtained in step 2, respectively to the training sample of three operation phase, returned with what step (3.2) obtained
Equation calculation is returned to go out estimated valueThen relative error is
Then its histogram is drawn, its distribution situation is observed；
Step (4.3) tests to test sample:
To test sample obtained in step 2, respectively to the test sample of three operation phase, returned with what step (3.2) obtained
Equation calculation is returned to go out estimated valueThen relative error is
Then respectively to the test sample of three operation phase, the estimated value of dependent variable axis temperature T, axis temperature T are drawn in one drawingThe line chart of relative error (relative error), and using double coordinate forms, relative error figure is able to reflect out model
The case where fitting effect, can be clearly seen that the effect of models fitting by the line chart of predicted value and true value in this figure
Fruit, and pass through relative error line chart it can be seen that prediction effect quality, if over time, relative error magnitudes become
It is increasing, then illustrate model to later period prediction effect not as good as early stage because predicting that error is in tolerance interval always,
Therefore this method can effectively predict axis temperature, so as to what the abnormal heating of axis temperature was detected as train hot box trouble
One discrimination standard, with the expansion for avoiding accident of maximum possible.
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