CN106599340A - Method for optimizing parameters of contact line and pantograph based on sensitivity analysis - Google Patents

Abstract

The invention discloses a method for optimizing parameters of a contact line and a pantograph based on sensitivity analysis. According to bow-net contact pressure during running of a high speed train, the existing problem is analyzed, level value design of the parameters is carried out through central composite design, and multi-factor and five-level parameters are obtained; an Spearman rank correlation coefficient method is adopted to compute correlation coefficients between the parameters of the contact line and the pantograph and the contact pressure to judge the correlation; and an Sobol method is adopted to compute sensitivity coefficients of the parameters of the contact line and the pantograph about the contact pressure, judge the impact of the parameters on the contact pressure and determine an optimization order of the parameters when the bow-net parameter optimization is carried out, after each index meets relevant standard requirements, optimization is ended and all bow-net parameter values are output. The method has reasonable optimization, and the parameters of the contact line and the pantograph can be adjusted quickly and reasonably, so that the contact pressure of the parameters of the contact line and the pantograph can be controlled reasonably.

Description

An Optimization Method of Catenary and Pantograph Parameters Based on Sensitivity Analysis

technical field

The invention relates to the technical field of high-speed rail pantograph-catenary current collection, in particular to an optimization method for catenary and pantograph parameters based on sensitivity analysis.

Background technique

When the train is running at a high speed, under the influence of wheel-rail and aerodynamic excitation, the vibration of the pantograph and the fluctuation of the catenary are serious, which affects the continuous and stable flow of the pantograph. Under the conditions of pantograph running speed and external excitation conditions, the quality of current receiving between pantograph and catenary is mainly affected by the parameters of catenary and pantograph. That is to say, the pantograph-catenary current receiving quality can be improved by adjusting the parameter values of catenary and pantograph. Then determining the changing direction of the parameters and the degree of influence of each parameter on the contact pressure becomes the key to optimize the pantograph-catenary flow quality.

But in the previous technology, most of them are based on engineering experience, or adopt multiple tests to adjust the catenary parameters and change the pantograph model to improve the current quality of the pantograph-catenary, and the amount of work is relatively large. This method is developed from two perspectives, the correlation between catenary and pantograph parameters and contact pressure, and the sensitivity of parameters to contact pressure, and proposes a method for quantitatively optimizing pantograph-catenary parameters to achieve good flow between pantograph-catenary.

Contents of the invention

The purpose of the invention is to provide a reasonable optimization method for the pantograph-catenary design of high-speed railway. And through the determination of the correlation between the catenary and pantograph parameters and the contact pressure and the sensitivity of the pantograph-catenary parameters, and then through the rapid and reasonable adjustment of the catenary and pantograph parameters to achieve.

When optimizing the structure of the catenary, the contact pressure and its statistics, that is, the standard deviation, average value, maximum value and minimum value of the contact pressure are used as the current receiving index, and the contact network and pantograph parameters are adjusted. The pressure is controlled within a reasonable range.

To achieve the above object, the present invention provides the following technical solutions:

A method for optimizing catenary and pantograph parameters based on sensitivity analysis, comprising the following steps:

Step 1: According to the design or initial pantograph-catenary model, according to the pantograph-catenary contact pressure when the high-speed train is running, calculate the average value, standard deviation, maximum value and minimum value of the contact pressure, and analyze the problems that arise;

Average contact pressure:

Contact Pressure Standard Deviation:

Maximum contact pressure:

F _max ＝Max(F _i ) (3)

Contact pressure min:

F _min ＝Min(F _i ) (4)

In formulas (1)-(4), F _i represents the contact pressure value (N) at each sampling point; n is the number of sampling points;

Step 2: Taking the current catenary-pantograph structure as the initial model, the level value design of the parameters is carried out through the central composite design, and the multi-factor five-level parameter combination and the set of level values of each parameter are obtained; respectively represent the standardized Catenary and pantograph design parameters Z _i , i=1, 2...n, n is the number of pantograph-catenary parameters;

Step 3: According to the combination of parameter levels obtained above, the correlation coefficient between catenary and pantograph parameters and contact pressure is calculated by Spearman rank correlation coefficient method, and the correlation between parameters and contact pressure is determined according to the sign of the correlation coefficient.

ρ represents the rank correlation coefficient, and -1≤ρ≤1; n is the number of simulation tests; a _j and b _j respectively represent the ranks of the set level values of catenary parameters and contact pressure indicators, 1≤j≤n;

Step 4: Using the Sobol method, calculate the sensitivity coefficient of the catenary and pantograph parameters to the contact pressure, and determine the degree of influence of this parameter on the contact pressure, so as to determine the optimization order of the parameters when optimizing the pantograph-catenary parameters.

The sensitivity coefficients of each order satisfy the Relationship;

Among them, partial variance D _i =∫f _i ² ( _xi )dx _i, total variance Si is the first-order sensitivity coefficient, indicating the degree of influence of a single catenary and pantograph parameter on the contact pressure; _Sij is the second-order sensitivity coefficient, indicating the influence of the pairwise interaction of catenary and pantograph parameters on the contact pressure influence level;

Step 5: For the problems in step 1, combine steps 3 and 4 to change the pantograph-catenary parameter value;

Step 6: According to the catenary and pantograph parameters adjusted in step 5, calculate in the simulation software, and obtain the pantograph-catenary contact pressure;

Step 7: According to the contact pressure value, count the standard deviation value, average value, maximum value, minimum value and offline rate of the contact pressure, and compare with the regulations in the corresponding standards. When the calculated value is within the range specified by the standard, stop the optimization , and output the parameter values of catenary and pantograph; otherwise, go to step 8;

Step 8: Continue to change the parameter value of catenary or pantograph, if it is still within the range of its maximum breaking force, repeat steps 6 and 7; otherwise, proceed to step 9;

Step 9: First judge whether the parameter has changed all parameter values, if not, continue to adjust the next parameter value, and then proceed to step 8; otherwise, proceed to step 10;

Step 10: Under the condition of adjusting all parameters, if each indicator still does not meet the requirements of the standard, add other parameters on the basis of the final parameter value, re-design the experiment, and repeat steps 2-9;

Step 11: Repeat all the above steps. After each index meets the requirements of the relevant standards, the optimization ends and all pantograph-catenary parameter values are output.

As a further solution of the present invention: in the step (3), when the rank correlation coefficient ρ>0, the pantograph-catenary parameter is positively correlated with the contact pressure; when the rank correlation coefficient ρ<0, the change of the contact pressure and the pantograph-catenary parameter into a negative correlation.

Compared with prior art, the beneficial effect of the present invention is:

The present invention provides a reasonable optimization method for pantograph-catenary design of high-speed railways, and through the determination of the correlation between catenary and pantograph parameters and contact pressure and the sensitivity of pantograph-catenary parameters, and then through rapid and reasonable adjustment of catenary and pantograph Pantograph parameters to achieve. When optimizing the catenary structure, the contact pressure and its statistics are used to control the contact pressure within a reasonable range by adjusting the parameter values of the catenary and pantograph.

Description of drawings

Figure 1 is a schematic diagram of the structure of the reference catenary.

Fig. 2 is a schematic structural diagram of the reference pantograph. (Among them, ①②③④ represent the numbers of different parts, and k represents the elastic coefficient of the spring)

Figure 3 is a flow chart of catenary structure optimization.

Figure 4 is a schematic diagram of the central composite design.

Figure 5 shows the example parameter sensitivity coefficient.

Figure 6 is the actual effect waveform diagram of the example.

Figures 7a, 7b, 7c, and 7d are actual effect diagrams of examples.

detailed description

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

Example

The optimization method of catenary parameters based on sensitivity analysis includes the following steps:

Step 1: According to the initial design scheme or the initial pantograph-catenary model, according to the pantograph-catenary contact pressure when the high-speed train is running, calculate the standard deviation, average value, maximum value and offline rate of the contact pressure, and analyze the problems that arise;

Initial pantograph-catenary model: The structural parameters in the figure refer to the Beijing-Tianjin intercity high-speed railway catenary and the Faiveley CX series pantograph, as shown in Figure 1 and Figure 2;

The average value, standard deviation and maximum value of contact pressure are used as evaluation indicators to analyze the change of contact pressure. Each index can be calculated according to the contact pressure shown in Figure 5, as follows:

Average contact pressure:

Contact Pressure Standard Deviation:

Maximum contact pressure:

F _max ＝Max(F _i ) (3)

Contact pressure min:

F _min ＝Min(F _i ) (4)

In formulas (1)-(4), F _i represents the contact pressure value (N) at each sampling point; n is the number of sampling points;

③ During the operation of the train, through the sliding contact between the pantograph and the contact wire, the pantograph-catenary contact pressure is the main index to evaluate the quality of the pantograph-catenary flow, and the contact pressure statistics such as the average value, standard deviation and maximum value of the contact pressure are generally used as a measure The index of contact pressure change; according to relevant standards, the flow quality between pantograph and catenate can be guaranteed only when the contact pressure is within a certain range;

Therefore, the problem here is that the indicators of contact pressure do not meet the requirements of relevant standards; for example, the standard deviation value is too large, the offline rate is too high, etc.;

Step 2: Taking the current catenary-pantograph structure as the initial model (given), the level value design of the parameters is carried out through the central composite design, and the multi-factor five-level parameter combination and the set of level values of each parameter are obtained; respectively represent the standardized catenary and pantograph design parameters Z _i , i=1, 2...n, n is the number of pantograph-catenary parameters;

Among them, the central composite design:

First of all, it is necessary to obtain the set of catenary parameters and contact pressure index level values, and use the central composite design method to design the combination of parameter level values for simulation experiments; in order to discuss the influence of contact pressure when the catenary design parameters change; the catenary in Figure 1 The design parameter is the initial value, set it as zero level, and change it by 0.1 times the initial value, and obtain the level value table of each parameter, as shown in Table 1;

Table 1 Catenary parameter value table

Standardize the zero-level value of the catenary design parameter to (1, 1, 1, 1), and then standardize the other level values of the parameter in turn, as shown in Table 2;

Table 2 Catenary parameter level coding table

Among them, Z _i (i=1, 2, 3, 4) respectively represent the design parameters of the standardized catenary;

According to the central composite design process and principles shown in Figure 3 and Figure 4, the combination design of each parameter level value is carried out, and the parameter combination of four factors and five levels is realized by Design-Expert software, and 30 combinations are obtained; Perform 30 simulation calculations in MSC.Marc software, and obtain the corresponding contact pressure average value, standard deviation and maximum value;

Step 3: According to the combination of parameter levels obtained above, the correlation coefficient between the contact line tension and the contact pressure is firstly calculated by the Spearman rank correlation coefficient method, and the correlation between the parameters and the contact pressure is determined according to the sign of the correlation coefficient.

In the formula, ρ represents the rank correlation coefficient, and -1≤ρ≤1; n is the number of simulation tests, n=30; a _j , b _j (1≤j≤30) represent the jth contact line tension value and The ordering, also known as the rank, of the standard deviation values in the set of contact line tensions and standard deviations. Use {T _cj } to represent the set of contact line tension level values, and use {S _j } to represent the set of standard deviations, where T _cj and S _j represent the elements in the two sets respectively. Arrange the elements in the two sets in ascending order to obtain the sets {a _j } and {b _j } of the ranks of the two series, and the elements of the two columns of variables are represented by a _j and b _j respectively;

The size of |ρ| indicates the degree of correlation between the tension of the contact line and the standard deviation. The closer |ρ| is to 1, the stronger the correlation between the tension of the contact line and the standard deviation is; the closer |ρ| is to 0, the relationship between the tension of the contact line and the standard deviation is stronger. The weaker the correlation between. When ρ>0, the contact line tension is positively correlated with the standard deviation, that is, the standard deviation increases with the increase of the contact line tension; when ρ<0, the contact line tension is negatively correlated with the standard deviation of the contact pressure, that is, the standard deviation Decreases with increasing contact line tension;

The above is the calculation process of the standard deviation of the contact line tension and contact pressure. In the same way, the correlation coefficient between the contact line tension and the average and maximum value of the contact pressure can be calculated. Furthermore, the correlation coefficients between the catenary cable tension, the linear density of the contact line and the linear density of the catenary cable and the standard deviation, average value and maximum value of the contact pressure were calculated.

Step 4: Using the Sobol method, calculate the sensitivity coefficient of the catenary parameters to the contact pressure, and determine the degree of influence of the parameter on the contact pressure according to the size of the sensitivity coefficient, so as to determine the optimization order of the parameters when optimizing the catenary parameters;

The functional relationship between the design parameters of the catenary and the contact pressure based on the Sobol method is expressed by formula (6);

f(X)=f(x ₁ , x ₂ , . . . , x _n ), i=1, 2, . . . , n (6)

In the formula, x _i represents each design parameter of catenary, n=4; f(X) represents the average value, standard deviation or maximum value of contact pressure. There is an obvious linear relationship between each design parameter of catenary and each index of contact pressure; under the influence of two parameters, the degree of correlation between each parameter and each index of contact pressure is different; therefore, a single catenary parameter is expressed in the form of first-order regression The linear relationship between the contact pressure and the product of two parameters is used to represent the relationship between the two-parameter interaction and the contact pressure, and f(X) is predicted to be in the form of a second-order interactive nonlinear model as shown in formula (6);

f(x)＝F ₀ +a ₁ x ₁ +a ₂ x ₂ +a ₃ x ₃ +a ₄ x ₄ +b ₁ x ₁ x ₂ +b ₂ x ₁ x ₃ +b ₃ x ₁ x ₄ +c ₁ x ₂ x ₃ +c ₂ x ₂ x ₄ +d ₁ x ₃ x ₄ (7)

Among them, f(x) represents the average value, standard deviation or maximum value; x ₁ represents the catenary tension, x ₂ represents the contact line tension, x ₃ represents the catenary line density, x ₄ represents the contact line line density; F ₀ Indicates the intercept of the equation; a ₁ , a ₂ , a ₃ ...c ₂ , d ₁ represent the regression coefficient of the equation; the intercept and regression coefficient of the regression equation can be calculated in the Design-Expert software by the parameter level values in Table 2 get;

The calculation formula of Sobol sensitivity coefficient is as follows:

S _1,2...n = D _1,2...s /D(8)

The sensitivity coefficients of each order satisfy the The relation of partial variance D _i ＝∫f _i ² ( _xi )dx _i , total variance S _i is the first-order sensitivity coefficient, indicating the degree of influence of a single catenary parameter on the contact pressure; the larger the sensitivity coefficient, the greater the influence of the parameter on the contact pressure; S _ij is the second-order sensitivity coefficient, indicating the contact pressure The influence degree of the pairwise interaction of network parameters on the contact pressure;

f _i (x _i ) and f _ij (x _i , x _j ) are sub-items of f(x ₁ , x ₂ ,…, x _n ), and each sub-item satisfies

Each sub-item can be calculated by the following method;

f ₀ =∫f(x ₁ ,x ₂ ,…x _n )dx ₁ dx ₂ …dx _n (10)

f _i (x _i )＝∫f(x ₁ ,x ₂ ,…x _n )dx ₁ …dx _i-1 dx _i+1 -f ₀ (11)

f _ij (x _i ,x _j )＝∫f(x ₁ ,x ₂ ,…x _n )dx ₁ …dx _i-1 dx _i+1 …dx _j - ₁ dx _j+1 -f ₀ -f _i ( x _i )-f _j (x _j ) (12)

Step 5: For the problems in step 1, combine steps 3 and 4 to change the pantograph-catenary parameter value;

Step 6: According to the catenary adjusted in step 5, calculate in the simulation software MSC.Marc, and obtain the pantograph-catenary contact pressure;

Step 7: According to the contact pressure value, count the standard deviation value, average value, maximum value and offline rate of the contact pressure, and compare it with the regulations in the corresponding standards. When the calculated value is within the range specified by the standard, stop the optimization and output Parameter values of catenary and pantograph; otherwise, go to step 8;

standard regulation:

Tb10621-2014

Table 3 Dynamic Contact Pressure Standards

Design speed(km/h) 250 300 350 Average contact force F _m (N) ≤130 ≤150 ≤180 Maximum contact force F _max (N) ≤250 ≤250 ≤350 Minimum contact force F _min (N) >0 >0 >0 offline rate ≤1% ≤1% ≤1%

EN50318 standard

Table 4 The statistical data of pantograph-catenary simulation results and the specified range of EN50318 standard

Since there is no relevant standard when the speed is greater than 400km/h, when the high-speed pantograph-catenary flow quality meets the low-speed requirements, the optimization can be stopped;

That is, the standard TB10621-2014, under the operating condition of 350km/h, the average contact pressure is not greater than 180N, the maximum value is not greater than 350N, and the off-line rate is not greater than 1%; European standard EN50318 stipulates that under the condition of operating speed of 300km/h The standard deviation of the contact pressure shall not exceed 40N;

Step 8: Continue to change the parameter value of catenary or pantograph, if it is still within the range of its maximum breaking force, repeat steps 6 and 7; otherwise, proceed to step 9;

Step 9: First judge whether the parameter has changed all parameter values, if not, continue to adjust the next parameter value, and then proceed to step 8; otherwise, proceed to step 10;

Step 10: Under the condition of adjusting all parameters, if each indicator still does not meet the requirements of the standard, add other parameters on the basis of the final parameter value, re-design the experiment, and repeat steps 2-9;

Step 11: Repeat all the above steps. After each index meets the requirements of the relevant standards, the optimization ends and all pantograph-catenary parameter values are output.

Test case

In the embodiment of the present invention, with reference to Fig. 3 and Fig. 4, an optimization test is carried out on the parameters of the catenary and pantograph.

In order to reduce the standard deviation value, maximum value and offline rate of contact pressure when the operating speed is 500 km/h, the Spearman rank correlation coefficient method in step 3 is first used to determine the optimization direction of catenary parameters, as shown in Table 5 and Table 6;

Table 5 Instance factor level table

Table 6 Correlation coefficient of the example

Then, use the Sobol method in step 4 to determine the optimization order of each parameter for the standard deviation and maximum value,

As shown in Figure 5. According to the above, for the standard deviation, it is necessary to increase the tension of the contact line, decrease the linear density of the contact line and the tension of the catenary cable, and increase the linear density of the catenary cable; for the maximum value, it is necessary to increase the tension of the contact line and reduce the bearing force cable tension and contact line density, increase load-bearing cable line density, and propose an optimization scheme as shown in Attached Table 7;

Table 7 Example policy scheme

Optimization step number change parameters parametric design 0 none Tc=21kN, Tj=27kN, mc=1.08kg/m, mj=1.08kg/m. 1 Tj Tc=21kN, Tj=34kN, mc=1.08kg/m, mj=1.08kg/m. 2 Tj, mj Tc=21kN, Tj=34kN, mc=1.08kg/m, mj=0.758kg/m. 3 Tj, mj, Tc Tc=14kN, Tj=34kN, mc=1.08kg/m, mj=0.758kg/m.

From Table 7, the actual effect diagrams shown in Figures 6 and 7 can be obtained. It can be seen that after gradually changing the catenary parameters, the standard deviation of the contact pressure is reduced to about 40N; the average value of the contact pressure is in the range of 70-110N within; the maximum contact pressure is reduced to below 250N; the off-line rate is reduced to below 1%. It can be seen that the optimized contact pressure indicators are all within the specified ranges of the EN50318 standard and the TB10621-2014 standard.

It can be seen from the examples that on the basis of the optimized process of the present invention, a catenary structure with good flow quality can be optimized. The description of the above example is only used to help understand the method of the present invention and its core idea; meanwhile, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation and application scope.

It will be apparent to those skilled in the art that the invention is not limited to the details of the above-described exemplary embodiments, but that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Accordingly, the embodiments should be regarded in all points of view as exemplary and not restrictive, the scope of the invention being defined by the appended claims rather than the foregoing description, and it is therefore intended that the scope of the invention be defined by the appended claims rather than by the foregoing description. All changes within the meaning and range of equivalents of the elements are embraced in the present invention. Any reference sign in a claim should not be construed as limiting the claim concerned.

Claims (2)

1. a kind of optimization method of the contact net and pantograph parameters based on sensitivity analysis, it is characterised in that including following step Suddenly：

Step 1：For design or initial bow net model, bow net contact pressure when being run according to bullet train, calculate and connect Touch pressure meansigma methodss, standard deviation, maximum and minima, analyze produced problem；

Contact pressure meansigma methodss：

$\stackrel{\&OverBar;}{F}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{F}_i---\left(1\right)$

Contact pressure standard deviation：

$F_{std}=\sqrt{\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(F_i-\stackrel{\&OverBar;}{F})}^2}---\left(2\right)$

Contact pressure maximum：

F_max=Max (F_i) (3)

Contact pressure minima：

F_min=Min (F_i) (4)

In formula (1)-(4), F_iRepresent the contact pressure value (N) of each sample point；N is sampling number；

Step 2：With current contact net-pantograph structure as initial model, by it is central composite design enter line parameter level Value design, draws the parameter combination of multifactor five level, and each parameter level value set；The contact after standardization is represented respectively Net and pantograph design parameter Z_i, i=1,2 ... n, n are bow net number of parameters；

Step 3：The parameter level combination drawn according to more than, contact net is calculated and by electricity using Spearman rank correlation coefficients method Bow parameter and contact pressure between correlation coefficient, and the sign determination parameter according to correlation coefficient to it is related between contact pressure Property,

$\mathrm{\&rho;}=1-\frac{6\mathrm{\&Sigma;}{(b_j-a_j)}^2}{n(n^2-1)}---\left(5\right)$

ρ represents rank correlation coefficient, and -1≤ρ≤1；N is the number of times of l-G simulation test；a_j、b_jBow net parameter and contact pressure are represented respectively The order of the set level value of power index, 1≤j≤n；

Step 4：Using Sobol methods, the sensitivity coefficient of contact net and pantograph parameters to contact pressure is calculated, judge the parameter Influence degree to contact pressure, so that it is determined that the optimization order of parameter when carrying out bow net parameter optimization,

$S_{\mathrm{12...}n}=D_{i_1{i}_2\mathrm{...}{i}_s}/D---\left(6\right)$

Each rank sensitivity coefficient is satisfied byRelation；

Wherein, partial variancePopulation varianceSi is single order sensitivity coefficient, represents single contact net and pantograph parameters Influence degree to contact pressure；S_ijFor second order sensitivity coefficient, the pairwise interaction of contact net and pantograph parameters is represented Influence degree to contact pressure；

Step 5：For produced problem in step 1, with reference to step 3 and 4, change bow net parameter value；

Step 6：According to the contact net and pantograph parameters that adjust in step 5, in simulation software, calculated, and drawn bow Net contact pressure；

Step 7：According to contact pressure value, contact pressure standard deviation value, meansigma methodss, maximum, minima and ratio of contact loss are counted, And contrasted with the regulation in respective standard, when value of calculation is in the range of standard regulation, then stop optimization, and export contact The parameter value of net and pantograph；Otherwise carry out step 8；

Step 8：Continue the parameter value for changing contact net or pantograph, if now still in the range of its maximum pull-off force, Then repeat step 6 and 7；Otherwise, then step 9 is carried out；

Step 9：The whether altered all of parameter value of parameter is first determined whether, if it is not, continuing to adjust next parameter Value, then proceeds by step 8；Otherwise carry out step 10；

Step 10：Under conditions of all parameters are adjusted, if each index is still unsatisfactory for the requirement of standard, in final parameter On the basis of being worth, other parameters are added again, re-start EXPERIMENTAL DESIGN, and repeat step 2-9；

Step 11：Repeat all of above step, each index is met after relevant criterion requirement, terminate optimization, and export all Bow net parameter value.

2. the optimization method of the contact net and pantograph parameters based on sensitivity analysis according to claim 1, its feature It is, in the step (3), as rank correlation coefficient ρ ＞ 0, bow net parameter and contact pressure positive correlation；As rank correlation coefficient ρ During ＜ 0, contact pressure is changing into negative correlation with bow net parameter.