Wheel polygon on-board quantitative diagnosis method based on frequency response function

Abstract

This invention provides an on-board quantitative diagnostic method for wheel polygons based on frequency response functions, belonging to the field of rail transit technology. This method first utilizes comb filtering to remove the influence of rail roughness, leaving a "purer" wheel polygon response component. Then, it uses the frequency response function to consider and correct the influence of the structure's inherent modes, thereby quantitatively diagnosing the polygon order and roughness level from the axle box vibration signal. This invention solves the problem of wheel and rail roughness vibration components being mixed in the axle box vibration response, leading to misjudgments between the wheel and rail during diagnosis, and the difficulty in quantitatively assessing wheel roughness in on-board wheel polygon detection methods.

Description

Technical Field

[0001] This invention belongs to the field of rail transit technology, and particularly relates to a quantitative on-board diagnostic method for wheel polygons based on frequency response functions. Background Technology

[0002] Polygonal wheel wear is a periodic abnormal wear pattern on the circumferential surface of the wheel tread. It has occurred in high-speed trains of all speed levels in recent years, seriously disrupting the safe and punctual operation of high-speed trains. Polygonal wheel wear significantly exacerbates the dynamic forces between the wheel and rail, leading to severe abnormal vibrations, noise, and structural vibration fatigue. Literature shows that polygonal wheel wear can increase the noise level inside the train by 11 dBA, and in severe cases, the vibration acceleration of the high-speed wheel axle box can even reach 800g. Furthermore, polygonal wheel wear can also cause serious structural failures such as wheelset lifting breakage, rail fastener breakage, and axle fatigue failure. Therefore, polygonal wheel wear is a type of failure that requires continuous and focused attention in railway operations.

[0003] To detect wheel polygons on high-speed trains as early as possible, various dynamic monitoring methods and equipment for wheel polygons have been deployed. Based on the difference in sensor location, they can be mainly divided into trackside monitoring methods and on-board detection methods. Trackside methods primarily identify the wheel polygon situation of passing trains by arranging stress and strain measurements on the side of the rail. On-board methods mainly detect and diagnose wheel polygons through axle box vibration acceleration. On-board methods have been widely adopted due to their higher signal-to-noise ratio, stronger tracking performance, and economic reliability. On-board monitoring of wheel polygons has become one of the essential on-board monitoring features for high-speed trains.

[0004] However, the wear problem of wheel polygons poses a challenge to the safe operation of high-speed trains. Currently, the accuracy of onboard wheel polygon monitoring remains far from satisfactory. This is mainly due to the highly dynamic and complex nature of axle box vibration signals, making signal processing and diagnostic algorithms for onboard wheel polygon diagnosis extremely difficult. In terms of wheel polygon fault feature extraction, empirical mode decomposition (EMD) and its improved methods are widely used to consider the modulation nonlinearity of wheel polygon responses, including EMD, improved ensemble EMD, variational mode decomposition (VMD), adaptive chirp mode decomposition (ACMD), and Hilbert-Huang transform. Existing technologies also include using discrete Fourier transform parameter spectrum estimation for wheel polygon identification under strong interference.

[0005] Furthermore, the quantitative diagnostic capability of wheel polygon roughness is an important indicator for evaluating the quality of diagnostic methods, and the quadratic integral method is currently the most commonly used quantitative diagnostic method for wheel polygons. However, traditional quantitative diagnostic methods for wheel polygons, represented by the quadratic integral method, have two limitations: interference from rail roughness and the influence of vehicle-track system coupling resonance. First, the axle box vibration acceleration is mainly affected by both wheel and rail roughness. If the rail roughness is greater than the wheel surface roughness, it will significantly interfere with the diagnostic results. Even if the vibration data used for diagnosis is taken from a section where the wheel has passed over rail corrugation, since rail corrugation and wheel polygons are both harmonic excitations and have certain similarities, there is a significant possibility of misjudgment. Second, the formation process of the wheel polygon is closely related to the high-frequency natural modes of the structure, and its vibration response is also greatly influenced by high-frequency modes. Both theoretical and experimental data show that the magnitude of the vibration response of the wheel polygon excitation within the natural mode frequency band and the non-natural mode frequency band differs significantly, with the former being significantly larger than the latter. However, the traditional quadratic integral method is based on the assumption that the wheel undergoes rigid inertial motion and the elastic deformation of the wheel and rail can be ignored. It does not take into account the influence of the inherent modes of the structure, making it difficult to take into account all orders and vehicle speeds. This is especially evident in high-speed trains.

[0006] In the field of indirect detection of rail roughness, methods based on acoustic vibration characteristic analysis are commonly used. These methods analyze vibration or noise data generated by train operation to indirectly assess the surface roughness of the rail, thereby determining whether abnormal wear such as rail corrugation exists. Although this monitoring task differs from the objective of on-board monitoring of wheel polygons, the two share similar technical methods. Currently, some research has attempted to detect rail surface roughness by establishing the frequency response function of the wheel-axle system. This method can effectively compensate for the influence of the inherent modes of the system's wheel-rail structure. However, similar techniques are rarely applied to the on-board monitoring and diagnosis of wheel polygons. Summary of the Invention

[0007] To address the aforementioned shortcomings in existing technologies, this invention provides an on-board quantitative diagnostic method for wheel polygons based on frequency response functions. This method solves the problem that the vibration components of wheel and track roughness are mixed together in the axle box vibration response, which easily leads to misjudgment between the wheel and track during diagnosis. It also addresses the difficulty in quantitatively assessing wheel roughness in on-board wheel polygon detection methods.

[0008] To achieve the above objectives, the technical solution adopted by this invention is: a vehicle-mounted quantitative diagnostic method for wheel polygons based on frequency response functions, comprising the following steps:

[0009] S1. Use comb filtering method to preprocess the vibration acceleration of the axle box and filter out the interference of rail roughness.

[0010] S2. Estimate the power spectral density of the pre-processed axle box vibration acceleration;

[0011] S3. Based on the estimated axle box vibration acceleration power spectral density, the wheel roughness power spectral density is calculated using the frequency response function between the axle box measuring point displacement and the wheel-rail roughness.

[0012] S4. Using the vehicle speed calculated from the rotational speed pulse signal, perform order slicing of the wheel roughness power spectral density.

[0013] S5. Based on the slicing results, calculate the wheel roughness order diagram;

[0014] S6. Based on the wheel roughness level order diagram, identify the roughness level and order of the wheel polygon disturbance, and obtain the distribution pattern of different orders according to the box-and-whisker diagram to complete the quantitative diagnosis of the wheel polygon on the vehicle.

[0015] Further, step S1 specifically includes:

[0016] S101. Based on the axle box vibration acceleration, use comb filtering to extract the length of one cycle from the axle box vibration signal;

[0017] S102. Add the axle box vibration signal extracted in this segment to the axle box vibration signal corresponding to the previous cycle;

[0018] S103. Repeat steps S101-S102 and suppress non-periodic noise and filter out rail roughness interference by averaging.

[0019] Furthermore, the time-domain difference equation of the comb filter is expressed as follows:

[0020] y[n] = x[n] - x[nN] + R·y[nN]

[0021] Where y[n] represents the axle box vibration signal output by the comb filter at time n, x[n] represents the axle box vibration signal input by the comb filter at time n, N represents the delay in the time-domain difference equation of the comb filter, y[nN] represents the axle box vibration signal output N time units ago, R represents the feedback coefficient, and x[nN] represents the axle box vibration signal input N time units ago.

[0022] The expression for the delay in the time-domain difference equation of the comb filter is as follows:

[0023]

[0024] Among them, f s f represents the sampling frequency. w This indicates the wheelset rotation frequency.

[0025] Furthermore, the frequency response of the comb filter is expressed as follows:

[0026]

[0027] Where H(f) represents the frequency response of the comb filter at frequency f, j represents the unit imaginary number, and f s Let R represent the sampling frequency, N represent the delay in the time-domain difference equation of the comb filter, and R represent the feedback coefficient. When R approaches 1, the comb filter retains the frequency components related to the period; when R approaches 0, the comb filter filters out the frequency components related to the period.

[0028] Furthermore, the expression for the frequency response function is as follows:

[0029] H(ω)=H ab (ω)H F (ω)

[0030]

[0031]

[0032]

[0033]

[0034] Where H(ω) represents the frequency response function between the displacement of the axle box measuring point and the wheel-rail roughness, H ab (ω) represents the admittance of wheel-rail force and axle box response point displacement, H F (ω) represents the frequency response function of wheel-rail roughness and wheel-rail contact force, Y w (ω) represents the vertical admittance of the wheel at the point of contact, Y c (ω) represents the admittance of the contact spring, Y r (ω) represents the displacement admittance of the rail under multi-wheelset constraints, Φ represents the normal mode shape at the nominal contact node, ω represents the excitation frequency, I represents the identity matrix, i represents the imaginary unit, C represents the damping coefficient matrix, and Ω represents the wheel rotation speed. This represents the matrix representing the rotational gyroscope effect of the wheelset. This represents the modal stiffness matrix of the wheelset system. The matrix indicates that the gyroscopic effect is related to the rotation of the wheelsets. The matrix M represents the relationship between the centrifugal effect and the matrix M. wh Indicates half the mass of the wheelset, T represents the transpose, K c This indicates the equivalent contact stiffness of the Hertz contact spring.

[0035] Furthermore, the expression for the total displacement response of the rail is as follows:

[0036]

[0037] Where z(x) represents the total displacement response of the rail at position x, α(x,x) a ) indicates when the rail is at x a When a unit force is applied at position x, the displacement at position x transfers admittance, K. wc N represents the dynamic stiffness of the wheelset connected in series with the contact spring. w Represents the number of wheelsets, z(x) wi' ) indicates that the rail is at x wi' The total displacement response at position x wi' Let α(x, x') represent the position of the i'th wheelset, N' represent the number of fasteners, and α(x, x') represent the position of the i'th wheelset. wi' ) indicates when the rail is at x wi' When a unit force is applied at position x, the displacement at position x transfers admittance. sn' K represents the position of the n'th fastener. s This represents the dynamic stiffness at each fastener support, z(x) sn' ) indicates that the rail is at x sn' The total displacement response at position α(x,x) sn' ) indicates when the rail is at x sn' When a unit force is applied at position x, the displacement at position x transfers admittance.

[0038] Furthermore, the expression for the wheel roughness power spectral density is as follows:

[0039] S aa (ω)=|-ω 2 H(ω)| 2 S xx (ω)

[0040] Among them, S aa (ω) represents the power spectral density of the axle box vibration acceleration, ω represents the excitation frequency, H(ω) represents the frequency response function of wheel-rail roughness and axle box acceleration, and S xx (ω) represents the power spectral density of wheel-rail roughness.

[0041] Furthermore, the expression for the wheel roughness order diagram is as follows:

[0042]

[0043] Among them, L r This represents the roughness order diagram of the wheel, where r represents the root mean square value of the roughness in the corresponding order zone. ref This represents the roughness level reference value.

[0044] The beneficial effects of this invention are:

[0045] (1) This invention proposes an online quantitative diagnostic method for wheel polygons based on frequency response functions. The method has the following two contributions: First, a comb filter is used in the data preprocessing stage to filter out the influence of rail roughness, reducing errors or even misjudgments caused by interference factors from the rail. Second, the frequency response function of the wheel-rail system is introduced to quantitatively estimate the roughness level of the wheel polygon, thereby taking into account the influence of the inherent modes of the structure, thus improving the accuracy of the diagnostic results across the entire order and speed range.

[0046] (2) In view of the problem that the vibration components of wheel and track roughness are mixed together in the vibration response of axle box, which easily leads to misjudgment between wheel and track during diagnosis, the present invention uses the wheel-track roughness separation method of comb filter to filter out the track response component from the vibration response of axle box, and retains the "purer" wheel vibration response component.

[0047] (3) This invention addresses the difficulty in quantitatively assessing wheel roughness in vehicle-mounted wheel polygon detection methods by proposing a frequency response function derived from a frequency domain vehicle-track system dynamics model to correlate wheel-rail roughness with axle box vibration spectrum. This frequency response function is then used for quantitative diagnosis of wheel polygons, achieving better adaptability and accuracy than traditional quadratic integral methods. Attached Figure Description

[0048] Figure 1 This is a flowchart of the method of the present invention.

[0049] Figure 2 This is a simplified dynamic model diagram of the wheelset-track system in this embodiment.

[0050] Figure 3 This is a schematic diagram of the frequency response function of wheel-rail roughness and axle box vibration acceleration in this embodiment. Detailed Implementation

[0051] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0052] Example

[0053] To address the limitations of traditional methods in the background art, this invention uses the frequency response function method for quantitative diagnosis of wheel polygons, providing a new perspective and solution for the accurate detection of wheel polygons, such as... Figure 1As shown, this invention provides a vehicle-mounted quantitative diagnostic method for wheel polygons based on frequency response functions, the implementation method of which is as follows:

[0054] S1. The comb filtering method is used to preprocess the axle box vibration acceleration and filter out rail roughness interference. The implementation method is as follows:

[0055] S101. Based on the axle box vibration acceleration, use comb filtering to extract the length of one cycle from the axle box vibration signal;

[0056] S102. Add the axle box vibration signal extracted in this segment to the axle box vibration signal corresponding to the previous cycle;

[0057] S103. Repeat steps S101-S102 and suppress non-periodic noise and filter out rail roughness interference by averaging.

[0058] S2. Estimate the power spectral density of the pre-processed axle box vibration acceleration;

[0059] S3. Based on the estimated axle box vibration acceleration power spectral density, the wheel roughness power spectral density is calculated using the frequency response function between the axle box measuring point displacement and the wheel-rail roughness.

[0060] S4. Using the vehicle speed calculated from the rotational speed pulse signal, perform order slicing of the wheel roughness power spectral density.

[0061] S5. Based on the slicing results, calculate the wheel roughness order diagram;

[0062] S6. Based on the wheel roughness level order diagram, identify the roughness level and order of the wheel polygon disturbance, and obtain the distribution pattern of different orders according to the box-and-whisker diagram to complete the quantitative diagnosis of the wheel polygon on the vehicle.

[0063] In this embodiment, as Figure 1 As shown, the main process of this invention includes signal noise reduction preprocessing based on comb filtering and quantitative estimation of wheel roughness level based on frequency response function: Comb filtering is used to preprocess the axle box vibration acceleration, filtering out most of the rail irregularities and leaving a purer wheel polygon component; power spectral density estimation is performed on the axle box vibration acceleration data preprocessed by the comb filter, such as using existing periodogram methods or Welch methods; the wheel roughness power spectral density is calculated from the axle box vibration acceleration power spectral density using the frequency response function H(ω); based on the vehicle speed converted from the rotational speed pulse signal, the wheel roughness power spectral density is sliced ​​into order segments, i.e., divided into frequency bands (order bands) corresponding to each order according to rotational speed, and the effective value within each order band is calculated; the wheel roughness level order map is calculated; the wheel polygonal excitation roughness level and order are identified, and the distribution pattern of different orders is obtained according to the box-and-whisker diagram.

[0064] In this embodiment, to filter out components from track irregularities in the axle box vibration acceleration, especially the potential impact of short-wave abnormal wear of the rails, a comb filter method is used for signal preprocessing. Based on the characteristics of wheel motion, the polygonal vibration component of the wheel in the axle box vibration response repeats periodically with wheel rotation, while the track disturbance component is not strictly periodic. A comb filter can be used to selectively extract the periodic repetitive components. In principle, a period is extracted from the axle box vibration signal, and this segment of the axle box vibration signal is added to the corresponding axle box vibration signal of the previous period. This process is repeated, and through cumulative averaging, the characteristics of the periodic signal are enhanced, while aperiodic noise tends to cancel each other out due to the uncertain phase relative to the periodic event. In digital processing, this process can be implemented using a comb filter, and the time-domain difference equation of the comb filter is:

[0065] y[n]=x[n]-x[nN]+R·y[nN] (1)

[0066] Where y[n] represents the axle box vibration signal output by the comb filter at time n, x[n] represents the axle box vibration signal input by the comb filter at time n, N represents the delay in the time-domain difference equation of the comb filter, y[nN] represents the axle box vibration signal output N time units ago, R represents the feedback coefficient, and x[nN] represents the axle box vibration signal input N time units ago.

[0067] The frequency response of the comb filter is shown in the following equation:

[0068]

[0069] Where H(f) represents the frequency response of the comb filter at frequency f, j represents the unit imaginary number, and f s Let R represent the sampling frequency, N represent the delay in the time-domain difference equation of the comb filter, and R represent the feedback coefficient. When R approaches 1, the comb filter retains the frequency components related to the period; when R approaches 0, the comb filter filters out the frequency components related to the period.

[0070] In this embodiment, according to equation (2), the comb filter will adjust the fundamental frequency f0 = f s The filter performs filtering or retention on the period (N). When R approaches 1, the zeros and poles will be nearly aligned, minimizing the loss of harmonic k·f0. Thus, the comb filter primarily retains frequency components related to the period (N). Conversely, when R approaches 0, the zeros will experience significant attenuation at integer multiples of f0. Therefore, the comb filter will preferentially filter out frequency components related to the period (N). Considering both effectiveness and comb filter stability, this invention sets the feedback coefficient R = 0.97.

[0071] In this embodiment, the wheelset rotation speed changes in real time during train operation, and the polygon excitation frequency also changes with the rotation speed. In order to filter out vibration interference components in real time, a frequency that varies with the wheelset rotation speed (f) is set. w The varying adaptive filter delay N:

[0072]

[0073] Where N represents the delay in the time-domain difference equation of the comb filter, f s f represents the sampling frequency. w This indicates the wheelset rotation frequency.

[0074] In this embodiment, the comb filter can extract periodic signals and suppress noise without increasing the computational burden too much. Therefore, it can filter out most of the rail excitation components and retain a purer periodic wheel polygon vibration response, thus ensuring the accuracy of on-board polygon detection.

[0075] In this embodiment, the key to quantitatively diagnosing the severity of polygonal wear on a wheel is to establish the transmission relationship between axle box vibration acceleration and wheel-rail roughness, assuming the frequency response function between the axle box measuring point displacement and wheel-rail roughness is H(ω):

[0076] S yy (ω)=|H(ω)| 2 S xx (ω) (4)

[0077] Where H(ω) represents the frequency response function between the displacement of the axle box measuring point and the wheel-rail roughness, S yy (ω) and S xx (ω) represents the power spectral density of the axle box measuring point displacement and the wheel-rail roughness, respectively.

[0078] By taking the second derivative of the displacement of the measuring point on the axle box, the power spectral density of the axle box vibration acceleration S can be obtained. aa (ω) for the power spectral density S of wheel-rail roughness xx The transitivity of (ω) is shown in equation (5).

[0079] S aa (ω)=|-ω 2 H(ω)| 2 S xx (ω) (5)

[0080] Among them, S aa (ω) represents the power spectral density of the axle box vibration acceleration, ω represents the excitation frequency, H(ω) represents the frequency response function of wheel-rail roughness and axle box acceleration, and S xx (ω) represents the power spectral density of wheel-rail roughness.

[0081] It is evident that if the transfer function H(ω) can be accurately derived, then the power spectral density of the axle box vibration acceleration S can be used to determine the optimal power spectral density. aa (ω), using equation (5), the magnitude of the wheel-rail roughness level is quantitatively estimated. This invention derives the frequency response function H(ω) of wheel-rail roughness and axle box acceleration from the wheelset-track frequency domain model, considering a simplified vehicle-track system such as... Figure 2 As shown, taking the second wheelset with polygonal wear as an example, the frequency response function H(ω) is derived from the frequency response function H of the wheel-rail roughness and the wheel-rail contact force. F (ω) and wheel-rail force and axle box response point displacement admittance H ab (ω) is determined by two parts.

[0082] H(ω)=H ab (ω)H F (ω) (6)

[0083] Frequency response function H of wheel-rail roughness and wheel-rail force in wheel-rail coupled system F Depends on the admittance Y of the wheelset at the contact point w The admittance Y of the contact spring c The admittance Y of the track at the contact point r The expression is as follows:

[0084]

[0085] Where H(ω) represents the frequency response function between the displacement of the axle box measuring point and the wheel-rail roughness, Y w (ω) represents the vertical admittance of the wheel at the point of contact, Y c (ω) represents the admittance of the contact spring, Y r (ω) represents the displacement admittance of the rail under multi-wheel pair constraint.

[0086] Vertical admittance Y of the wheel at the contact point w (ω) is:

[0087]

[0088] Where Φ represents the normal mode shape at the nominal contact node, ω represents the excitation frequency, I represents the identity matrix, i represents the imaginary unit, C represents the damping coefficient matrix, and Ω represents the wheel rotational speed. This represents the matrix representing the rotational gyroscope effect of the wheelset. This represents the modal stiffness matrix of the wheelset system. The matrix indicates that the gyroscopic effect is related to the rotation of the wheelsets. The matrix M represents the relationship between the centrifugal effect and the matrix M. wh This indicates half the mass of the wheelset, and T indicates transpose.

[0089] The wheel-rail contact spring is considered as an equivalent linear spring, Y c (ω) can be expressed as:

[0090]

[0091] Among them, K c This represents the equivalent contact stiffness of the Hertz contact spring, typically taken as 1.1 × 10⁻⁶. 9 N / m.

[0092] Rail displacement admittance Y under multiple wheel pair constraints r (ω) can be obtained by referring to the classical frequency domain model. Consider the rail as an infinitely long Timoshenko beam. Since the rail is discretely supported, the fasteners are treated as linear stiffness and damping elements. Also, assume there are N... w Each wheelset is coupled to the rail, and each wheelset acts as a constraint on the rail. This constraint alters the transmission path of vibration waves within the rail, thus affecting the rail admittance. Therefore, at rail position x... a When a unit harmonic excitation with frequency ω is applied, the total displacement response at any position x of the rail can be written as:

[0093]

[0094] Where z(x) represents the total displacement response of the rail at position x, α(x,x) a ) indicates when the rail is at x a When a unit force is applied at position x, the displacement at position x transfers admittance, K. wc N represents the dynamic stiffness of the wheelset connected in series with the contact spring. w Represents the number of wheelsets, z(x) wi' ) indicates that the rail is at x wi' The total displacement response at position x wi' Let α(x, x') represent the position of the i'th wheelset, N' represent the number of fasteners, and α(x, x') represent the position of the i'th wheelset. wi' ) indicates when the rail is at x wi' When a unit force is applied at position x, the displacement at position x transfers admittance. sn' K represents the position of the n'th fastener. s This represents the dynamic stiffness at each fastener support, z(x) sn' ) indicates that the rail is at x sn' The total displacement response at position α(x,x) sn' ) indicates when the rail is at x sn' When a unit force is applied at position x, the displacement at position x transfers admittance.

[0095] Let x = {x} in the above formula sn' ,x wm},(n'=-N',…,-1,0,1,…,N'+1,m=1,2,3,…,N w This constructs a 2N"+N w A system of linear equations with +1 dimension can be used to calculate the displacement response vectors of the rail at the wheelset position and the fastener position. Substituting these back into equation (10) yields the rail transmit admittance Y under multi-wheelset coupling. r (ω), where x wm N represents the position of the m-th wheel pair. w N' represents the number of wheelsets, N' represents the number of fasteners, and n' represents the n'th fastener.

[0096] In this embodiment, the frequency response function H of the displacement at the axle box measuring point with respect to the wheel-rail contact force is... ab (ω) can be written as the sum of the rigid and flexible parts, as shown in (11). Note that this expression is similar in form to equation (8), but slightly different, where Φ ab Indicates the normal mode shape at the measuring point of the axle box:

[0097]

[0098] Finally, according to (6), the system frequency response function H(ω) can be obtained, as follows: Figure 3 As shown, there is a first high-frequency resonance band in the 600-700Hz range, a second high-frequency resonance band around 400Hz, and a P2 force resonance band around 50Hz.

[0099] In this embodiment, the expression for the wheel roughness order diagram is as follows:

[0100]

[0101] Among them, L r This represents the roughness order diagram of the wheel, where r represents the root mean square value of the roughness in the corresponding order zone. ref This represents the roughness level reference value.

[0102] This invention can not only accurately identify the order of polygons, but also quantitatively estimate the roughness level of wheel polygons, which has strong practicality and engineering value.

Claims

1. A vehicle-mounted quantitative diagnostic method for wheel polygons based on frequency response function, characterized in that, Includes the following steps: S1. Use comb filtering method to preprocess the vibration acceleration of the axle box and filter out the interference of rail roughness. S2. Estimate the power spectral density of the pre-processed axle box vibration acceleration; S3. Based on the estimated axle box vibration acceleration power spectral density, the wheel roughness power spectral density is calculated using the frequency response function between the axle box measuring point displacement and the wheel-rail roughness. The expression for the frequency response function is as follows: in, The frequency response function representing the relationship between the displacement of the axle box measuring point and the wheel-rail roughness. This represents the admittance of wheel-rail force and axle box response point displacement. This represents the frequency response function of wheel-rail roughness and wheel-rail contact force. This indicates the vertical admittance of the wheel at the point of contact. This represents the admittance of the contact spring. This represents the displacement admittance of the rail under multi-wheel constraint. This represents the normal mode shape at the nominal contact node. Indicates the excitation frequency. Represents the identity matrix. Represents the imaginary unit. Represents the damping coefficient matrix. Indicates the rotational speed of the wheel. This represents the matrix representing the rotational gyroscope effect of the wheelset. This represents the modal stiffness matrix of the wheelset system. The matrix indicates that the gyroscopic effect is related to the rotation of the wheelsets. The matrix indicates that it is related to the centrifugal effect. Indicates half the mass of the wheelset. Indicates transpose. This indicates the equivalent contact stiffness of the Hertz contact spring. This indicates the normal mode shape at the measuring point of the axle box; S4. Using the vehicle speed calculated from the rotational speed pulse signal, perform order slicing of the wheel roughness power spectral density. S5. Based on the slicing results, calculate the wheel roughness order diagram; S6. Based on the wheel roughness level order diagram, identify the roughness level and order of the wheel polygon disturbance, and obtain the distribution pattern of different orders according to the box-and-whisker diagram to complete the quantitative diagnosis of the wheel polygon on the vehicle.

2. The on-board quantitative diagnostic method for wheel polygons based on frequency response function according to claim 1, characterized in that, Step S1 specifically involves: S101. Based on the axle box vibration acceleration, use comb filtering to extract the length of one cycle from the axle box vibration signal; S102. Add the axle box vibration signal extracted in this segment to the axle box vibration signal corresponding to the previous cycle; S103. Repeat steps S101-S102 and suppress non-periodic noise and filter out rail roughness interference by averaging.

3. The on-board quantitative diagnostic method for wheel polygons based on frequency response function according to claim 2, characterized in that, The expression for the time-domain difference equation of the comb filter is as follows: in, Indicates the comb filter at time... n The output axle box vibration signal, Indicates the comb filter at time... n Input axle box vibration signal, The delay in the time-domain difference equation of the comb filter is represented by... express The axle box vibration signal output a certain time unit ago Indicates the feedback coefficient. express The axle box vibration signal input one time unit ago; The expression for the delay in the time-domain difference equation of the comb filter is as follows: in, Indicates the sampling frequency. This indicates the wheelset rotation frequency.

4. The on-board quantitative diagnostic method for wheel polygons based on frequency response function according to claim 3, characterized in that, The expression for the frequency response of a comb filter is as follows: in, This indicates that the comb filter is at a frequency f Frequency response at that point, j Represents the imaginary unit. Indicates the sampling frequency. N The delay in the time-domain difference equation of the comb filter is represented by... Represents the feedback coefficient, when Approaching 1, the comb filter retains frequency components related to the period. As the value approaches 0, the comb filter removes frequency components that are related to the period.

5. The on-board quantitative diagnostic method for wheel polygons based on frequency response function according to claim 1, characterized in that, The expression for the total displacement response of the rail is as follows: in, Indicates that the rails are in The total displacement response at the position. Indicates when the rail is Apply a unit force at the location, Displacement transfer admittance at the location. This indicates the dynamic stiffness of the wheelset connected in series with the contact spring. Indicates the number of wheelsets. Indicates that the rails are in Total displacement response at the location. Indicates the first The position of each wheel pair Indicates the number of fasteners. Indicates when the rail is Apply a unit force at the location, Displacement transfer admittance at location. Indicates the first The location of the fastener, This indicates the dynamic stiffness at each fastener support. Indicates that the rails are in Total displacement response at the location. Indicates when the rail is Apply a unit force at the location, Displacement transfer admittance at the location.

6. The on-board quantitative diagnostic method for wheel polygons based on frequency response function according to claim 1, characterized in that, The expression for the power spectral density of the wheel roughness is as follows: in, This represents the power spectral density of the axle box vibration acceleration. Indicates the excitation frequency. The frequency response function representing the relationship between wheel-rail roughness and axle box acceleration. This represents the power spectral density of wheel-rail roughness.

7. The on-board quantitative diagnostic method for wheel polygons based on frequency response function according to claim 1, characterized in that, The expression for the wheel roughness order diagram is as follows: in, This represents the roughness order diagram of the wheel. This represents the root mean square value of the roughness in the corresponding zone. This represents the roughness level reference value.

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