CN116150918B - Intelligent rail profile optimization method considering distribution characteristics of contact positions of wheel and rail on rail - Google Patents
Intelligent rail profile optimization method considering distribution characteristics of contact positions of wheel and rail on rail Download PDFInfo
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Abstract
The intelligent rail profile optimizing method disclosed by the invention adopts the distribution of wheel-rail contact points at the contact point positions of the rails as an objective function, and calculates the rail profile optimizing method which meets the requirements by taking a multi-objective approximation method as an optimizing method, so that the aim of improving the wheel-rail matching relation is fulfilled. The method adopts the direct wheel-rail contact relation of adjusting the contact point distribution of the contact point on the steel rail as a target, and the target can intuitively show the distribution of the wheel-rail contact on the steel rail and indirectly show the contact stress distribution. The method adopts the multi-objective approximate optimization method which has the advantages of simple operation, good convergence and short calculation time, and is improved into a simpler and faster multi-objective linear approximate optimization method. The method can be applied to the new rail profile optimization design and the rail profile design suitable for polishing in the operation line, and has the characteristics of wide application range, simple optimization method, high calculation efficiency and the like.
Description
Technical Field
The invention relates to the technical field of railway engineering, in particular to an intelligent rail profile optimization method considering distribution characteristics of contact positions of wheel rails on rails.
Background
With the continuous improvement of the operation speed of railway systems in China, the interaction of wheel and rail is continuously enhanced, and the profile of the steel rail is used as a key ring, so that the running stability, the safety, the transportation cost and the like are greatly affected. The reasonable profile of the steel rail can improve the contact relationship of the wheel rail, reduce the power action and the abrasion of the wheel rail generated when a train passes, delay the development of fatigue damage of the steel rail and prolong the service life of the steel rail; the running quality of the train can be improved, and the riding comfort is improved.
At present, the main objective function of the rail profile optimization design in China is a wheel set rolling circle radius difference curve (RRD), the wheel set rolling circle radius difference is one of the main wheel-rail contact geometric parameters closely related to the dynamic performance of the vehicle, and the contact relationship of the wheel rail can be obviously improved by improving the rolling circle radius difference curve of the wheel rail. RRD is defined as the difference value of rolling circles of left and right contact positions of the wheel pair, is an indirect objective function in the contact relation of the wheel and the rail, and can improve the dynamic performance of running of the wheel pair on the rail through the design of RRD. However, RRD mainly reflects the change of the contact point at the wheel position, and cannot intuitively reflect the change of the rail contact in rail profile optimization.
Disclosure of Invention
In order to solve the technical problems, the invention provides an intelligent rail profile optimizing method considering the distribution characteristics of wheel-rail contact positions on a rail, which comprises the following steps:
s1: establishing a target contact point position distribution curve of the steel rail and the wheel rail, and establishing a target function according to the distribution curve;
s2: selecting design points on the steel rail, dividing the profile of the steel rail into an optimized region and a non-optimized region, establishing a constraint equation function, and determining a constraint range of the design points;
s3: determining a search subarea of the iterative step, and randomly generating in the search subareaGroup test protocol, new rail profiles are formed for each group, wherein->Is a positive integer;
s4: calculating the geometric relationship between the newly generated steel rail and the wheel rail contact, and obtaining the calculation resultObjective function value of the new test protocol of group, will +.>Fitting the target values of the experimental schemes to obtain a linear approximation equation of the target function;
s5: solving an optimal solution of a linear approximation target function in a constraint range meeting a constraint equation and a design point, and performing error analysis on the linear approximation target equation of the target function;
s6: and judging whether the optimal solution meets the termination condition, and if not, repeating the steps from S3 to S5 until the optimal profile is found.
Based on the above scheme, in the step S1, the method for determining the target contact point position distribution curve is:
based on a vehicle and rail power interaction model, carrying out dynamics simulation analysis according to an actual operation scene, extracting a vehicle body lateral movement amount of simulation operation, determining the contact position of an actual steel rail according to the lateral movement amount, and obtaining a position distribution curve of a steel rail contact point;
the objective function formula is as follows:
wherein ,、/>the distribution curves of the contact points of the target steel rails at the left side and the right side are respectively; />、Respectively calculating a steel rail contact point position distribution curve according to the optimized steel rail profile; />Is a design variable; />Is the transverse movement amount of the wheel set; />The number of the transverse movement quantity calculation points is calculated; />、/>The contact weight coefficients are respectively on the left side and the right side.
Based on the above scheme, the S2 specifically is:
s1, determining an adjustment optimization range of the profile of the steel rail according to the target contact point position set in the step S1, and determining a fixed point;
dividing the whole steel rail profile into an optimized region and a non-optimized region;
in the process of optimizing design, the transverse vertical coordinates of the profile of the steel rail in the non-optimized area at the fixed point and the two sides are unchanged all the time;
selecting a plurality of points in the optimization area as design points, wherein the abscissa is unchanged, the vertical coordinate is variable, and the vertical coordinate of the design points is a design variable in the optimization design:
establishing a constraint equation according to the determined design points, and establishing a constraint equation function through the convex shape constraint of the steel rail profile curve after the fixed points and the design points are determined;
the constraint relation of the rail profile optimization design is as follows:
wherein ,is->Data points and->Slope of data point line, +.>Is->Data point and the firstSlope of the line between data points; />Including fixed points and all design points.
On the basis of the scheme, the left steel rail profile and the right steel rail profile are considered to be respectively designed;
wherein, the left side design point constraint equation is as follows:
in the formula ,、/>respectively the abscissa and the +.A +.>、/>Respectively the vertical coordinates of two fixed points of the left steel rail.
Based on the above scheme, the S3 specifically is: when the iterative step is the initial step, searching the subarea as the total constraint range of the design points, and in the second and subsequent iterative steps of the optimization process, the constraint range of the design points passes through the upper and lower limits of the boundary of the search area and />To determine;
according to the optimal solution of each iteration step in the optimization process, the size and the position of the search subarea are adjusted, and the search subarea of each design variable is determined by the following formula:
wherein ,is the latest optimal solution; />Is the optimal solution of the previous time; />Determining the change direction of the search range;
for the moving step length of the design variable, determining according to the adjacent two optimal solutions and the relative moving step length:
the steps are performedThe group test scheme adopts a non-uniform rational B spline curve fitting curve to form each new steel rail profile;
wherein, the B spline curve adopts a B spline basis function to describe complex shapes and local properties thereof, and the equation of the B spline curve is as follows:
wherein ,is a control point; />B-spline basis functions are normalized k times.
Based on the above scheme, the S4 specifically is:
calculating a wheel-rail contact relation by adopting a space trace method, scanning in a steel rail range according to the position of the steel rail, iterating until a vertical minimum distance point of a left wheel pair and a right wheel pair is found, calculating to obtain each characteristic parameter of the wheel-rail contact relation, obtaining a steel rail contact point position distribution curve corresponding to an objective function, and obtaining objective function values of each group of test schemes;
wherein, the space trace coordinates are as follows:
fitting target values of all groups of experimental schemes according to a least square method to obtain a linear approximation equation of an objective function;
defining an approximation equation by adopting a single parameter according to a multiple linear regression method, and expressing the approximation equation as a linear function of a design variable;
the linear approximation objective equation of the objective function is:
combining steps S2 to S4 to obtain a linear approximation objective function:
obtaining a linear approximation constraint equation:
obtaining boundary constraint conditions:
and (3) solving an optimal solution of the approximate objective function in a constraint range meeting a constraint equation and a design point by using a linear programming solving method.
Based on the above scheme, the S5 specifically is: performing error analysis on the linear approximation target equation of the target function;
the method comprises the steps of approximation equation error analysis, dead pixel analysis, approximation solution oscillation analysis and iteration direction error analysis;
the approximation equation error analysis concretely comprises the following steps:
if it meetsThe error analysis results are: meets the requirements;
the dead pixel analysis concretely comprises the following steps:
if the condition is not satisfiedThen the search subarea is reduced by the reduction coefficient, and then one-step optimization calculation is carried out, namely +.>；
The approximate solution oscillation analysis concretely comprises the following steps:
if the condition is satisfiedWhen searching the boundary of the subarea, the optimal solution carries out oscillation factor evaluation, and according to the calculation result of the latest two optimal approximate solutions, an oscillation factor is defined>Is that
Wherein if itIndicating that no oscillation occurs in the optimization process; if->The search sub-area is then reduced by a reduction factor, i.e. +.>；
The iteration direction error analysis concretely comprises the following steps:
in the process of multiple iterations, the latest is judgedThe search direction of the calculation is optimized by the next iteration,
if it meets，
Expand the search sub-area to。
Based on the above scheme, the S6 specifically is:
if the condition is satisfiedWhen the optimal solution is not in the boundary of the search subarea, the obtained approximate solution is the optimal approximate solution of the optimization problem, and the multi-point approximate optimization iterative computation is terminated;
if the condition is not satisfiedChanging the search subarea by changing the moving step length, and repeating the steps from S3 to S6 until the optimal profile is found;
wherein the change of the movement step is a reduction coefficient obtained by the above error analysisThe realization is as follows:
the invention has the beneficial effects that:
the invention provides an intelligent rail profile optimization method considering distribution characteristics of contact positions of wheel rails on rails. The optimization target can intuitively show the distribution of the wheel-rail contact on the steel rail, and can indirectly show the contact stress distribution; the optimization method adopts an improved multi-objective linear approximation method, and has the characteristics of simplicity in operation, good convergence and short calculation time; the method can quickly and efficiently calculate the optimized profile meeting the target requirement, and provides a concise and efficient rail profile optimizing way for the design of the new rail profile and the design of the rail polishing profile of the operation line.
Drawings
The invention has the following drawings:
FIG. 1 is a diagram of an optimized front wheel-rail contact relationship;
FIG. 2 is a graph comparing the position distribution curves of the original contact point and the target contact point;
FIG. 3 is a comparison of the rail profiles before and after optimization;
FIG. 4 is a graph comparing the optimized contact point position distribution curves with the target contact point position distribution curves;
FIG. 5 is a graph of optimized rear wheel-rail contact relationship.
Detailed Description
The present invention will be described in further detail with reference to fig. 1-5 and the detailed description of the invention, in order to make the objects, advantages and features of the invention more apparent.
S1: establishing a target contact point position distribution curve of the steel rail and the wheel rail, and establishing a target function according to the distribution curve;
the established target rail contact point position distribution can be a single-side (left side or right side) rail contact point position distribution curve or a two-side rail contact point position distribution curve.
The target contact point position profile determination method may generally be determined empirically and actual wear position. A scientific determination method is as follows: based on a vehicle and rail power interaction model, dynamics simulation analysis is carried out according to an actual operation scene, the transverse movement amount of a vehicle body which is simulated and operated is extracted, the contact position of an actual steel rail is determined according to the transverse movement amount, and a position distribution curve at a steel rail contact point in a wheel-rail contact relation is designed by comprehensive consideration.
The established objective function is used for meeting the minimization of the difference between the position distribution curve of the contact point of the target steel rail and the position distribution curve of the contact point of the calculated steel rail in the optimization process, and the formula is as follows:
in the formula ,、/>the distribution curves of the contact points of the target steel rails at the left side and the right side are respectively; />、Respectively calculating a steel rail contact point position distribution curve according to the optimized steel rail profile; />Is a design variable; />Is the transverse movement amount of the wheel set; />The number of the transverse movement quantity calculation points is calculated; />、/>The contact weight coefficients are respectively on the left side and the right side.
S2: selecting design points on the steel rail, dividing the profile of the steel rail into an optimized region and a non-optimized region, establishing a constraint equation function, and determining a constraint range of the design points;
the selected design variables are required to be analyzed and determined according to the optimization design target set in the step S1 to determine the adjustment optimization range of the steel rail profile, so as to determine a fixed point, and the whole steel rail profile is divided into an optimized area and a non-optimized area. In the process of optimizing design, the transverse vertical coordinates of the steel rail profile of the non-optimized area at the fixed point and at the two sides are unchanged all the time.
Selecting a plurality of points in the optimization area as design points, wherein the abscissa is unchanged, the vertical coordinate is variable, and the vertical coordinate of the design points is the design variable in the optimization design:
the positions of the design points can be freely selected, and the positions of the design points can be automatically determined according to the number and the range of the control points.
And establishing a constraint equation according to the determined design points, and automatically establishing a constraint equation function through the convex shape constraint of the steel rail profile curve after the fixed points and the design points are determined. The constraint relation of the rail profile optimization design is as follows:
in the formula ：is->Data points and->Slope of data point line, +.>Is->Data point and the firstSlope of the line between data points; wherein (1)>Including fixed points and all design points.
The left and right rail profiles should be considered separately. Wherein, the left side design point constraint equation is as follows:
in the formula ,、/>respectively the abscissa and the +.A +.>、/>Respectively the vertical coordinates of two fixed points of the left steel rail.
Determining a constraint range of the design points according to the selected design points, wherein the operation units generally put forward design requirements: the new design profile can set the upper and lower limits of design variables, the upper limit of the design variables of the polishing profile is basically the vertical coordinate of the original profile, and the lower limit of the design variables is generally the maximum polishing amount control provided by a polishing unit.
S3: determining a search subarea of the iterative step, and randomly generating in the search subareaGroup test protocol, new rail profiles are formed for each group, wherein->Is a positive integer.
Determining a search subarea in the current iteration step, wherein the search subarea is the total constraint range of the design points when the iteration step is the initial step, and the constraint range of the design points needs to pass through the upper limit and the lower limit of the boundary of the search area in the second step of the optimization process and the subsequent iteration steps and />To determine. And continuously adjusting the size and the position of the search subarea according to the optimal solution of each iteration step in the optimization process, thereby ensuring the effectiveness of the approximation equation. Search sub-intervals for each design variableCan be determined by the following formula:
wherein ,is the latest optimal solution; />Is the optimal solution of the previous time; />Determining the change direction of the search range; />For the moving step length of the design variable, the moving step length can be determined according to the adjacent two optimal solutions and the relative moving step length:
specifying the step length of the movementWhen (I)>，/>；/>When (I)>，/>。
Generated byA group of test schemes, wherein the first initial scheme is the optimal solution in the optimization process of the last step, and the rest is->Group test protocol is determined from the initial protocol and the design variable movement step size, altogether +.>And optimizing the test scheme.
The steps are performedAnd adopting a group test scheme to form each new steel rail profile by adopting a non-uniform rational B-spline curve fitting curve. Wherein, the B spline curve adopts a B spline basis function to describe complex shapes and local properties thereof, and the B spline curve equation can be written as:
in the formula ,is a control point; />B-spline basis functions are normalized k times.
S4: calculating the geometric relationship between the newly generated steel rail and the wheel rail contact, and obtaining the calculation resultObjective function value of the new test protocol of group, will +.>The target values of the set of experimental protocols are fitted to obtain a linear approximation equation of the objective function.
The wheel-rail contact geometrical relationship is calculated by adopting a space trace method, scanning is carried out within the range of the steel rail according to the position of the steel rail, iteration is continued until the vertical minimum distance point of the left wheel pair and the right wheel pair is found, each characteristic parameter of the wheel-rail contact relationship can be obtained by calculation, namely, the position distribution curve of the steel rail contact point corresponding to the objective function can be obtained, and the objective function value of each group of test schemes is obtained according to the position distribution curve. Wherein, the space trace coordinates are as follows:
and fitting target values of all groups of experimental schemes according to a least square method to obtain a linear approximation equation of the objective function. The approximation equation is defined using a single parameter according to a multiple linear regression method, and expressed as a linear function of the design variables. The linear approximation objective equation of the objective function is:
and (3) combining the step (S2) to obtain a linear approximation constraint equation, the step (S3) to obtain a design point boundary constraint condition, and the step (S4) to obtain a linear approximation target equation, and converting the obtained rail optimization problem into an optimization problem of each approximation equation, namely a simple and easy-to-solve linear programming solution problem.
In step S4, a linear approximation objective function is obtained:
in step S2, a linear approximation constraint equation is obtained:
boundary constraint conditions obtained in step S3:
and (3) obtaining an optimal solution of the approximate objective function in a constraint range meeting a constraint equation and a design point by using a linear programming solving method.
S5: solving an optimal solution of the linear approximation objective function in a constraint range meeting a constraint equation and a design point; performing error analysis on the linear approximation target equation of the target function;
whether the optimal solution meets each error requirement is judged. Because the approximation equation is adopted to replace the original function, error analysis is needed to be carried out on the approximation equation, wherein, for the kth iterative computation, the error analysis of the approximation equation, the dead point analysis, the oscillation analysis and the error analysis of the iteration direction are needed to be carried out.
Approximation equation error analysis:
if it meetsThe obtained approximation solution is sufficiently accurate.
And (3) dead pixel analysis:
if the condition is not satisfiedThe search sub-area needs to be reduced by a reduction coefficient and then one-step optimization calculation is performed, namely +.>。
Approximate solution oscillation analysis:
if the condition is satisfiedWhen searching the boundary of the subarea, the optimal solution needs to evaluate the oscillation factor, and according to the calculation result of the latest two optimal approximate solutions, the oscillation factor is defined>The method comprises the following steps:
wherein if itIndicating that no oscillation occurs in the optimization process; if->The oscillation phenomenon occurs in the optimization process, and the search subarea is required to be reduced by a reduction coefficient, namely +.>。
Iterative direction error analysis:
in the process of multiple iterations, the latest is judgedThe search direction of the sub-iterative optimization calculation is described as being close if the following formula is satisfiedThe search direction of the iterative optimization calculation is the same, and the search subarea needs to be enlarged at the moment, namely +.>。
And S6, judging whether the optimal solution meets the termination condition, and if not, repeating the steps S3 to S5 until the optimal profile is found.
Termination condition analysis: if the condition is satisfiedAnd when the optimal solution is not in the boundary of the search subarea, the obtained approximate solution is the optimal approximate solution of the optimization problem, and the multi-point approximate optimization iterative computation is terminated.
If the condition is not satisfiedThe search sub-area needs to be changed by changing the movement step and steps S3 to S6 are repeated until an optimal profile is found. Wherein the change of the movement step is by the reduction factor obtained by the above error analysis>The realization is as follows:
the present invention will be described in further detail with reference to test examples and specific embodiments below:
taking a standard rail CHN60 profile as an example, calculating a pre-polished design profile matched with the LM wheel tread under the condition of bilateral symmetry.
And calculating the contact relation between the LM and the CHN60 profile wheel rail, determining an original steel rail contact point position distribution curve, wherein the designed steel rail profile is bilaterally symmetrical, so that only a single-side target contact point position distribution curve is required to be established, the right steel rail profile is designed, the transverse movement amount is minus 12-12 mm, a target right steel rail contact point position distribution Curve (CPR) is established, and a linear distribution curve is adopted, as shown in figure 2.
Determining a selection design variable: the fixed point and the design point are freely selected on the right steel rail profile, and the taking point is shown in table 1:
design variables in the optimization design:
establishing an objective function, and for meeting the minimum difference between the target steel rail contact point position distribution curve and the calculated steel rail contact point position distribution curve in the optimization process, the formula is as follows:
in the formula ,is a right side target rail contact point position distribution curve; />Respectively calculating a steel rail contact point position distribution curve according to the optimized steel rail profile; />Is a design variable; />Is the transverse movement amount of the wheel set; />The number of the traversing amount calculation points is calculated.
And establishing a constraint equation, wherein the value of a design variable needs to meet the convex constraint of the steel rail profile curve, and the left steel rail profile and the right steel rail profile should be separately considered. The right design point constraint equation is as follows:
in the formula ,、/>respectively the abscissa and the +.A +.>、/>Respectively the vertical coordinates of two fixed points of the right steel rail.
The constraint range of the design points is determined according to the selected design points, in this embodiment, a pre-polishing mode is adopted, and the maximum polishing amount is 1.5mm, so that the upper limit and the lower limit of each design point are shown in table 2:
and S3, determining the search subarea of the iterative step, wherein the search subarea of the initial step is the upper limit and the lower limit of the design variable, as shown in the table 2.
Random generation within search sub-regionsGroup test protocol.
And adopting a non-uniform rational B-spline curve to fit a curve to form each new steel rail profile.
And calculating the contact geometric relationship between the wheel set and the new wheel rail according to a trace method, and calculating the objective function value of each group of new test schemes.
And fitting target values of all groups of experimental schemes according to a least square method to obtain a linear approximation equation of the objective function.
And (3) solving an optimal solution of the approximate objective function in a constraint range meeting a constraint equation and a design point by using a linear programming method.
Judging whether the optimal solution meets the termination condition, if not, repeating the steps until the optimal profile is found, wherein the calculated design variable results of the optimal profile are shown in the table 3:
the optimum profile thus obtained is shown in fig. 3.
Fig. 4 is a graph of the contact point position profile matched by the calculated optimal profile versus the target profile.
Fig. 5 shows the calculated optimal profile versus the track contact geometry of the tread of the wheel LM.
Compared with the original contact relation, the optimized steel rail profile eliminates uneven contact distribution, the steel rail contact points are distributed more uniformly in the whole contact range, the conformality of the wheel set and the steel rail is increased, thereby playing a better control role on local stress concentration and prolonging the service life of the steel rail.
According to the description of the embodiment, the intelligent rail profile optimization method considering the distribution characteristics of the wheel-rail contact positions on the rail disclosed by the invention has the advantages of simple operation method and high calculation efficiency, and can be well applied to the rail profile optimization design in the railway industry.
The above embodiments are only for illustrating the present invention and not for limiting the present invention, and various changes and modifications may be made by one skilled in the relevant art without departing from the spirit and scope of the present invention, so that all equivalent technical solutions fall within the scope of the present invention, which is defined by the claims.
Claims (6)
1. An intelligent rail profile optimizing method considering distribution characteristics of wheel-rail contact positions on a rail is characterized by comprising the following steps:
s1: establishing a target contact point position distribution curve of the steel rail and the wheel rail, and establishing a target function according to the distribution curve;
s2: selecting design points on the steel rail, dividing the profile of the steel rail into an optimized region and a non-optimized region, establishing a constraint equation function, and determining a constraint range of the design points;
s3: determining the iterative step search subarea, and randomly generating N in the search subarea mov +1 set of test protocols, wherein N mov Is a positive integer;
s4: calculating the geometric relationship between the newly generated steel rail and the wheel rail contact, and calculating to obtain N mov Objective function value of +1 set of new protocol, N mov Fitting the target values of the +1 group experimental scheme to obtain a linear approximation equation of the objective function;
s5: solving an optimal solution of a linear approximation target function in a constraint range meeting a constraint equation and a design point, and performing error analysis on the linear approximation target equation of the target function;
s6: judging whether the optimal solution meets the termination condition, if not, repeating the steps from S3 to S5 until the optimal profile is found;
in the step S1, the method for determining the target contact point position distribution curve is as follows:
based on a vehicle and rail power interaction model, carrying out dynamics simulation analysis according to an actual operation scene, extracting a vehicle body lateral movement amount of simulation operation, determining the contact position of an actual steel rail according to the lateral movement amount, and obtaining a position distribution curve of a steel rail contact point;
the objective function formula is as follows:
wherein DeltaCPL t 、ΔCPR t The distribution curves of the contact points of the target steel rails at the left side and the right side are respectively; ΔCPL c 、ΔCPR c Respectively calculating a steel rail contact point position distribution curve according to the optimized steel rail profile; z is a design variable; y is w Is the transverse movement amount of the wheel set; n is the number of the lateral movement calculation points; a, a 1 、a 2 The weight coefficients of the left contact and the right contact are respectively;
the step S2 is specifically as follows:
s1, determining an adjustment optimization range of the profile of the steel rail according to the target contact point position set in the step S1, and determining a fixed point;
dividing the whole steel rail profile into an optimized region and a non-optimized region;
in the process of optimizing design, the transverse vertical coordinates of the profile of the steel rail in the non-optimized area at the fixed point and the two sides are unchanged all the time;
selecting a plurality of points in the optimization area as design points, wherein the abscissa is unchanged, the vertical coordinate is variable, and the vertical coordinate of the design points is a design variable in the optimization design:
Z＝[z 1 ,z 2 ,...,z n ]
establishing a constraint equation according to the determined design points, and establishing a constraint equation function through the convex shape constraint of the steel rail profile curve after the fixed points and the design points are determined;
the constraint relation of the rail profile optimization design is as follows:
k i ＞k i+1 (i＝A,1,2,...n)
wherein ,ki Slope, k, of the line connecting the ith data point and the (i+1) th data point i+1 Slope of the line between the i+1st data point and the i+2nd data point; i includes the fixed point and all design points.
2. The intelligent rail profile optimizing method considering the distribution characteristics of wheel rail contact positions on rails according to claim 1, wherein the left rail profile and the right rail profile are designed respectively;
wherein, the left side design point constraint equation is as follows:
K L ·Z L ＜b L
in the formula ,yi 、z i Respectively the abscissa and the z of each design point of the left steel rail A 、z B Respectively the vertical coordinates of two fixed points of the left steel rail.
3. A consideration according to claim 1The intelligent rail profile optimizing method for the distribution characteristics of the contact positions of the wheel and the rail on the rail is characterized in that the S3 is specifically as follows: when the iterative step is the initial step, searching the subarea as the total constraint range of the design points, and in the second and subsequent iterative steps of the optimization process, the constraint range of the design points passes through the upper and lower limits of the boundary of the search area and />To determine;
according to the optimal solution of each iteration step in the optimization process, the size and the position of the search subarea are adjusted, and the search subarea of each design variable is determined by the following formula:
wherein ,is the latest optimal solution; />Is the optimal solution of the previous time; />Determining the change direction of the search range;
for the moving step length of the design variable, determining according to the adjacent two optimal solutions and the relative moving step length:
n generated in the above steps mov +1 group of test schemes, adopting non-uniform rational B spline curve fitting curves to form new rail profiles of each group;
wherein, the B spline curve adopts a B spline basis function to describe complex shapes and local properties thereof, and the equation of the B spline curve is as follows:
wherein ,di Is a control point; n (N) i,k (u) is a k-degree canonical B-spline basis function.
4. The intelligent optimization method for the profile of the steel rail taking into account the distribution characteristics of the contact positions of the wheel rail on the steel rail according to claim 1, wherein the step S4 is specifically:
calculating a wheel-rail contact relation by adopting a space trace method, scanning in a steel rail range according to the position of the steel rail, iterating until a vertical minimum distance point of a left wheel pair and a right wheel pair is found, calculating to obtain each characteristic parameter of the wheel-rail contact relation, obtaining a steel rail contact point position distribution curve corresponding to an objective function, and obtaining objective function values of each group of test schemes;
wherein, the space trace coordinates are as follows:
fitting target values of all groups of experimental schemes according to a least square method to obtain a linear approximation equation of an objective function;
defining an approximation equation by adopting a single parameter according to a multiple linear regression method, and expressing the approximation equation as a linear function of a design variable;
the linear approximation objective equation of the objective function is:
combining steps S2 to S4 to obtain a linear approximation objective function:
obtaining a linear approximation constraint equation:
obtaining boundary constraint conditions:
and (3) solving an optimal solution of the approximate objective function in a constraint range meeting a constraint equation and a design point by using a linear programming solving method.
5. The intelligent optimization method for the profile of the steel rail taking into account the distribution characteristics of the contact positions of the wheel and the rail on the steel rail according to claim 4, wherein the step S5 is specifically: performing error analysis on the linear approximation target equation of the target function;
the method comprises the steps of approximation equation error analysis, dead pixel analysis, approximation solution oscillation analysis and iteration direction error analysis;
the approximation equation error analysis concretely comprises the following steps:
if satisfy r k ≤ε k The error analysis results are: meets the requirements;
the dead pixel analysis concretely comprises the following steps:
if the condition r is not satisfied i m ≤ε k The search sub-area is reduced by the reduction coefficient, and then one-step optimization calculation is performed, i.e. t=t bad ，T bad ＞1；
The approximate solution oscillation analysis concretely comprises the following steps:
if the condition r is satisfied i m ≤ε k When searching the boundary of the subarea, the optimal solution carries out oscillation factor evaluation, and according to the calculation result of the latest two optimal approximate solutions, an oscillation factor theta is defined m Is that
Wherein if theta m ∈[0,1]Indicating that no oscillation occurs in the optimization process; if theta is m ∈[-1,0]The search sub-area is then reduced by a reduction factor, i.e. t=t osc ；
The iteration direction error analysis concretely comprises the following steps:
in the process of multiple iterations, judging the searching direction of the latest iteration optimization calculation,
if 1- ρ is less than or equal to |θ i |≤1,i＝k,k-1,…,k-l+1，
Then expand the search sub-region to t=t enlr 。
6. The intelligent optimization method for the profile of the steel rail taking into account the distribution characteristics of the contact positions of the wheel and the rail on the steel rail according to claim 1, wherein the step S6 is specifically:
if the condition r is satisfied i m ≤ε k When the optimal solution is not in the boundary of the search subarea, the obtained approximate solution is the optimal approximate solution of the optimization problem, and the multi-point approximate optimization iterative computation is terminated;
if not full ofFoot condition r i m ≤ε k Changing the search subarea by changing the moving step length, and repeating the steps from S3 to S6 until the optimal profile is found;
wherein the change of the moving step length is realized by the reduction coefficient T obtained by each error analysis:
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| CN114218643A (en) * | 2021-12-16 | 2022-03-22 | 上海应用技术大学 | Rapid design method of steel rail profile |
| CN115510735A (en) * | 2022-08-22 | 2022-12-23 | 北京交通大学 | Rail grinding target profile optimization design method based on wheel-rail contact parameters |
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| CN114218643A (en) * | 2021-12-16 | 2022-03-22 | 上海应用技术大学 | Rapid design method of steel rail profile |
| CN115510735A (en) * | 2022-08-22 | 2022-12-23 | 北京交通大学 | Rail grinding target profile optimization design method based on wheel-rail contact parameters |
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