CN106528940A - A method for evaluation and early warning for train axle properties based on mathematical models - Google Patents

Abstract

The invention provides a method for evaluation and early warning for train axle properties based on mathematical models and belongs to the field of methods for evaluation and early warning of high speed train axle properties. The method comprises the steps of establishing an axle temperature variation mathematical model for axle operation in each of the latest 30 days, and obtaining a group of parameters for evaluating the axle properties with respect to each model; performing smoothing processing on each group of parameters, and performing abrupt change detection and trend detection for the axle properties based on the smoothed property parameters. The qualitative method can assist train maintainers in accurately and reliably judging whether axle temperature alarm signals belong to short-period false alarms capable of self-recovery, and further provide important reference bases for maintenance decisions thereof.

Description

Train axle performance is evaluated based on mathematical model and early warning method

Technical field

The invention belongs to the evaluation of EMU axletree performance and method for early warning field, and in particular to a kind of to be based on mathematics Model train axle performance is evaluated and early warning method.

Background technology

TCMS (TrainControlandManagementSystem) Train Controls and management that EMU has System has the functions such as intelligentized distributed information collection, storage, logical judgment, police instruction and man-machine interaction, its except Collect daily and store beyond the shaft temperature sensor data of each train axle, also received by other sensors respectively simultaneously Collection and train car speed of service data and outside vehicle ambient temperature data.The axle temperature feature of axletree can be anti-to a certain extent Reflect the behavior pattern of axletree, which is most important for the judgement of axle failures property, but existing TCMS system do not have it is right The intellectual analysis function of bearing temperature alarm signal, which generally only carries out the logical judgment of temperature over-range and sends axle temperature to axle temperature data High temperature alarm signal, maintainer can be transferred and be analyzed to the historical data of bearing temperature alarm in car inspection and repair, so as to right The axletree of sent high temperature alarm carries out failture evacuation.

However, under vehicle operating condition complicated and changeable, vehicle-mounted shaft temperature sensor, road speed sensor and outside Environment temperature sensor, the signal gathered by its three kinds of onboard sensors are possible to jolted concussion, circumstance of temperature difference, electromagnetism Interference etc. the impact of factor and send the rub-out signal of substantial deviation actual value once in a while, therefore, many times, TCMS system institute The axle temperature high temperature alarm signal for sending is the axle temperature false alarm signal that just voluntarily can recover at short notice, especially, at some Under special interference effect, send the axletree of warning and actually check in train advances way and be not out of order, and Train Stopping inspection When repairing, induce the driving objective condition of warning in driving way at that time and but do not existed, this cause maintainer be difficult directly with Completely and accurately judge by means of experience the bearing temperature alarm in historical data whether belong to voluntarily can recover, or can be temporary When ignore the false alarm not processed, thereby result in maintainer and cannot assert whether the phenomenon of such warning axletree needs subsequently Long-term follow observation, and then cause the bearing temperature alarm phenomenon that should arouse vigilance of part to be inadvertently omitted, its warning message The potential risk for being reflected is not taken seriously in time and is investigated early.

Additionally, the axle temperature data of axletree are also affected and are subject to by the static temperature difference of axletree temperature and ambient temperature respectively Impact of the train running speed to the signals collecting precision of shaft temperature sensor, ambient temperature are bigger with the difference of axletree actual temperature Then the thermolysis of axletree is more notable, and train running speed change can then cause the change of the signals collecting precision of shaft temperature sensor Change.But above-mentioned ambient temperature or road speed are difficult to precise quantification to the influence degree of axletree temperature, especially, ambient temperature with Caused by driving latitude, height above sea level or seasonal law institute, Changing Pattern is complicated and very long, is difficult to summarize.And it is subject to sensing element The detection error accumulation factor such as aging impact, axletree temperature data, road speed data and environment that sensor is gathered The collection result of temperature data can also occur slow drift, produce long-term tendency change, but these factors are often difficult Accurately considered by artificial experience, especially for possess it is numerous wheel to permutation motor train unit train for, summarized to every one by one One is taken turns what the judgement experience to axletree performance cannot almost be realized, and this is further to maintainer to the accurate of bearing temperature alarm Judgement causes obstacle.

On the other hand, if the axletree temperature history that can be stored to TCMS system and descending speed of corresponding time period Degree historical data and ambient temperature historical data are compared, by the variation tendency of its three of comprehensive consideration, so as to sum up Mapping relations with certain regularity, then can be used for judgement of the auxiliary repair personnel to axle temperature qualitative change, help which more For being efficiently completed routine servicing and the maintenance work of axletree and its related sensor, and more scrupulously complete part replacement Plan or bearing temperature alarm investigation task.

Therefore, design a kind of mathematical model for axle temperature associated arguments so as to axletree can be reflected by quantitative target Overall performance, and to study and judge the real property of train axle temperature alarm signal or for the performance to axle temperature related sensor part Investigate and whether the performance for axletree being followed the trail of in the case of to characterizing without obvious fault has potential potential safety hazard, it has also become The emphasis research direction of scientific research personnel.

The content of the invention

In order to solve the existing quantizating index because lacking the overall performance for reflecting axletree, and the shadow of train axle temperature The factor of sound is more, complex genesis, and rule is extremely difficult, causes whether the attribute of bearing temperature alarm signal belongs to of short duration false alarm problem It is difficult to experience quickly identification and the judgement by maintainer；Temporarily no obvious fault is characterized but has been pointed out potential hidden for part The bearing temperature alarm phenomenon of trouble cannot be by timely and effectively identification, attention, investigation or later stage tracking；And can be to axletree due to lacking The summary method of temperature, three kinds of data mapping principles of road speed and ambient temperature, causes the maintainer cannot be to axletree itself And the performance change trend of axle temperature related transducer device is investigated, therefore component capabilities Changing Pattern can not be grasped in time Or the technical problem of part replacement plan is scrupulously drafted, the present invention is provided one kind and train axle performance is entered based on mathematical model Row evaluates the method with early warning.

The technical scheme taken by present invention solution technical problem is as follows：

The present invention train axle performance is evaluated based on mathematical model and the method for early warning comprises the steps：

Step one, to axletree run it is nearest 30 days in set up within the 1st day axle temperature change mathematical model before data screening

Step 1.1：The 1st day in axletree operation is nearest 30 days, gathers respectively according to the onboard sensor of three kinds of parameters Train exterior ambient temperature M_d(d represents the number of ambient temperature sampling time node, and d takes natural number), road speed V_j(j tables Show the number of road speed sampling time node, j takes natural number), the axle temperature T of axletree_i(i represents axle temperature sampling time node Number, i take natural number), generate train exterior ambient temperature M with regard to time t_dContinuous data curve, road speed V_jCompany Continuous data and curves, axle temperature T_iContinuous data curve, and be stored in the raw data base of EMUs TCMS system；

Step 1.2：Abnormal data of three kinds of parameters each on continuous data curve is screened out in step 1.1 respectively：

Reject road speed V_jV on corresponding continuous data curve_jThe data segment and V that 0,000 m/hour of ＜_j400 kms of ＞/ When data segment, obtain road speed V_jWith regard to the normal data curve of time t；

Reject train exterior ambient temperature M_dM on corresponding continuous data curve_dThe data segment and M of≤- 80 degree_d>=80 degree Data segment, obtain train exterior ambient temperature M_dWith regard to the normal data curve of time t；

Reject axle temperature T_iT on corresponding continuous data curve_iThe data segment of≤- 80 degree, obtains axle temperature T_iWith regard to time t's Normal data curve；

Step 1.3：In road speed V that step 1.2 is obtained_jWith regard to filter out on the normal data curve of time t according to It is multiple with regard to road speed V that time span is sorted from long to short_jSection continuous time, and retain these continuous times of Duan Suofen Not corresponding road speed V_jData segment on normal data curve；

Step 1.31：To road speed V_jWith regard on the normal data curve of time t any two consecutive number strong point when Between be spaced and screened, obtain multiple sections continuous time；

The method of above-mentioned screening is：If the time interval at two consecutive number strong points is less than or equal to 5 minutes, this two adjacent Data point is in same section continuous time；If the time interval at two consecutive number strong points is more than 5 minutes, this two consecutive numbers Strong point is respectively in former and later two different sections continuous time；

Step 1.32：Time span is picked out in multiple sections continuous time obtained from step 1.31 and is all higher than 1 hour Multiple sections continuous time；

Step 1.33：To road speed V in a data segment corresponding to each section in step 1.32 continuous time_jTake Arithmetic average, if road speed V in certain data segment_jArithmetic average be less than or equal to 15,000 ms/hour, then reject the number According to section continuous time corresponding to section；If road speed V in certain data segment_jArithmetic average be more than 15,000 ms/hour, then Retain section continuous time corresponding to the data segment；

Step 1.34：Order of the section according to time span from long to short continuous time retained in step 1.33 is arranged Sequence, and retain road speed V of each after sequence corresponding to section continuous time_jData segment on normal data curve；

Step 1.4：Each with regard to road speed Vj filtered out in step 1.34 is in section continuous time, to step 1.2 The axle temperature T of acquisition_iNormal data curve and train exterior ambient temperature M with regard to time t_dWith regard to the normal data curve of time t The screening of section continuous time is carried out respectively, finds most long public section continuous time；

Step 1.41：In the first long section continuous time with regard to road speed Vj that step 1.34 is filtered out, using step Screening technique in rapid 1.31, to axle temperature T_iScreening acquisition is carried out with regard to axle temperature T with regard to the normal data curve of time t_iIt is multiple Continuous time section；

Step 1.42：Company of the time span more than 1 hour is picked out in multiple sections continuous time obtained from step 1.41 Continuous time period, and execution step 1.44；If there is no axle temperature T of the length more than 1 hour_iContinuous time, section, then rejected and step Corresponding road speed Vj of current first long section continuous time and axle temperature T described in 1.34_iTotal data, then execution step 1.43；

Step 1.43：In the residue obtained in step 1.34 each of section, again according to time span from growing to continuous time Short order, in the first new long section continuous time, using the screening technique in step 1.31, to axle temperature T_iWith regard to time t Normal data curve carry out screening obtain with regard to axle temperature T_iMultiple sections continuous time, and from obtaining with regard to axle temperature T_iIt is many Continuous time section of the time span more than 1 hour, and execution step 1.44 is selected in individual section continuous time；If no length is more than Section continuous time of 1 hour, then reject corresponding road speed V of the first new long section continuous time aforementioned with this step_jWith Axle temperature T_iTotal data, then re-execute this step, until time span can be selected more than section continuous time of 1 hour Afterwards, execution step 1.44；If failing all the time to find satisfactory section continuous time, day data, execution step three are worked as in deletion；

Step 1.44, step 1.42 or step 1.43 filter out with regard to axle temperature T_iContinuous time in section, using step Screening technique in rapid 1.31, to train exterior ambient temperature M_dWith regard to time t normal data curve carry out screening closed In train exterior ambient temperature M_dMultiple sections continuous time；

Step 1.45：From step 1.44 obtain with regard to train exterior ambient temperature M_dMultiple sections continuous time in select Go out continuous time section of the time span more than 1 hour, execution step 1.46；If there is no continuous time section of the length more than 1 hour, Road speed V corresponding with this of section is rejected continuous time then_j, axle temperature T_iWith train exterior ambient temperature M_dTotal data, so Execution step 1.43, find out again with regard to axle temperature T afterwards_iTime span more than section continuous time of 1 hour, then execution step 1.44 and this step, until continuous time of the time span with regard to train exterior ambient temperature Md more than 1 hour can be found out Duan Hou, execution step 1.46；

Step 1.46：In continuous time of the time span that step 1.45 finds more than 1 hour in section, will be three parameters same When there is most long section common time of data as most long public section continuous time；

Step 1.5：The data segment of three parameters corresponding to most long public section continuous time that step 1.46 is obtained is folded It is added under coordinate system at the same time, and supplies the value lacked in each supplemental characteristic section using linear interpolation respectively so that most Each time in public section continuous time of length can three parameters of correspondence data, then, preserve with this most it is long it is public continuously Road speed V corresponding to time period_jStable data and curves, axle temperature T_iStable data and curves and train exterior environment temperature Degree M_dStable data and curves；

Step 2, to axletree run it is nearest 30 days in set up within the 1st day axle temperature change mathematical model

Step 2.1：According to the radiating equation in physicss, and after considering speed to the impact of axle temperature, set up the axle of axletree Warm rate of change function, i.e. axle temperature change mathematical model is as follows：

In formula (1),Original value of the axle temperature rate of change of the 1st day to speed sensitivity in representing nearest 30 days, In representing nearest 30 days under the static environment of the 1st day by the temperature difference caused axletree rate of heat dispation original value, T_i(i represents axle The number of warm sampling time node, i take natural number) be axletree correspondence current time axle temperature,；V_j(j represents that road speed is sampled The number of timing node, j take natural number) represent the road speed for corresponding to current time；M_d(d represents the ambient temperature sampling time The number of node, d take natural number) represent the train exterior ambient temperature for corresponding to current time；

Step 2.2：SolveWithValue：

Step 2.21：Formula (1) is integrated, is then had

In formula (2),Original value of the axle temperature rate of change of the 1st day to speed sensitivity in representing nearest 30 days, In representing nearest 30 days under the static environment of the 1st day by the temperature difference caused axletree rate of heat dispation original value, T_iRepresent axletree The axle temperature at correspondence current time, V_jRepresent the road speed at correspondence current time；M_dRepresent the train exterior ring at correspondence current time Border temperature；Q represents axletree in t_nThe axle temperature of time, Q₁Represent axletree in t₁The axle temperature of time；Q-Q₁Represent in t₁To t_nTime The temperature approach of axletree temperature change in section；

Step 2.22：By the data obtained by step 2.21 integrationWithTo Q-Q₁ Linear fit is carried out, can be tried to achieveWithValue, process is as follows：

Make the matrix that X is n row three row, n is the number of data time point t, the expression form of matrix X is as follows：

Wherein, t₁To t_nFor time t in most long public section continuous time that step 1.46 is obtained all possible value；

The matrix that Y is a n row string is made, the column data is Q-Q₁；

Wherein, Q_iRespectively Q is in t_iThe value at moment, the number of i=1,2,3 ... n, n for data time point t；

Calculation expression β (X^TX)^-1X^TY, wherein, β represents the needed fitting parameter for solving, X^TIt is the transposed matrix of X, Subscript -1 is matrix inversion, and expression formula β is finally calculated the matrix of three row string, and the second row of matrix is's It is worth, the third line of matrix isValue, will be calculatedValue andValue correspondence natural law be stored in EMUs In the raw data base of TCMS system；

Step 2.23：By the data obtained by step 2.21 integrationWithTo Q-Q₁ Linear fit is carried out, the sensitivity of the axle temperature rate of change of the 1st day to speed is tried to achieveBy the temperature difference under value and static environment And the rate of heat dispation of caused axletreeThe p of model is calculated while value₁Value andValue, p₁Value has reacted the V of the 1st day_j (T_i-M_d) impact to axle temperature whether significantly, p₁Value includesP corresponding to₁Value andP corresponding to₁Value,P corresponding to₁Value is designated asP corresponding to₁Value is designated asIfRepresent current Road speed V at moment_jImpact for f (s) be it is significant, ifRepresent the environment static temperature difference (T_i-M_d) right In the impact of f (s) be significant；The goodness of fit of the 1st dayValueRepresent the excellent of the whole models fitting of assessment Bad degree；Value,Value andThe calculating process of value is as follows：

First, make RSS=(Y-X β)^T(Y-Xβ)……(3)

By the value of X, Y, β and the n obtained in step 2.22, the pr tried to achieve to formula (5) by formula (3)_βFor three rows one The matrix of row, the first row of matrix is 1, and the second row isThe third line isWherein, RSS represents the residuals squares of fitting With var_βRepresent the error of fitting parameter, pr_βThe statistical indicator of the whether notable non-zero of fitting parameter is represented, if pr_β<0.05 Regard notable non-zero as, show correspondence parameter be it is influential, otherwise without impact；Function p is represented and for the t values in t-distribution to be converted into p The function of value, the function are calculated by the standard t-distribution table looked into statistically；

Make again

In formula, SYY is the variance of Y, weighs the fluctuating margin of data Y,For the meansigma methodss of Y, obtained by step 2.22 Y value and formula (3) in the value of RSS that obtains, then can be in the hope of by formula (6) and formula (7)Value, will be calculated 'sValue,Value andValue correspondence natural law be stored in the raw data base of EMUs TCMS system；

Step 3：The train exterior ambient temperature that gathered respectively for 29 days in the residue of nearest 30 days with onboard sensor, Road speed, axle temperature are initial data, with every day as a time range, according to the mode of step one and step 2 to each It sets up an axle temperature change mathematical model, and corresponding each axle temperature change mathematical model is calculated oneValue, OneValue, oneValue, oneIt is worth and oneValue, and will be above-mentioned calculated numerical value corresponding with natural law It is stored in the raw data base of EMUs TCMS system, wherein,The axle temperature rate of change pair of kth day in representing nearest 30 days The original value of speed sensitivity,In representing nearest 30 days under the static environment of kth day by the temperature difference caused axletree Rate of heat dispation original value,Whether impact of the road speed of reaction kth day to axle temperature be notable,The ring of reaction kth day Whether impact of the border static state temperature difference to axle temperature be notable,The fit value of expression kth day, k=2,3 ... ..., 30, k take from So count；

Step 4：Performance parameter in the multiple axle temperature change mathematical models set up to step 2 and step 3WithAdaptive smooth process is carried out, the performance parameter after being smoothed is corresponded toWithAnd the performance parameter after smoothingWithCorresponding with natural law to be stored in the raw data base of EMUs TCMS system, adaptive smooth process is as follows：

Define binary function f (p, a r²) cause p ＞ 0.05 when, binary function value be 0, p≤0.05 when, binary function It is worth for r²；By the smooth original performance parameter of following recurrence formulas：

Wherein,Original value of the axle temperature rate of change of the 1st day to speed sensitivity in representing nearest 30 days,Table In showing nearest 30 days under the static environment of the 1st day by the temperature difference caused axletree rate of heat dispation original value,Represent nearest Original value of the axle temperature rate of change of kth day to speed sensitivity in 30 days,The static ring of kth day in representing nearest 30 days Under border by the temperature difference caused axletree rate of heat dispation original value,Reacting impact of the road speed of kth day to axle temperature is It is no notable,Whether impact of the environment static temperature difference of reaction kth day to axle temperature be notable,Represent the goodness of fit of kth day Value, k=2,3 ... ..., 30, k take natural number；

Step 5, nearest 30 days of the correspondence that obtained with step 4 it is smooth after performance parameterWithData be Basis, using mutation probe algorithm pairWithThe two performance parameters do the detection with the presence or absence of numerical value mutation；Instead Axle temperature rate of change has been answered to speed sensitivity,Represent the rate of heat dispation of the caused axletree by the temperature difference under static environment；If DetectOr/andNumerical value undergo mutation, then show that corresponding axletree performance has a mutation, and by the mutation for detecting Feed back to EMUs TCMS system and show；The processing procedure of above-mentioned mutation probe algorithm is as follows：

First, the performance parameter after smooth correspondenceIt is divided into two sections, the last period is the performance of first 27 days ParameterData, its average that counts is designated as μ₁, its standard deviation is designated as σ, and latter section is the performance parameter of nearest 3 days's Data, its average are designated as μ₂If, | μ₁-μ₂|>2 σ, then defining the average of nearest 3 days and comparing first 27 days has mutation, otherwise does not then have There is mutation；

Secondly, the performance parameter after smooth correspondenceIt is divided into two sections, the last period is the performance ginseng of first 27 days NumberData, its average is designated as μ₁, its standard deviation is designated as σ, and latter section is the performance parameter of nearest 3 daysData, its Average is designated as μ₂If, | μ₁-μ₂|>2 σ, then defining the average of nearest 3 days and comparing first 27 days has mutation, otherwise is not then mutated；

Step 6, nearest 30 days of the correspondence that obtained with step 4 it is smooth after performance parameterWithData be Basis, using trend probe algorithm pairWithThe two performance parameters do the detection with the presence or absence of Long-term change trend；Instead Axle temperature rate of change has been answered to speed sensitivity,Represent the rate of heat dispation of the caused axletree by the temperature difference under static environment；If DetectOrThe change of numerical value occurrence tendency, then show that corresponding axletree performance has a Long-term change trend, and will detect Long-term change trend feeds back to EMUs TCMS system and shows；The processing procedure of above-mentioned trend probe algorithm is as follows：

With time k as independent variable, with the nearest 30 days performance parameters after smoothWithSingle argument is carried out for dependent variable Linear fit, obtain the corresponding time parameter significance p values of time k and goodness of fit r²Value；If p<0.05 and r²> 0.5, then show the performance parameter of nearest 30 daysOrThere is a Long-term change trend, on the contrary then no Long-term change trend；Linear fit mistake Journey is as follows：

Order

DetectionTrend when, order

DetectionTrend when, order

By each expression formula of following linear fit：

β=(X^TX)^-1X^TY

RSS=(T-X β)^T(Y-Xβ)

Corresponding Y is calculated respectively for the goodness of fit r of time k=1 to 30², and time parameter significance p Value.

Beneficial effects of the present invention are as follows：

The method of the present invention is true by the summary to axletree temperature, three kinds of data mapping principles of road speed and ambient temperature A set of axletree performance evaluation and early warning mathematical model for including mutation probe algorithm and trend probe algorithm is found, its mutation is visited Method of determining and calculating can realize respectively to axle temperature rate of change to speed sensitivity and under static environment by the temperature difference caused car The qualitative judgement of the rate of heat dispation change of axle, so that more accurately and reliably judge axle with qualitatively method auxiliary repair personnel Whether warm alarm signal belongs to the short-term false alarm that voluntarily can recover, and then is that its maintenance and Maintenance Decision making provide important ginseng Examine foundation.The quantitative checking computation results of the trend probe algorithm of this method characterize the accumulative change institute of endogenous cause of ill under non-exopathogenic factor interference Gradual tendency change is caused, therefore, it is possible to realize doing the evolutionary change degree of axle temperature and its axle temperature detection related sensor Go out rational judgment, so as to auxiliary repair personnel are to more efficiently completing routine servicing and the maintenance of axletree and its related sensor Work, and more scrupulously complete part replacement plan or bearing temperature alarm investigation task.

The axletree performance carry out evaluate and early warning method its can as reflection axletree overall performance quantizating index, So as to solve whether the bearing temperature alarm signal caused because of factors such as the impact complex genesis of train axle temperature belongs to false alarm The old problem of quick judgement is difficult to, and causes any axle temperature pointed out potential risk but temporarily do not had obvious fault to characterize Warning phenomenon is subject to timely and effectively early warning, recording and tracking monitoring, and this causes this method in the short duration failure to axletree performance Investigation and the equal effect is significant of potential risk two aspects of early warning at a specified future date, can yet be regarded as a kind of outstanding axletree performance quantitatively evaluating side Method.

Additionally, the present invention train axle performance is evaluated based on mathematical model and early warning method also summarize car Axle performance variation law, intelligent early-warning risk and the raising aspect such as maintenance level and efficiency are respectively provided with stronger outstanding advantage, and Can the creation of value in terms of saving analysis time, cutting down axletree maintenance cost etc. in advance, in addition, the method can also be greatly lowered Skill requirement and technical ability threshold to maintainer, therefore there is extensive promotion and application prospect.

Specific embodiment

The present invention is described in further details with reference to embodiment.

The present invention train axle performance is evaluated based on mathematical model and the method for early warning comprises the steps：

Step one, to axletree run it is nearest 30 days in set up within the 1st day axle temperature change mathematical model before data screening

Step 1.1：The 1st day in axletree operation is nearest 30 days, gathers respectively according to the onboard sensor of three kinds of parameters Train exterior ambient temperature M_d(d represents the number of ambient temperature sampling time node, and d takes natural number), road speed V_j(j tables Show the number of road speed sampling time node, j takes natural number), the axle temperature T of axletree_i(i represents axle temperature sampling time node Number, i take natural number), generate train exterior ambient temperature M with regard to time t_dContinuous data curve, road speed V_jCompany Continuous data and curves, axle temperature T_iContinuous data curve, and be stored in the raw data base of EMUs TCMS system；

Step 1.2：Abnormal data of three kinds of parameters each on continuous data curve is screened out in step 1.1 respectively：

Reject the V on continuous data curve corresponding to road speed Vj_jThe data segment and V that 0,000 m/hour of ＜_j400 kms of ＞/ When data segment, obtain road speed V_jWith regard to the normal data curve of time t；

Reject train exterior ambient temperature M_dM on corresponding continuous data curve_dThe data segment and M of≤- 80 degree_d>=80 degree Data segment, obtain train exterior ambient temperature M_dWith regard to the normal data curve of time t；

Reject axle temperature T_iT on corresponding continuous data curve_iThe data segment of≤- 80 degree, obtains axle temperature T_iWith regard to time t's Normal data curve；

Step 1.3：In road speed V that step 1.2 is obtained_jWith regard to filter out on the normal data curve of time t according to It is multiple with regard to road speed V that time span is sorted from long to short_jSection continuous time, and retain these continuous times of Duan Suofen Not corresponding road speed V_jData segment on normal data curve；

Step 1.31：To road speed V_jWith regard on the normal data curve of time t any two consecutive number strong point when Between be spaced and screened, obtain multiple sections continuous time；

The method of above-mentioned screening is：If the time interval at two consecutive number strong points is less than or equal to 5 minutes, this two adjacent Data point is in same section continuous time；If the time interval at two consecutive number strong points is more than 5 minutes, this two consecutive numbers Strong point is respectively in former and later two different sections continuous time；

Step 1.32：Time span is picked out in multiple sections continuous time obtained from step 1.31 and is all higher than 1 hour Multiple sections continuous time；

Step 1.33：To road speed V in a data segment corresponding to each section in step 1.32 continuous time_jTake Arithmetic average, if road speed V in certain data segment_jArithmetic average be less than or equal to 15,000 ms/hour, then reject the number According to section continuous time corresponding to section；If road speed V in certain data segment_jArithmetic average be more than 15,000 ms/hour, then Retain section continuous time corresponding to the data segment；

Step 1.34：Order of the section according to time span from long to short continuous time retained in step 1.33 is arranged Sequence, and retain road speed V of each after sequence corresponding to section continuous time_jData segment on normal data curve；

Step 1.4：Step 1.34 filter out with regard to road speed V_jEach in section continuous time, to step 1.2 The axle temperature T of acquisition_iNormal data curve and train exterior ambient temperature M with regard to time t_dWith regard to the normal data curve of time t The screening of section continuous time is carried out respectively, finds most long public section continuous time；

Step 1.41：Step 1.34 filter out with regard to road speed V_jThe first long section continuous time in, using step Screening technique in rapid 1.31, to axle temperature T_iScreening acquisition is carried out with regard to axle temperature T with regard to the normal data curve of time t_iIt is multiple Continuous time section；

Step 1.42：Company of the time span more than 1 hour is picked out in multiple sections continuous time obtained from step 1.41 Continuous time period, and execution step 1.44；If there is no axle temperature T of the length more than 1 hour_iContinuous time, section, then rejected and step Corresponding road speed V of current first long section continuous time described in 1.34_jWith axle temperature T_iTotal data, then execution step 1.43；

Step 1.43：In the residue obtained in step 1.34 each of section, again according to time span from growing to continuous time Short order, in the first new long section continuous time, using the screening technique in step 1.31, to axle temperature T_iWith regard to time t Normal data curve carry out screening obtain with regard to axle temperature T_iMultiple sections continuous time, and from obtaining with regard to axle temperature T_iIt is many Continuous time section of the time span more than 1 hour, and execution step 1.44 is selected in individual section continuous time；If no length is more than Section continuous time of 1 hour, then reject corresponding road speed V of the first new long section continuous time aforementioned with this step_jWith Axle temperature T_iTotal data, then re-execute this step, until time span can be selected more than section continuous time of 1 hour Afterwards, execution step 1.44；If failing all the time to find satisfactory section continuous time, day data, execution step three are worked as in deletion；

Step 1.44, step 1.42 or step 1.43 filter out with regard to axle temperature T_iContinuous time in section, using step Screening technique in rapid 1.31, to train exterior ambient temperature M_dWith regard to time t normal data curve carry out screening closed In train exterior ambient temperature M_dMultiple sections continuous time；

Step 1.45：From step 1.44 obtain with regard to train exterior ambient temperature M_dMultiple sections continuous time in select Go out continuous time section of the time span more than 1 hour, execution step 1.46；If there is no continuous time section of the length more than 1 hour, Road speed V corresponding with this of section is rejected continuous time then_j, axle temperature T_iWith train exterior ambient temperature M_dTotal data, so Execution step 1.43, find out again with regard to axle temperature T afterwards_iTime span more than section continuous time of 1 hour, then execution step 1.44 and this step, until finding out with regard to train exterior ambient temperature M_dTime span more than continuous time of 1 hour Duan Hou, execution step 1.46；

Step 1.46：In continuous time of the time span that step 1.45 finds more than 1 hour in section, will be three parameters same When there is most long section common time of data as most long public section continuous time；

Step 1.5：The data segment of three parameters corresponding to most long public section continuous time that step 1.46 is obtained is folded It is added under coordinate system at the same time, and supplies the value lacked in each supplemental characteristic section using linear interpolation respectively so that most Each time in public section continuous time of length can three parameters of correspondence data, then, preserve with this most it is long it is public continuously Road speed V corresponding to time period_jStable data and curves, axle temperature T_iStable data and curves and train exterior environment temperature Degree M_dStable data and curves；

Step 2, to axletree run it is nearest 30 days in set up within the 1st day axle temperature change mathematical model

Step 2.1：According to the radiating equation in physicss, and after considering speed to the impact of axle temperature, set up the axle of axletree Warm rate of change function, i.e. axle temperature change mathematical model is as follows：

In formula (1),Original value of the axle temperature rate of change of the 1st day to speed sensitivity in representing nearest 30 days, In representing nearest 30 days under the static environment of the 1st day by the temperature difference caused axletree rate of heat dispation original value, T_i(i represents axle The number of warm sampling time node, i take natural number) be axletree correspondence current time axle temperature,；V_j(j represents that road speed is sampled The number of timing node, j take natural number) represent the road speed for corresponding to current time；M_d(d represents the ambient temperature sampling time The number of node, d take natural number) represent the train exterior ambient temperature for corresponding to current time；

Step 2.2：SolveWithValue：

Step 2.21：Formula (1) is integrated, is then had

In formula (2),Original value of the axle temperature rate of change of the 1st day to speed sensitivity in representing nearest 30 days, In representing nearest 30 days under the static environment of the 1st day by the temperature difference caused axletree rate of heat dispation original value, T_iRepresent axletree The axle temperature at correspondence current time, V_jRepresent the road speed at correspondence current time；M_dRepresent the train exterior ring at correspondence current time Border temperature；Q represents axletree in t_nThe axle temperature of time, Q₁Represent axletree in t₁The axle temperature of time；Q-Q₁Represent in t₁To t_nTime The temperature approach of axletree temperature change in section；

Step 2.22：By the data obtained by step 2.21 integrationWithTo Q-Q₁ Linear fit is carried out, can be tried to achieveWithValue, process is as follows：

Make the matrix that X is n row three row, n is the number of data time point t, the expression form of matrix X is as follows：

Wherein, t₁To t_nFor time t in most long public section continuous time that step 1.46 is obtained all possible value；

The matrix that Y is a n row string is made, the column data is Q-Q₁；

Wherein, Q_iRespectively Q is in t_iThe value at moment, the number of i=1,2,3 ... n, n for data time point t；

Calculation expression β=(X^TX)^-1X^TY, wherein, β represents the needed fitting parameter for solving, X^TIt is the transposition square of X Battle array, subscript -1 are matrix inversion, and expression formula β is finally calculated the matrix of three row string, and the second row of matrix isValue, the third line of matrix isValue, will be calculatedValue andValue correspondence natural law be stored in it is dynamic In the raw data base of car group TCMS system；

Step 2.23：By the data obtained by step 2.21 integrationWithTo Q-Q₁ Linear fit is carried out, the sensitivity of the axle temperature rate of change of the 1st day to speed is tried to achieveBy the temperature difference under value and static environment And the rate of heat dispation of caused axletreeThe p of model is calculated while value₁Value andValue, p₁Value has reacted the V of the 1st day_j (T_i-M_d) impact to axle temperature whether significantly, p₁Value includesP corresponding to₁Value andP corresponding to₁Value,P corresponding to₁Value is designated asP corresponding to₁Value is designated asIfRepresent current Road speed V at moment_jImpact for f (s) be it is significant, ifRepresent the environment static temperature difference (T_i-M_d) right In the impact of f (s) be significant；The goodness of fit of the 1st dayValueRepresent the excellent of the whole models fitting of assessment Bad degree；Value,Value andThe calculating process of value is as follows：

First, make RSS=(Y-X β)^T(Y-Xβ)……(3)

By the value of X, Y, β and the n obtained in step 2.22, the pr tried to achieve to formula (5) by formula (3)_βFor three rows one The matrix of row, the first row of matrix is 1, and the second row isThe third line isWherein, RSS represents the residuals squares of fitting With var_βRepresent the error of fitting parameter, pr_βThe statistical indicator of the whether notable non-zero of fitting parameter is represented, if pr_β<0.05 Regard notable non-zero as, show correspondence parameter be it is influential, otherwise without impact；Function p is represented and for the t values in t-distribution to be converted into p The function of value, the function are calculated by the standard t-distribution table looked into statistically；

Make again

In formula, SYY is the variance of Y, weighs the fluctuating margin of data Y,For the meansigma methodss of Y, obtained by step 2.22 Y value and formula (3) in the value of RSS that obtains, then can be in the hope of by formula (6) and formula (7)Value, will be calculated 'sValue,Value andValue correspondence natural law be stored in the raw data base of EMUs TCMS system；

Step 3：The train exterior ambient temperature that gathered respectively for 29 days in the residue of nearest 30 days with onboard sensor, Road speed, axle temperature are initial data, with every day as a time range, according to the mode of step one and step 2 to each It sets up an axle temperature change mathematical model, and corresponding each axle temperature change mathematical model is calculated oneValue, OneValue, oneValue, oneIt is worth and oneValue, and will be above-mentioned calculated numerical value corresponding with natural law It is stored in the raw data base of EMUs TCMS system, wherein,The axle temperature rate of change pair of kth day in representing nearest 30 days The original value of speed sensitivity,In representing nearest 30 days under the static environment of kth day by the temperature difference caused axletree Rate of heat dispation original value,Whether impact of the road speed of reaction kth day to axle temperature be notable,The ring of reaction kth day Whether impact of the border static state temperature difference to axle temperature be notable,The fit value of expression kth day, k=2,3 ... ..., 30, k take from so Number；

Step 4：Performance parameter in the multiple axle temperature change mathematical models set up to step 2 and step 3WithAdaptive smooth process is carried out, the performance parameter after being smoothed is corresponded toWithAnd the performance parameter after smoothingWithCorresponding with natural law to be stored in the raw data base of EMUs TCMS system, adaptive smooth process is as follows：

Define binary function f (p, a r²) cause p ＞ 0.05 when, binary function value be 0, p≤0.05 when, binary function It is worth for r²；By the smooth original performance parameter of following recurrence formulas：

Wherein,Original value of the axle temperature rate of change of the 1st day to speed sensitivity in representing nearest 30 days,Table In showing nearest 30 days under the static environment of the 1st day by the temperature difference caused axletree rate of heat dispation original value,Represent nearest Original value of the axle temperature rate of change of kth day to speed sensitivity in 30 days,The static ring of kth day in representing nearest 30 days Under border by the temperature difference caused axletree rate of heat dispation original value,Reacting impact of the road speed of kth day to axle temperature is It is no notable,Whether impact of the environment static temperature difference of reaction kth day to axle temperature be notable,Represent the goodness of fit of kth day Value, k=2,3 ... ..., 30, k take natural number；

Step 5, nearest 30 days of the correspondence that obtained with step 4 it is smooth after performance parameterWithData be Basis, using mutation probe algorithm pairWithThe two performance parameters do the detection with the presence or absence of numerical value mutation；Instead Axle temperature rate of change has been answered to speed sensitivity,Represent the rate of heat dispation of the caused axletree by the temperature difference under static environment；If DetectOr/andNumerical value undergo mutation, then show that corresponding axletree performance has a mutation, and by the mutation for detecting Feed back to EMUs TCMS system and show；The processing procedure of above-mentioned mutation probe algorithm is as follows：

First, the performance parameter after smooth correspondenceIt is divided into two sections, the last period is the performance of first 27 days ParameterData, its average that counts is designated as μ₁, its standard deviation is designated as σ, and latter section is the performance parameter of nearest 3 days's Data, its average are designated as μ₂If, | μ₁-μ₂|>2 σ, then defining the average of nearest 3 days and comparing first 27 days has mutation, otherwise does not then have There is mutation；

Secondly, the performance parameter after smooth correspondenceIt is divided into two sections, the last period is the performance ginseng of first 27 days NumberData, its average is designated as μ₁, its standard deviation is designated as σ, and latter section is the performance parameter of nearest 3 daysData, its Average is designated as μ₂If, | μ₁-μ₂|>2 σ, then defining the average of nearest 3 days and comparing first 27 days has mutation, otherwise is not then mutated；

Step 6, nearest 30 days of the correspondence that obtained with step 4 it is smooth after performance parameterWithData be Basis, using trend probe algorithm pairWithThe two performance parameters do the detection with the presence or absence of Long-term change trend；Instead Axle temperature rate of change has been answered to speed sensitivity,Represent the rate of heat dispation of the caused axletree by the temperature difference under static environment； If detectingOrNumerical value occurrence tendency change, then show that corresponding axletree performance has Long-term change trend, and will detect Long-term change trend feed back to EMUs TCMS system and show；The processing procedure of above-mentioned trend probe algorithm is as follows：

With time k as independent variable, with the nearest 30 days performance parameters after smoothWithSingle argument is carried out for dependent variable Linear fit, obtain the corresponding time parameter significance p values of time k and goodness of fit r²Value；If p<0.05 and r²> 0.5, then show the performance parameter of nearest 30 daysOrThere is a Long-term change trend, on the contrary then no Long-term change trend；Linear fit mistake Journey is as follows：

Order

DetectionTrend when, order

DetectionTrend when, order

By each expression formula of following linear fit：

β=(X^TX)^-1X^TY

RSS=(Y-X β)^T(Y-Xβ)

Corresponding Y is calculated respectively for the goodness of fit r of time k=1 to 30², and time parameter significance p Value.

Concrete application the present invention train axle performance is evaluated based on mathematical model and early warning method when, to row Each axletree of car respectively sets up a set of exclusive independent performance evaluation and Early-warning Model using the method, and by they Data are collected into TCMS system display, are preserved and standby by the vehicle netbios of EMU.

It is during train day-to-day operation, corresponding to each axletree isolated operation daily to evaluate and early warning mathematical model, with Mutation probe algorithm and the trend probe algorithm data of same day renewal are tried to achieve, and these results are preserved again, finally to each Individual independent axletree adds up to generate axletree performance evaluation and the early warning that a whole set of can be used for qualitative and quantitative assessment its axletree performance Mathematical model.

When Train Stopping is overhauled, maintainer can arbitrarily transfer some axletree according to the actual requirements from TCMS system Mathematical model historical data, and be mutated the result of probe algorithm and trend probe algorithm to which and be analyzed.

By be mutated the axletree performance that found of probe algorithm be mutated index show the axletree performance of nearest 3 days compared to 27 days before this axletree performance averages there occurs the great change of obvious exception, should be considered non-exopathogenic factor interference, and in a short time Caused by expendable endogenous cause of ill, it is necessary to cause enough vigilance and attention, and maintainer must be to car that mutation situation occur Axle carries out comprehensively malfunction elimination and test.

Therefore, it is mutated warning algorithm to be realized to axle temperature rate of change respectively to speed sensitivityAnd to static state Under environment by the temperature difference caused axletree rate of heat dispationQualitative judgement, so as to auxiliary repair personnel are more accurate and can Judge whether bearing temperature alarm signal belongs to the short-term false alarm that voluntarily can recover or can temporarily ignore what is do not processed by ground False alarm, and then be that its maintenance and Maintenance Decision making provide important reference frame.

The axletree performance trend found by trend probe algorithm shows the axletree performance of nearest 3 days compared to before this 27 days axletree performance averages there occurs that obvious the accumulative of exception sexually revises, and which should be considered the endogenous cause of ill change institute under non-exopathogenic factor interference Gradual tendency change is caused, the tendency change reflects that the shaft temperature sensor or environmental sensor of train occur in that detection The temperature drift of signal or velocity sensor occur in that the wear and aging situation of the passivation of sensitivity or axletree itself recent Acceleration is occurred in that inside.

Therefore trending early warning algorithm can be realized detecting axle temperature and its axle temperature the evolutionary change degree of related sensor Rational judgment is made, so as to auxiliary repair personnel are to more efficiently completing routine servicing and the dimension of axletree and its related sensor Work is repaiied, and more scrupulously completes part replacement plan or bearing temperature alarm investigation task.

Claims (1)

1. train axle performance is evaluated based on mathematical model and early warning method, it is characterised in that the method include as Lower step：

Step one, to axletree run it is nearest 30 days in set up within the 1st day axle temperature change mathematical model before data screening

Step 1.1：The 1st day in axletree operation is nearest 30 days, according to the row that the onboard sensor of three kinds of parameters is gathered respectively Car ambient temperature M_d(d represents the number of ambient temperature sampling time node, and d takes natural number), road speed V_j(j represents capable The number of vehicle speed sampling time node, j take natural number), the axle temperature T of axletree_i(i represents the number of axle temperature sampling time node, I takes natural number), generate train exterior ambient temperature M with regard to time t_dContinuous data curve, road speed V_jConsecutive numbers According to curve, axle temperature T_iContinuous data curve, and be stored in the raw data base of EMUs TCMS system；

Step 1.2：Abnormal data of three kinds of parameters each on continuous data curve is screened out in step 1.1 respectively：

Reject road speed V_jV on corresponding continuous data curve_jThe data segment and V that 0,000 m/hour of ＜_j400,000 ms/hour of ＞'s Data segment, obtains road speed V_jWith regard to the normal data curve of time t；

Reject train exterior ambient temperature M_dM on corresponding continuous data curve_dThe data segment and M of≤- 80 degree_d>=80 degree of number According to section, train exterior ambient temperature M is obtained_dWith regard to the normal data curve of time t；

Reject axle temperature T_iT on corresponding continuous data curve_iThe data segment of≤- 80 degree, obtains axle temperature T_iWith regard to the normal of time t Data and curves；

Step 1.3：In road speed V that step 1.2 is obtained_jIt is long according to the time with regard to filtering out on the normal data curve of time t It is multiple with regard to road speed V that degree is sorted from long to short_jSection continuous time, and retain these of section continuous times and correspond to respectively Road speed V_jData segment on normal data curve；

Step 1.31：To road speed V_jWith regard to the time interval at any two consecutive number strong point on the normal data curve of time t Screened, obtained multiple sections continuous time；

The method of above-mentioned screening is：If the time interval at two consecutive number strong points is less than or equal to 5 minutes, this two adjacent datas Point is in same section continuous time；If the time interval at two consecutive number strong points is more than 5 minutes, this two consecutive number strong points Respectively in former and later two different sections continuous time；

Step 1.32：Time span is picked out in multiple sections continuous time obtained from step 1.31 is all higher than 1 hour multiple Continuous time section；

Step 1.33：To road speed V in a data segment corresponding to each section in step 1.32 continuous time_jTake and count Meansigma methodss, if road speed V in certain data segment_jArithmetic average be less than or equal to 15,000 ms/hour, then reject the data segment Corresponding section continuous time；If road speed V in certain data segment_jArithmetic average be more than 15,000 ms/hour, then retain Section continuous time corresponding to the data segment；

Step 1.34：Order of the section according to time span from long to short continuous time retained in step 1.33 is ranked up, And retain road speed V of each after sequence corresponding to section continuous time_jData segment on normal data curve；

Step 1.4：Step 1.34 filter out with regard to road speed V_jEach in section continuous time, step 1.2 is obtained Axle temperature T_iNormal data curve and train exterior ambient temperature M with regard to time t_dEnter with regard to the normal data curve of time t respectively The screening of row section continuous time, finds most long public section continuous time；

Step 1.41：Step 1.34 filter out with regard to road speed V_jThe first long section continuous time in, using step 1.31 In screening technique, to axle temperature T_iScreening acquisition is carried out with regard to axle temperature T with regard to the normal data curve of time t_iMultiple consecutive hourss Between section；

Step 1.42：Consecutive hours of the time span more than 1 hour is picked out in multiple sections continuous time obtained from step 1.41 Between section, and execution step 1.44；If there is no axle temperature T of the length more than 1 hour_iContinuous time, section, then rejected and step 1.34 institute State corresponding road speed V of the current first long section continuous time_jWith axle temperature T_iTotal data, then execution step 1.43；

Step 1.43：In the residue obtained in step 1.34 each of section, again according to time span from long to short continuous time Sequentially, in the first new long section continuous time, using the screening technique in step 1.31, to axle temperature T_iWith regard to time t just Regular data curve carries out screening and obtains with regard to axle temperature T_iMultiple sections continuous time, and from obtaining with regard to axle temperature T_iMultiple companies Continuous time section of the time span more than 1 hour, and execution step 1.44 is selected in the continuous time period；If no length is little more than 1 When section continuous time, then reject corresponding road speed V of the first long section continuous time newly aforementioned with this step_jAnd axle temperature T_iTotal data, then re-execute this step, until continuous time of the time span more than 1 hour can be selected after section, Execution step 1.44；If failing all the time to find satisfactory section continuous time, day data, execution step three are worked as in deletion；

Step 1.44, step 1.42 or step 1.43 filter out with regard to axle temperature T_iContinuous time in section, using step 1.31 In screening technique, to train exterior ambient temperature M_dScreening acquisition is carried out with regard to train with regard to the normal data curve of time t Ambient temperature M_dMultiple sections continuous time；

Step 1.45：From step 1.44 obtain with regard to train exterior ambient temperature M_dMultiple sections continuous time in when picking out Between length more than section continuous time of 1 hour, execution step 1.46；If there is no continuous time section of the length more than 1 hour, pick Except road speed V corresponding with this of section continuous time_j, axle temperature T_iWith train exterior ambient temperature M_dTotal data, then hold Row step 1.43, is found out again with regard to axle temperature T_iTime span more than section continuous time of 1 hour, then 1.44 He of execution step This step, until finding out with regard to train exterior ambient temperature M_dContinuous time of the time span more than 1 hour after section, hold Row step 1.46；

Step 1.46：, three parameters are deposited simultaneously in section in continuous time of the time span that step 1.45 finds more than 1 hour Data most long section common time as most long public section continuous time；

Step 1.5：The data segment of three parameters corresponding to most long public section continuous time that step 1.46 is obtained is added to At the same time under coordinate system, and supply the value lacked in each supplemental characteristic section using linear interpolation respectively so that in most long public affairs Each time in the co-continuous time period can correspond to the data of three parameters, then, preserve and the most long public continuous time Road speed V corresponding to section_jStable data and curves, axle temperature T_iStable data and curves and train exterior ambient temperature M_d Stable data and curves；

Step 2, to axletree run it is nearest 30 days in set up within the 1st day axle temperature change mathematical model

Step 2.1：According to the radiating equation in physicss, and after considering speed to the impact of axle temperature, the axle temperature for setting up axletree becomes Rate function, i.e. axle temperature change mathematical model is as follows：

$f\left(s\right)=\frac{aT}{dt}=c_{V_1}\&times;V_j+c_{T_1}\&times;(T_i-M_d)\mathrm{......}\left(1\right)$

In formula (1),Original value of the axle temperature rate of change of the 1st day to speed sensitivity in representing nearest 30 days,Represent In nearest 30 days under the static environment of the 1st day by the temperature difference caused axletree rate of heat dispation original value, T_i(i represents that axle temperature is adopted The number of sample timing node, i take natural number) be axletree correspondence current time axle temperature,；V_j(j represents the road speed sampling time The number of node, j take natural number) represent the road speed for corresponding to current time；M_d(d represents ambient temperature sampling time node Number, d takes natural number) represent the train exterior ambient temperature at correspondence current time；

Step 2.2：SolveWithValue：

Step 2.21：Formula (1) is integrated, is then had

${\&Integral;}_{t_1}^{t_n}f\left(s\right)=Q-Q_1=c_{V_1}{\&Integral;}_{t_1}^{t_n}{V}_{1}dt+c_{T_1}{\&Integral;}_{t_1}^{t_n}(T_i-M_d)dt\mathrm{......}\left(2\right)$

In formula (2),Original value of the axle temperature rate of change of the 1st day to speed sensitivity in representing nearest 30 days,Represent In nearest 30 days under the static environment of the 1st day by the temperature difference caused axletree rate of heat dispation original value, T_iRepresent axletree correspondence The axle temperature at current time, V_jRepresent the road speed at correspondence current time；M_dRepresent the train exterior environment temperature at correspondence current time Degree；Q represents axletree in t_nThe axle temperature of time, Q₁Represent axletree in t₁The axle temperature of time；Q-Q₁Represent in t₁To t_nTime period in The temperature approach of axletree temperature change；

Step 2.22：By the data obtained by step 2.21 integrationWithTo Q-Q₁Carry out Linear fit, can try to achieveWithValue, process is as follows：

Make the matrix that X is n row three row, n is the number of data time point t, the expression form of matrix X is as follows：

$X=\left(\begin{array}{ccc}1& {\&Integral;}_{t_1}^{t_1}{V}_{j}dt& {\&Integral;}_{t_1}^{t_1}(T_i-M_d)dt\\ 1& {\&Integral;}_{t_1}^{t_2}{V}_{j}dt& {\&Integral;}_{t_1}^{t_2}(T_i-M_d)dt\\ .& .& .\\ .& .& .\\ .& .& .\\ 1& {\&Integral;}_{t_1}^{t_n}{V}_{j}dt& {\&Integral;}_{t_1}^{t_n}(T_i-M_d)dt\end{array}\right)$

Wherein, t₁To t_nFor time t in most long public section continuous time that step 1.46 is obtained all possible value；

The matrix that Y is a n row string is made, the column data is Q-Q₁；

$Y=\left(\begin{array}{c}{Q}_1-Q_1\\ Q_2-Q_1\\ .\\ .\\ .\\ Q_n-Q_1\end{array}\right)$

Wherein, Q_iRespectively Q is in t_iThe value at moment, the number of i=1,2,3 ... n, n for data time point t；

Calculation expression β=(X^TX)^-1X^TY, wherein, β represents the needed fitting parameter for solving, X^TIt is the transposed matrix of X, on - 1 is marked for matrix inversion, expression formula β is finally calculated the matrix of three row string, and the second row of matrix is's It is worth, the third line of matrix isValue, will be calculatedValue andValue correspondence natural law be stored in EMUs In the raw data base of TCMS system；

Step 2.23：By the data obtained by step 2.21 integrationWithTo Q-Q₁Carry out Linear fit, tries to achieve the sensitivity of the axle temperature rate of change of the 1st day to speedLed by the temperature difference under value and static environment The rate of heat dispation of the axletree of causeThe p of model is calculated while value₁Value andValue, p₁Value has reacted the V of the 1st day_jWith (T_i-M_d) impact to axle temperature whether significantly, p₁Value includesP corresponding to₁Value andP corresponding to₁Value, P corresponding to₁Value is designated as P corresponding to₁Value is designated asIfRepresent current time Road speed V_jImpact for f (s) be it is significant, ifRepresent the environment static temperature difference (T_i-M_d) for f (s) Impact be significant；The goodness of fit of the 1st dayValueRepresent the good and bad degree of the whole models fitting of assessment；Value,Value andThe calculating process of value is as follows：

First, make RSS=(Y-X β)^T(Y-Xβ)……(3)

${\mathrm{var}}_{\mathrm{\&beta;}}=\frac{RSS}{n-3}{\left(X^{T}X\right)}^{-1}\mathrm{......}\left(4\right)$

${\mathrm{pr}}_{\mathrm{\&beta;}}=p\left(\frac{\mathrm{\&beta;}}{\sqrt{{\mathrm{var}}_{\mathrm{\&beta;}}}}\right)\mathrm{......}\left(5\right)$

By the value of X, Y, β and the n obtained in step 2.22, the pr tried to achieve to formula (5) by formula (3)_βFor the square of three row string Battle array, the first row of matrix is 1, and the second row isThe third line isWherein, RSS represents the residual sum of squares (RSS) of fitting, var_β Represent the error of fitting parameter, pr_βThe statistical indicator of the whether notable non-zero of fitting parameter is represented, if pr_β<0.05 regard as it is aobvious Write non-zero, show correspondence parameter be it is influential, otherwise without impact；Function p represents the letter that the t values in t-distribution are converted into p value Number, the function are calculated by the standard t-distribution table looked into statistically；

Make again

In formula, SYY is the variance of Y, weighs the fluctuating margin of data Y,For the meansigma methodss of Y, by the Y value obtained in step 2.22 With the value of the RSS obtained in formula (3), then can be in the hope of by formula (6) and formula (7)Value, will be calculatedValue,Value andValue correspondence natural law be stored in the raw data base of EMUs TCMS system；

Step 3：The train exterior ambient temperature that gathered respectively for 29 days in the residue of nearest 30 days with onboard sensor, driving Speed, axle temperature are initial data, with every day as a time range, are built to every day according to the mode of step one and step 2 A vertical axle temperature changes mathematical model, and corresponding each axle temperature change mathematical model is calculated oneValue, oneValue, oneValue, oneIt is worth and oneValue, and by preservation above-mentioned calculated numerical value corresponding with natural law In the raw data base of EMUs TCMS system, wherein,In representing nearest 30 days, the axle temperature rate of change of kth day is to speed The original value of sensitivity,In representing nearest 30 days under the static environment of kth day by the temperature difference caused axletree radiating Speed original value,Whether impact of the road speed of reaction kth day to axle temperature be notable,The environment of reaction kth day is quiet Whether impact of the state temperature difference to axle temperature be notable,The fit value of expression kth day, k=2,3 ... ..., 30, k take natural number；

Step 4：Performance parameter in the multiple axle temperature change mathematical models set up to step 2 and step 3WithEnter The process of row adaptive smooth, corresponds to the performance parameter after being smoothedWithAnd the performance parameter after smoothingWithCorresponding with natural law to be stored in the raw data base of EMUs TCMS system, adaptive smooth process is as follows：

Define binary function f (p, a r²) cause p ＞ 0.05 when, binary function value be 0, p≤0.05 when, binary function value is r²；By the smooth original performance parameter of following recurrence formulas：

$S_{V_1}=C_{V_1}$

$S_{T_1}=C_{T_1}$

$s_{V_k}=(1-f(p_{V_k},r_k^2\left)\right)*s_{V_{k-1}}+f(p_{V_k},r_k^2)*c_{V_k}$

$s_{T_k}=(1-f(p_{T_k},r_k^2\left)\right)*s_{T_{k-1}}+f(p_{T_k},r_k^2)*c_{T_k}$

Wherein,Original value of the axle temperature rate of change of the 1st day to speed sensitivity in representing nearest 30 days,Represent most In nearly 30 days under the static environment of the 1st day by the temperature difference caused axletree rate of heat dispation original value,Represent nearest 30 days Original value of the axle temperature rate of change of middle kth day to speed sensitivity,In representing nearest 30 days under the static environment of kth day The rate of heat dispation original value of caused axletree by the temperature difference,Whether impact of the road speed of reaction kth day to axle temperature shows Write,Whether impact of the environment static temperature difference of reaction kth day to axle temperature be notable,Represent the fit value of kth day, k =2,3 ... ..., 30, k take natural number；

Step 5, nearest 30 days of the correspondence that obtained with step 4 it is smooth after performance parameterWithData based on, Using mutation probe algorithm pairWithThe two performance parameters do the detection with the presence or absence of numerical value mutation；React Axle temperature rate of change to speed sensitivity,Represent the rate of heat dispation of the caused axletree by the temperature difference under static environment；If detection ArriveOr/andNumerical value undergo mutation, then show that corresponding axletree performance has a mutation, and the mutation for detecting fed back To EMUs TCMS system and show；The processing procedure of above-mentioned mutation probe algorithm is as follows：

First, the performance parameter after smooth correspondenceIt is divided into two sections, the last period is the performance parameter of first 27 daysData, its average that counts is designated as μ₁, its standard deviation is designated as σ, and latter section is the performance parameter of nearest 3 daysData, Its average is designated as μ₂If, | μ₁-μ₂|>2 σ, then defining the average of nearest 3 days and comparing first 27 days has mutation, otherwise does not then dash forward Become；

Secondly, the performance parameter after smooth correspondenceIt is divided into two sections, the last period is the performance parameter of first 27 daysData, its average is designated as μ₁, its standard deviation is designated as σ, and latter section is the performance parameter of nearest 3 daysData, which is equal Value is designated as μ₂If, | μ₁-μ₂|>2 σ, then defining the average of nearest 3 days and comparing first 27 days has mutation, otherwise is not then mutated；

Step 6, nearest 30 days of the correspondence that obtained with step 4 it is smooth after performance parameterWithData based on, Using trend probe algorithm pairWithThe two performance parameters do the detection with the presence or absence of Long-term change trend；React Axle temperature rate of change to speed sensitivity,Represent the rate of heat dispation of the caused axletree by the temperature difference under static environment；If visiting MeasureOrThe change of numerical value occurrence tendency, then show that corresponding axletree performance has a Long-term change trend, and by becoming for detecting Gesture change feeds back to EMUs TCMS system and shows；The processing procedure of above-mentioned trend probe algorithm is as follows：

With time k as independent variable, with the nearest 30 days performance parameters after smoothWithUnivariate line is carried out for dependent variable Property fitting, obtain the corresponding time parameter significance p values of time k and goodness of fit r²Value；If p<0.05 and r²>0.5, then Show the performance parameter of nearest 30 daysOrThere is a Long-term change trend, on the contrary then no Long-term change trend；Linear fitting procedure is such as Under：

Order

DetectionTrend when, order

DetectionTrend when, order

By each expression formula of following linear fit：

β=(X^TX)^-1X^TY

RSS=(Y-X β)^T(Y-Xβ)

$\mathrm{var}=\frac{RSS}{28}{\left(X^{T}X\right)}^{-1}$

$p=p\left(\frac{\mathrm{\&beta;}}{\sqrt{var}}\right)$

$SYY={(Y-\stackrel{\&OverBar;}{Y})}^T(Y-\stackrel{\&OverBar;}{Y})$

$r^2=\frac{SYY-RSS}{SYY}$

Corresponding Y is calculated respectively for the goodness of fit r of time k=1 to 30², and time parameter significance p value.