Method and system for identifying higher-order transverse modes of steel rails for measuring longitudinal forces

Abstract

A method for identifying a high-order transverse mode of a steel rail so as to measure longitudinal force, comprising: equally distributing a plurality of sensors at a neutral axis position of a steel rail, each sensor serving as a monitoring point; equally selecting a plurality of excitation points at the neutral axis position of the steel rail, and laterally exciting a plurality of excitation points by means of an impact hammer; collecting response data of transverse excitation recorded at a plurality of monitoring points, and analyzing modal features of the steel rail according to the response data; and performing modal analysis on sensor arrangement and data processing, and calculating according to the modal analysis result of transverse vibration to obtain the longitudinal force of the steel rail. The described method has good testing quality, and can effectively identify transverse modal features of a steel rail. Moreover, the comparability between test data is good, and test data from different times and different places can be effectively compared and analyzed, verifying one another, thus the validity of the data is ensured. Further provided is a system for identifying a high-order transverse mode of a steel rail so as to measure longitudinal force.

Description

Method and system for identifying high-order transverse modes of rails to measure longitudinal forces Technical Field

[0001] The present invention belongs to the technical field of rail health detection, and in particular relates to a method and system for identifying high-order transverse modes of rails to measure longitudinal forces. Background Art

[0002] How to conveniently and accurately measure the longitudinal forces within rails is a key concern for railway operations and maintenance departments. Measuring temperature stress using the relationship between longitudinal forces and rail modal properties is a viable measurement method. Previous studies have shown that rail modes dominated by transverse vibration are most sensitive to changes in temperature stress. Hammer testing is used to stably and conveniently identify transverse rail modes sensitive to longitudinal force changes. Existing rail modal feature identification methods have the following shortcomings:

[0003] The scope of measurement point layout is not clear, and it is set randomly based on experience during testing. If the measurement point range is small, the required modal characteristics cannot be effectively tested. If the measurement point range is too large, the test efficiency will be greatly reduced. The number of hammer excitation points is not clear, and it is set randomly based on experience during testing. If the excitation points are too few or too concentrated, the data will be poor and the modal characteristics cannot be effectively obtained. If there are too many excitation points, the test efficiency will be reduced. The sensor layout position is not clear, and it is laid on the rail head or rail bottom, and the torsional mode is measured. The torsional mode is the main component and is coupled with the lateral mode, affecting the identification effect. The position of the hammer excitation point is not clear, and the rail head or rail bottom is stimulated, which excites the torsional mode that is the main component, affecting the identification effect. The modal identification range is not clear, and a single frequency such as pin-pin frequency is usually measured, and the influence of track structure factors such as fastener spacing and stiffness cannot be ignored. The modal identification method is not clear, and it is not easy to identify effective modes.

[0004] Summary of the Invention

[0005] In order to solve the above problems, the present invention discloses a method for identifying high-order transverse modes of a rail to measure longitudinal force, the method comprising:

[0006] Multiple sensors are evenly spaced at the neutral axis of the rail, with each sensor serving as a monitoring point.

[0007] Selecting multiple excitation points at equal distances from the neutral axis of the rail and laterally exciting the multiple excitation points with a hammer;

[0008] collecting response data of lateral excitation recorded at a plurality of monitoring points, and analyzing modal characteristics of the rail based on the response data;

[0009] Analyzing the modal characteristics of the rail according to the response data includes:

[0010] Perform noise reduction on the response data of lateral excitation recorded at multiple monitoring points;

[0011] According to the noise reduction processing results, a modal identification method is used to output multiple modal parameters;

[0012] Filter the output multiple modal parameters and output the complex modal frequency ω mi A set of

[0013] For each complex modal frequency ω in set A mi Perform validation processing and output the effective natural frequency ω mi有效 ;

[0014] According to the effective natural frequency ω mi有效 As well as the relationship between the natural frequency and the longitudinal force, the longitudinal force of the rail is calculated.

[0015] Preferably, the distance between two adjacent fasteners on the rail is set as a span, the multiple sensors are arranged in the same span, and the multiple excitation points are selected in adjacent spans.

[0016] Preferably, the laterally exciting the multiple excitation points by a hammer comprises:

[0017] The multiple excitation points are struck one by one and multiple times by a hammer, and a time interval is set between each strike.

[0018] Preferably, the step of outputting a plurality of modal parameters using a modal identification method according to the noise reduction processing result includes:

[0019] The modal identification algorithm is used to identify all modes in the range of 500-4000Hz and output the modal parameters of each order; among them,

[0020] Complex modal frequency Complex modal damping ratio:

[0021] Among them, ω mdi represents the complex modal damping natural frequency, σ mi represents the complex modal damping attenuation coefficient.

[0022] Preferably, the complex modal damping ratio ξ in the output modal parameters of each order is mi The value is between 0 and 0.3.

[0023] Preferably, the output multiple modal parameters are screened and the complex modal frequency ω is output. mi The steps of the set A include:

[0024] Using frequency response function, output peak natural frequency ω fi ;

[0025] The first threshold Δω1 is preset to filter out the mi -ω fi Complex modal frequency ω |≤Δω1 mi ;

[0026] Secondary screening of multiple-occurring complex modal frequencies ω mi .

[0027] Preferably, each complex modal frequency ω in the pair A mi The steps to carry out the validation process include:

[0028] Preset the second threshold Δω2 and filter out the complex modal frequencies ω in set A that are lower than the second threshold Δω2 mi ;

[0029] For the selected complex mode frequency ω mi Take the average value and output the effective natural frequency ω mi有效 .

[0030] On the other hand, the present invention also discloses a system for identifying high-order transverse modes of a rail to measure longitudinal force, the system comprising:

[0031] A monitoring unit, comprising a plurality of sensors preset on the rail, configured to monitor response data of the rail when the hammer laterally excites the plurality of excitation points, and transmit the response data to the calculation processing unit;

[0032] The calculation and processing unit is used to receive the response data transmitted by the monitoring unit and analyze the modal characteristics of the rail according to the response data.

[0033] The computing processing unit includes:

[0034] A noise reduction module is used to perform noise reduction processing on the response data of the lateral excitation recorded at multiple monitoring points and output multiple modal parameters;

[0035] The screening module is used to screen the output multiple modal parameters and output the complex modal frequency ω mi A set of

[0036] An effective processing module for each complex modal frequency ω in the set A mi Perform validation processing and output the effective natural frequency ω mi有效 ;

[0037] A calculation module is used for calculating the effective natural frequency ω according to the mi有效 As well as the relationship between the natural frequency and the longitudinal force, the longitudinal force of the rail is calculated.

[0038] Preferably, the noise reduction module performs the noise reduction processing on the response data of the lateral excitation recorded at the plurality of monitoring points, including the following steps:

[0039] The modal identification algorithm is used to identify all modes in the range of 500-4000Hz and output the modal parameters of each order; among them,

[0040] Complex modal frequency Complex modal damping ratio:

[0041] Among them, ω mdi represents the complex modal damping natural frequency, σ mi represents the complex modal damping attenuation coefficient.

[0042] Preferably, the complex modal damping ratio ξ output by the noise reduction module is mi The value is between 0 and 0.3.

[0043] Preferably, the screening module performs the screening of the output multiple modal parameters and outputs the complex modal frequency ω mi The set A includes the following steps:

[0044] Using frequency response function, output peak natural frequency ω fi ;

[0045] The first threshold Δω1 is preset to filter out the mi -ω fi Complex modal frequency ω |≤Δω1 mi ;

[0046] Secondary screening of multiple-occurring complex modal frequencies ω mi ,ω mi ∈A.

[0047] Preferably, the effective processing module performs the following operation on each complex modal frequency ω in the set A: mi Perform validation processing and output the effective natural frequency ω mi有效 The following steps are involved:

[0048] Preset the second threshold Δω2 to filter the complex mode frequency ω below the second threshold Δω2 mi ;

[0049] For the selected complex mode frequency ω mi Take the average value and output the effective natural frequency ω mi有效 .

[0050] The present invention has fixed measuring points and, through sensor arrangement and data processing, can stably measure response data within the range of 500-4000 Hz. Modal analysis with lateral vibration as the main component is performed based on the response data, and the longitudinal force of the rail is calculated based on the modal analysis results of the lateral vibration. The test quality is good and the lateral modal characteristics of the rail can be effectively identified. The test efficiency is high and multiple operations can be performed within the maintenance time window. The test data are highly comparable and test data from different times and locations can be effectively compared and analyzed, mutually verified, and the validity of the data is ensured.

[0051] Other features and advantages of the present invention will be described in the following description, and in part will become apparent from the description, or will be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures pointed out in the description, claims and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0053] FIG1 shows a flow chart of identifying rail high-order modes according to an embodiment of the present invention;

[0054] FIG2 is a schematic diagram showing an example of arrangement of sensors according to an embodiment of the present invention;

[0055] FIG3 is a schematic diagram showing an example of arrangement of excitation points according to an embodiment of the present invention;

[0056] FIG4 shows a frequency response function curve diagram of the natural frequency of a rail according to an embodiment of the present invention. DETAILED DESCRIPTION

[0057] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0058] The present invention proposes a method for rapidly identifying high-order transverse modes of rails to measure longitudinal forces. Referring to the flow chart shown in FIG1 , by rationally arranging excitation points and sensors, rail modes in the range of 500-4000 Hz can be stably detected.

[0059] In one embodiment of the present invention, before using this method to quickly identify the high-order transverse modes of the rail to measure the longitudinal force, the monitoring unit needs to be installed and arranged. As shown in Figure 2, the monitoring unit is provided with three sensors. First, sensors 1, 2 and 3 are arranged in order on the rail waist between two adjacent fasteners of the rail. At the same time, the space between two adjacent fasteners on the rail is set as a span, and the above three sensors are arranged in the same span, which is set as the first span, and the fastener spacing is set as D2. In addition, as shown in Figure 3, the adjacent span is set as the second span, and the fastener spacing is set as D1. Five excitation points are preset in the second span, namely excitation point 1 to excitation point 5. The five excitation points are arranged at equal intervals and are located at the positions of 0, 0.25, 0.5, 0.75 and 1 of the crotch width respectively. In real life, the fastener spacing D1 and D2 of two adjacent spans cannot be completely equal. In this embodiment, the excitation points and sensors are set at the neutral axis position of the two adjacent spans of the rail.

[0060] Specifically, after the monitoring units are deployed, the rail is stimulated multiple times at excitation point 1, and the excitation and corresponding response data are collected. This excitation process is repeated for excitation points 2, 3, 4, and 5, respectively. A modal identification algorithm is used to extract the effective natural frequencies within the 500-4000 Hz range. Furthermore, a certain amount of time is required between each excitation to prevent residual vibration in the rail from the previous strike, which could affect the validity of the response data collected during subsequent excitation processes.

[0061] Referring to the flow chart shown in Figure 1, the present invention can stably measure response data in the 500-4000 Hz range by arranging multiple sensors and collecting response data. Modal analysis with lateral vibration as the primary component can then be performed based on this response data. By setting multiple sets of excitation points and arranging multiple sensors, multiple sets of response data can be obtained through lateral excitation at these multiple excitation points. This allows for the acquisition of multiple sets of highly stable response data while maintaining test efficiency. This ensures the stability of the modal analysis results.

[0062] In one embodiment of the present invention, after a rail is subjected to transverse excitation, response data of the transverse excitation recorded at multiple monitoring points are collected, and the modal characteristics of the rail are analyzed based on the response data. The following steps are included:

[0063] Analyzing the modal characteristics of the rail according to the response data includes:

[0064] Perform noise reduction on the response data of lateral excitation recorded at multiple monitoring points;

[0065] According to the noise reduction processing results, a modal identification method is used to output multiple modal parameters;

[0066] Filter the output multiple modal parameters and output the complex modal frequency ω mi A set of

[0067] For each complex modal frequency ω in set A mi Perform validation processing and output the effective natural frequency ω mi有效 ;

[0068] According to the effective natural frequency ω mi有效 As well as the relationship between the natural frequency and the longitudinal force, the longitudinal force of the rail is calculated.

[0069] According to the noise reduction processing result, in the range of 500-4000 Hz, a modal identification method is used to output multiple modal parameters, including the following steps:

[0070] Step 1: Where: ΔY k =ω k H k -ω k-1 H k-1 ; ΔH k =H k -H k-1

[0071] According to the collected response data, a set of frequency response function values ​​H in the resonance area are obtained. k and H k-1 , combined with the above formula, we can identify ω mdi , σ mi (i=1,2,…,m) as the initial modal parameters.

[0072] Among them, ω k is the kth order natural frequency; H k is the corresponding frequency response function value; σ mi and ω mdi is the complex modal damping attenuation coefficient and the complex modal damping natural frequency.

[0073] Step 2: Set the actual measured frequency points ω within the fitting frequency band k Frequency response function value at (k=1,2,…,s) Initial nonlinear parameter ω mdi , σ mi (i=1,2,…,m)

[0074] Among them, the initial nonlinear parameter ω mdi , σ mi (i=1,2,…,m) is identified by step 1. The corresponding real k-th order natural frequency ω k Set the theoretical value of the frequency response function to H ef (ωk ), (k=1,2,…,s). According to the above settings, the frequency response function matrix expression within the fitting frequency band is:

[0075]

[0076]

[0077] Linear parameter: P = [Y R Y I U1 V1 U2 V2 … U m V m Z R Z I ] T

[0078] Among them, the formulas (1) and (2) Represents the frequency response function H ef The real part of (ω), Represents the frequency response function H ef The imaginary part of (ω), ω = ω mdi (i=1,2,…,m); linear parameter Y R , Y I , U i , V i (i=1,2,…,m), Z R , Z I is a linear parameter related to the vibration mode.

[0079] All parameters: Q = [P T σ m1 ω md1 σ m2 ω md2 ··· σ mm ω mdm ] T

[0080] Set to h p (p=1,2,…,2m+4) represents the linear parameter Y R 、Y I 、U i 、V i (i=1,2,…,m), Z R , Z I , the above frequency response function matrix expressions (1) and (2) are expressed as partial derivatives:

[0081]

[0082]

[0083] in:

[0084]

[0085] e(ω)=[e1(ω) e2(ω) … e 2m+4 (ω)] T ;

[0086] f(ω)=[f1(ω) f2(ω) … f 2m+4 (ω)] T

[0087] Step 3: Due to the initial nonlinear parameter ω mdi , σ mi (i=1,2,…,m) has been calculated in step 1. The parameter P is obtained by the least squares method:

[0088]

[0089] in:

[0090] Represents the matrix E p The transposed matrix of Represents the matrix F p The transposed matrix of

[0091] Get the full estimate:

[0092] Step 4: Using Taylor series, expand equations (1) and (2) to obtain:

[0093]

[0094]

[0095] Construct the optimization target matrix (total variance):

[0096]

[0097] in:

[0098]

[0099] The optimization direction of parameter Q is given by the least squares principle:

[0100] The increment of parameter Q:

[0101] Step 5: Use formula (9) to find the parameter increment ΔQ1 and the variance E Δ, then the parameter increment after the first iteration is:

[0102] Q1=Q0+ΔQ1 (10)

[0103] Step 6: Given the error precision μ, test the variance E Δ If not, repeat step 5 based on parameter Q1 until the accuracy requirement is met. Q is the identification parameter.

[0104] Step 7: The modal parameters of each order can be obtained from the identification parameter Q. Including the complex modal frequency Complex modal damping ratio:

[0105] In one embodiment of the present invention, after a modal identification method is used to output a plurality of modal parameters, the collected plurality of modal parameters are screened. The screening specifically includes the following steps:

[0106] According to the complex mode frequency ω mi The complex modal damping ratio ξ is obtained mi The value ranges from 0 to 0.3;

[0107] Refer to the frequency response function curve shown in Figure 4, which is the amplitude-frequency curve corresponding to multiple excitations obtained for the three sensors. The complex modal frequency ω is obtained according to the frequency response function curve. mi . Find the peak natural frequency ω corresponding to the peak point fi The first threshold Δω1 is preset to filter out the mi -ω fi Complex modal frequency ω under the condition |≤Δω1 mi ;

[0108] Secondary screening of multiple-occurring complex modal frequencies ω mi .

[0109] Among them, multiple occurrences are set to occur at least three times, and the complex mode frequency ω that occurs more than three times is repeated mi It has better stability and can accurately convert the actual rail longitudinal force after screening.

[0110] In one embodiment of the present invention, the complex mode frequency ω after screening mi Form a set A, each complex mode frequency ω in set A mi All need to be processed effectively to output the effective natural frequency ω mi有效 The validation process includes:

[0111] Preset the second threshold Δω2 to filter the complex mode frequency ω below the second threshold Δω2 mi ;

[0112] For the multiple complex mode frequencies ω selected mi Take the average value and output the effective natural frequency ω mi有效 ;

[0113] Since there is a linear relationship between the natural frequency and the longitudinal force of the rail, the effective natural frequency ω can be obtained according to the above linear relationship. mi有效 Calculate the longitudinal force of the rail.

[0114] The present invention has fixed measuring points and, through sensor arrangement and data processing, can stably measure response data within the range of 500-4000 Hz. Modal analysis with lateral vibration as the main component is performed based on the response data, and the longitudinal force of the rail is calculated based on the modal analysis results of the lateral vibration. The test quality is good and the lateral modal characteristics of the rail can be effectively identified. The test efficiency is high and multiple operations can be performed within the maintenance time window. The test data are highly comparable and test data from different times and locations can be effectively compared and analyzed, mutually verified, and the validity of the data is ensured.

[0115] Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for identifying high-order transverse modes of rails to measure longitudinal forces, the method include: Multiple sensors are arranged at equal distances on the neutral axis of the rail, and each sensor serves as a monitoring point; Select multiple excitation points at equal distances from the neutral axis of the rail, and laterally excite the multiple excitation points by a hammer; Collecting response data of lateral excitation recorded at multiple monitoring points, and analyzing the modal characteristics of the rail according to the response data, characterized in that; Analyzing the modal characteristics of the rail according to the response data includes: Perform noise reduction on the response data of lateral excitation recorded at multiple monitoring points; According to the denoising results, a modal identification method is used to output multiple modal parameters; Filter the output multiple modal parameters and output the complex modal frequency ω mi A set of For each complex mode frequency ω in set A mi Perform validation processing and output the effective natural frequency ω mi有效 ; According to the effective natural frequency ω mi有效 As well as the relationship between the natural frequency and the longitudinal force, the longitudinal force of the rail is calculated.

2. The method for measuring longitudinal force according to claim 1, It is characterized in that The space between two adjacent fasteners on the rail is set as a span, the multiple sensors are arranged in the same span, and the multiple excitation points are selected in adjacent spans.

3. The method for measuring longitudinal force according to claim 1, It is characterized in that The step of laterally exciting the plurality of excitation points by means of a force hammer comprises: The multiple excitation points are struck one by one and multiple times by a hammer, and a time interval is set between each strike.

4. A method for measuring longitudinal force according to any one of claims 1 to 3, It is characterized in that The step of outputting a plurality of modal parameters using a modal identification method according to the noise reduction processing result comprises: The modal identification algorithm is used to identify all modes in the range of 500-4000Hz, and the modal parameters of each order are output; among them, Complex modal frequency Complex modal damping ratio: Among them, ω mdi represents the complex modal damping natural frequency, σ mi represents the complex mode damping attenuation coefficient.

5. The method for measuring longitudinal force according to claim 4, It is characterized in that The complex modal damping ratio ξ in the output modal parameters of each order mi The value is between 0 and 0.

3.

6. The method for measuring longitudinal force according to claim 1, It is characterized in that The output multiple modal parameters are screened and the complex modal frequency ω is output. mi The steps of the set A include: Using frequency response function, the output peak natural frequency ω fi ; Preset first threshold Δω 1 , filter out the ones that meet |ω mi -ω fi |≤Δω 1 The complex modal frequency ω mi ; Secondary screening of multiple occurrences of complex modal frequencies ω mi .

7. The method for measuring longitudinal force according to claim 1, It is characterized in that For each complex modal frequency ω in the set A mi The steps to implement the effective treatment include: Preset the second threshold Δω 2 , filter out the set A below the second threshold Δω 2 The complex modal frequency ω mi ; For the selected complex mode frequency ω mi Take the average value and output the effective natural frequency ω mi有效 .

8. A system for identifying high-order transverse modes of rails to measure longitudinal forces, It is characterized in that The system comprises: A monitoring unit, the monitoring unit comprising a plurality of sensors preset on the rail, for monitoring response data of the rail when the hammer laterally excites the plurality of excitation points, and transmitting the response data to the calculation processing unit; A computing and processing unit, configured to receive the response data transmitted by the monitoring unit, and analyze the modal characteristics of the rail according to the response data; The computing processing unit comprises: A noise reduction module is used to perform noise reduction processing on the response data of the lateral excitation recorded at multiple monitoring points, and output multiple modal parameters; The screening module is used to screen the output multiple modal parameters and output the complex modal frequency ω mi A set of An effective processing module is used to process each complex modal frequency ω in the set A. mi Perform validation processing and output the effective natural frequency ω mi有效 ; A calculation module is used for calculating the effective natural frequency ω according to the mi有效 As well as the relationship between the natural frequency and the longitudinal force, the longitudinal force of the rail is calculated.

9. The system for measuring longitudinal force according to claim 8, It is characterized in that The noise reduction module performs the noise reduction processing on the response data of the lateral excitation recorded at the multiple monitoring points, including the following steps: The modal identification algorithm is used to identify all modes in the range of 500-4000Hz, and the modal parameters of each order are output; among them, Complex modal frequency Complex modal damping ratio: Among them, ω mdi represents the complex modal damping natural frequency, σ mi represents the complex mode damping attenuation coefficient.

10. The system for measuring longitudinal force according to claim 8, It is characterized in that The complex modal damping ratio ξ output by the noise reduction module mi The value is between 0 and 0.

3.

11. The system for measuring longitudinal force according to claim 8, It is characterized in that The screening module performs the screening of the output multiple modal parameters and outputs the complex modal frequency ω mi The set A includes the following steps: Using frequency response function, the output peak natural frequency ω fi ; Preset first threshold Δω 1 , filter out the ones that meet |ω mi -ω fi |≤Δω 1 The complex modal frequency ω mi ; Secondary screening of multiple occurrences of complex modal frequencies ω mi ,ω mi ∈A.

12. The system for measuring longitudinal force according to claim 8, It is characterized in that The effective processing module performs a mi Perform validation processing and output the effective natural frequency ω mi有效 The following steps are involved: Preset the second threshold Δω 2 , screening below the second threshold Δω 2 The complex modal frequency ω mi ; For the selected complex mode frequency ω mi Take the average value and output the effective natural frequency ω mi有效 .

Images