CN108229045B - High-speed pantograph key parameter identification method based on sensitivity analysis - Google Patents

High-speed pantograph key parameter identification method based on sensitivity analysis Download PDF

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CN108229045B
CN108229045B CN201810039385.0A CN201810039385A CN108229045B CN 108229045 B CN108229045 B CN 108229045B CN 201810039385 A CN201810039385 A CN 201810039385A CN 108229045 B CN108229045 B CN 108229045B
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pantograph
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speed pantograph
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bow
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张静
段甫川
程肥肥
刘志刚
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Southwest Jiaotong University
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Abstract

The invention discloses a high-speed pantograph key parameter identification method based on sensitivity analysis, which adopts a Sobol' global sensitivity analysis method to deduce and calculate a first-order sensitivity value, a second-order sensitivity value and a total sensitivity value of a high-speed pantograph structure parameter to a pantograph head motion track, and analyzes the influence of different high-speed pantograph structure parameters on the dynamic lifting displacement of a high-speed pantograph, thereby determining a key structure parameter influencing the current collection quality of a high-speed pantograph network; and further determining which design parameter is most effective to adjust, and reasonably selecting the design parameter. Compared with the traditional high-speed pantograph optimal design method, the method can greatly simplify the optimal design process so as to improve the sliding contact characteristic of the high-speed pantograph net to the maximum extent.

Description

High-speed pantograph key parameter identification method based on sensitivity analysis
Technical Field
The invention relates to the technical field of high-speed pantograph parameter identification, in particular to a sensitivity analysis-based high-speed pantograph key parameter identification method.
Background
The pantograph-catenary relationship of the high-speed railway is one of important factors influencing safe and reliable operation of the railway, and parameter optimization design of a contact network and a high-speed pantograph is always the key point of research on the pantograph-catenary relationship. In order to improve the current collection quality of the high-speed pantograph-catenary, part of documents propose optimization schemes of design parameters of the catenary, such as Song ocean and the like, and propose a method for establishing a three-dimensional model of the catenary, and nonlinear solution is carried out under the condition of considering windage yaw. However, most of the solutions require the reconstruction of the contact system, which requires high cost. Compared with a parameter optimization scheme of a contact network, the parameter design optimization scheme of the high-speed pantograph is more convenient to implement, and therefore the high-speed pantograph parameter design optimization scheme has higher feasibility and practical significance. For example, a multi-quality model is adopted in terms of Zhongning, single parameter change is researched, and the influence of high-speed pantograph structure parameters on pantograph-catenary contact force is analyzed; and the horseshoe and the like establish a high-speed pantograph-catenary coupling simulation model by adopting multi-body system dynamics software Simpack, and the influence of the high-speed pantograph-catenary coupling simulation model on the dynamic characteristics of the pantograph is researched by utilizing high-speed pantograph mass block model parameters. However, in existing high-speed pantograph parameter optimization schemes, the influence degree of different design parameters of the high-speed pantograph on the pantograph-catenary sliding contact characteristics is not considered in analysis. In the parameter optimization design process, the overall parameters of the high-speed pantograph are optimized and designed, so that the current collection quality of a high-speed pantograph-catenary system can be improved to a certain extent, but the optimization target of the scheme is too general, the cost is increased easily in the implementation process, and the optimization degree of the performance of the high-speed pantograph cannot reach the optimum.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a pantograph control device that can improve the precision of movement of a high-speed pantograph; and meanwhile, the influence of each parameter and the mutual influence among the parameters are considered, so that the accuracy and the reliability of the optimization design of the high-speed pantograph structure are better, and the sensitivity analysis-based high-speed pantograph key parameter identification research method is provided. The technical scheme is as follows:
a high-speed pantograph key parameter identification method based on sensitivity analysis is characterized by comprising the following steps:
step 1: random errors of the high-speed pantograph kinematic pair gaps are counted, a pantograph head motion nonlinear model of the high-speed pantograph is established, and a pantograph head motion trajectory equation is deduced according to a frame model of the high-speed pantograph;
step 2: simulating a design variable random sample of the high-speed pantograph by adopting a Latin hypercube sampling method;
and step 3: adopting a Sobol' global sensitivity analysis method to deduce and calculate a first-order sensitivity value, a second-order sensitivity value and a total sensitivity value of the high-speed pantograph design variable to the movement locus of the pantograph head;
and 4, step 4: deducing a high-speed pantograph reduction mass model, and calculating the frame mass and the frame damping under the influence of different design variables;
and 5: substituting the deduced frame quality and frame damping of the high-speed pantograph into a simulation model, analyzing the contact pressure change of the high-speed pantograph-catenary under the influence of different design variables, and verifying the sensitivity analysis result of the key design variables of the high-speed pantograph.
Further, an included angle β between the bow balancing rod and the horizontal direction in the bow motion nonlinear model of the high-speed pantograph is as follows:
Figure BDA0001549031370000021
wherein (E)x，Ey)、(Hx，Hy) Respectively are x and y coordinate components of a bow balancing rod;
the motion track of the bow head is as follows:
Figure BDA0001549031370000022
wherein E isx(i) Is the x-coordinate component of discrete points of the trajectory curve of the E point of the bow head, Ey(i) Is a Y coordinate component of discrete points of a track curve of a bow E point, beta (i) is an included angle between the ith position of the bow balance arm and the horizontal direction, and n is the total number of the discrete points; x is the number of1,x2,...,x11Representing design variables, x, of high-speed pantographs1Is the length l of the lower arm ACAC；x2Length l of CD section for upper arm rodCD；x3Is the length l of the push rod BG sectionBG；x4For the length l of the push rod BD segmentBD；x5Length l of upper arm rod DE sectionDE；x6For the upper frame controlling the length l of the rod GHGH；x7For the length l of the bow balancing rod EHEH；x8Is composed of two fixed hinged supports A and BDistance of point center lAB；x9Is the included angle between the CD rod and the DE rod of the upper frame; x is the number of10Is an included angle, x, between a BG rod and a BD rod on the push rod11Is the angle between the central line of A and B and the x-axis.
Furthermore, the method for simulating the random sample of the design variables of the high-speed pantograph comprises the following steps: the simulation times are N, the uniform distribution functions of all design variables are divided into N non-overlapping subintervals, independent equal probability sampling is carried out in each subinterval, only one random number is generated in each subinterval, then an inverse transformation method is adopted, N random variable sampling values are obtained from the random numbers generated in the N subintervals, and the serial numbers of the intervals to which the sampling values of all the random variables belong are randomly arranged.
Furthermore, the method for calculating the first-order sensitivity value and the total sensitivity value of the high-speed pantograph design variable to the pantograph head motion trajectory comprises the following steps:
decomposing the curve of the motion trail of the E point of the bow head into the following parts:
Figure BDA0001549031370000023
Ωn＝(xi|ximin<xi<ximax,i＝1,2,…,n,n＝11)
wherein E isy0Is a constant, the integral of the other addend terms to any of the variables it contains being zero, i.e.
Figure BDA0001549031370000024
The addition terms are orthogonal as known from the expressions (3) and (4), i.e. if
(i1,i2,…is)≠(j1,j2,…jl)
Then
Figure BDA0001549031370000031
Thus, it is possible to provide
Figure BDA0001549031370000032
Wherein dx represents dx1；…；dxn；
The decomposition in equation (3) is unique and the addend term is found by multiple integration:
Figure BDA0001549031370000033
Figure BDA0001549031370000034
wherein x is～i，x～ijRespectively represent the division by xiAnd remove xiAnd xjA variable other than;
Ey(x) The total variance D is:
Figure BDA0001549031370000035
the bias variance is obtained from each addend term of equation (3):
Figure BDA0001549031370000036
wherein, 1 is less than or equal to i1<…isN and s is 1,2, …, n; the pair formula (3) is in the whole omeganAnd (4) field squaring and integration to obtain:
Figure BDA0001549031370000037
sensitivity of the device
Figure BDA0001549031370000038
Expressed as:
Figure BDA0001549031370000039
by definition, this is obtained from equation (11):
Figure BDA00015490313700000310
wherein S isiX of the representationiA first order sensitivity; sijDenotes xiAnd xjSecond order sensitivity of (1), i ≠ j;
the sensitivity of the total system is the sum of sensitivity coefficients of each order of a variable and is expressed as
Figure BDA00015490313700000311
Wherein the content of the first and second substances,
Figure BDA0001549031370000041
wherein E isy0、D、DiAnd D～iThe following were obtained by the monte carlo integration method:
Figure BDA0001549031370000042
Figure BDA0001549031370000043
Figure BDA0001549031370000044
Figure BDA0001549031370000045
Figure BDA0001549031370000046
according to equations (12), (16), (17) and (18), xiThe first order sensitivity coefficient of (d) is:
Figure BDA0001549031370000047
according to equations (14), (16), (17) and (19), xiThe total sensitivity coefficient of (a) is:
Figure BDA0001549031370000048
where k is the number of samples in the Monte Carlo method, xmAt omeganSampling points of the domain; the superscripts (1) and (2) in equations (19) and (20) represent two k × m-dimensional sample arrays of X;
finally, the above method is used to derive Ex(i)＝Ex(x1,x2,...,x11) The sensitivity of (2).
Further, the detailed process of step 4 is as follows:
establishing a frame part motion equation according to a Lagrange motion equation and a pull equation:
Figure BDA0001549031370000049
wherein, alpha represents the pantograph angle,
Figure BDA00015490313700000410
yethe longitudinal coordinate of the E point of the bow head is obtained by the geometrical relationship:
ye＝csinγ+x1sinα (24)
wherein c is the length of the CE rod,
Figure BDA00015490313700000411
s2＝x1 2+x8 2+2x1x8cos(α+x11)；
k10is an intermediate variable obtained according to the principle of imaginary displacement variation, and k10＝k4ccosγ+x1cosα，
Figure BDA0001549031370000051
e. f is the ordinate and abscissa of the point B respectively;
performing Taylor series expansion on the working height of the pantograph head to obtain an equivalent linear motion differential equation of the pantograph frame at the working position accessory:
Figure BDA0001549031370000052
wherein M isFFor high speed pantograph frame quality, KH、KFRespectively high speed pantograph bow and frame stiffness, Bh、BFFriction, U, of the head and frame of the high-speed pantograph, respectivelyH、UFDamping of the head and frame, respectively, of the high-speed pantographe、yhRespectively are longitudinal coordinates of a bow head E point and a bow head H point;
wherein, yhFrom the geometric relationship:
yh＝e+x3sinξ+x6sinλ (26)
wherein xi is the negative included angle between the GB rod and the x axis, and lambda is the included angle between the HG rod and the x axis;
therefore, the regression parameters of the pantograph linearization model are obtained:
Figure BDA0001549031370000053
Figure BDA0001549031370000054
wherein M is equalEffective frame mass, MxThe moment of raising the bow.
The invention has the beneficial effects that: when the high-speed pantograph is researched and designed, a Sobol' global sensitivity analysis method is adopted to calculate the first-order sensitivity value, the second-order sensitivity value and the total sensitivity value of the head trajectory in the x direction and the y direction according to different structural parameters of the high-speed pantograph. Compared with the traditional high-speed pantograph optimization design method, the method adopts the actual structure parameter model of the high-speed pantograph, and can improve the motion precision of the high-speed pantograph; meanwhile, the influence of each parameter and the mutual influence among the parameters are considered, so that the accuracy and the reliability of the optimized design of the high-speed pantograph structure are better, and the optimized design cost is effectively reduced.
Drawings
Fig. 1 is a flowchart of a method for identifying parameters of a key structure of a high-speed pantograph.
Fig. 2 is a schematic view of the geometry of a high-speed pantograph.
Fig. 3 shows the total sensitivity (x-direction) of the structural parameters of the high-speed pantograph.
Fig. 4 shows the total sensitivity (y-direction) of the structural parameters of the high-speed pantograph.
Fig. 5 shows a high-speed pantograph-catenary coupling model.
FIG. 6 shows the results of contact pressure changes at 350km/h for pantograph nets with different structural parameters.
Detailed Description
The invention is described in further detail below with reference to the figures and specific embodiments. In this embodiment, a Sobol' global sensitivity analysis method is adopted to derive and calculate a first-order sensitivity value, a second-order sensitivity value and a total sensitivity value of a high-speed pantograph structural parameter on a pantograph head motion trajectory, and analyze the influence of different high-speed pantograph structural parameters on the dynamic lifting displacement of the high-speed pantograph, so as to determine a key structural parameter influencing the current collection quality of the high-speed pantograph-catenary. The method flow is shown in fig. 1, and the specific content and design method steps are as follows:
step 1: a high-speed pantograph nonlinear motion model is adopted to replace a traditional mass block model, a kinematic pair gap error is introduced into the mass block model, and a geometric relation schematic diagram of the high-speed pantograph is shown in figure 2. On the basis, the derivation of the motion trail equation of the head of the high-speed pantograph is carried out according to the geometric relationship among the structural parameters of the high-speed pantograph. The relation of the included angle between the bow balancing rod and the horizontal direction is shown as a formula (1), and the bow track is shown as a formula (2).
Figure BDA0001549031370000061
Figure BDA0001549031370000062
Wherein beta is an included angle between the bow balance rod and the horizontal direction; (E)x,Ey)、(Hx,Hy) Respectively, the x and y coordinate components of the bow balancing pole. In the formula (2), Ex(i) The x coordinate component of the discrete point of the trajectory curve of the bow E point is taken as the component of the X coordinate; ey(i) A discrete point y coordinate component of a trajectory curve of a bow E point is obtained; beta (i) is the included angle of the bow balance arm at the ith position and the horizontal direction; n is the total number of discrete points taken. x is the number of1,x2,...,x11Representing design variables of a high-speed pantograph, wherein x1Is the length l of the lower arm ACAC；x2Length l of CD section for upper arm rodCD；x3Is the length l of the push rod BG sectionBG；x4For the length l of the push rod BD segmentBD；x5Length l of upper arm rod DE sectionDE；x6For the upper frame controlling the length l of the rod GHGH；x7For the length l of the bow balancing rod EHEH；x8The center distance l between two points A and B of the two fixed hinged supportsAB；x9Is the included angle between the CD rod and the DE rod of the upper frame; x is the number of10Is an included angle, x, between a BG rod and a BD rod on the push rod11Is the angle between the central line of A and B and the x-axis.
Step 2: adopts a Latin hypercube sampling method aiming at a high-speed pantograph x1,x2,……，x11A total of 11 design variables were sampled for random samples:
(1) taking the simulation times N as 20, dividing normal distribution functions of all design variables into 20 non-overlapping subintervals, and respectively carrying out independent equal probability sampling in each subinterval;
(2) in order to ensure that the random number extracted belongs to each subinterval, the random number V in the ith intervaliIt should satisfy:
Figure BDA0001549031370000071
Figure BDA0001549031370000072
(3) generating only one random number in each subinterval, then obtaining N random variable sample values by the random numbers generated in the N subintervals by adopting an inverse transformation method, and randomly arranging the sequence numbers of the intervals to which the sample values of the random variables belong.
And step 3: adopting a Sobol' global sensitivity analysis method to deduce and calculate a first-order sensitivity value, a second-order sensitivity value and a total sensitivity value of the structural parameters of the high-speed pantograph to the movement locus of the pantograph head:
decomposing the trajectory curve of the E point of the bow into the following components:
Figure BDA0001549031370000073
Ωn＝(xi|ximin<xi<ximax,i＝1,2,…,n,n＝11)
wherein E isy0Is a constant, and the integral of any variable contained by other addend terms is zero;
Figure BDA0001549031370000074
the respective addend terms are orthogonal if, as can be derived from equations (5) and (6), that is to say if
(i1,i2,…is)≠(j1,j2,…jl)
Then
Figure BDA0001549031370000075
Thus, it is possible to provide
Figure BDA0001549031370000076
Wherein dx represents dx1；…；dxn。
The decomposition in equation (5) is unique and the addend term can be found by multiple integration
Figure BDA0001549031370000077
Figure BDA0001549031370000078
Wherein x is～i，x～ijRespectively represent the division by xiAnd remove xiAnd xjOther variables, higher order terms can be similarly found.
Ey(x) The total variance D is:
Figure BDA0001549031370000081
the variance can be determined from the respective addend terms of equation (5):
Figure BDA0001549031370000082
where 1. ltoreq. i1<…isN and s is 1,2, …, n. The pair formula (5) is in the whole omeganAnd (4) field squaring and integration to obtain:
Figure BDA0001549031370000083
thus, the sensitivity
Figure BDA0001549031370000084
Expressed as:
Figure BDA0001549031370000085
from the definition and equation (13) we can get:
Figure BDA0001549031370000086
wherein S isiX of the representationiFirst order sensitivity, Sij(i ≠ j) represents xiAnd xjSecond order sensitivity of (c), and so on. The sensitivity of the total system is the sum of the sensitivity coefficients of each order of a variable, expressed as:
Figure BDA0001549031370000087
wherein the content of the first and second substances,
Figure BDA0001549031370000088
Ey0、D、Diand D～iThe following can be obtained by the monte carlo integration method:
Figure BDA0001549031370000089
Figure BDA00015490313700000810
Figure BDA00015490313700000811
Figure BDA0001549031370000091
Figure BDA0001549031370000092
according to equations (14), (18), (19) and (20), xiThe first order sensitivity coefficient of (d) is:
Figure BDA0001549031370000093
according to equations (16), (18), (19) and (21), xiThe total sensitivity coefficient of (a) is:
Figure BDA0001549031370000094
where k is the number of samples in the Monte Carlo method, xmAt omeganSampling points in space. Superscripts (1) and (2) in equations (21) and (22) represent two k × m-dimensional sample arrays of X.
Derivation of E by the method described abovex(i)＝Ex(x1,x2,...,x11) The sensitivity of (2).
And 4, step 4: according to the sensitivity analysis result of the structural parameters of the high-speed pantograph, deducing a high-speed pantograph reduction quality model, and calculating the frame quality and the frame damping under the influence of different structural parameters:
establishing a frame part motion equation according to a Lagrange motion equation and a pull equation:
Figure BDA0001549031370000095
wherein, alpha represents the pantograph angle,
Figure BDA0001549031370000096
yefor the longitudinal coordinate of the bow E point, it can be derived from the geometrical relationship:
ye＝csinγ+x1sinα (26)
wherein c is the length of the CE rod,
Figure BDA0001549031370000097
s2＝x1 2+x8 2+2x1x8cos(α+x11)。
k10intermediate variables obtained according to the principle of virtual displacement variation:
k10＝k4ccosγ+x1cosα (27)
wherein the content of the first and second substances,
Figure BDA0001549031370000098
e. f is the ordinate and abscissa of the point B respectively.
Performing Taylor series expansion on the working height of the pantograph head to obtain an equivalent linear motion differential equation of the pantograph frame at the working position accessory:
Figure BDA0001549031370000101
wherein M isFFor high speed pantograph frame quality, KH、KFRespectively high speed pantograph bow and frame stiffness, Bh、BFFriction, U, of the head and frame of the high-speed pantograph, respectivelyH、UFDamping of the head and frame, respectively, of the high-speed pantographe、yhRespectively are longitudinal coordinates of a bow head E point and a bow head H point;
wherein, yhThe geometric relationship can be derived as:
yh＝e+x3sinξ+x6sinλ (29)
and xi is an included angle between the GB rod and the x axis in the negative direction, and lambda is an included angle between the HG rod and the x axis.
Therefore, the regression parameters of the pantograph linearization model are obtained:
Figure BDA0001549031370000102
Figure BDA0001549031370000103
wherein M is the equivalent frame mass, MxThe moment of raising the bow.
And 5: substituting the deduced different high-speed pantograph frame masses and frame damping into a high-speed pantograph-catenary coupling model, calculating pantograph-catenary dynamic contact pressure under the influence of different structural parameters, analyzing the obtained contact pressure simulation result, and comparing the analysis result with the high-speed pantograph structural parameter sensitivity calculation result to verify the sensitivity analysis result.
In this example, the distribution of the high-speed pantograph structure parameters in the x and y directions, which can be obtained by the sensitivity calculation, can be classified into the strong influence parameters (l) as shown in tables 1,2, 3, 4, 3, and 4AC lCD lBD) Medium influencing parameter (l)DElEH) And a weak influence parameter (l)AB lBG lGH)。
TABLE 1 first order sensitivity analysis of Pantograph parameters (x-direction)
Figure BDA0001549031370000104
Figure BDA0001549031370000111
TABLE 2 second order sensitivity values (x-direction) of Pantograph parameters
Figure BDA0001549031370000112
TABLE 3 first order sensitivity analysis of Pantograph parameters (y-direction)
Figure BDA0001549031370000113
TABLE 4 second order sensitivity values (y-direction) of Pantograph parameters
Figure BDA0001549031370000121
Results of analysis of contact pressure at 5350 km/h
Figure BDA0001549031370000122
And then calculating the mass and the frame damping of the high-speed pantograph frame under the influence of different structural parameters according to the steps 4 and 5, substituting the mass and the frame damping into the high-speed pantograph-catenary coupling model shown in fig. 5 for subsequent simulation, wherein the simulation results are shown in table 5 and fig. 6. The simulation result is analyzed, in this example, the structural parameter affecting the larger contact pressure ratio is the upper arm lever lCDAnd lDEThe contact pressure variation is 6.81%, 6.69%, respectively, followed by a balance bar lEH(4.87%) and push rod lBD(4.63%), which is substantially consistent with the sensitivity calculation. This shows that the sensitivity analysis result of the high-speed pantograph structural parameter obtained by the Sobol' global sensitivity analysis method basically accords with the actual dynamics analysis result, and compared with the traditional high-speed pantograph parameter optimization scheme, the adoption of the scheme can realize the pertinence of the high-speed pantograph structural parameter optimization and effectively improve the high-speed pantograph optimization design efficiency.

Claims (4)

1. A high-speed pantograph key parameter identification method based on sensitivity analysis is characterized by comprising the following steps:
step 1: random errors of the high-speed pantograph kinematic pair gaps are counted, a pantograph head motion nonlinear model of the high-speed pantograph is established, and a pantograph head motion trajectory equation is deduced according to a frame model of the high-speed pantograph;
the included angle beta between the bow balancing rod and the horizontal direction in the bow motion nonlinear model of the high-speed pantograph is as follows:
Figure FDA0002975991700000011
wherein (E)x，Ey)、(Hx，Hy) Respectively are x and y coordinate components of a bow balancing rod;
the motion track of the bow head is as follows:
Figure FDA0002975991700000012
wherein E isx(i) Is the x-coordinate component of discrete points of the locus curve of the bow (E) point, Ey(i) Is a Y coordinate component of a discrete point of a curve of a point track of the bow head (E), beta (i) is an included angle between the ith position of the bow head balance arm and the horizontal direction, and n is the total number of the discrete points; x is the number of1,x2,...,x11Representing design variables, x, of high-speed pantographs1Is the length l of the lower arm ACAC；x2Length l of CD section for upper arm rodCD；x3Is the length l of the push rod BG sectionBG；x4For the length l of the push rod BD segmentBD；x5Length l of upper arm rod DE sectionDE；x6For the upper frame controlling the length l of the rod GHGH；x7For the length l of the bow balancing rod EHEH；x8The center distance l between two points A and B of the two fixed hinged supportsAB；x9Is the included angle between the CD rod and the DE rod of the upper frame; x is the number of10Is an included angle, x, between a BG rod and a BD rod on the push rod11Is the included angle between the central connecting line of A and B and the x axis;
step 2: simulating a design variable random sample of the high-speed pantograph by adopting a Latin hypercube sampling method;
and step 3: adopting a Sobol' global sensitivity analysis method to deduce and calculate a first-order sensitivity value, a second-order sensitivity value and a total sensitivity value of the high-speed pantograph design variable to the movement locus of the pantograph head;
and 4, step 4: deducing a high-speed pantograph reduction mass model, and calculating the frame mass and the frame damping under the influence of different design variables;
and 5: substituting the deduced frame quality and frame damping of the high-speed pantograph into a simulation model, analyzing the contact pressure change of the high-speed pantograph-catenary under the influence of different design variables, and verifying the sensitivity analysis result of the key design variables of the high-speed pantograph.
2. The method for identifying key parameters of a high-speed pantograph based on sensitivity analysis according to claim 1, wherein the method for simulating the random sample of design variables of the high-speed pantograph comprises the following steps: the simulation times are N, the uniform distribution functions of all design variables are divided into N non-overlapping subintervals, independent equal probability sampling is carried out in each subinterval, only one random number is generated in each subinterval, then an inverse transformation method is adopted, N random variable sampling values are obtained from the random numbers generated in the N subintervals, and the serial numbers of the intervals to which the sampling values of all the random variables belong are randomly arranged.
3. The method for identifying key parameters of a high-speed pantograph based on sensitivity analysis according to claim 1, wherein the method for calculating the first-order sensitivity value, the second-order sensitivity value and the total sensitivity value of the design variables of the high-speed pantograph to the motion trajectory of the pantograph head comprises the following steps:
decomposing the motion track curve of the bow (E) point into:
Figure FDA0002975991700000021
Ωn＝(xi|ximin<xi<ximax,i＝1,2,…,n,n＝11)
wherein E isy0Is a constant, the integral of the other addend terms to any variable contained therein being zeroI.e. by
Figure FDA0002975991700000022
The addition terms are orthogonal as known from the expressions (3) and (4), i.e. if
(i1,i2,…is)≠(j1,j2,…jl)
Then
Figure FDA0002975991700000023
Thus, it is possible to provide
Figure FDA0002975991700000024
Wherein dx represents dx1；…；dxn；
The decomposition in equation (3) is unique and the addend term is found by multiple integration:
Figure FDA0002975991700000025
Figure FDA0002975991700000026
wherein x is～i，x～ijRespectively represent the division by xiAnd remove xiAnd xjA variable other than;
Ey(x) The total variance D is:
Figure FDA0002975991700000027
the bias variance is obtained from each addend term of equation (3):
Figure FDA0002975991700000031
wherein, 1 is less than or equal to i1＜…isN and s is 1,2, …, n; the pair formula (3) is in the whole omeganAnd (4) field squaring and integration to obtain:
Figure FDA0002975991700000032
sensitivity of the device
Figure FDA0002975991700000033
Expressed as:
Figure FDA0002975991700000034
by definition, this is obtained from equation (11):
Figure FDA0002975991700000035
wherein S isiX of the representationiA first order sensitivity; sijDenotes xiAnd xjSecond order sensitivity of (1), i ≠ j;
the sensitivity of the total system is the sum of sensitivity coefficients of each order of a variable and is expressed as
Figure FDA0002975991700000036
Wherein the content of the first and second substances,
Figure FDA0002975991700000037
wherein E isy0、D、DiAnd D:iThe following were obtained by the monte carlo integration method:
Figure FDA0002975991700000038
Figure FDA0002975991700000039
Figure FDA00029759917000000310
Figure FDA00029759917000000311
Figure FDA00029759917000000312
according to equations (12), (16), (17) and (18), xiThe first order sensitivity coefficient of (d) is:
Figure FDA00029759917000000313
according to equations (14), (16), (17) and (19), xiThe total sensitivity coefficient of (a) is:
Figure FDA0002975991700000041
where k is the number of samples in the Monte Carlo method, xmAt omeganSampling points of the domain; the superscripts (1) and (2) in equations (19) and (20) represent two k × m-dimensional sample arrays of X;
finally using the above-mentioned methodDerivation Ex(i)＝Ex(x1,x2,...,x11) The sensitivity of (2).
4. The method for identifying key parameters of a high-speed pantograph based on sensitivity analysis according to claim 3, wherein the detailed process of the step 4 is as follows:
establishing a frame part motion equation according to a Lagrange motion equation and a pull equation:
Figure FDA0002975991700000042
wherein, alpha represents the pantograph angle,
Figure FDA0002975991700000043
yeas the longitudinal coordinate of the bow (E) point, the geometrical relationship is as follows:
ye＝csinγ+x1sinα (24)
wherein c is the length of the CE rod,
Figure FDA0002975991700000044
s2＝x1 2+x8 2+2x1x8cos(α+x11)；
k10is an intermediate variable obtained according to the principle of imaginary displacement variation, and k10＝k4ccosγ+x1cosα，
Figure FDA0002975991700000045
e. f is the ordinate and abscissa of the point B respectively;
performing Taylor series expansion on the working height of the pantograph head to obtain an equivalent linear motion differential equation of the pantograph frame at the working position accessory:
Figure FDA0002975991700000046
wherein M isFFor high speed pantograph frame quality, KH、KFRespectively high speed pantograph bow and frame stiffness, Bh、BFFriction, U, of the head and frame of the high-speed pantograph, respectivelyH、UFDamping of the head and frame, respectively, of the high-speed pantographe、yhRespectively are longitudinal coordinates of a bow head E point and a bow head H point;
wherein, yhFrom the geometric relationship:
yh＝e+x3sinξ+x6sinλ (26)
wherein xi is the negative included angle between the GB rod and the x axis, and lambda is the included angle between the HG rod and the x axis;
therefore, the regression parameters of the pantograph linearization model are obtained:
Figure FDA0002975991700000051
Figure FDA0002975991700000052
wherein M is the equivalent frame mass, MxThe moment of raising the bow.
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