CN106202635A - A kind of dynamic axle temperature Forecasting Methodology of bullet train based on multivariate regression models - Google Patents

Abstract

The invention discloses a kind of dynamic axle temperature Forecasting Methodology of bullet train based on multivariate regression models, specifically implement according to following steps: step 1, initial data to train are classified；Step 2: step 1 is carried out sorted data and carries out multidomain treat-ment；Step 3: the data after the multidomain treat-ment obtaining step 2 set up the flow model that axle temperature is analyzed；Step 4: the flow model obtaining step 3 is tested, the present invention solves the problem that can realize axletree temperature prediction based on axle temperature change mechanism present in prior art.

Description

A kind of dynamic axle temperature Forecasting Methodology of bullet train based on multivariate regression models

Technical field

The invention belongs to bullet train technical field of data prediction, be specifically related to a kind of high speed based on multivariate regression models Train Dynamic axle temperature Forecasting Methodology.

Background technology

In recent years, along with being becoming better and approaching perfection day by day of four cross lines indulged by railway four, train becomes the first-selection of most people trip, And high ferro because it is convenient, fast, safe, on schedule etc. advantage be more exposed to go on a journey the favor of personage.By the end of 2015 the end of the year China High ferro operation mileage reach 1.9 ten thousand kilometers, rank first in the world, account for more than the 60% of world's high ferro total kilometrage.Along with China is high The fast development of speed train, being continuously increased of operation mileage, the safety problem of bullet train receives much concern, wherein the safety of axletree Particularly important.Train often causes locomotive breakage, locomotive failure in the process of moving because train axle temperature is too high, even causes great Train derailment accident, thus axle temperature become axle failures detection core index.Complicated, such as owing to affecting the factor of axletree Bearing produces the main cause of hot axle to be had: bearing inner race or retainer burst apart, and quality of lubrication oil does not meets standard-required, lubricating oil Denseness is too high, mechanism's assembling tension, loads excessive etc. so that axletree temperature prediction based on mechanism there is no solution.For This problem, based on big data and the thinking of data mining, turning causal analysis is dependency relation analysis, and data are being carried out pretreatment During, find train axle temperature and speed v, primitive axis temperature value T0 in a start-stop stage, ambient temperature C, run time t with And load-carrying L has obvious relation.

Summary of the invention

It is an object of the invention to provide a kind of dynamic axle temperature Forecasting Methodology of bullet train based on multivariate regression models, solve The problem that can realize axletree temperature prediction based on axle temperature change mechanism present in prior art.

The technical solution adopted in the present invention is, a kind of dynamic axle temperature prediction side of bullet train based on multivariate regression models Method, specifically implements according to following steps:

Step 1, initial data to train are classified；

Step 2: step 1 is carried out sorted data and carries out multidomain treat-ment；

Step 3: the data after the multidomain treat-ment obtaining step 2 set up the flow model that axle temperature is analyzed；

Step 4: the flow model obtaining step 3 is tested.

The feature of the present invention also resides in,

Step 1 is specifically implemented according to following steps:

Step (1.1), collection train original axle temperature data, put in set " Num.1 ", train original axle temperature packet Include: train speed v, axle temperature T, the initial axle temperature T in each start-stop stage₀, ambient temperature C, run time t and load-carrying L；

Step (1.2), by the train original axle temperature data acquisition system " Num.1 " that collects in described step (1.1) according to speed Degree is divided into n start-stop stage, and each start-stop stage all includes n boost phase, n even running stage and n deceleration rank Section；

Step (1.3), the data of n boost phase in step (1.2) are put into the table sheet1 in set " Num.2 " In, then by table sheet1 RNTO " boost phase ", the data in n even running stage are put in set " Num.2 " Table sheet2 in, then by sheet2 RNTO " even running stage ", the data in n decelerating phase are put into set In table sheet3 in " Num.2 ", then by table sheet3 RNTO " decelerating phase ".

N=9 in step (1.1).

Step 2 is specifically implemented according to following steps:

For the operation time point t of three operation phase in " Num.2 " in step 1, make t=random (10), at random Produce one 0～10 random number be assigned to variable t, if t ＞ 3, be "true", be otherwise "false", and derive comprise t ＞ 3 correspondence Variable as " training sample " data set, is derived and is not comprised the variable of t ＞ 3 correspondence as " test sample " data set, with this side Method will respectively obtain " accelerating training sample .xls ", " steady training sample .xls ", " deceleration training sample .xls ", " accelerates Test sample .xls ", " steady test sample .xls ", " deceleration test sample .xls ".

Step 3 is specifically implemented according to following steps:

Step (3.1), the dependency of predictor variable:

To " accelerating training sample .xls " after described step 2 processes, " steady training sample .xls " and " instruction of slowing down Practice sample .xls " in predictor variable carry out correlation analysis, the i.e. initial axle temperature T in speed v, each start-stop stage₀, environment temperature Degree C, the relative coefficient run between time t and load-carrying L and axle temperature T, based on the following:

$r=\frac{{\mathrm{N\Σx}}_i{y}_i-{\mathrm{\Σx}}_i{\mathrm{\Σy}}_i}{\sqrt{{{\mathrm{N\Σx}}_i}^2-{\left({\mathrm{\Σx}}_i\right)}^2}\sqrt{{{\mathrm{N\Σy}}_i}^2-{\left({\mathrm{\Σy}}_i\right)}^2}}$

Wherein, N is the number of variable, x_iFor independent variable, y_iIt is that Pearson came Pearson is correlated with for dependent variable axle temperature T, r Coefficient, when

During (1) 0.8≤r≤1, variable is extremely strong relevant；

During (2) 0.6≤r ＜ 0.8, variable is strong correlation；

During (3) 0.4≤r ＜ 0.6, variable is moderate relevant；

During (4) 0.2≤r ＜ 0.4, variable is weak relevant；

During (5) 0.0≤r ＜ 0.2, variable is the most weak relevant or without relevant,

Because affecting the many factors of axle temperature, therefore the most weak relevant or unrelated shadow can be weeded out according to correlation coefficient r The factor of sound；

Step (3.2), the calculating of regression coefficient:

The training sample data of the three phases obtained after step 2 processes are carried out regression analysis, regression mould The matrix table of type is shown asWherein, e is the measured value difference with estimated value of dependent variable,For partial regression coefficient, table Show when other independent variable values are fixed, independent variable x_iY when often changing a unit_iVariable quantity, by three operation phase Variable speed v (x_1i), the initial axle temperature T in each start-stop stage₀(x_2i), ambient temperature C (x_3i), run time t (x_4i) and carry Weight L (x_5i) as the independent variable x in regression model_ki, and it is as follows to generate independent variable matrix X:

$X=\left[\begin{array}{c}{\left(x_{1i}\right)}^T\\ {\left(x_{2i}\right)}^T\\ ...\\ {\left(x_{ki}\right)}^T\end{array}\right]$

In above formula, k is the number of independent variable, and i is first prime number that each independent variable comprises,

By axle temperature T (y_i) as the dependent variable y in regression model_i, and generate comprise the k dimensional vector Y of all object sets such as Under:

$Y=\left[\begin{array}{c}{y}_1\\ y_2\\ ...\\ y_k\end{array}\right]$

WithFormula draws each regression coefficientAnd then obtain dependent variable yⁱEstimated value Wherein, X' is the transposition of the matrix X that independent variable forms；

Step (3.3), in Data Mining Tools SPSS Modeler, set up flow model:

In SPSS Modeler, inside " source " tab, first select " excel " node, by " training sample .xls " Import in this node, inside " Field Options " tab, then select " filtration " node filter and " type " node type, " filtering " node with this and can filter out " moment " item of train operation, " type " node is in order to arrange the role of each variable, so After inside " modeling " tab, select " feature selection " feature selection and " recurrence " regression node, connect Get off in " field " tab, select " derivation " node export, the axle temperature value obtained in order to reduced model and original axle temperature pair The table of ratio and block diagram.

Step 4 is specifically implemented according to following steps:

Step (4.1), model collect inspection:

The quality that model is overall, wherein, coefficient of multiple correlation R, coefficient of determination R is weighed by equation below², the decision system of correction Number R_adj ²:

$R^2=\frac{SSR}{{\mathrm{SS}}_{total}}=\frac{\Σ{({\hat{y}}_i-{\stackrel{\‾}{y}}_i)}^2}{\Σ{(y_i-{\stackrel{\‾}{y}}_i)}^2}$

${R^2}_{adj}=1-\frac{n-1}{n-p-1}(1-R^2)$

Wherein, independent variable and the level of intimate of dependent variable linear relationship during coefficient of multiple correlation R represents model.Wherein y_iFor because of Variable axle temperature T,For the y obtained in described step (3.2)_iEstimator, actually it is y_iSimple linear with its estimator Correlation coefficient, its span is (0,1), does not has negative value, and R value is the biggest, illustrates that linear regression relation is the closest, coefficient of determination R² Represent the ratio shared by part explained in total variation of dependent variable, the explanation strengths one of regression equation by independent variable in regression model As be by coefficient of determination R²Measure, the most generally R²Being the bigger the better, wherein SSR is regression sum of square, SS_totalFor Total quadratic sum,For the average of dependent variable axle temperature T, the coefficient of determination R of correction_adj ²It it is the important finger weighing institute's established model quality One of mark, wherein, what n represented is the content of sample, and what p represented is the number of independent variable, R_adj ²The biggest, the effect of model is more Good；

Step (4.2), the relative error rectangular histogram of training sample:

To the training sample obtained in step 2, the training sample to three operation phase respectively, obtain by step (3.2) Regression equation calculation go out estimated valueThen relative error is

$\begin{array}{cc}relative& error=abs(y_i-{\hat{y}}_i)/y_i\end{array}$

Then draw its rectangular histogram, observe its distribution situation；

Step (4.3), test sample is tested:

To the test sample obtained in step 2, the test sample to three operation phase respectively, obtain by step (3.2) Regression equation calculation go out estimated valueThen relative error is

$\begin{array}{cc}relative& error=abs(y_i-{\hat{y}}_i)/y_i\end{array},$

Test sample to three operation phase the most respectively, draws dependent variable axle temperature T, the estimating of axle temperature T in one drawing EvaluationThe broken line graph of relative error (relative error), and use double coordinate form, relative error figure can reflect The situation of models fitting effect, in this figure, can be clearly seen that models fitting by the broken line graph of predictive value and actual value Effect, and by relative error broken line graph it can be seen that the quality of prediction effect, if over the passage of time, relative error Value becomes increasing, then explanation model to later stage prediction effect not as early stage because forecast error is in acceptable all the time Scope, therefore axle temperature can be effectively predicted by the method, such that it is able to by the abnormal intensification of axle temperature as train hot box trouble One discrimination standard of detection, with the expansion avoiding accident of maximum possible.

The invention has the beneficial effects as follows, a kind of dynamic axle temperature Forecasting Methodology of bullet train based on multivariate regression models, right High ferro train axle temperature data sectional is analyzed, it is achieved that bullet train axle temperature Forecasting Methodologies based on data, uses to return and divides Axle temperature data can effectively be approximated by analysis method, it was predicted that error be in acceptable all the time within the scope of.Will be real Border detection axle temperature is compared with the prediction axle temperature that this regression model obtains, and analyzes its difference degree and can set up based on axle temperature Axle failures discrimination model, farthest avoids the accident of train operation.

Accompanying drawing explanation

Fig. 1 is the overall procedure of the present invention dynamic axle temperature Forecasting Methodology of a kind of bullet train based on multivariate regression models Figure；

Fig. 2 is to set up subregion stream in the present invention dynamic axle temperature Forecasting Methodology of a kind of bullet train based on multivariate regression models Cheng Tu；

Fig. 3 is to set up in the present invention dynamic axle temperature Forecasting Methodology of a kind of bullet train based on multivariate regression models to return mould Type flow chart；

Fig. 4 is to test sample in the present invention dynamic axle temperature Forecasting Methodology of a kind of bullet train based on multivariate regression models The flow chart tested；

Fig. 5 is to boost phase in the present invention dynamic axle temperature Forecasting Methodology of a kind of bullet train based on multivariate regression models The relative error rectangular histogram that training sample is tested；

Fig. 6 is to even running in the present invention dynamic axle temperature Forecasting Methodology of a kind of bullet train based on multivariate regression models The relative error rectangular histogram that stage-training sample is tested；

Fig. 7 is to the decelerating phase in the present invention dynamic axle temperature Forecasting Methodology of a kind of bullet train based on multivariate regression models The relative error rectangular histogram that training sample is tested；

Fig. 8 is to boost phase in the present invention dynamic axle temperature Forecasting Methodology of a kind of bullet train based on multivariate regression models The curve chart tested of test sample；

Fig. 9 is to even running in the present invention dynamic axle temperature Forecasting Methodology of a kind of bullet train based on multivariate regression models The curve chart that stage test sample is tested；

Figure 10 is to deceleration rank in the present invention dynamic axle temperature Forecasting Methodology of a kind of bullet train based on multivariate regression models The curve chart that section test sample is tested.

Detailed description of the invention

The present invention is described in detail with detailed description of the invention below in conjunction with the accompanying drawings.

The present invention dynamic axle temperature Forecasting Methodology of a kind of bullet train based on multivariate regression models, idiographic flow such as Fig. 1 institute Show, specifically implement according to following steps:

Step 1, initial data to train are classified；

Step 2: step 1 is carried out sorted data and carries out multidomain treat-ment；

Step 3: the data after the multidomain treat-ment obtaining step 2 set up the flow model that axle temperature is analyzed；

Step 4: the flow model obtaining step 3 is tested.

Wherein, step 1 is specifically implemented according to following steps:

Step (1.1), collection train original axle temperature data, put in set " Num.1 ", train original axle temperature packet Include: train speed v, axle temperature T, the initial axle temperature T in each start-stop stage₀, ambient temperature C, run time t and load-carrying L；

Step (1.2), by the train original axle temperature data acquisition system " Num.1 " that collects in described step (1.1) according to speed Degree is divided into n start-stop stage, n=9, and each start-stop stage all includes that n boost phase, n even running stage and n subtracts The speed stage；

Step (1.3), the data of n boost phase in step (1.2) are put into the table sheet1 in set " Num.2 " In, then by table sheet1 RNTO " boost phase ", the data in n even running stage are put in set " Num.2 " Table sheet2 in, then by sheet2 RNTO " even running stage ", the data in n decelerating phase are put into set In table sheet3 in " Num.2 ", then by table sheet3 RNTO " decelerating phase ".

Step 2 idiographic flow is as in figure 2 it is shown, implement according to following steps:

For the operation time point t of three operation phase in " Num.2 " in step 1, make t=random (10), at random Produce one 0～10 random number be assigned to variable t, if t ＞ 3, be "true", be otherwise "false", and derive comprise t ＞ 3 correspondence Variable as " training sample " data set, is derived and is not comprised the variable of t ＞ 3 correspondence as " test sample " data set, with this side Method will respectively obtain " accelerating training sample .xls ", " steady training sample .xls ", " deceleration training sample .xls ", " accelerates Test sample .xls ", " steady test sample .xls ", " deceleration test sample .xls ".

Step 3 is specifically implemented according to following steps:

Step (3.1), the dependency of predictor variable:

To " accelerating training sample .xls " after described step 2 processes, " steady training sample .xls " and " instruction of slowing down Practice sample .xls " in predictor variable carry out correlation analysis, the i.e. initial axle temperature T in speed v, each start-stop stage₀, environment temperature Degree C, the relative coefficient run between time t and load-carrying L and axle temperature T, based on the following:

$r=\frac{{\mathrm{N\Σx}}_i{y}_i-{\mathrm{\Σx}}_i{\mathrm{\Σy}}_i}{\sqrt{{{\mathrm{N\Σx}}_i}^2-{\left({\mathrm{\Σx}}_i\right)}^2}\sqrt{{{\mathrm{N\Σy}}_i}^2-{\left({\mathrm{\Σy}}_i\right)}^2}}$

Wherein, N is the number of variable, x_iFor independent variable, y_iIt is that Pearson came Pearson is correlated with for dependent variable axle temperature T, r Coefficient, when

During (1) 0.8≤r≤1, variable is extremely strong relevant；

During (2) 0.6≤r ＜ 0.8, variable is strong correlation；

During (3) 0.4≤r ＜ 0.6, variable is moderate relevant；

During (4) 0.2≤r ＜ 0.4, variable is weak relevant；

During (5) 0.0≤r ＜ 0.2, variable is the most weak relevant or without relevant,

Because affecting the many factors of axle temperature, therefore the most weak relevant or unrelated shadow can be weeded out according to correlation coefficient r The factor of sound；

Step (3.2), the calculating of regression coefficient, idiographic flow as shown in Figure 3:

The training sample data of the three phases obtained after step 2 processes are carried out regression analysis, regression mould The matrix table of type is shown asWherein, e is the measured value difference with estimated value of dependent variable,For partial regression coefficient, table Show when other independent variable values are fixed, independent variable x_iY when often changing a unit_iVariable quantity, by three operation phase Variable speed v (x_1i), the initial axle temperature T in each start-stop stage₀(x_2i), ambient temperature C (x_3i), run time t (x_4i) and carry Weight L (x_5i) as the independent variable x in regression model_ki, and it is as follows to generate independent variable matrix X:

$X=\left[\begin{array}{c}{\left(x_{1i}\right)}^T\\ {\left(x_{2i}\right)}^T\\ ...\\ {\left(x_{ki}\right)}^T\end{array}\right]$

In above formula, k is the number of independent variable, and i is first prime number that each independent variable comprises,

By axle temperature T (y_i) as the dependent variable y in regression model_i, and generate comprise the k dimensional vector Y of all object sets such as Under:

$Y=\left[\begin{array}{c}{y}_1\\ y_2\\ ...\\ y_k\end{array}\right]$

WithFormula draws each regression coefficientAnd then obtain dependent variable yⁱEstimated value Wherein, X' is the transposition of the matrix X that independent variable forms；

In the present invention, the regression equation 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), in Data Mining Tools SPSS Modeler, set up flow model:

In SPSS Modeler, inside " source " tab, first select " excel " node, by " training sample .xls " Import in this node, inside " Field Options " tab, then select " filtration " node filter and " type " node type, " filtering " node with this and can filter out " moment " item of train operation, " type " node is in order to arrange the role of each variable, so After inside " modeling " tab, select " feature selection " feature selection and " recurrence " regression node, connect Get off in " field " tab, select " derivation " node export, the axle temperature value obtained in order to reduced model and original axle temperature pair The table of ratio and block diagram.

Step 4 is specifically implemented according to following steps:

Step (4.1), model collect inspection:

The quality that model is overall, wherein, coefficient of multiple correlation R, coefficient of determination R is weighed by equation below², the decision system of correction Number R_adj ²:

$R^2=\frac{SSR}{{\mathrm{SS}}_{total}}=\frac{\Σ{({\hat{y}}_i-{\stackrel{\‾}{y}}_i)}^2}{\Σ{(y_i-{\stackrel{\‾}{y}}_i)}^2}$

${R^2}_{adj}=1-\frac{n-1}{n-p-1}(1-R^2)$

Wherein, independent variable and the level of intimate of dependent variable linear relationship during coefficient of multiple correlation R represents model.Wherein y_iFor because of Variable axle temperature T,For the y obtained in described step (3.2)_iEstimator, actually it is y_iSimple linear with its estimator Correlation coefficient, its span is (0,1), does not has negative value, and R value is the biggest, illustrates that linear regression relation is the closest, coefficient of determination R² Represent the ratio shared by part explained in total variation of dependent variable, the explanation strengths one of regression equation by independent variable in regression model As be by coefficient of determination R²Measure, the most generally R²Being the bigger the better, wherein SSR is regression sum of square, SS_totalFor Total quadratic sum,For the average of dependent variable axle temperature T, the coefficient of determination R of correction_adj ²It it is the important finger weighing institute's established model quality One of mark, wherein, what n represented is the content of sample, and what p represented is the number of independent variable, R_adj ²The biggest, the effect of model is more Good；

Step (4.2), the relative error rectangular histogram of training sample:

To the training sample obtained in step 2, the training sample to three operation phase respectively, obtain by step (3.2) Regression equation calculation go out estimated valueThen relative error is

$\begin{array}{cc}relative& error=abs(y_i-{\hat{y}}_i)/y_i\end{array}$

Then drawing its rectangular histogram, the graphic result obtained, as shown in Fig. 5, Fig. 6, Fig. 7, observes its distribution situation, by scheming 5, Fig. 6, Fig. 7 are it will be seen that more relative error is in a smaller scope, therefore permissible by the figure exported Find out that this model has reached certain precision；

Step (4.3), test sample is tested, concrete flow chart as shown in Figure 4:

To the test sample obtained in step 2, the test sample to three operation phase respectively, obtain by step (3.2) Regression equation calculation go out estimated valueThen relative error is

$\begin{array}{cc}relative& error=abs(y_i-{\hat{y}}_i)/y_i\end{array},$

Test sample to three operation phase the most respectively, draws dependent variable axle temperature T, the estimating of axle temperature T in one drawing EvaluationThe broken line graph of relative error (relative error), and use double coordinate form, relative error figure can reflect The situation of models fitting effect.The graphic result obtained is as shown in Fig. 8, Fig. 9, Figure 10, in this figure, by predictive value with true The broken line graph of value can be clearly seen that the effect of models fitting, and by relative error broken line graph it can be seen that prediction effect Quality, if over the passage of time, relative error magnitudes becomes increasing, then later stage prediction effect is not so good as early by explanation model Phase, because forecast error is in tolerance interval all the time, therefore axle temperature can be effectively predicted by the method, such that it is able to by axle The abnormal intensification of temperature is as a discrimination standard of train hot box trouble detection, with the expansion avoiding accident of maximum possible.

Claims (6)

1. the dynamic axle temperature Forecasting Methodology of bullet train based on multivariate regression models, it is characterised in that specifically according to following Step is implemented:

Step 1, initial data to train are classified；

Step 2: described step 1 is carried out sorted data and carries out multidomain treat-ment；

Step 3: the data after the multidomain treat-ment obtain described step 2 set up the flow model that axle temperature is analyzed；

Step 4: the flow model obtaining described step 3 is tested.

A kind of dynamic axle temperature Forecasting Methodology of bullet train based on multivariate regression models the most according to claim 1, it is special Levying and be, described step 1 is specifically implemented according to following steps:

Step (1.1), collection train original axle temperature data, put in set " Num.1 ", and train original axle temperature packet includes: row Vehicle speed v, axle temperature T, the initial axle temperature T in each start-stop stage₀, ambient temperature C, run time t and load-carrying L；

Step (1.2), the train original axle temperature data acquisition system " Num.1 " collected in described step (1.1) is divided according to speed Being segmented into n start-stop stage, each start-stop stage all includes n boost phase, n even running stage and n decelerating phase；

Step (1.3), the data of n boost phase in described step (1.2) are put into the table sheet1 in set " Num.2 " In, then by table sheet1 RNTO " boost phase ", the data in n even running stage are put in set " Num.2 " Table sheet2 in, then by sheet2 RNTO " even running stage ", the data in n decelerating phase are put into set In table sheet3 in " Num.2 ", then by table sheet3 RNTO " decelerating phase ".

A kind of dynamic axle temperature Forecasting Methodology of bullet train based on multivariate regression models the most according to claim 2, it is special Levy and be, n=9 in described step (1.1).

A kind of dynamic axle temperature Forecasting Methodology of bullet train based on multivariate regression models the most according to claim 1, it is special Levying and be, described step 2 is specifically implemented according to following steps:

For the operation time point t of three operation phase in " Num.2 " in described step 1, make t=random (10), at random Produce one 0～10 random number be assigned to variable t, if t ＞ 3, be "true", be otherwise "false", and derive comprise t ＞ 3 correspondence Variable as " training sample " data set, is derived and is not comprised the variable of t ＞ 3 correspondence as " test sample " data set, with this side Method will respectively obtain " accelerating training sample .xls ", " steady training sample .xls ", " deceleration training sample .xls ", " accelerates Test sample .xls ", " steady test sample .xls ", " deceleration test sample .xls ".

A kind of dynamic axle temperature Forecasting Methodology of bullet train based on multivariate regression models the most according to claim 1, it is special Levying and be, described step 3 is specifically implemented according to following steps:

Step (3.1), the dependency of predictor variable:

To " accelerating training sample .xls " after described step 2 processes, " steady training sample .xls " and " deceleration training sample This .xls " in predictor variable carry out correlation analysis, the i.e. initial axle temperature T in speed v, each start-stop stage₀, ambient temperature C, Relative coefficient between operation time t and load-carrying L and axle temperature T, based on the following:

$r=\frac{{\mathrm{N\Σx}}_i{y}_i-{\mathrm{\Σx}}_i{\mathrm{\Σy}}_i}{\sqrt{{{\mathrm{N\Σx}}_i}^2-{\left({\mathrm{\Σx}}_i\right)}^2}\sqrt{{{\mathrm{N\Σy}}_i}^2-{\left({\mathrm{\Σy}}_i\right)}^2}}$

Wherein, N is the number of variable, x_iFor independent variable, y_iIt is the phase relation of Pearson came Pearson for dependent variable axle temperature T, r Number, when

During (1) 0.8≤r≤1, variable is extremely strong relevant；

During (2) 0.6≤r ＜ 0.8, variable is strong correlation；

During (3) 0.4≤r ＜ 0.6, variable is moderate relevant；

During (4) 0.2≤r ＜ 0.4, variable is weak relevant；

During (5) 0.0≤r ＜ 0.2, variable is the most weak relevant or without relevant,

Because affecting the many factors of axle temperature, thus can according to correlation coefficient r weed out the most weak relevant or unrelated affect because of Element；

Step (3.2), the calculating of regression coefficient:

The training sample data of the three phases obtained after described step 2 processes are carried out regression analysis, regression mould The matrix table of type is shown asWherein, e is the measured value difference with estimated value of dependent variable,For partial regression coefficient, table Show when other independent variable values are fixed, independent variable x_iY when often changing a unit_iVariable quantity, by three operation phase Variable speed v (x_1i), the initial axle temperature T in each start-stop stage₀(x_2i), ambient temperature C (x_3i), run time t (x_4i) and carry Weight L (x_5i) as the independent variable x in regression model_ki, and it is as follows to generate independent variable matrix X:

$X=\left[\begin{array}{c}{\left(x_{1i}\right)}^T\\ {\left(x_{2i}\right)}^T\\ ...\\ {\left(x_{ki}\right)}^T\end{array}\right]$

In above formula, k is the number of independent variable, and i is first prime number that each independent variable comprises,

By axle temperature T (y_i) as the dependent variable y in regression model_i, and it is as follows to generate the k dimensional vector Y comprising all object sets:

$Y=\left[\begin{array}{c}{y}_1\\ y_2\\ ...\\ y_k\end{array}\right]$

WithFormula draws each regression coefficientAnd then obtain dependent variable y_iEstimated value Wherein, X' is the transposition of the matrix X that independent variable forms；

Step (3.3), in Data Mining Tools SPSS Modeler, set up flow model:

In SPSS Modeler, inside " source " tab, first select " excel " node, " training sample .xls " is imported In this node, inside " Field Options " tab, then select " filtration " node filter and " type " node type, use this " filtering " node and can filter out " moment " item of train operation, " type " node, in order to arrange the role of each variable, then exists " model " and inside tab, select " feature selection " feature selection and " recurrence " regression node, next " derivation " node export, the axle temperature value obtained in order to reduced model and the contrast of original axle temperature is selected in " field " tab Table and block diagram.

A kind of dynamic axle temperature Forecasting Methodology of bullet train based on multivariate regression models the most according to claim 1, it is special Levying and be, described step 4 is specifically implemented according to following steps:

Step (4.1), model collect inspection:

The quality that model is overall, wherein, coefficient of multiple correlation R, coefficient of determination R is weighed by equation below², the coefficient of determination of correction R_adj ²:

$R^2=\frac{SSR}{{\mathrm{SS}}_{total}}=\frac{\Σ{({\hat{y}}_i-{\stackrel{\‾}{y}}_i)}^2}{\Σ{(y_i-{\stackrel{\‾}{y}}_i)}^2}$

${R^2}_{adj}=1-\frac{n-1}{n-p-1}(1-R^2)$

Wherein, coefficient of multiple correlation R represents independent variable and the level of intimate of dependent variable linear relationship, wherein y in model_iFor dependent variable Axle temperature T,For the y obtained in described step (3.2)_iEstimator, actually it is y_iRelevant to the simple linear of its estimator Coefficient, its span is (0,1), does not has negative value, and R value is the biggest, illustrates that linear regression relation is the closest, coefficient of determination R²Represent The ratio shared by part explained by independent variable in regression model in total variation of dependent variable, the explanation strengths of regression equation is usually By coefficient of determination R²Measure, the most generally R²Being the bigger the better, wherein SSR is regression sum of square, SS_totalFor total Quadratic sum,For the average of dependent variable axle temperature T, the coefficient of determination R of correction_adj ²Be weigh institute established model quality important indicator it One, wherein, what n represented is the content of sample, and what p represented is the number of independent variable, R_adj ²The biggest, the effect of model is the best；

Step (4.2), the relative error rectangular histogram of training sample:

To the training sample obtained in step 2, the training sample to three operation phase respectively, with returning that step (3.2) obtains Equation for Calculating is returned to go out estimated valueThen relative error is

$\begin{array}{cc}relative& error=abs(y_i-{\hat{y}}_i)/y_i\end{array}$

Then draw its rectangular histogram, observe its distribution situation；

Step (4.3), test sample is tested:

To the test sample obtained in step 2, the test sample to three operation phase respectively, with returning that step (3.2) obtains Equation for Calculating is returned to go out estimated valueThen relative error is

$\begin{array}{cc}relative& error=abs(y_i-{\hat{y}}_i)/y_i\end{array},$

Test sample to three operation phase the most respectively, draws dependent variable axle temperature T, the estimated value of axle temperature T in one drawingThe broken line graph of relative error (relative error), and use double coordinate form, relative error figure can reflect model The situation of fitting effect, in this figure, can be clearly seen that the effect of models fitting by the broken line graph of predictive value and actual value Really, and passing through relative error broken line graph it can be seen that the quality of prediction effect, if over the passage of time, relative error magnitudes becomes Increasing, then explanation model to later stage prediction effect not as early stage because forecast error is in tolerance interval all the time, Therefore axle temperature can be effectively predicted by the method, such that it is able to by the abnormal intensification of axle temperature as the detection of train hot box trouble One discrimination standard, with the expansion avoiding accident of maximum possible.