CN106372450A - High-speed train axle temperature prediction method based on stepwise regression analysis - Google Patents

Abstract

The invention discloses a high-speed train axle temperature prediction method based on stepwise regression analysis. Interpolation processing and standardized transformation are conducted on axle temperature acquired from a high-speed train and data of factors affecting axle temperature change, and a correlation coefficient matrix R(0) is established; through the stepwise regression analysis, the factors remarkably affecting axle temperature change are screened out; the factors and a standardized regression equation are utilized to establish an axle temperature prediction equation; finally, the data of relevant factors obtained after screening are substituted into the axle temperature prediction equation to obtain an axle temperature prediction value. By the adoption of the prediction method, the change trend of the axle temperature can be accurately predicted, and a certain theoretical basis is provided for axle operation and maintenance.

Description

High-speed train axle temperature predicting method based on stepwise regression analysiss

Technical field

The invention belongs to data mining technology field is and in particular to a kind of bullet train axletree based on stepwise regression analysiss Temperature predicting method.

Background technology

In recent years, the continuous popularization with bullet train and development, bullet train becomes more and more popular trip mode, Its appearance shortens the time-space matrix between each city, is that the trip of people brings great convenience.Meanwhile, it promotes The development of regional economy along the line, promotes the raising of people's living standard.But, with the development of bullet train, bullet train Safe operation receives huge challenge, how to ensure that the safe operation of bullet train becomes research topic important now.

Train bogie is the important component part of train, and it is used for supporting car body and in-vehicle device, and train is moved Mechanical property, security performance and hauling ability all play decisive role.And the key that train axle is train bogie is held Carry position, be also the strength member of impact safe train operation, axletree temperature is that axletree situation is the most directly reacted, in train fortune During row, axletree needs the enormous impact born huge gravity load and turned, caused by road basin etc. due to train, Thus axletree temperature can constantly raise.When abnormal intensification in axletree temperature it is possible to cause off-axis, overheating of axle bearing etc. existing As causing the major accidents such as train derailing, bringing on a disaster property consequence.

It is mainly the real-time monitoring to axletree temperature and the inspection to axletree currently for the maintenance measure that axletree is taken Survey.Monitoring to axletree temperature, mainly uses axle temperature annunciator.Axle temperature annunciator is when axletree temperature occurs extremely When, send warning, crew can reaffirm warning message after receiving the report for police service, and takes corresponding measure after finding failure cause.But It is that, because axle temperature annunciator is easily affected by extraneous factor, sensing point is because affecting it for axle temperature situations such as the swing of vehicle body The Real-time Collection of data, leads to axle temperature precaution device often to occur reporting by mistake, is unfavorable for discovery and the process of axle failures.Meanwhile, to car The detection work of axle, Railway Bureau and each related scientific research institutes propose and take multinomial maintenance maintenance measure, but main at present Around be still maintenance after periodic inspection and fault occur, lack promptness and effectiveness, this is all unfavorable for ensureing train Safe operation.Both the above maintenance maintenance measure all can only detect the situation of current axletree temperature and axletree, and cannot be pre- The variation tendency of measuring car axle temperature degree.But the Accurate Prediction for axletree temperature, has important to the safe operation ensureing train Meaning.

Content of the invention

It is an object of the invention to provide a kind of high-speed train axle temperature predicting method based on stepwise regression analysiss, solve High-speed train shaft detection present in prior art can only reflect current axletree in real time with the work of axletree temperature monitoring Situation, and cannot furnish a forecast, the problem of warning function.

The technical solution adopted in the present invention is, based on the high-speed train axle temperature predicting method of stepwise regression analysiss, Comprise the following steps:

Step 1, from the data of bullet train collecting vehicle axle temperature degree and the factor of impact axletree temperature change, to having vacant position Data carry out interpolation processing；

Step 2, carry out data normalization conversion to completing the data after interpolation processing, set up correlation matrix r⁽⁰⁾；

Step 3, pass through stepwise regression analysiss, regression equation will be introduced on the axletree temperature larger factor of impact successively, and draw The condition entering is that the sum of squares of partial regression of this factor is maximum in factor to be selected, meanwhile, often introduces one to axletree temperature change Affect significant factor, be required for the significance of the factor having been incorporated into regression equation is tested, reject and axle temperature is changed Affect inapparent factor, until not having factor can introduce, also do not have factor to need to reject, now, the factor staying is right Axletree temperature change affects significant factor；

Step 4, using what screening obtained, significant factor and standardized regression equation are affected on axletree temperature change, build Vertical shaft temperature predictive equation；

Step 5, the data substitution axle temperature predictive equation of the correlative factor that will obtain after screening, obtain the prediction of axletree temperature Value.

The feature of the present invention also resides in:

Step 3 is specifically implemented according to following steps:

1) calculate the sum of squares of partial regression q of each factor of impact axle temperature change, find out sum of squares of partial regression maximum because Plain x_k；

2) to factor x that sum of squares of partial regression is maximum_kCarry out f inspection, if f >=f^*, then by x_kIntroduce regression equation, lay equal stress on The new correlation matrix r of new calculating, execution step 3)；If f is ＜ f^*, then factor screening terminate；

3) to originally having determined the factor introducing regression equation, calculate the minimum factor of its sum of squares of partial regression, carry out f Inspection, if f >=f^*, show the new factor x introducing_kChecked by f, then retain the factor originally having been incorporated into regression equation, continue Execution step 1)；If f is ＜ f^*, then reject x_k, recalculate new correlation matrix r, be then further continued for carrying out step 3), inspection Test the significance that residue has been incorporated into the variable of regression equation, until not having factor to need to reject；If now still suffering to be screened Factor, then return execution step 1)；If now there is not the factor needing to introduce or reject, stepwise regression analysiss execute Finish；

Above-mentioned steps 2, recalculating of 3 correlation matrix r are carried out by eliminating conversion, disappear when r passes through l-1 time Go to convert, when needing to carry out l conversion, conversion process is as follows:

$\left\{\begin{array}{cc}{r}_{ki}^{\left(l\right)}=\frac{r_{ki}^{(l-1)}}{r_{kk}^{(l-1)}}& (i\&notequal;k)\\ r_{ji}^{\left(l\right)}=r_{ji}^{(l-1)}-\frac{r_{jk}^{(l-1)}{r}_{ki}^{(l-1)}}{r_{kk}^{(l-1)}}& (i\&notequal;k,j\&notequal;k)\\ r_{kk}^{\left(l\right)}=\frac{1}{r_{kk}^{(l-1)}}& \\ r_{jk}^{(l-1)}=-\frac{r_{jk}^{(l-1)}}{r_{kk}^{(l-1)}}& (j\&notequal;k)\end{array}\right.$

Wherein, interpolation processing described in step 1 adopts the processing mode of nearest neighbour interpolation, is specifically divided into following two situations:

1) as j ＜ n and when j-th data is vacancy value, the factor of axle temperature data y (j) or impact axletree temperature change Data x_iJ the value of () is the value of -1 data of jth；

2) as j=n and when j-th data is vacancy value, the factor of axle temperature data y (j) or impact axletree temperature change Data x_iJ the value of () is the value of+1 data of jth.

Wherein, step 2 carries out data normalization using regular method, obtains normal equation group, with its coefficient matrix r and Constant coefficient matrix r sets up correlation matrix r⁽⁰⁾.

Wherein, step 4 is specifically implemented according to following steps:

Staying p axle temperature is changed after step 3 screening affects significant factor, and obtained standardized regression equation is as follows Shown:

z_y=d₁z₁+d₂z₂+…+d_pz_p(12)

Obtain each factor and standard deviation s of axle temperature data₁, s₂... s_p, s_y, obtain p factor using below equation Coefficient in predictive equation,

$b_q=\frac{s_y}{s_q}{d}_q,(q=1,...,p)---\left(13\right)$

Substituted into meansigma methodss, obtain b₀, obtaining axle temperature predictive equation is:

Y=b₀+b₁x₁+b₂x₂+…b_px_p(14).

The present invention proposes using stepwise regression analysiss method, axletree temperature to be predicted.The basic think of of stepwise regression analysiss Think it is to introduce the factor one by one, the condition being introduced into is that the sum of squares of partial regression of this factor is maximum in all factors to be selected；Simultaneously.Often Introduce a factor, the factor that script will be had been incorporated into carries out significance test, rejects the wherein inapparent factor.Due to It is a complicated process that axletree temperature rises, and it is related with a lot of other factors, such as speed, load-carrying, ambient temperature etc., by Step returns and can filter out the factor larger on axle temperature change impact from many factors, sets up axle temperature predictive equation.The present invention Invention is intended to find the rule of axle temperature change in bullet train running, filter out larger on axle temperature change impact because Element, reacts other with the related data collecting and can not survey the impact to axle temperature for the physical factor, to realize the prediction to axle temperature, Safe operation for the operation and maintenance of train axle, vehicle provides theories integration.

The invention has the beneficial effects as follows, (1) is present invention achieves high-speed train axle temperature degree and other correlative factor numbers According to interpolation processing, by the process to high-speed train axle temperature degree and its related data, supplement the vacancy value in data, be The foundation of subsequent prediction equation and inspection are provided convenience.(2) method based on stepwise regression analysiss for the present invention, by progressively returning Return and filter out the factor larger on the impact of axletree temperature change from the factor of numerous impact axle temperature changes, predicting for axle temperature provides Theories integration.(3) present invention utilizes the measurable factor related to axle temperature change, replaces other immesurable physical factors countershaft The impact of temperature change.(4) present invention achieves prediction to high-speed train axle temperature changing trend, and set up axle temperature prediction side Journey；Meanwhile, the operation for axletree and maintenance provide certain theoretical basiss.

Brief description

Fig. 1 is the block diagram based on the high-speed train axle temperature predicting method of stepwise regression analysiss for the present invention；

Fig. 2 is that the present invention on axle temperature and affects axle based on the high-speed train axle temperature predicting method of stepwise regression analysiss The flow chart that the related data of temperature change carries out data prediction；

Fig. 3 is the stepwise regression analysiss based on the high-speed train axle temperature predicting method of stepwise regression analysiss for the present invention Flow chart；

Fig. 4 is the axle temperature prediction curve based on the high-speed train axle temperature predicting method of stepwise regression analysiss for the present invention Figure；

Fig. 5 is the axle temperature actual curve based on the high-speed train axle temperature predicting method of stepwise regression analysiss for the present invention Figure；

Fig. 6 is the axle temperature curve comparison based on the high-speed train axle temperature predicting method of stepwise regression analysiss for the present invention Figure.

Specific embodiment

The present invention is described in further detail with reference to the accompanying drawings and detailed description, but the present invention is not limited to These embodiments.

The high-speed train axle temperature predicting method based on stepwise regression analysiss of the present invention is as shown in figure 1, according to following Step is implemented:

Step 1, using sensor from bullet train collecting vehicle axle temperature degree and impact axletree temperature change factor number According to.Because sensor is during carrying out data acquisition, by extraneous factor interference it may appear that the feelings that do not collect of data Condition, therefore, on axle temperature data y (j) and impact axletree temperature change factor data x_iJ the span of (), wherein i is 1～m, i are the number of the factor of impact axletree temperature change, and j is sampling time point, and the value of j is 1～n；Checking in data is No have vacancy value.As shown in Figure 2.

First, it is determined that whether there is vacancy value in axle temperature data y (j).If existing, carry out interpolation processing；If not existing, Then continue checking for affecting factor x of axle temperature change_iWhether there is vacancy value in the data of (j).Until all of data check is complete Finish and interpolation processing is carried out to data and complete.

Sensor is to gather once for each second to the collection of data, therefore the change between adjacent data is little.Therefore, to height Vacancy value present in the data of factor of the axle temperature data of fast train and impact axle temperature change, uses nearest neighbour interpolation Processing mode, is specifically divided into following two situations:

1) as j ＜ n and when j-th data is vacancy value, y (j) or x_iJ the value of () is the value of -1 data of jth；

2) as j=n and when j-th data is vacancy value, y (j) or x_iJ the value of () is the value of+1 data of jth；

Data after interpolation is no longer free missing value, can preferably reflect Changing Pattern in time interval for the data.

Step 2, carry out data normalization conversion to completing the data after interpolation processing, to overcome the impact of dimension.

The present invention uses regular method and carries out data normalization, and the core concept of this method is using data Average and standard deviation, initial data x is normalized into x ' using z-score.Specific step is:

1) obtain the arithmetic mean of instantaneous value of axle temperature dataWith standard deviation s_y, then the data obtaining the factor of impact axle temperature change Arithmetic mean of instantaneous valueWith standard deviation s_i(i=1 ..., m).

2) it is standardized processing.

$z_{jy}=\frac{y_j-\stackrel{\&overbar;}{y}}{s_y},1\≤j\≤n---\left(1\right)$

$z_{ji}=\frac{x_{ij}-{\stackrel{\&overbar;}{x}}_i}{s_i},1\≤j\≤n---\left(2\right)$

Wherein, z_jyAnd z_jiFor the numerical value after standardization, y_jAnd x_jiFor the numerical value before standardization.For writing conveniently, make z_jy= z_j(m+1), wherein m is the number of the factor of impact axle temperature change.

The coefficient matrix a of normal equation group and constant term b are respectively

$a=\left(\begin{array}{cccc}{\mathrm{\σz}}_{j1}^2& {\mathrm{\σz}}_{j1}{z}_{j2}& ...& {\mathrm{\σz}}_{j1}{z}_{jm}\\ {\mathrm{\σz}}_{j2}{z}_{j1}& {\mathrm{\σz}}_{j2}^2& ...& {\mathrm{\σz}}_{j2}{z}_{jm}\\ ...& ...& ...& ...\\ {\mathrm{\σz}}_{jm}{z}_{j1}& {\mathrm{\σz}}_{jm}{z}_{j2}& ...& {\mathrm{\σz}}_{jm}^2\end{array}\right)---\left(3\right)$

$b=\left(\begin{array}{c}{\mathrm{\σz}}_{j1}{z}_{j(m+1)}\\ {\mathrm{\σz}}_{j2}{z}_{j(m+1)}\\ \·\\ \·\\ \·\\ {\mathrm{\σz}}_{jm}{z}_{j(m+1)}\end{array}\right)---\left(4\right)$

Thus can obtain

$\underset{j}{\σ}{z}_{jk}^2=(n-1)\frac{s_{kk}}{s_k\·s_k}=(n-1)r_{kk},(k=1,2,...,m)---\left(5\right)$

$\underset{j}{\σ}{z}_{ji}{z}_{jk}=(n-1)\frac{s_{ik}}{s_i\·s_k}=(n-1)r_{ik},(i,k=1,2,...,m)---\left(6\right)$

Can obtain from formula (5) and formula (6),Coefficient matrix r and constant coefficient matrix r are respectively as follows:

$r=\left(\begin{array}{cccc}{r}_{11}& r_{12}& ...& r_{1m}\\ r_{21}& r_{22}& ...& r_{2m}\\ ...& ...& ...& ...\\ r_{m1}& r_{m2}& ...& r_{mm}\end{array}\right)---\left(7\right)$

$r_y=\left(\begin{array}{c}{r}_{1(m+1)}\\ r_{2(m+1)}\\ \·\\ \·\\ \·\\ r_{m(m+1)}\end{array}\right)---\left(8\right)$

Step 3, using the coefficient matrix r obtaining and constant coefficient matrix r, set up correlation matrix r⁽⁰⁾, using r⁽⁰⁾Enter Row stepwise regression analysiss, filter out the factor having notable contribution to axletree temperature change.

Stepwise regression analysiss refer in multiple linear regression analysis, are inverted compact converter technique and double check using solution Method, to study and to set up optimal regression equation, the present invention using the purpose of stepwise regression analysiss be intended to axle temperature change have shadow Filter out the factor that axle temperature change is had a significant impact in the factor rung, set up optimal predictive equation.Utilize matrix for this Elementary transformation, introduces effective factor, and the significance of each factor of sequential test, one by one to ensure in last regression equation Comprise whole significant factors.The regression equation of several transition will be experienced during this.The flow process of stepwise regression analysiss such as Fig. 3 Shown, the process of Factor Selection is realized by stepwise regression analysiss, specific as follows shown:

First, determine in stepwise regression analysiss check factor significance f inspection marginal value f*, marginal value big The little size depending on the sample data volume carrying out successive Regression.

Then, start with correlation matrix and carry out stepwise regression analysiss, the process of realization is broadly divided into following four steps:

1) calculate the contribution of all independent variables to be selected, that is, the sum of squares of partial regression q of each factor of impact axle temperature change, looks for Go out maximum factor x of sum of squares of partial regression_k.The computing formula of sum of squares of partial regression is:

$q_k=\frac{r_{k(m+1)}^2}{r_{kk}}---\left(9\right)$

2) to factor x that sum of squares of partial regression is maximum_kCarry out f inspection.According to correlation matrix r, obtain x_kStatistic F, the computing formula of statistic f is:

$f=\frac{q_k}{(r_{(m+1)(m+1)}-q_k)/(n-1-\∂)}---\left(10\right)$

WhereinThe number of the factor being changed significantly for the impact axle temperature having been incorporated into.Now, if f >=f^*, show x_kPass through F checks, then by x_kIntroduce regression equation, and recalculate new correlation matrix r (correlation matrix r⁽⁰⁾Refer to first The correlation matrix of secondary generation, the correlation matrix subsequently obtaining all is replaced by r), then execution step 3)；If f is ＜ f^*, table Bright x_kChecked by f, then factor screening terminates.

3) determining one new factor x of introducing_kAfterwards, need the factor originally having determined introducing regression equation is carried out Significance test, i.e. f inspection.It is calculated the minimum factor of sum of squares of partial regression, its statistic f is obtained by formula (10), If f >=f^*, show that this factor is checked by f, then retain the factor originally having been incorporated into regression equation, continue executing with step 1)； If f is ＜ f^*, show that this factor is checked by f, and after introducing new factor, the significance of this factor reduce, then reject this because Element, recalculates new correlation matrix r, is then further continued for carrying out step 3), inspection residue has been incorporated into regression equation The significance of variable, until not having factor to need to reject.If now still suffering from factor to be screened, return execution step 1)； If now there is not the factor needing to introduce or reject, stepwise regression analysiss are finished.

Step 2) and step 3) in, often introduce or reject a factor, be required for recalculating correlation matrix r. Converted by eliminating, can introduce or reject correlated variabless.Eliminate conversion when r passes through l-1 time, need to carry out l change When changing, conversion process is as follows:

$\left\{\begin{array}{cc}{r}_{ki}^{\left(l\right)}=\frac{r_{ki}^{(l-1)}}{r_{kk}^{(l-1)}}& (i\&notequal;k)\\ r_{ji}^{\left(l\right)}=r_{ji}^{(l-1)}-\frac{r_{jk}^{(l-1)}{r}_{ki}^{(l-1)}}{r_{kk}^{(l-1)}}& (i\&notequal;k,j\&notequal;k)\\ r_{kk}^{\left(l\right)}=\frac{1}{r_{kk}^{(l-1)}}& \\ r_{jk}^{(l-1)}=-\frac{r_{jk}^{(l-1)}}{r_{kk}^{(l-1)}}& (j\&notequal;k)\end{array}\right.---\left(11\right)$

New correlation matrix r thus can be regenerated.

By above step, just complete the screening of the factor to impact axletree temperature.

Step 4, obtained using screening be changed significantly related notable factor to axle temperature and stepwise regression analysiss obtain Standardized regression equation, obtain axle temperature predictive equation.Specific as follows:

Staying p axle temperature is changed after screening affects significant factor, and obtained standardized regression equation is as follows:

z_y=d₁z₁+d₂z₂+…+d_pz_p(12)

Obtain each factor and standard deviation s of axle temperature data₁, s₂... s_p, s_y, obtain p factor using below equation Coefficient in predictive equation.

$b_q=\frac{s_y}{s_q}{d}_q,(q=1,...,p)---\left(13\right)$

Substituted into meansigma methodss, obtain b₀, obtaining axle temperature predictive equation is:

Y=b₀+b₁x₁+b₂x₂+…b_px_p(14)

Step 5, take screening after the data of each factor that obtains, after carrying out data prediction (interpolation processing and standardization), Substitute into predictive equation, obtain the predictive value of axle temperature.Complete the prediction to high-speed train axle temperature degree.

Embodiment

Forecasting Methodology using the present invention is predicted to certain high-speed train axle temperature degree.

Step 1: interpolation processing is carried out on the data of axle temperature data and impact axle temperature change.

Take data x of the factor of axle temperature data y (j) collecting and impact axletree temperature change_iJ (), wherein i are shadow Ring the number of the factor of axletree temperature change, j is sampling time point, j=24.List axletree temperature at this as space is limited, Degree and the corresponding value of 24 sampling time points corresponding to this factor of speed of impact axletree temperature change, respectively as table 1 He Shown in table 2.

Table 1 high-speed train axle temperature degree initial data

Table 2 ambient temperature initial data

Sampling time point j	1	2	3	4	5	6	7	8
									Speed km/h	289.1	288	287	286.5		286	286	285.4
Sampling time point j	9	10	11	12	13	14	15	16
									Speed km/h	285.3		285	284.3	284	284	283.6	283
Sampling time point j	17	18	19	20	21	22	23	24
									Speed km/h	282.5	282	282	281.8	281.5	281.5	281.1	281

Respectively high-speed train axle temperature degrees of data and ambient temperature initial data are carried out with the lookup of vacancy value, Ke Yifa Existing, in y (7), y (13), y (21), x₁(5), x₁(10) there is vacancy value in this five points.

Using the method for nearest neighbour interpolation, except last point, other points are all being supplemented with a rear numerical value of employing The method of previous numerical value, due to y (8), y (14), y (22), x₁(6), x₁(11) this five points are not empty, therefore can be by Numerical value is attached to the previous point for vacancy value, completes interpolation processing.Carry out the tables of data after interpolation processing as shown in Table 3 and Table 4.

Data after table 3 high-speed train axle temperature degree interpolation processing

Data after table 2 ambient temperature interpolation processing

Sampling time point j	1	2	3	4	5	6	7	8
									Speed km/h	289.1	288	287	286.5	286	286	286	285.4
Sampling time point j	9	10	11	12	13	14	15	16
									Speed km/h	285.3	285	285	284.3	284	284	283.6	283
Sampling time point j	17	18	19	20	21	22	23	24
									Speed km/h	282.5	282	282	281.8	281.5	281.5	281.1	281

Step 2: data is standardized process.

Using normalized method, the data after interpolation processing is standardized.First, obtain axletree temperature data Meansigma methodssWith standard deviation s_y, and the meansigma methodss of impact axletree temperature variation factorsWith standard deviation s_i, then utilizeEach data is standardized convert, obtains regular The coefficient matrix a of equation group and constant term b, because the value of specimen sample point j is larger, here does not just list this two matrixes.

Correlation matrix can be obtained by the covariance between variable.Correlation coefficient in correlation matrix r byObtain.Correlation matrix r is:

$r=\left(\begin{array}{ccccc}{r}_{11}& r_{12}& ...& r_{1m}& r_{1(m+1)}\\ r_{21}& r_{22}& ...& r_{2m}& r_{2(m+1)}\\ ...& ...& ...& ...& ...\\ r_{m1}& r_{m2}& ...& r_{mm}& r_{m(m+1)}\\ r_{(m+1)1}& r_{(m+1)2}& ...& r_{(m+1)m}& r_{(m+1)(m+1)}\end{array}\right)$

Step 3: the factor of impact axletree temperature change is screened using stepwise regression analysiss.

Successive Regression is by factor screening, axle temperature will be changed with the significant factor of impact and stay, and reject and axle temperature is changed Affect inapparent factor.It requires the factor being introduced into regression equation each time must be that in all factors to be screened, partial regression is put down Side and maximum factor, sum of squares of partial regression byObtain.Then checked by f, check this factor that equation is shown The size of work property.The computing formula of statistic f is as follows:

$f=\frac{q_k}{(r_{(m+1)(m+1)}-q_k)/(n-1-\∂)}$

Sample data volume due to carrying out stepwise regression analysiss is very big, therefore it is stipulated that being used for marginal value f of f inspection^*For 5, Be equivalent to significance

If f >=f^*, then this factor is introduced regression equation, and correlation matrix is carried out with solution and invert compact conversion, Obtain new correlation matrix, the mode of compact conversion of inverting is as follows:

$\left\{\begin{array}{cc}{r}_{ki}^{\left(l\right)}=\frac{r_{ki}^{(l-1)}}{r_{kk}^{(l-1)}}& (i\&notequal;k)\\ r_{ji}^{\left(l\right)}=r_{ji}^{(l-1)}-\frac{r_{jk}^{(l-1)}{r}_{ki}^{(l-1)}}{r_{kk}^{(l-1)}}& (i\&notequal;k,j\&notequal;k)\\ r_{kk}^{\left(l\right)}=\frac{1}{r_{kk}^{(l-1)}}& \\ r_{jk}^{(l-1)}=-\frac{r_{jk}^{(l-1)}}{r_{kk}^{(l-1)}}& (j\&notequal;k)\end{array}\right.$

After obtaining new correlation matrix, that is, need the factor originally having determined introducing regression equation is carried out again Significance test, to avoid reducing the significance on axle temperature change impact for the old factor due to the introducing of new factor.

For the factor that may need rejecting, it is also to calculate its sum of squares of partial regression first, selects sum of squares of partial regression Little factor carries out f inspection.If the minimum factor of sum of squares of partial regression has also passed through f inspection, illustrate not need to reject any Factor, proceeds factor to be selected introduces the calculating of regression equation；If the factor now carrying out f inspection is checked by f, Reject this factor from regression equation, and correlation matrix is carried out eliminate conversion, after obtaining new correlation matrix, Continue to select the minimum factor of sum of squares of partial regression to carry out f inspection, until not having factor can reject or certain factor must not Till rejecting.

If f is ＜ f^*, then factor screening terminate.

By stepwise regression analysiss, screening successively obtains ambient temperature, load-carrying, speed, pull strength, pull strength current transformer work( This five factors of rate, the impact to axletree temperature change is notable.Trying to achieve the standardized regression equation corresponding to five factors is:

z_y=0.8025z₁+0.2156z₂-0.0842z₃-0.0340z₄-0.0130z₅

Wherein z₁, z₂, z₃, z₄, z₅It is respectively ambient temperature, load-carrying, speed, pull strength, pull strength current transformer power.Obtain This five factors and the standard deviation of axle temperature data, obtain this coefficient in predictive equation for five factors using below equation.

$b_q=\frac{s_y}{s_q}{d}_q,(q=1,...,p)$

Substituted into meansigma methodss, obtain b₀=-211.2244, obtaining axle temperature predictive equation is:

Y=-211.2244-0.0122x₁+2.5510x₂+0.9614x₃-0.0124x₄-0.0002x₅

Wherein x₁, x₂, x₃, x₄, x₅It is respectively speed, ambient temperature, load-carrying, pull strength, pull strength current transformer power.

Step 5: the value of speed, ambient temperature, load-carrying, pull strength, pull strength this five factors of current transformer power is substituted into Predictive equation, obtains the predictive value of axletree temperature.

Wherein Fig. 4 is the prediction curve of the axletree temperature being obtained by axle temperature predictive equation, and Fig. 5 for axletree temperature in institute The actual measured value of the axletree temperature that corresponding sampling time point is collected.Fig. 6 is then predictive value and the reality of axletree temperature The comparison diagram of value, it will be appreciated from fig. 6 that passing through axle temperature predictive equation calculated axletree temperature prediction value, can reflect axletree The variation tendency of temperature, is the safe operation of vehicle, and the inspection of axletree is supported with safeguarding to provide.By axle temperature predictive equation, just The prediction to axletree temperature can be completed.

Claims (6)

1. the high-speed train axle temperature predicting method based on stepwise regression analysiss is it is characterised in that comprise the following steps:

Step 1, from bullet train collecting vehicle axle temperature degree and impact axletree temperature change factor data, to the number having vacant position According to carrying out interpolation processing；

Step 2, carry out data normalization conversion to completing the data after interpolation processing, set up correlation matrix；

Step 3, pass through stepwise regression analysiss, regression equation will be introduced on the axletree temperature larger factor of impact successively, introducing Condition is that the sum of squares of partial regression of this factor is maximum in factor to be selected, and meanwhile, often introducing one affects on axletree temperature change Significantly factor, is required for the significance of the factor having been incorporated into regression equation is tested, and rejects and changes impact to axle temperature Inapparent factor, until not having factor can introduce, does not have factor to need to reject, now, the factor staying is to axletree yet Temperature change affects significant factor；

Step 4, using what screening obtained, significant factor and standardized regression equation are affected on axletree temperature change, set up axle Warm predictive equation；

Step 5, the data substitution axle temperature predictive equation of the correlative factor that will obtain after screening, obtain the predictive value of axletree temperature.

2. the high-speed train axle temperature predicting method based on stepwise regression analysiss according to claim 1, its feature exists In described step 3 is specifically implemented according to following steps:

1) calculate the sum of squares of partial regression q of each factor of impact axle temperature change, find out maximum factor x of sum of squares of partial regression_k；

2) to factor x that sum of squares of partial regression is maximum_kCarry out f inspection, if f >=f^*, then by x_kIntroduce regression equation, and again count New correlation matrix, execution step 3)；If f is ＜ f^*, then factor screening terminate；

3) to originally having determined the factor introducing regression equation, calculate the minimum factor of its sum of squares of partial regression, carry out f inspection Test, if f >=f^*, show the new factor x introducing_kChecked by f, then retain the factor originally having been incorporated into regression equation, continue to hold Row step 1)；If f is ＜ f^*, then reject x_k, recalculate new correlation matrix, be then further continued for carrying out step 3), inspection is surplus The significance of the remaining variable having been incorporated into regression equation, until not having factor to need to reject；If now still suffer to be screened because Element, then return execution step 1)；If now there is not the factor needing to introduce or reject, stepwise regression analysiss have executed Finish.

3. the high-speed train axle temperature predicting method based on stepwise regression analysiss according to claim 2, its feature exists In recalculating of described correlation matrix r is carried out by eliminating conversion, eliminates conversion when r passes through l-1 time, needs When carrying out l conversion, conversion process is as follows:

.

4. the high-speed train axle temperature predicting method based on stepwise regression analysiss according to claim 1, its feature exists Adopt the processing mode of nearest neighbour interpolation in, interpolation processing described in step 1, be specifically divided into following two situations:

1) as j ＜ n and when j-th data is vacancy value, data x of the factor of axle temperature data y (j) or impact axletree temperature change_i J the value of () is the value of -1 data of jth；

2) as j=n and when j-th data is vacancy value, the data of the factor of axle temperature data y (j) or impact axletree temperature change x_iJ the value of () is the value of+1 data of jth.

5. the high-speed train axle temperature predicting method based on stepwise regression analysiss according to claim 1, its feature exists In described step 2 carries out data normalization using regular method, obtains normal equation group, with its coefficient matrix and constant coefficient Matrix sets up correlation matrix.

6. the high-speed train axle temperature predicting method based on stepwise regression analysiss according to claim 1, its feature exists In described step 4 is specifically implemented according to following steps:

Staying p axle temperature is changed after step 3 screening affects significant factor, the following institute of obtained standardized regression equation Show:

z_y=d₁z₁+d₂z₂+…+d_pz_p(12)

Obtain each factor and standard deviation s of axle temperature data₁, s₂... s_p, s_y, obtain p factor in prediction using below equation Coefficient in equation,

Substituted into meansigma methodss, obtain b₀, obtaining axle temperature predictive equation is:

Y=b₀+b₁x₁+b₂x₂+…b_px_p(14).