CN110029544B - Method and device for measuring track irregularity - Google Patents

Abstract

The application provides a measuring method and a measuring device for rail irregularity, wherein the measuring method based on a multi-measuring-point multi-order chord measuring method comprises the steps of measuring a plurality of groups of combined chord measuring values in a target section according to a preset sampling step length, establishing a measuring model for measuring rail short wave irregularity based on the measuring process of the multi-measuring-point multi-order chord measuring method and the condition that a plurality of groups of combined chord measuring value matrixes are equal to the product of a measuring matrix and a matrix formed by adjacent discretization of the geometric configuration and position of a steel rail, and obtaining the rail irregularity by constructing an optimized model of the measuring model and carrying out inversion solution on the optimized model. Therefore, the detection data of a plurality of measuring points can be effectively fused, the measurement error control is realized by solving through a linear system, and the measurement precision is improved while the smaller measurement wavelength resolution is ensured; and moreover, the maximum utilization of the sensor at the measuring point is realized through the combined optimization of the measuring point positions by the chord measuring method, and a measuring result with higher precision is obtained.

Description

Method and device for measuring track irregularity

Technical Field

The application relates to the technical field of steel rail measurement, in particular to a method and a device for measuring track irregularity.

Background

The rail irregularity comprises steel rail short wave irregularity and steel rail long wave irregularity in rail traffic. Taking rail short wave irregularity as an example, the rail short wave irregularity mainly comprises rail surface roughness, rail surface irregularity and wheel tread irregularity, and the rail short wave irregularity can not only excite rolling vibration and noise of a wheel rail, but also cause high-frequency wheel rail contact force and impact force, and further cause damages such as Guidong contact fatigue crack, rail corrugation and the like on the surface of a wheel or the rail. Therefore, the detection and analysis of the irregularity of the rail are the premise and the foundation for reasonably maintaining and repairing the steel rail, controlling the vibration and noise of the wheel rail and prolonging the service life of the steel rail.

The related technology provides a chord measuring system measuring method based on the geometric principle to measure the track irregularity, the method generally adopts an asymmetric three-point chord measuring method to measure the corresponding vector deviation value, and the restoration of the short wave irregularity is realized by a method of designing a digital inverse filter. By the method, on one hand, data loss at two ends of a measurement section can be caused in the filtering process, and on the other hand, the design of the filter under the asymmetric condition is too complex, errors can be generated in the measurement result due to the design of the filter, and the problem of data fusion under the condition of multiple measuring points cannot be solved.

The related art also provides an acceleration quadratic integration method based on dynamic response, which needs to keep a certain measuring speed, requires that a measuring instrument is in an excitation state, and has poor measuring effect under the condition of low speed.

Disclosure of Invention

In view of this, an object of the embodiments of the present application is to provide a method and an apparatus for measuring track irregularity, which measure the track irregularity by using a multi-point method, improve a measurable wavelength range of a track, have high measurement result precision, are not limited by a detection speed, and have good operability.

In a first aspect, an embodiment of the present application provides a method for measuring track irregularity, including:

measuring a plurality of groups of combined chord measuring values in a target section according to a preset sampling step length based on a measuring method of a multi-measuring-point multi-order chord measuring method; wherein the combined chord value comprises detailed shape information of the measurement object;

establishing a measurement model for measuring short-wave irregularity of the steel rail based on the measurement process of a multi-measuring-point multi-order chord measuring method and the condition that a plurality of groups of combined chord measuring value matrixes are equal to the product of a measurement matrix and a matrix formed by adjacent discretization of the geometric shape and position of the steel rail;

reconstructing a least square optimization model corresponding to the measurement model and comprising the target orbit geometric form and position based on the principle that the error of the optimal target orbit geometric form and position and the measured multiple groups of combined measured values is minimum;

and carrying out inversion solving on the least square optimization model to obtain the track irregularity.

With reference to the first aspect, an embodiment of the present application provides a first possible implementation manner of the first aspect, where the method for measuring a multi-point and multi-order chord survey includes:

according to the determined chord measuring method order, carrying out equal division processing on the measured chord length to obtain a plurality of equal division points;

if the number of the target measuring points to be measured is one, determining an optimal single measuring point chord measuring method arrangement mode from multiple arrangement modes of the target measuring point at different equally-divided points;

if the number of the target measuring points to be measured is more than one, determining an optimal double-measuring-point chord measuring method arrangement mode by adjusting the position of an added measuring point to be added on the basis of the optimal single-measuring-point chord measuring method arrangement mode; and judging whether the number of target measuring points in the optimal double-measuring-point chord measuring method arrangement mode meets the requirement, if not, continuously obtaining the optimal three-measuring-point chord measuring method arrangement mode by adjusting the position of one added measuring point to be added on the basis of the optimal double-measuring-point chord measuring method arrangement mode until the number of the target measuring points in the current optimal target measuring-point chord measuring method arrangement mode meets the requirement.

With reference to the first possible implementation manner of the first aspect, this application provides a second possible implementation manner of the first aspect, where the determining an optimal single-measurement-point chord measurement method arrangement manner from multiple arrangement manners of the one target measurement point at different equally-divided points includes:

calculating an error amplification coefficient of each group of double-measuring-point chord measuring method arrangement modes aiming at the long-wave track, and selecting the double-measuring-point chord measuring method arrangement mode with the minimum error amplification coefficient from the groups of error amplification coefficients as an optimal double-measuring-point chord measuring method arrangement mode; wherein the double measuring points in the arrangement mode of each group of double measuring point chord measuring method are positioned at different equally-divided points;

and calculating the critical wavelength of each group of double-measuring-point chord measuring method arrangement modes aiming at the short wave track, and selecting the double-measuring-point chord measuring method arrangement mode with the largest critical wavelength from the multiple groups of critical wavelengths as the optimal double-measuring-point chord measuring method arrangement mode.

With reference to the first aspect, an embodiment of the present application provides a third possible implementation manner of the first aspect, where the establishing a measurement model for measuring rail short wave irregularity based on a measurement process of a multi-point and multi-level chord measurement method and a product of a plurality of groups of combined chord measurement value matrixes equal to a product of a measurement matrix and a matrix formed by adjacent discretization of rail geometric positions includes:

establishing a mathematical expression of a measuring process of a multi-measuring-point multi-order chord measuring method:

k＝c₁,c₂,…,c_w(ii) a Wherein s represents the number of sensors; c. C_wIndicating the location of the w-th sensor; the k value corresponds to s measuring points, h_kChord, lambda, obtained for the kth station position_kThe proportional value of the sensor arranged at the kth measuring point is a negative number;

y_kas the value of the track irregularity at position k, y₀The value of the track irregularity at the beginning of the chord line, y_n+1The track irregularity value at the end of the chord line, and N is the chord measuring order;

based on a mathematical expression of a measuring process of a multi-measuring-point multi-order chord measuring method and a product that a plurality of groups of combined chord measuring value matrixes are equal to a measuring matrix and a matrix formed by adjacent discretization of the geometric shape and position of the steel rail, a measuring model is established: h is M.F;

whereinH represents a combined chord measurement value matrix; m represents a measurement matrix, the first line of M corresponds to the information of the 1 st measuring point, the c1+1 th element of the midpoint is 1, the second line corresponds to the information of the 2 nd measuring point, wherein the c2+1 th element of the midpoint is 1, and the values of the elements in the 3 rd line are the same; c1 denotes the first row of matrix H, c2 denotes the second row of matrix H, and so on, c_wRepresents the w rows of matrix H; N-N-2 represents the N-N-2 column of the matrix H, and N-N-1 represents the N-N-1 column of the matrix H; n represents the chord measuring order number, and N represents the column number of the matrix H;

the F matrix is a matrix formed by measurement objects y and has the following structure:

the matrix F (y) is the combination of the measurement objects y, the number of independent unknowns of the matrix is only size (y), and size (y) is the length of the vector y; n represents the number of columns of the matrix F and N represents the chordal order.

With reference to the third possible implementation manner of the first aspect, this application provides an example of a fourth possible implementation manner of the first aspect, where reconstructing a least-squares optimization model corresponding to the measurement model and including the target orbit geometry based on a principle that an error between the optimal target orbit geometry and the measured multiple sets of combined measured values is minimum includes:

based on the principle that the error between the optimal track geometry y and the measured combined chord value H is minimum, a least square optimization model comprising the optimal track geometry y is constructed:

wherein M represents a measurement matrix, the matrix F (y) represents a combination of the rail irregularity objects y to be measured, and H represents a combined chord measurement value matrix.

With reference to the fourth possible implementation manner of the first aspect, an embodiment of the present application provides a fifth possible implementation manner of the first aspect, where the performing inversion solution on the least squares optimization model to obtain the orbit irregularity includes:

splitting the measurement matrix M according to rows to obtain a matrix A_k(k＝c₁,c₂,…,c_w) (ii) a Wherein A is_kRepresenting the matrix after the matrix M is split according to rows; c. C_wRepresents the w rows of matrix M; m represents a measurement matrix;

splitting the combined chord measuring value matrix H according to rows to obtain a vector H_k(k＝c₁,c₂,…,c_w) (ii) a Wherein h is_kRepresenting the matrix H split according to rows; c. C_wRepresents the w rows of matrix H; m represents a combined chord measurement value matrix;

based on matrix A_kSum vector h_kTwo independent systems of linear equations are obtained: a. the_k·y＝h_k；k＝c₁,c₂,…,c_w(ii) a Wherein y represents the rail irregularity object to be measured;

based on the linear equation set, the least square optimization model is converted to obtain a conversion model:

wherein E represents a total residual value objective function, the optimization objective is to minimize the total residual value objective function, and U represents a matrix;

based on a system of linear equations

Solving the conversion model; wherein i represents a number from c₁To c_wOf an arbitrary value selected from A_iRepresents from A_kOf an arbitrary value selected from A_i ^TIs A_iTranspose of (A)_k ^TIs represented by A_kTranspose of (y)^*And the optimal solution is the optimal solution of the measured object, namely the track irregularity measurement result.

With reference to the first aspect, the first possible implementation manner of the first aspect, to the fifth possible implementation manner of the first aspect, an embodiment of the present application provides a sixth possible implementation manner of the first aspect, where the performing an inversion solution on the least squares optimization model to obtain an orbit irregularity includes:

and filtering the obtained track irregularity according to the high-pass filtering of the preset filtering wavelength to obtain the original track irregularity.

In a second aspect, an embodiment of the present application further provides a device for measuring track irregularity, including:

the measuring module is used for measuring a plurality of groups of combined chord measuring values in a target section according to a preset sampling step length based on a measuring method of a multi-point multi-order chord measuring method; the combined chord value includes detailed shape information of the measurement object;

the building module is used for building a measuring model for measuring short-wave irregularity of the steel rail based on the measuring process of a multi-point multi-order chord measuring method and the condition that a plurality of groups of combined chord measuring value matrixes are equal to the product of a measuring matrix and a matrix formed by adjacent discretization of the geometrical shape and position of the steel rail;

the reconstruction module is used for reconstructing a least square optimization model which corresponds to the measurement model and comprises the target orbit geometric form and position on the basis of the principle that the error between the optimal target orbit geometric form and the measured multiple groups of combined chord measurement values is minimum;

and the calculation module is used for carrying out inversion solving on the least square optimization model to obtain the track irregularity.

With reference to the second aspect, the present application provides a first possible implementation manner of the second aspect, where the track irregularity measuring device provided by the present application further includes:

the halving processing module is used for performing halving processing on the measured chord length according to the determined chord measuring order to obtain a plurality of halving points;

the determining module is used for determining an optimal single-measuring-point chord measuring method arrangement mode from multiple arrangement modes of one target measuring point at different equally-divided points if the number of the target measuring points to be measured is one; if the number of the target measuring points to be measured is more than one, determining an optimal double-measuring-point chord measuring method arrangement mode by adjusting the position of an added measuring point to be added on the basis of the optimal single-measuring-point chord measuring method arrangement mode; and judging whether the number of target measuring points in the optimal double-measuring-point chord measuring method arrangement mode meets the requirement, if not, continuously obtaining the optimal three-measuring-point chord measuring method arrangement mode by adjusting the position of one added measuring point to be added on the basis of the optimal double-measuring-point chord measuring method arrangement mode until the number of the target measuring points in the current optimal target measuring-point chord measuring method arrangement mode meets the requirement.

With reference to the first possible implementation manner of the second aspect, an embodiment of the present application provides a second possible implementation manner of the second aspect, where the determining module is specifically configured to:

calculating an error amplification coefficient of each group of double-measuring-point chord measuring method arrangement modes aiming at the long-wave track, and selecting the double-measuring-point chord measuring method arrangement mode with the minimum error amplification coefficient from the groups of error amplification coefficients as an optimal double-measuring-point chord measuring method arrangement mode; wherein the double measuring points in the arrangement mode of each group of double measuring point chord measuring method are positioned at different equally-divided points;

and calculating the critical wavelength of each group of double-measuring-point chord measuring method arrangement modes aiming at the short wave track, and selecting the double-measuring-point chord measuring method arrangement mode with the largest critical wavelength from the multiple groups of critical wavelengths as the optimal double-measuring-point chord measuring method arrangement mode.

The method and the device for measuring the track irregularity are based on a measuring method of a multi-measuring-point multi-order chord measuring method, a plurality of groups of combined chord measuring values in a target section are measured according to preset sampling step length, a measuring model for measuring the short-wave irregularity of the steel rail is established based on the measuring process of the multi-measuring-point multi-order chord measuring method and the fact that a plurality of groups of combined chord measuring value matrixes are equal to the product of a measuring matrix and a matrix formed by adjacent discretization of the geometric shape and position of the steel rail, the track irregularity is obtained by constructing an optimized model of the measuring model and performing inversion solution on the optimized model, the detection data of a plurality of measuring points can be effectively fused, measurement error control is realized through a linear system, and the measurement precision is improved while smaller measurement wavelength resolution is ensured; and moreover, the maximum utilization of the sensor at the measuring point is realized through the combined optimization of the measuring point positions by the chord measuring method, and a measuring result with higher precision is obtained.

In order to make the aforementioned objects, features and advantages of the present application more comprehensible, preferred embodiments accompanied with figures are described in detail below.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained from the drawings without inventive effort.

FIG. 1 is a schematic structural diagram illustrating a basic concept of an N-order optimal chord measurement method provided by an embodiment of the present application;

FIG. 2 is a schematic structural diagram of an S-point Nth order chord measuring method provided by an embodiment of the present application;

FIG. 3 is a schematic diagram illustrating a 2-point Nth order chord measurement process provided by an embodiment of the present application;

FIG. 4 is a schematic diagram illustrating another 2-point Nth order chord measurement process provided by the embodiment of the present application;

FIG. 5 is a flow chart illustrating a method for measuring rail irregularity according to an embodiment of the present disclosure;

FIG. 6 is a flow chart of another track irregularity measuring method provided by embodiments of the present application;

FIG. 7 is a schematic diagram illustrating distribution of chord survey patterns at a single measurement point according to an embodiment of the present application;

FIG. 8 is a schematic diagram showing the distribution of chord survey patterns at two survey points provided by the embodiment of the present application;

FIG. 9 is a schematic diagram illustrating a distribution of s-point chord survey measurements provided by an embodiment of the present application;

FIG. 10 is a flow chart illustrating an optimization method of the optimal S-point chord measurement method provided by an embodiment of the present application;

FIG. 11 is a schematic structural diagram of another track irregularity measuring device provided by an embodiment of the present application;

fig. 12 shows a schematic structural diagram of a computer device 40 provided in an embodiment of the present application.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all the embodiments. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present application, presented in the accompanying drawings, is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present application without making any creative effort, shall fall within the protection scope of the present application.

This application embodiment is arranged in measuring the short wave irregularity in the track geometry irregularity, and the wavelength of the rail short wave irregularity of general concern is between 1mm to 3000mm, and the amplitude is at submillimeter level. The basic idea of measuring rail irregularity by a chord survey method is shown in fig. 1, which includes two core processes, a measurement process and a reconstruction process. As shown in fig. 2, in order to obtain the short-wave irregularity of the steel rail, the embodiment of the present application is implemented by an "S-point N-order chord measurement method", which includes two main processes, 1) a S-point N-order chord measurement method measurement process; 2) and (4) post-processing the data by an S-point N-order chord measuring method to obtain the short-wave irregularity of the steel rail.

The embodiment of the application provides a method and a device for measuring rail irregularity, in particular to a method for measuring short wave grinding detection of a steel rail based on a chord measuring system.

In the embodiment of the application, the chord measuring method is used for measuring the geometric irregularity of the track (namely the steel rail), and the layout mode of the chord measuring system is as follows: the method comprises the steps of selecting a measuring reference chord line with a certain length, enabling two ends of the chord line to be in contact with a steel rail, measuring the vertical distance between the middle point (or an equal ratio point or a plurality of measuring points) of the chord line and the corresponding steel rail position, namely a chord value, recording the chord value with a certain sampling step length delta l along the movement of the chord line along the steel rail direction (any direction of the steel rail), and forming a chord value vector (or a combined chord value vector).

For the nth order chord length measurement method, the nth order chord length measurement method is defined in the embodiment of the present application as being called the nth order chord length measurement method when, for a given measurement reference chord length L, chord measurement value measurement points are arranged at N +1 bisectors of the chord line (N possible positions in total), and the sampling step length Δ l is equal to or less than L/(N + 1).

For example, in the case of measuring a reference chord length of 1m, if the chord measurement value is located at some 9 bisector of the chord line and the sampling step size is 0.1m, the measurement method may be referred to as a 10 th order chord measurement method. The detection effect of the chord measuring method with different orders is related to the number and the arrangement position of the measuring points.

For the S point N order chord measurement method, for an N order chord measurement method, if only one measuring point is located at a certain N +1 equally divided point, the method is called a 1 point N order chord measurement method, when the number of the measuring points is S (S is an integer greater than or equal to 1), the method is called an S point N order chord measurement method, a schematic diagram of the measuring process of a 2 point N order chord measurement method is respectively shown in FIG. 3 and FIG. 4, two measuring points in the diagram are respectively located at the ith and jth N +1 equally divided points, and the measuring step length is L/(N + 1).

As shown in fig. 5, based on the chord measuring system, the method for measuring track irregularity provided in the embodiment of the present application includes the following steps:

s101, measuring a plurality of groups of combined chord measuring values in a target section according to a preset sampling step length by using a measuring method based on a multi-point multi-order chord measuring method; wherein the combined chord value comprises detailed shape information of the measurement object.

In the embodiment of the present application, a group of combined chord values is measured at each preset sampling step, and the target segment may correspond to a plurality of preset sampling steps, so that a plurality of groups of combined chord values are obtained. Wherein, each group of combined chord measuring values comprises the detailed shape information of the measuring object (namely the steel rail).

S102, establishing a measuring model for measuring short-wave irregularity of the steel rail based on a measuring process of a multi-measuring-point multi-order chord measuring method and the fact that a plurality of groups of combined chord measuring value matrixes are equal to the product of a measuring matrix and a matrix formed by adjacent discretization of geometrical configuration and position of the steel rail.

In the embodiment of the application, the measurement process of the multi-point and multi-order chord measurement method is described by a mathematical method, multiple groups of measured chord value vectors are subjected to matrix integration based on the mathematical description of the measurement process, the integration aims to adopt a matrix to uniformly describe, and the measurement results are integrated into a linear equation set so as to facilitate the establishment of a post-processing model. Then, defining a measurement matrix, and establishing a measurement model for measuring the short wave irregularity of the steel rail based on the idea that the product of the measurement matrix and a matrix formed by adjacent discretization of the geometric configuration of the steel rail is equal to a plurality of groups of combined chord measurement value matrixes.

S103, reconstructing a least square optimization model including the target orbit geometric shape and position corresponding to the measurement model based on the principle that the error of the optimal target orbit geometric shape and position and the measured multiple groups of combined measured values is minimum.

In the embodiment of the application, the process of inverting the track irregularity based on the established measurement model is the inverse process of the measurement process, and in practice, the establishment of the measurement model is based on the principle of least squares. It should be emphasized here that, under the condition of not considering the measurement error, a single measurement point is enough to invert to obtain the original track irregularity, that is, the measurement model itself is accurate, but the actual measurement process inevitably results in the measurement error due to the accuracy of the sensor at the measurement point position, the state of the measurement equipment and the change of the environment, the measurement error will be amplified in the inversion process, resulting in the decrease of the result accuracy, and at this time, the accumulation of the error can be effectively controlled by adopting a higher sampling frequency (i.e. a smaller adopted step length) and arranging more measurement points. This is the original intention of the embodiments of the present application to use the S-point N-th order chord measurement method (i.e., the idea of the embodiments of the present application is to control error accumulation).

In the embodiment of the application, an optimal orbit geometric form and position is sought for the established measurement model, so that the error between the optimal orbit geometric form and position and the measured combined chord value is minimized.

And S104, carrying out inversion solving on the least square optimization model to obtain the track irregularity.

In the embodiment of the application, inversion of track irregularity corresponds to a measurement model, the inversion of the track irregularity is realized by establishing a least square optimization model of redundant data fusion and solving a linear equation set, and finally, a digital high-pass filtering method is adopted to obtain the short wave irregularity.

The measuring method for the track irregularity provided by the embodiment of the application is based on a measuring method of a multi-measuring-point multi-order chord measuring method, a plurality of groups of combined chord measuring values in a target section are measured according to a preset sampling step length, a measuring model for measuring the short-wave irregularity of the steel rail is established based on the measuring process of the multi-measuring-point multi-order chord measuring method and the condition that a plurality of groups of combined chord measuring value matrixes are equal to the product of a measuring matrix and a matrix formed by adjacent discretization of the geometric configuration and the position of the steel rail, the track irregularity is obtained by constructing an optimized model of the measuring model and performing inversion solution on the optimized model, the detection data of a plurality of measuring points can be effectively fused, the measurement error control is realized by solving through a linear system, and the measurement precision is improved; and moreover, the maximum utilization of the sensor at the measuring point is realized through the combined optimization of the measuring point positions by the chord measuring method, and a measuring result with higher precision is obtained.

In the embodiment of the application, the track irregularity is obtained by solving a linear equation set equivalent to the constructed least square optimization model.

Further, as shown in fig. 6, in the measurement method for measuring the track irregularity provided in the embodiment of the present application, a general measurement method is provided, and the measurement method may be used in different detection situations, and is not specific to a certain type of detection device, nor a certain specific chord length and order N. In the measurement process, the chord measurement value vector at the corresponding measurement point is required to be obtained. The specific measurement method comprises the following steps:

and S201, according to the determined chord measuring method order, carrying out equal division processing on the measured chord length to obtain a plurality of equal division points.

In the embodiment of the application, a chord measuring order N of a measured chord length is predetermined, and the determined measured chord length is equally divided through the determined chord measuring order N to obtain a plurality of equal division points on a plurality of measured chord lengths.

S202, if the number of the target measuring points to be measured is one, determining an optimal single measuring point chord measuring method arrangement mode from multiple arrangement modes of the target measuring point at different equally-divided points.

In the embodiment of the application, an optimal measuring point arrangement scheme for a single-measuring-point N-order chord measuring method is as follows, for a single-measuring-point situation, for a measured chord length L and an order N of the chord measuring method, target measuring points (i.e. possible measuring points) are distributed at N +1 equal divisions of the N chord lines, that is, the N equal divisions equally divide the chord line L into N +1 equal divisions, as shown in fig. 7, assuming that the left side of the target measuring points is z parts and the right side is t, the following steps are provided:

z+t＝N+1；

wherein, z, t ∈ N⁺And z and t are integral parts of two parts divided by a single measuring point.

The optimal single-point chord measurement method is provided in the embodiment of the application in an arrangement mode as follows:

the minimum measurement wavelength resolution can reach 2L/(N +1) under the condition that z and t are relatively prime, namely the greatest common divisor is 1 and is recorded as (z, t) being 1, wherein Δ w represents the minimum measurement wavelength resolution, L represents the measurement chord length L, and N represents the order of the chord measuring method, and the condition that the highest measurement precision is ensured on the basis that z and t need to meet the following optimal condition:

min|z-t|；

in particular when N is an even number, there are:

in fact, through the calculation model provided by the embodiment of the application, even if the calculation model is not an optimal point distribution mode, the track geometric irregularity (short wave) can be measured, and only the optimal conditions can ensure that the control effect on the error is optimal.

Note that, in the optimal single-point chord measurement method, a local boundary effect occurs, and data of a shorter range (the data length is the chord length L) at both ends may be discarded.

S203, if the number of the target measuring points to be measured is more than one, determining an optimal double-measuring-point chord measuring method arrangement mode by adjusting the position of an added measuring point to be added on the basis of the optimal single-measuring-point chord measuring method arrangement mode; and judging whether the number of target measuring points in the optimal double-measuring-point chord measuring method arrangement mode meets the requirement, if not, continuously obtaining the optimal three-measuring-point chord measuring method arrangement mode by adjusting the position of one added measuring point to be added on the basis of the optimal double-measuring-point chord measuring method arrangement mode until the number of the target measuring points in the current optimal target measuring-point chord measuring method arrangement mode meets the requirement.

As shown in FIG. 8, for the case of two measuring points, for measuring the chord length L and the chord measuring order N, the target measuring point (i.e. the possible measuring point) is distributed at the N +1 equal division point of the N chord lines, that is, the N equal division points equally divide the chord line L into N +1 parts, the two measuring points divide the N +1 into r parts, z parts and t parts, wherein r, z and t are integer parts divided by the two measuring points into three parts.

Similarly, the embodiment of the application provides an optimal arrangement mode of a two-point chord measuring method:

the minimum measurement wavelength resolution can reach Δ w of 2L/(N +1) under the condition that the greatest common divisor of r, z and t is 1, and is marked as (r, z, t) ═ 1:, Δ w represents the minimum measurement wavelength resolution, L represents the measurement chord length L, and N represents the order of the chord measuring method

r＝round(0.34·N)；

Where round (·) represents a rounding operation. In particular when N is an odd number, there are:

r＝round(0.34·N)；

for S (S is more than or equal to 2) point N order chord measurement method, the optimal measuring point optimization method of the S point N order chord measurement method is as follows:

as shown in FIG. 9, for the case of multiple measuring points (the number of measuring points S is greater than 2), for measuring the chord length L and the chord length measurement order N, the possible measuring points are distributed at the N +1 equal divisions of the N chord lines, that is, the N equal divisions equally divide the chord line L into N +1, and the S measuring points are set to divide N +1 into r₁Portion, r₂Parts and r_s+1And (4) portions are obtained.

As shown in FIG. 10, for the optimal s-point chord method, the condition that the minimum measurement wavelength resolution can reach Δ w of 2L/(N +1) is that (r)₁,r₂,…,r_s+1) 1, i.e. the greatest common divisor of the s +1 integers is 1; wherein r is₁、r₂And r_s+1Is an integral number of parts divided into s +1 parts by s measuring points. With the increase of the number of the measuring points, the absolutely optimal point distribution mode is too complex, and the embodiment of the application provides a general optimal multipoint chord measuring method optimization mode: and adding an optimal measuring point on the basis of the optimal two-measuring-point chord measuring method to form an optimal three-measuring-point chord measuring method, adding an optimal measuring point on the basis of the optimal three-measuring-point chord measuring method to form an optimal four-measuring-point chord measuring method, and repeating the steps to form an optimal s-point chord measuring method by adding an optimal measuring point on the basis of the optimal s-1 measuring-point chord measuring method.

Further, in the method for measuring rail irregularity provided in the embodiment of the present application, in step 102, the step of establishing a measurement model for measuring rail short-wave irregularity based on the measurement process of the multi-point and multi-level chord measurement method and the product of the multiple groups of combined chord measurement value matrixes equal to the measurement matrix and the matrix formed by the geometric discretization of the rail, includes:

establishing a mathematical expression of a measuring process of a multi-measuring-point multi-order chord measuring method:

k＝c₁,c₂,…,c_w(ii) a Wherein s represents the number of sensors; c. C_wIndicating the location of the w-th sensor; the k value corresponds to s measuring points, h_kChord, lambda, obtained for the kth station position_kThe proportional value of the sensor arranged at the kth measuring point is a negative number;

the above-mentioned-represents a symbol, y_kAs the value of the track irregularity at position k, y₀The value of the track irregularity at the beginning of the chord line, y_n+1The value of the track irregularity at the end of the chord line, and N is the chord gauging order.

And integrating the matrixes of the measured chord value vectors, wherein the integration aims to adopt the matrixes to uniformly describe, and integrates the measured results into a linear equation set so as to facilitate the establishment of a post-processing model. Based on a mathematical expression of a measuring process of a multi-measuring-point multi-order chord measuring method and a product that a plurality of groups of combined chord measuring value matrixes are equal to a measuring matrix and a matrix formed by adjacent discretization of the geometric shape and position of the steel rail, a measuring model is established: h is M.F;

wherein H represents a combined chord measurement value matrix; m represents a measurement matrix, the first line of M corresponds to the information of the 1 st measuring point, the c1+1 th element of the midpoint is 1, the second line corresponds to the information of the 2 nd measuring point, wherein the c2+1 th element of the midpoint is 1, and the values of the elements in the 3 rd line are the same; c1 denotes the first row of matrix H, c2 denotes the second row of matrix H, and so on, c_wRepresents the w rows of matrix H; N-N-2 denotes the N-N-2 column of the matrix H, and N-N-1 denotes the matrixColumn N-N-1 of H; n represents the chord measuring order number, and N represents the column number of the matrix H; the above-mentioned-represents a symbol, specifically,

the F matrix is a matrix formed by measurement objects y and has the following structure:

the matrix F (y) is the combination of the measurement objects y, the number of independent unknowns of the matrix is only size (y), and size (y) is the length of the vector y; n represents the number of columns of the matrix F and N represents the chordal order.

Further, in the method for measuring track irregularity provided in the embodiment of the present application, S103, reconstructing a least-squares optimization model including the target track geometry corresponding to the measurement model based on a principle that an error between the optimal target track geometry and the measured multiple groups of combined measured values is minimum includes:

and constructing a least square optimization model comprising the optimal track geometry y based on the principle that the error between the optimal track geometry y and the measured combined chord value H is minimum. The least squares optimization model can be simply described as finding an optimal orbit geometry y such that its error with the measured combined chord value H is minimal, i.e.:

the optimization model of the above formula implies partial constraints, that is, the matrix F (y) is coupled, and the optimization solution needs to decouple the matrix F (y) first; wherein M represents a measurement matrix; the matrix F (y) represents the combination of the rail irregularity objects y to be measured; h represents a combined chord measurement value matrix; the matrix is formed by reading of a plurality of measuring point sensors (namely, a combined chord measuring value matrix), each row corresponds to the reading of one sensor along the mileage direction, and each column corresponds to the reading of all the sensors after a certain movement.

In step 104, the inversion solving is performed on the least square optimization model, and the process of obtaining the track irregularity is as follows:

the least square optimization model belongs to a convex optimization problem with constraint, but the constraint is hidden in an objective function, so that the direct solution is inconvenient, and the matrix F (y) is decoupled firstly.

Therefore, in the embodiment of the present application, the measurement matrix M is divided into rows, and the matrix a is defined based on the rows_k(k＝c₁,c₂,…,c_w)：

k＝c₁,c₂,…,c_w；

Wherein A is_kRepresenting the matrix after the matrix M is split according to rows; c. C_wRepresents the w rows of matrix M; m represents a measurement matrix;

splitting chord value matrix H according to rows and defining vector H based on the split chord value matrix H_k(k＝c₁,c₂,…,c_w)：

h_k＝{h_k,1h_k,2… h_k,N-n-1h_k,N-n}^T(ii) a k ═ i, j; wherein h is_kRepresenting the matrix H split according to rows; c. C_wRepresents the w rows of matrix H; m represents a combined chord measurement value matrix; i represents h_kThe number of rows of (a), j represents h_kThe number of columns.

Based on matrix A_kSum vector h_kThe following two independent systems of linear equations can be obtained:

A_k·y＝h_k；k＝c₁,c₂,…,c_w；

the least squares optimization model can be converted into:

where E represents the total residual value objective function, the objective of the optimization is to minimize it, U represents the matrix, in U, A_c1To A_cwCan representIs A_i(i ═ c1, …, cw, as follows:

based on a system of linear equations

Solving the conversion model; wherein i represents a number from c₁To c_wOf an arbitrary value selected from A_iRepresents from A_kOf an arbitrary value selected from A_i ^TIs A_iTranspose of (A)_k ^TIs represented by A_kTranspose of (y)^*And the optimal solution is the optimal solution of the measured object, namely the track irregularity measurement result.

At a single station, the optimization model can be described simply as:

corresponding, single-point time least-squares solution y^*This is achieved by solving the following system of linear equations: a. the_i ^TA_i·y^*＝A_i ^Th_i. Wherein A is_iRepresents from A_kOf an arbitrary value selected from A_i ^TIs A_iTranspose of (A)_k ^TIs represented by A_kTranspose of (y)^*And the optimal solution is the optimal solution of the measured object, namely the track irregularity measurement result.

The process of solving the transformation model is as follows: the optimization model belongs to a typical convex optimization model, and the optimal solution y^*It can be calculated by the following linear operator:

wherein,

a simplified operator for the inverse model; h is a chord measuring value matrix obtained by measurement; m is smallMarking a corresponding measurement matrix (determined by a multipoint arrangement form); a. the_iRepresents the diagonal matrix generated from the ith row of the measurement matrix M, of the form:

A_i ^Tis A_iTranspose of h_kTransposed vector, y, representing the k-th row vector of the measurement matrix H^*And the optimal solution is the optimal solution of the measured object, namely the track irregularity measurement result.

The above formula can be understood as that for a given multipoint chord arrangement form, only the corresponding chord value matrix needs to be measured, that is, the inversion operator can be used

The described calculation expression yields the optimum estimation y of the track irregularity^*. It should be noted that if the matrix is a matrix

Irreversible, then adopt

The pseudo-inverse of (1).

Further, in step 202, the method for measuring track irregularity provided in this embodiment of the present application, where the determining an optimal single-measuring-point chord measurement method arrangement manner from multiple arrangement manners of the target measuring point at different equally-divided points includes:

calculating an error amplification coefficient of each group of double-measuring-point chord measuring method arrangement modes aiming at the long-wave track, and selecting the double-measuring-point chord measuring method arrangement mode with the minimum error amplification coefficient from the groups of error amplification coefficients as an optimal double-measuring-point chord measuring method arrangement mode; wherein the double measuring points in the arrangement mode of each group of double measuring point chord measuring method are positioned at different equally-divided points.

In the embodiment of the present application, the embodiment of the present application proposes an S-point N-order chord measuring method, and the measuring method of the measuring accuracy under different measuring point combinations is to optimize the weight of the measuring point combinationsThe foundation is needed. Because the derivation process is complicated, the measurement index C of the S point N order chord measurement method measurement accuracy is directly given_k. This index is also referred to as the error amplification factor, and the index k corresponds to the kth sampling position of the measurement section. The index gives the law of accumulation of errors over different measurement zones, and in general, the error amplification coefficient will take a maximum value near the middle of a measurement zone. For the given measuring point number S and the determined chord measuring method order N, the error amplification coefficients of different chord measuring combinations have obvious difference.

Wherein, C_kA measurement index of S point N order chord measurement accuracy, C_kAnd D_ki ²The index k in (a) denotes the kth sampling position of the measurement section, k ═ c₁,c₂,…,c_w(ii) a i denotes from c₁To c_wN represents the chord measuring method order, and N represents the multipoint chord measuring method order; d represents a matrix and D ═ BA_c1 ^TBA_c2 ^T… BA_cw ^T](ii) a Wherein, the measurement matrix M is split according to rows to obtain a matrix A_k(k＝c₁,c₂,…,c_w) (ii) a Wherein A is_kRepresenting the matrix after the matrix M is split according to rows; c. C_wRepresents the w rows of matrix M; m represents a measurement matrix; b is a matrix and satisfies the following conditions:

wherein I is an identity matrix, A_i(i＝c₁,c₂,…,c_w) Splitting the measurement matrix M according to rows and corresponding to the c-th₁The line structure is obtained, i denotes from c₁To c_wOf an arbitrary value selected from A_iRepresents from A_kOf an arbitrary value selected from A_i ^TIs A_iThe transposing of (1). If matrix

Irreversible, then B here is

The pseudo-inverse of (1). Wherein A is_kIs represented as follows:

k＝c₁,c₂,…,c_w。

and calculating the critical wavelength of each group of double-measuring-point chord measuring method arrangement modes aiming at the short wave track, and selecting the double-measuring-point chord measuring method arrangement mode with the largest critical wavelength from the multiple groups of critical wavelengths as the optimal double-measuring-point chord measuring method arrangement mode.

The definition calculation method of the critical wavelength comprises the following steps:

it should be understood that the critical wavelength is a description of the basic characteristics of the error in a specific multi-point chord arrangement, and the cumulative coefficient of the error at the critical wavelength position is 1. That is, errors of the long-wave component sensor exceeding the wavelength are accumulated, accuracy is deteriorated, and errors of the short-wave component sensor falling below the wavelength are suppressed, and accuracy is improved.

First, consider the inversion operator

The measurement error can be described as:

wherein,

for the inversion operator, E measures the random error for each sensor as white noise, i.e., a normal distribution with a variance of 0-mean-1, y is the true orbital irregularity,

is a measurement error term. Lower partSurface consideration error term

The discrete fourier transform is obtained:

wherein subscript p represents a position coordinate of a track measurement direction, and w represents a wavelength;

representing a measurement error term corresponding to a certain wavelength

The fourier transform value (being a complex number).

Further, the critical wavelength is defined as a certain wavelength w_cWhich makes it correspond to

The mathematical expectation of the modulus of (a) is equal to 1, i.e.:

where Amp (. cndot.) is modulo a complex number and E (. cndot.) is a mathematical expectation. The above formula can be estimated by a numerical simulation method.

Further, in the method for measuring an orbit irregularity provided in the embodiment of the present application, in step 104, performing inversion solving on the least square optimization model to obtain an orbit irregularity, the method includes:

and filtering the obtained track irregularity according to the high-pass filtering of the preset filtering wavelength to obtain the original track irregularity.

In the embodiment of the application, the short wave irregularity of the steel rail is obtained through high-pass filtering. The track irregularity solved by the method comprises various wavelength components from the resolution of the minimum measurement wavelength to the total length of the measurement section. Since each measuring point has a measurement error, and the error will be amplified in the inversion process, the error amplification law can be described as follows:

1) the total error (i.e. the error in the inversion to obtain the track irregularity) is the smallest at the start and end of the measurement zone, close to the measurement accuracy of the sensor, and accumulates most significantly near the midpoint of the zone, if the error magnification of the midpoint of the zone is used to describe the measurement accuracy, denoted as C_n/2Then the total accuracy of the measurement is approximated by the following relation:

the method comprises the steps of measuring a section length, measuring a chord length, and measuring a number of measured points, wherein l is the measured section length, L is the measured reference chord length, N is the chord length, and S is the number of measured points.

2) In the total error, the error terms with different wavelengths have different amplitudes, the short wave precision is generally higher, the main component of the error is long wave irregularity, the speed of the wavelength is increased at the power of 1.85 along with the increase of the wavelength, and the longer wavelength component error is larger.

Therefore, in the short wave irregularity measurement process, the long wave error term is filtered by a high-pass filter, which is necessary. The wavelength range of the high-pass filter is 0-3000 mm, that is, only the wavelength components below 3m are reserved. The specific filter construction method is quite various, and no specific limitation is made in the embodiment of the present application.

According to the method for measuring the track irregularity, an S-point N-order chord measuring method is adopted, the combined chord measuring value of the track is detected in a point distribution mode of the optimal position of the S-point N-order chord measuring method measuring point combination, vectors of the chord measuring values of multiple measuring points are fused by using the least square principle, a track geometric irregularity detection value is obtained through solving of a linear equation set, detection data of multiple measuring points can be effectively fused, measurement error control is achieved through solving of a linear system, and the measurement precision is improved while the smaller measurement wavelength resolution is guaranteed; and moreover, the maximum utilization of the sensor at the measuring point is realized through the combined optimization of the measuring point positions by the chord measuring method, and a measuring result with higher precision is obtained.

As shown in fig. 11, an apparatus for measuring track irregularity provided in the embodiment of the present application is configured to perform the method for measuring track irregularity, where the apparatus includes:

the measurement module 11 is used for measuring a plurality of groups of combined chord measuring values in a target section according to a preset sampling step length based on a measurement method of a multi-point multi-order chord measuring method; wherein the combined chord value comprises detailed shape information of the measurement object;

the establishing module 12 is used for establishing a measuring model for measuring short wave irregularity of the steel rail based on the measuring process of a multi-point multi-order chord measuring method and the condition that a plurality of groups of combined chord measuring value matrixes are equal to the product of a measuring matrix and a matrix formed by adjacent discretization of the geometrical shape and position of the steel rail;

a reconstruction module 13, configured to reconstruct a least square optimization model including the target orbit geometric form and position corresponding to the measurement model based on a principle that an error between the optimal target orbit geometric form and the measured multiple groups of combined chord measurement values is minimum;

and the calculation module 14 is used for performing inversion solving on the least square optimization model to obtain the track irregularity.

Further, this application embodiment provides a measuring device of track irregularity, the device still includes:

the halving processing module is used for performing halving processing on the measured chord length according to the determined chord measuring order to obtain a plurality of halving points;

the determining module is used for determining an optimal single-measuring-point chord measuring method arrangement mode from multiple arrangement modes of one target measuring point at different equally-divided points if the number of the target measuring points to be measured is one;

if the number of the target measuring points to be measured is more than one, determining an optimal double-measuring-point chord measuring method arrangement mode by adjusting the position of an added measuring point to be added on the basis of the optimal single-measuring-point chord measuring method arrangement mode; and judging whether the number of target measuring points in the optimal double-measuring-point chord measuring method arrangement mode meets the requirement, if not, continuously obtaining the optimal three-measuring-point chord measuring method arrangement mode by adjusting the position of one added measuring point to be added on the basis of the optimal double-measuring-point chord measuring method arrangement mode until the number of the target measuring points in the current optimal target measuring-point chord measuring method arrangement mode meets the requirement.

Further, the determination module of the measuring device for track irregularity provided in the embodiment of the present application is specifically configured to:

calculating an error amplification coefficient of each group of double-measuring-point chord measuring method arrangement modes aiming at the long-wave track, and selecting the double-measuring-point chord measuring method arrangement mode with the minimum error amplification coefficient from the groups of error amplification coefficients as an optimal double-measuring-point chord measuring method arrangement mode; wherein the double measuring points in the arrangement mode of each group of double measuring point chord measuring method are positioned at different equally-divided points;

and calculating the critical wavelength of each group of double-measuring-point chord measuring method arrangement modes aiming at the short wave track, and selecting the double-measuring-point chord measuring method arrangement mode with the largest critical wavelength from the multiple groups of critical wavelengths as the optimal double-measuring-point chord measuring method arrangement mode.

Further, the measuring device of track irregularity that this application embodiment provided still includes:

and the filtering module is used for filtering the obtained track irregularity according to the high-pass filtering of the preset filtering wavelength to obtain the original track irregularity.

Further, the track irregularity measuring device provided in the embodiment of the present application establishes the module 12, and is specifically configured to:

establishing a mathematical expression of a measuring process of a multi-measuring-point multi-order chord measuring method:

k＝c₁,c₂,…,c_w(ii) a Wherein s represents the number of sensors; c. C_wIndicating the location of the w-th sensor; the k value corresponds to s measuring points, h_kChord, lambda, obtained for the kth station position_kThe proportional value of the sensor arranged at the kth measuring point is a negative number;

y_kas the value of the track irregularity at position k, y₀The value of the track irregularity at the beginning of the chord line, y_n+1The track irregularity value at the end of the chord line, and N is the chord measuring order;

based on a mathematical expression of a measuring process of a multi-measuring-point multi-order chord measuring method and a product that a plurality of groups of combined chord measuring value matrixes are equal to a measuring matrix and a matrix formed by adjacent discretization of the geometric shape and position of the steel rail, a measuring model is established: h is M.F;

wherein H represents a combined chord measurement value matrix; m represents a measurement matrix, the first line of M corresponds to the information of the 1 st measuring point, the c1+1 th element of the midpoint is 1, the second line corresponds to the information of the 2 nd measuring point, wherein the c2+1 th element of the midpoint is 1, and the values of the elements in the 3 rd line are the same; c1 denotes the first row of matrix H, c2 denotes the second row of matrix H, and so on, cw denotes the w rows of matrix H; N-N-2 represents the N-N-2 column of the matrix H, and N-N-1 represents the N-N-1 column of the matrix H; n represents the chord measuring order number, and N represents the column number of the matrix H;

the F matrix is a matrix formed by measurement objects y and has the following structure:

wherein the matrix F (y) is the object of measurementy, the number of independent unknowns of the matrix is only size (y), and size (y) is the length of the vector y; n represents the number of columns of the matrix F and N represents the chordal order.

Further, in the measurement apparatus for track irregularity provided in the embodiment of the present application, the reconstruction module 13 is specifically configured to:

based on the principle that the error between the optimal track geometry y and the measured combined chord value H is minimum, a least square optimization model comprising the optimal track geometry y is constructed:

wherein M represents a measurement matrix, the matrix F (y) represents a combination of the rail irregularity objects y to be measured, and H represents a combined chord measurement value matrix.

Further, in the measurement apparatus for track irregularity provided in the embodiment of the present application, the calculation module 14 is specifically configured to:

splitting the measurement matrix M according to rows to obtain a matrix A_k(k＝c₁,c₂,…,c_w) (ii) a Wherein A is_kRepresenting the matrix after the matrix M is split according to rows; c. C_wRepresents the w rows of matrix M; m represents a measurement matrix;

splitting the combined chord measuring value matrix H according to rows to obtain a vector H_k(k＝c₁,c₂,…,c_w) (ii) a Wherein h is_kRepresenting the matrix H split according to rows; c. C_wRepresents the w rows of matrix H; m represents a combined chord measurement value matrix;

based on matrix A_kSum vector h_kTwo independent systems of linear equations are obtained: a. the_k·y＝h_k；k＝c₁,c₂,…,c_w(ii) a Wherein y represents the rail irregularity object to be measured;

based on the linear equation set, the least square optimization model is converted to obtain a conversion model:

wherein E represents a total residual value objective function, the optimization objective is to minimize the total residual value objective function, and U represents a matrix;

based on a system of linear equations

Solving the conversion model; wherein i represents a number from c₁To c_wOf an arbitrary value selected from A_iRepresents from A_kOf an arbitrary value selected from A_i ^TIs A_iTranspose of (A)_k ^TIs represented by A_kTranspose of (y)^*And the optimal solution is the optimal solution of the measured object, namely the track irregularity measurement result.

The measuring device for the track irregularity, which is provided by the embodiment of the application, is based on a measuring method of a multi-measuring-point multi-order chord measuring method, a plurality of groups of combined chord measuring values in a target section are measured according to a preset sampling step length, a measuring model for measuring the short-wave irregularity of the steel rail is established based on the measuring process of the multi-measuring-point multi-order chord measuring method and the condition that a plurality of groups of combined chord measuring value matrixes are equal to the product of a measuring matrix and a matrix formed by adjacent discretization of the geometric shape and position of the steel rail, the track irregularity is obtained by constructing an optimized model of the measuring model and performing inversion solution on the optimized model, the detection data of a plurality of measuring points can be effectively fused, the measurement error control is realized by solving through a linear system, and the measurement; and moreover, the maximum utilization of the sensor at the measuring point is realized through the combined optimization of the measuring point positions by the chord measuring method, and a measuring result with higher precision is obtained.

Fig. 12 is a schematic structural diagram of a computer device 40 according to an embodiment of the present application, as shown in fig. 12, configured to execute the method for measuring track irregularity in fig. 5, where the device includes a memory 401, a processor 402, and a computer program stored in the memory 401 and executable on the processor 402, where the processor 402 implements the steps of the method for measuring track irregularity when executing the computer program.

Specifically, the memory 401 and the processor 402 can be general-purpose memory and processor, which are not limited to specific embodiments, and the processor 402 can execute the track irregularity measuring method when executing the computer program stored in the memory 401.

Corresponding to the method for measuring the track irregularity in fig. 5, an embodiment of the present application further provides a computer-readable storage medium, on which a computer program is stored, and the computer program is executed by a processor to perform the steps of the method for measuring the track irregularity.

In particular, the storage medium can be a general-purpose storage medium, such as a removable disk, a hard disk, or the like, on which a computer program can be executed to perform the above-mentioned method for measuring track irregularity.

The track irregularity measuring device provided by the embodiment of the application can be specific hardware on equipment or software or firmware installed on the equipment. The device provided by the embodiment of the present application has the same implementation principle and technical effect as the foregoing method embodiments, and for the sake of brief description, reference may be made to the corresponding contents in the foregoing method embodiments where no part of the device embodiments is mentioned. It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the foregoing systems, apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.

In the embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions when actually implemented, and for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection of devices or units through some communication interfaces, and may be in an electrical, mechanical or other form.

The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.

In addition, functional units in the embodiments provided in the present application may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit.

The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present application or portions thereof that substantially contribute to the prior art may be embodied in the form of a software product stored in a storage medium and including instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.

It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus once an item is defined in one figure, it need not be further defined and explained in subsequent figures, and moreover, the terms "first", "second", "third", etc. are used merely to distinguish one description from another and are not to be construed as indicating or implying relative importance.

Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present application, and are used for illustrating the technical solutions of the present application, but not limiting the same, and the scope of the present application is not limited thereto, and although the present application is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope disclosed in the present application; such modifications, changes or substitutions do not depart from the spirit and scope of the present disclosure, which should be construed in light of the above teachings. Are intended to be covered by the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims (10)

1. A method of measuring rail irregularity, comprising:

measuring a plurality of groups of combined chord measuring values in a target section according to a preset sampling step length based on a measuring method of a multi-measuring-point multi-order chord measuring method; wherein the combined chord value comprises detailed shape information of the measurement object;

establishing a measurement model for measuring short-wave irregularity of the steel rail based on the measurement process of a multi-measuring-point multi-order chord measuring method and the condition that a plurality of groups of combined chord measuring value matrixes are equal to the product of a measurement matrix and a matrix formed by adjacent discretization of the geometric shape and position of the steel rail;

reconstructing a least square optimization model corresponding to the measurement model and comprising the target orbit geometric form and position based on the principle that the error of the optimal target orbit geometric form and position and the measured multiple groups of combined measured values is minimum;

and carrying out inversion solving on the least square optimization model to obtain the track irregularity.

2. The method as claimed in claim 1, wherein the method for measuring the track irregularity comprises:

according to the determined chord measuring method order, carrying out equal division processing on the measured chord length to obtain a plurality of equal division points;

if the number of the target measuring points to be measured is one, determining an optimal single measuring point chord measuring method arrangement mode from multiple arrangement modes of the target measuring point at different equally-divided points;

if the number of the target measuring points to be measured is more than one, determining an optimal double-measuring-point chord measuring method arrangement mode by adjusting the position of an added measuring point to be added on the basis of the optimal single-measuring-point chord measuring method arrangement mode; and judging whether the number of target measuring points in the optimal double-measuring-point chord measuring method arrangement mode meets the requirement, if not, continuously obtaining the optimal three-measuring-point chord measuring method arrangement mode by adjusting the position of one added measuring point to be added on the basis of the optimal double-measuring-point chord measuring method arrangement mode until the number of the target measuring points in the current optimal target measuring-point chord measuring method arrangement mode meets the requirement.

3. The method for measuring the unevenness of the track according to claim 2, wherein the step of determining the optimal single-point chord measuring method arrangement mode from the multiple arrangement modes of the target measuring point at different equally-divided points comprises the following steps:

calculating an error amplification coefficient of each group of double-measuring-point chord measuring method arrangement modes aiming at the long-wave track, and selecting the double-measuring-point chord measuring method arrangement mode with the minimum error amplification coefficient from the groups of error amplification coefficients as an optimal double-measuring-point chord measuring method arrangement mode; wherein the double measuring points in the arrangement mode of each group of double measuring point chord measuring method are positioned at different equally-divided points;

and calculating the critical wavelength of each group of double-measuring-point chord measuring method arrangement modes aiming at the short wave track, and selecting the double-measuring-point chord measuring method arrangement mode with the largest critical wavelength from the multiple groups of critical wavelengths as the optimal double-measuring-point chord measuring method arrangement mode.

4. The method for measuring the unevenness of the track according to claim 1, wherein the establishment of the measurement model for measuring the short wave unevenness of the steel rail based on the measurement process of the multi-point and multi-order chord measuring method and the fact that the matrix of the plurality of groups of combined chord measuring values is equal to the product of the measurement matrix and the matrix formed by the geometric form and position adjacent discretization of the steel rail comprises:

establishing multi-measuring-point multi-order stringMathematical expression of the measurement process of the method:

the multi-measuring point multi-order chord measuring method is characterized in that the multi-measuring point multi-order chord measuring method is correspondingly provided with s measuring points, and each measuring point is provided with a sensor, so that the total number of the sensors is s; c. C_wIndicating the location of the w-th sensor; k represents the position of the measuring point corresponding to each measuring point, k corresponds to s measuring points, h_kChord, lambda, obtained for the kth station position_kThe proportional value of the sensor arranged at the kth measuring point is a negative number;

y_kas the value of the track irregularity at the measuring point position k, y₀The value of the track irregularity at the beginning of the chord line, y_N+1The track irregularity value at the end of the chord line, and N is the chord measuring order;

based on a mathematical expression of a measuring process of a multi-measuring-point multi-order chord measuring method and a product that a plurality of groups of combined chord measuring value matrixes are equal to a measuring matrix and a matrix formed by adjacent discretization of the geometric shape and position of the steel rail, a measuring model is established: h is M.F;

wherein H represents a combined chord measurement value matrix; m represents a measurement matrix, the first line of M corresponds to the information of the 1 st measuring point, the c1+1 th element of the midpoint is 1, the second line corresponds to the information of the 2 nd measuring point, wherein the c2+1 th element of the midpoint is 1, and the values of the elements in the 3 rd line are the same; c1 denotes the first row of matrix H, c2 denotes the second row of matrix H, and so on, c_wRepresents the w rows of matrix H; N-N-2 represents the N-N-2 column of the matrix H, and N-N-1 represents the N-N-1 column of the matrix H; n represents the chord measuring order number, and N represents the column number of the matrix H;

the F matrix is a matrix formed by measurement objects y and has the following structure:

the matrix F (y) is the combination of the measurement objects y, the number of independent unknowns of the matrix is only size (y), and size (y) is the length of the vector y; n represents the number of columns of the matrix F and N represents the chordal order.

5. The method of claim 4, wherein reconstructing a least squares optimization model corresponding to the measurement model and including the target orbit geometry based on the principle that the error between the optimal target orbit geometry and the measured sets of combined chord measurements is minimal comprises:

based on the principle that the error between the optimal track geometry and the measured combined chord measuring value H is minimum, a least square optimization model comprising the optimal track geometry is constructed:

wherein M represents a measurement matrix, the matrix F (y) represents a combination of the rail irregularity objects y to be measured, and H represents a combined chord measurement value matrix.

6. The method of claim 5, wherein the inverse solution of the least squares optimization model to obtain the rail irregularity comprises:

splitting the measurement matrix M according to rows to obtain a matrix A_k(ii) a Wherein A is_kRepresenting the matrix after the matrix M is split according to rows; c. C_wRepresents the w rows of matrix M; m represents a measurement matrix; k is c₁,c₂,…,c_w；

Splitting the combined chord measuring value matrix H according to rows to obtain a vector H_k(ii) a Wherein h is_kRepresenting the matrix H split according to rows; c. C_wRepresents the w rows of matrix H; m represents a combined chord measurement value matrix; k is c₁,c₂,…,c_w；

Based on matrix A_kSum vector h_kTwo independent systems of linear equations are obtained: a. the_k·y＝h_k；k＝c₁,c₂,…,c_w(ii) a Wherein y represents the rail irregularity object to be measured;

based on the linear equation set, the least square optimization model is converted to obtain a conversion model:

wherein E represents a total residual value objective function, the optimization objective is to minimize the total residual value objective function, and U represents a matrix;

based on a system of linear equations

Solving the conversion model; wherein i represents a number from c₁To c_wOf an arbitrary value selected from A_iRepresents from A_kOf an arbitrary value selected from A_i ^TIs A_iTranspose of (A)_k ^TIs represented by A_kTranspose of (y)^*And the optimal solution is the optimal solution of the measured object, namely the track irregularity measurement result.

7. The method for measuring the rail irregularity according to any one of claims 1 to 6, wherein the inversion solving of the least square optimization model after the rail irregularity is obtained comprises:

and filtering the obtained track irregularity according to the high-pass filtering of the preset filtering wavelength to obtain the original track irregularity.

8. A rail irregularity measuring device, comprising:

the measuring module is used for measuring a plurality of groups of combined chord measuring values in a target section according to a preset sampling step length based on a measuring method of a multi-point multi-order chord measuring method; the combined chord value includes detailed shape information of the measurement object;

the building module is used for building a measuring model for measuring short-wave irregularity of the steel rail based on the measuring process of a multi-point multi-order chord measuring method and the condition that a plurality of groups of combined chord measuring value matrixes are equal to the product of a measuring matrix and a matrix formed by adjacent discretization of the geometrical shape and position of the steel rail;

the reconstruction module is used for reconstructing a least square optimization model which corresponds to the measurement model and comprises the target orbit geometric form and position on the basis of the principle that the error between the optimal target orbit geometric form and the measured multiple groups of combined chord measurement values is minimum;

and the calculation module is used for carrying out inversion solving on the least square optimization model to obtain the track irregularity.

9. The apparatus for measuring rail irregularity of claim 8, further comprising:

the halving processing module is used for performing halving processing on the measured chord length according to the determined chord measuring order to obtain a plurality of halving points;

the determining module is used for determining an optimal single-measuring-point chord measuring method arrangement mode from multiple arrangement modes of one target measuring point at different equally-divided points if the number of the target measuring points to be measured is one;

if the number of the target measuring points to be measured is more than one, determining an optimal double-measuring-point chord measuring method arrangement mode by adjusting the position of an added measuring point to be added on the basis of the optimal single-measuring-point chord measuring method arrangement mode; and judging whether the number of target measuring points in the optimal double-measuring-point chord measuring method arrangement mode meets the requirement, if not, continuously obtaining the optimal three-measuring-point chord measuring method arrangement mode by adjusting the position of one added measuring point to be added on the basis of the optimal double-measuring-point chord measuring method arrangement mode until the number of the target measuring points in the current optimal target measuring-point chord measuring method arrangement mode meets the requirement.

10. The device according to claim 9, characterized in that the determination module is specifically configured to:

calculating an error amplification coefficient of each group of double-measuring-point chord measuring method arrangement modes aiming at the long-wave track, and selecting the double-measuring-point chord measuring method arrangement mode with the minimum error amplification coefficient from the groups of error amplification coefficients as an optimal double-measuring-point chord measuring method arrangement mode; wherein the double measuring points in the arrangement mode of each group of double measuring point chord measuring method are positioned at different equally-divided points;

and calculating the critical wavelength of each group of double-measuring-point chord measuring method arrangement modes aiming at the short wave track, and selecting the double-measuring-point chord measuring method arrangement mode with the largest critical wavelength from the multiple groups of critical wavelengths as the optimal double-measuring-point chord measuring method arrangement mode.

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