A theoretical detection method for determining local voids in a monolithic track bed

Abstract

The present application relates to a kind of theoretical detection methods for determining local void of monolithic track bed, comprising the steps of: obtaining train-monolithic track bed-lining-ground coupling vibration equation according to the control equation of rail, monolithic track bed and lining and the dynamic balance equation of train, the vertical acceleration of car body is calculated using Newmark algorithm;The Hilbert-Huang transform spectrum of the vertical acceleration of car body is obtained;According to the energy change of the Hilbert-Huang transform spectrum of the imf2 decomposition curve under the void state, the position of the local void area of monolithic track bed is judged.The beneficial effects of the present application are: the position of the local void area of monolithic track bed can be judged according to the energy value change of the Hilbert-Huang transform spectrum of the vertical acceleration of car body imf2;Whether there is track bed void and the starting position of void can be judged, and the severity of void length can be qualitatively estimated according to the length of energy value change, which helps to reduce the operation and maintenance cost of subway track.

Description

Technical Field

[0001] This invention belongs to the field of underground engineering technology, and in particular relates to a theoretical detection method for determining local voids in an overall track bed. Background Technology

[0002] In densely populated cities where land is extremely valuable, utilizing underground transportation space has become an inevitable trend in future urban planning and development. Subways play a crucial role in maintaining daily urban operations and facilitating urban expansion. However, under long-term operation, subway tracks may experience defects such as delamination. During subway track pouring, the integral track bed is poured directly onto the surface of the tunnel segments, resulting in weak surface adhesion. Influenced by soil properties, surrounding construction, and tunnel depth, subway shield tunnels in soft soil areas are prone to significant deformation. This mismatch in deformation between the tunnel segments and the integral track bed can lead to localized separation and delamination. Delamination and delamination of the track bed and tunnel segments have occurred in the subway operations of many medium and large cities, affecting not only the structural lifespan of the subway tunnels but also passenger comfort and posing significant safety hazards to urban subway operations. Therefore, timely detection and identification of localized track bed delamination, allowing for early prevention and treatment of these early defects, is of great significance for ensuring the integrity and operational safety of the subway track system.

[0003] Currently, the identification of track bed voids mainly relies on modern geophysical exploration technologies, including ground-penetrating radar, shock echo method, and ultrasonic method.

[0004] Ground Penetrating Radar (GPR) Method: Li Youyun et al. used GPR to detect defects in the overall track bed of railway tunnels. They also conducted mathematical simulation analysis based on drilling and sampling data, and used GPR non-destructive testing to determine the specific location of the overall track bed void.

[0005] Impact echo method: Li Xing et al. used the impact echo method to determine the presence of defects such as stripping and voids in the track bed.

[0006] Ultrasonic method: Zhao Yanshun used nonlinear ultrasonic mixing technology to excite the track bed before and after the jacking with different mixing signals, and used FFT transformation to obtain the signal frequency components. The jacking position of the track bed was identified based on the frequency components.

[0007] However, these methods for detecting track bed voids have obvious shortcomings: first, the testing methods are time-consuming and costly; second, the detection has certain limitations and it is difficult to monitor the entire operating section in real time. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a theoretical detection method for determining local voids in the overall track bed.

[0009] This theoretical detection method for determining local voids in the overall track bed includes the following steps:

[0010] S1. Based on the control equations of the rail, integral track bed and lining and the dynamic balance equation of the train, the coupled vibration equations of the train-integral track bed-lining-foundation are obtained, and the vertical acceleration of the car body is calculated using the Newmark algorithm.

[0011] S2. Perform Hilbert-Huang transform on the vertical acceleration of the vehicle body to obtain the Hilbert-Huang transform spectrum of the decomposition curves imf1 to imf6, and use the color scale values ​​of the curves to represent the magnitude of the energy value.

[0012] S3. By comparing the Hilbert-Huang transform spectra of the vertical acceleration of the vehicle body from IMF1 to IMF6 when it is not detached, the location of the local detachment area of ​​the overall track bed is determined based on the energy change of the Hilbert-Huang transform spectrum of the IMF2 decomposition curve under the detached state.

[0013] Preferably, step S1 specifically involves: establishing the dynamic balance equations of the train based on d'Alembert's principle.

[0014]

[0015] Where M, C, and K are the mass matrix, damping matrix, and stiffness matrix of the train, respectively; v is the displacement vector of the train; and F is the matrix of external forces acting on each part of the train.

[0016] The rails are simulated using Euler beams simply supported at both ends. The fasteners below the rails are discretely distributed at equal intervals and simulated using spring-damping elements. The integral track bed and lining are simulated using Timoshenko beams simply supported at both ends. The interface bonding between the integral track bed and the lining is simulated using discrete spring-damping elements distributed at equal intervals. The foundation is considered to be uniformly distributed spring-damping elements directly connected to the lining.

[0017] Using the modal superposition method and orthogonal decomposition, the ordinary differential vibration equations of the rail, the integral track bed, and the lining are obtained. The ordinary differential vibration equations of the rail, track bed, and lining are combined with the dynamic balance equations of the train to obtain the coupled vibration equations of the train-integral track bed-lining-foundation. Finally, the Newmark algorithm is used to numerically calculate the equations to obtain the vertical acceleration of the car body.

[0018] Preferably, in step S1: the rail is simulated by a Euler beam simply supported at both ends, and its governing equation is:

[0019]

[0020] In the formula:

[0021] E r I rThe bending stiffness of the rail is expressed in N·m. 2 ;v r x represents the vertical displacement of the rail, with the unit symbol being meters (m). rs,j ρ represents the position of the j-th fastener, with the unit symbol being m; r A r The distributed mass of the rail, with the unit symbol kg / m; n rs For the number of fasteners; x w,i (t) represents the position of the i-th round at time t; n c P represents the number of train formations. rs,j The fastening force of the j-th fastener is calculated using the following formula:

[0022]

[0023] Among them, K rs C represents the stiffness of the fastener, with the unit symbol N / m; rs For fastener damping, the unit symbol is N·s / m; P a,i (x w,i (t) represents the wheel-rail contact force of the i-th wheelset of the a-th vehicle, calculated using the following formula:

[0024] P a,i (x w,i (t))=K wr (z w,a,i (t)-ε(x w,a,i )v r (x w,a,i ,t))

[0025] Where K wr This refers to the wheel-rail contact stiffness, with the unit symbol N / m; z w,a,i Let be the vertical displacement of the i-th wheelset of vehicle a, with the unit symbol m;

[0026]

[0027] Preferably, in step S1: the track bed is simulated using a Timoshenko beam with simply supported ends, and its governing equation is:

[0028]

[0029] In the formula:

[0030] κ h A h G h The shear stiffness of the overall track bed is expressed in N.

[0031] F h (x,t) represents the vertical external force acting on the entire track bed, with the unit symbol N;

[0032]

[0033] m h (x,t) represents the external bending moment applied to the entire track bed, with the unit symbol N·m;

[0034] ρ h The density of the entire track bed is expressed in kg / m³. 3 ;ρ h A h The total mass of the track bed is expressed in kg / m.

[0035] I h The moment of inertia of the integral track bed section is expressed in meters (m). 4 E h I h The overall flexural stiffness of the track bed is expressed in N·m. 2 ;

[0036] v h The vertical displacement of the entire track bed is expressed in meters (m).

[0037] This represents the angular displacement of the entire track bed, with the unit symbol being rad.

[0038] As a preferred option, in step S1: the lining is also simulated using a Timoshenko beam with simple support at both ends, and its governing equation is the same as that of the overall track bed, except that the subscript in the formula and variables changes from h to t.

[0039] Preferably, in step S2: the Hilbert-Huang transform spectrum of the vehicle body's vertical acceleration, from top to bottom, are the Hilbert-Huang transform spectra of the IMF1 to IMF6 decomposition curves, where the color scale values ​​of each curve are negative, and the absolute value of the color scale value is negatively correlated with the energy value. The smaller the absolute value of the color scale value, the greater the energy value.

[0040] Preferably, in step S3: comparing the Hilbert-Huang transform spectra of the vertical acceleration of the car body from imf1 to imf6 under the condition of not being detached, the frequency value curve of the Hilbert-Huang transform spectrum of the imf2 decomposition curve changes with time under the condition of detachment. Specifically, before reaching the detachment area, the frequency in the imf2 curve oscillates periodically; when approaching the detachment area, the imf2 frequency curve fluctuates significantly, specifically, the frequency value increases for a short time and then decreases by more than 15% to a minimum point. The time corresponding to the above minimum point is the time when the center of the front bogie of the first car reaches the starting point of the detachment area. By calculating the center position of the front bogie of the first car at this time, the coordinates of the starting point of the overall track bed detachment area can be obtained.

[0041] Preferably, in step S3: the color mark value of curve imf2 decreases as the length of the voided area increases, and the decreasing trend of the color mark value of imf2 in the non-voided area is greater than that in the voided area. Based on the changes in the color mark value of curve imf2 at different time periods, if the absolute value of the external color mark value decreases by more than 15% in a certain time period, it is determined that there is a void in the overall track bed section passed by the train in that time period. Based on the first minimum value point with a decrease of more than 15% closest to that time period and the train speed, the starting position of the overall track bed voided area is calculated.

[0042] The beneficial effects of this invention are:

[0043] 1) By examining the impact of overall track bed delamination on the dynamic characteristics of the vehicle and track, the vertical acceleration of the vehicle body is used as a sensitive indicator for delamination identification. Based on this, the Hilbert-Huang transform method is used to identify the delamination section of the overall track bed. The location of the local delamination area of ​​the overall track bed is determined by the change in the energy value of the Hilbert-Huang transform spectrum of the vertical acceleration imf2 of the vehicle body.

[0044] 2) By utilizing vibration signals during vehicle operation, real-time identification of the entire operational track section can be achieved. By combining the energy value change of IMF2 and the train speed, it is possible to determine whether there is track bed delamination and the starting position of the delamination. Furthermore, the severity of the delamination length can be qualitatively estimated based on the length of energy value change. This provides a new and convenient method for track inspection, which helps to reduce the operating and maintenance costs of subway tracks and provides a theoretical basis for future research on local delamination of the overall track bed. Attached Figure Description

[0045] Figure 1 This invention relates to a section of the subway track bed where the track is partially derailed.

[0046] Figure 2 This invention provides a calculation model for coupled vibration between subway trains and tracks.

[0047] Figure 3 The Hilbert-Huang transform spectrum of the vehicle body's vertical acceleration when it is not airborne according to the present invention;

[0048] Figure 4 The Hilbert-Huang transform spectrum of the vehicle body's vertical acceleration under a 0.4m air gap condition according to the present invention;

[0049] Figure 5 The Hilbert-Huang transform spectrum of the vehicle body's vertical acceleration under a 0.8m air gap condition according to the present invention;

[0050] Figure 6 The Hilbert-Huang transform spectrum of the vehicle body's vertical acceleration under a 1.2m free-fall condition according to the present invention;

[0051] Figure 7The Hilbert-Huang transform spectrum of the vehicle body's vertical acceleration under the condition of being 1.6m free from air is shown. Detailed Implementation

[0052] The present invention will be further described below with reference to embodiments. The description of the embodiments below is only for the purpose of helping to understand the present invention. It should be noted that those skilled in the art can make several modifications to the present invention without departing from the principle of the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

[0053] Example 1

[0054] As one embodiment, a theoretical detection method for determining local voids in the overall track bed is proposed, specifically including the following steps:

[0055] S1. Based on the control equations of the rail, integral track bed and lining and the dynamic balance equation of the train, the coupled vibration equations of the train-integral track bed-lining-foundation are obtained, and the vertical acceleration of the car body is calculated using the Newmark algorithm.

[0056] The simulation conditions for the car body, rails, monolithic track bed, and lining are as follows: The car body adopts a 20-DOF rigid body model of two carriages, that is, the car body and bogies consider vertical and nodding displacements, while the wheelsets only consider vertical displacements. The bogies and wheelsets, and the carriages and bogies are connected by primary and secondary suspensions, respectively. The rails are simulated using Euler beams simply supported at both ends, with the fasteners under the rails being discretely distributed at equal intervals and simulated using spring-damped elements. The monolithic track bed and lining are simulated using Timoshenko beams simply supported at both ends. The interface bonding between the monolithic track bed and the lining is simulated using discretely distributed spring-damped elements at equal intervals. The foundation is considered to be uniformly distributed spring-damped elements directly connected to the lining. The rail condition is ideal, and track irregularities are not considered. In the void area, the stiffness coefficient and damping coefficient of the discrete spring-damped elements between the monolithic track bed and the lining are set to 0, and nonlinear contact is not considered.

[0057] Define the following parameters:

[0058] v c This represents the vertical displacement of the vehicle body, with the unit symbol being meters (m).

[0059] ψ c The displacement of the vehicle body at the nose is expressed in rad.

[0060] m c The mass of the vehicle body is expressed in kg.

[0061] J c The moment of inertia of the vehicle body, with the unit symbol kg·m 2 ;

[0062] k2 is the second-order suspension stiffness, with the unit symbol N / m;

[0063] c2 is the secondary suspension damping, with the unit symbol N·s / m;

[0064] m b The mass of the bogie is expressed in kg.

[0065] J b The moment of inertia of the bogie is expressed in kg·m. 2 ;

[0066] v b This represents the vertical displacement of the bogie, with the unit symbol being meters (m).

[0067] ψ b The bogie head-up displacement is expressed in rad.

[0068] k1 is the primary suspension stiffness, with the unit symbol N / m;

[0069] c1 is the primary suspension damping, with the unit symbol N·s / m;

[0070] z wi (i = 1, ..., 8) represents the vertical displacement of the eight wheelsets, with the unit symbol being meters;

[0071] E r I r The bending stiffness of the rail is expressed in N·m. 2 ;

[0072] ρ r A r The mass distributed along the rails is expressed in kg / m.

[0073] ρ h A h The total mass of the track bed is expressed in kg / m.

[0074] κ h A h G h The shear stiffness of the overall track bed is expressed in N.

[0075] E h I h The overall flexural stiffness of the track bed is expressed in N·m. 2 ;

[0076] ρ t A t The mass distributed in the tunnel lining is expressed in kg / m.

[0077] κ t A t Gt Shear stiffness of tunnel lining, with the unit symbol N;

[0078] E t I t The flexural stiffness of the tunnel lining, with the unit symbol N·m. 2 ;

[0079] K hs The bond stiffness between track bed linings is expressed in N / m.

[0080] C hs The bonding damping between track bed lining sections is represented by the unit symbol N·s / m;

[0081] K ts This represents the equivalent stiffness of the foundation, with the unit symbol N / m.

[0082] C ts The equivalent damping of the foundation is represented by the unit N·s / m;

[0083] Based on d'Alembert's principle, the dynamic balance equations of the train are established as follows:

[0084]

[0085] In the formula: M, C and K are the mass matrix, damping matrix and stiffness matrix of the train, respectively; v is the displacement vector of the train; and F is the external force matrix of each part of the train.

[0086] The rail is simulated by a simply supported Euler beam at both ends, and its governing equations are:

[0087]

[0088] In the formula:

[0089] E r I r The bending stiffness of the rail is expressed in N·m. 2 ;v r x represents the vertical displacement of the rail, with the unit symbol being meters (m). rs,j ρ represents the position of the j-th fastener, with the unit symbol being m; r A r The distributed mass of the rail, with the unit symbol kg / m; n rs For the number of fasteners; x w,i (t) represents the position of the i-th round at time t; n c P represents the number of train formations. rs,j The fastening force of the j-th fastener is calculated using the following formula:

[0090]

[0091] Among them, Krs C represents the stiffness of the fastener, with the unit symbol N / m; rs For fastener damping, the unit symbol is N·s / m; P a,i (x w,i (t) represents the wheel-rail contact force of the i-th wheelset of the a-th vehicle, calculated using the following formula:

[0092] P a,i (x w,i (t))=K wr (z w,a,i (t)-ε(x w,a,i )v r (x w,a,i ,t))

[0093] Where K wr This refers to the wheel-rail contact stiffness, with the unit symbol N / m; z w,a,i Let be the vertical displacement of the i-th wheelset of vehicle a, with the unit symbol m;

[0094]

[0095] The track bed is simulated using a Timoshenko beam with simply supported ends, and its governing equations are as follows:

[0096]

[0097] In the formula:

[0098] κ h A h G h The shear stiffness of the overall track bed is expressed in N.

[0099] F h (x,t) represents the vertical external force acting on the entire track bed, with the unit symbol N;

[0100]

[0101] m h (x,t) represents the external bending moment applied to the entire track bed, with the unit symbol N·m;

[0102] ρ h The density of the entire track bed is expressed in kg / m³. 3 ;ρ h A h The total mass of the track bed is expressed in kg / m.

[0103] I h The moment of inertia of the integral track bed section is expressed in meters (m). 4 E h I h The overall flexural stiffness of the track bed is expressed in N·m.2 ;

[0104] v h The vertical displacement of the entire track bed is expressed in meters (m).

[0105] This represents the angular displacement of the entire track bed, with the unit symbol being rad.

[0106] The lining is also simulated using a Timoshenko beam with simple support at both ends. Its governing equations are the same as those of the overall track bed, except that the subscripts in the formula and variables are changed from h to t.

[0107] Then, using the modal superposition method and orthogonal decomposition, the ordinary differential vibration equations of the rail, integral track bed, and lining are obtained. By combining these equations with the dynamic equations of the subway train, the coupled vibration equations of the train-integral track bed-lining-foundation can be obtained. Finally, the Newmark algorithm is used to numerically calculate the vertical acceleration of the car body using the equations.

[0108] S2. Perform Hilbert-Huang transform on the vertical acceleration of the vehicle body to obtain the Hilbert-Huang transform spectrum of the decomposition curves imf1 to imf6, and use the color scale values ​​of the curves to represent the energy values. The Hilbert-Huang transform spectrum of the decomposition curves imf1-imf6 is shown from top to bottom in the Hilbert-Huang transform spectrum. The color scale values ​​of each curve are negative, and the absolute value of the color scale value is negatively correlated with the energy value. The smaller the absolute value of the color scale value, the greater the energy value.

[0109] S3. Determine the location of the local voiding area of ​​the overall track bed based on the energy change of the Hilbert-Huang transform spectrum of IMF2. The specific method is as follows: Compare the Hilbert-Huang transform spectrum of the car body vertical acceleration from IMF1 to IMF6 under the condition of not being voided. Under the condition of voiding, the frequency value curve of the Hilbert-Huang transform spectrum of the IMF2 decomposition curve changes significantly with time. Specifically, before reaching the voiding area, the frequency in the IMF2 curve oscillates periodically, and the oscillation center value is consistent with the frequency center value of IMF2 under the condition of not being voided. When approaching the voiding area, the frequency curve of IMF2 fluctuates significantly. After the frequency value increases for a short time, it decreases significantly by more than 15%. The time corresponding to the minimum value point of the above significant decrease is the time when the center of the front bogie of the first car reaches the starting point of the voiding area. By calculating the center position of the front bogie of the first car at this time, the coordinates of the starting point of the voiding area of ​​the overall track bed can be obtained.

[0110] The color scale value of curve imf2 decreases as the length of the voided area increases, and the decreasing trend of the color scale value of imf2 in the non-voided area is greater than that in the voided area. Based on the changes of the color scale value of curve imf2 in different time periods, if the absolute value of the color scale value outside a certain time period decreases by more than 15%, it is determined that there is a void in the overall track bed section passed by the train in that time period. Based on the first minimum value point with a decrease of more than 15% closest to that time period and the train speed, the starting position of the overall track bed voided area is calculated.

[0111] Example 2

[0112] This embodiment presents an example of the application of the theoretical detection method for determining local voids in the overall track bed given in Embodiment 1:

[0113] Numerical simulations were conducted on a train traveling through a voided area at a speed of 72 km / h, under the assumption that the stiffness and damping coefficients of the discrete spring-damped elements between the track bed and lining in the voided area were both set to 0, and that nonlinear contact was not considered. The void lengths were taken as 0.4 m, 0.8 m, 1.2 m, and 1.6 m, respectively, corresponding to... Figure 1 The delamination regions of the spring-damping unit section are numbered 1622 to 1625, 1622 to 1629, 1622 to 1633, and 1622 to 1637, thereby analyzing the Hilbert-Huang transform spectrum of the vehicle's vertical acceleration.

[0114] Hilbert-Huang transform spectra of vehicle body acceleration at different decoupling lengths are as follows Figures 4 to 7 As shown: Vertical acceleration of the vehicle body imf1 ( Figures 4 to 7 The frequency values ​​of the Hilbert-Huang transform spectrum of the first curve from top to bottom in the middle do not change significantly, but the color of the curve gradually darkens, indicating that the energy value decreases with the increase of the de-emptying length. In particular, the change is most significant when the de-emptying length changes from 1.2m to 1.6m.

[0115] In the non-empty region, imf2( Figures 4 to 7 The frequency value of the Hilbert-Huang transform spectrum (the second curve from top to bottom) remains stable, but the energy value decreases with increasing gap length. Furthermore, the decreasing trend of the color scale value of IMF2 is greater in the non-gap region than in the gap region. Significant changes in energy value occur when the train approaches the gap position and when the entire train leaves the gap position, indicating that the time point of significant energy change is related to the location of the gap section. Therefore, the location of the gap region can be determined by segmenting the energy change region of the Hilbert-Huang transform spectrum of IMF2.

[0116] At the same time imf2( Figures 4 to 7The frequency values ​​of the Hilbert-Huang transform spectrum of the second curve from top to bottom in the middle all show a phenomenon of first periodic oscillation, then a significant increase in the maximum frequency value at a certain moment, and then a significant decrease in the minimum frequency value. Moreover, the time period of this phenomenon coincides with the time period of energy change in the Hilbert-Huang transform spectrum of imf2. According to the theoretical detection method for determining the local voiding of the overall track bed given in Example 1, the time corresponding to the significantly decreased minimum value is the time when the center of the front bogie of the first car reaches the starting point of the voiding area. By calculating the center position of the front bogie of the first car at this time, the coordinates of the starting point of the voiding area of ​​the overall track bed can be obtained.

[0117] In summary, the location of the starting point of local delamination of the overall track bed can be roughly determined based on the time point when the energy value of the Hilbert-Huang transform spectrum of IMF2 begins to change significantly. Alternatively, the coordinates of the starting point of the delamination area of ​​the overall track bed can be obtained based on the frequency value change of IMF2. In addition, the severity of the overall track bed delamination length can be qualitatively determined based on the energy value changes of the Hilbert-Huang transform spectra of the vehicle body's vertical acceleration IMF1 and IMF2, as well as the length of the significant change segment of IMF2.

[0118] The results show that, theoretically, this invention can determine whether local voids exist in the overall track bed and the location of the voided area. It provides a new and simple method for track inspection, enabling real-time identification of the entire operational track section using vibration signals from vehicle operation. Furthermore, it provides a theoretical basis for future research on local voids in the overall track bed, and helps reduce the operating and maintenance costs of subway tracks.

Claims

1. A theoretical detection method for determining local voids in an overall track bed, characterized in that, Includes the following steps: S1. Based on the control equations of the rail, integral track bed and lining and the dynamic balance equation of the train, the coupled vibration equations of the train-integral track bed-lining-foundation are obtained, and the vertical acceleration of the car body is obtained using the Newmark algorithm. Based on d'Alembert's principle, establish the dynamic balance equations for the train. in, M , C and K These are the train's mass matrix, damping matrix, and stiffness matrix, respectively. v Let be the displacement vector of the train. F This represents the matrix of external forces acting on each part of the train. The rails are simulated using Euler beams simply supported at both ends, and the fasteners below the rails are discretely distributed at equal intervals and simulated using spring-damping elements. The integral track bed and lining are simulated using Timoshenko beams simply supported at both ends, and the interface bonding between the integral track bed and the lining is simulated using discrete spring-damping elements distributed at equal intervals. The foundation is considered to be uniformly distributed spring-damping elements directly connected to the lining. Using the modal superposition method and orthogonal decomposition, the ordinary differential vibration equations of the rail, monolithic track bed, and lining are obtained. These equations are then combined with the train's dynamic equilibrium equations to derive the coupled vibration equations of the train, monolithic track bed, lining, and foundation. Finally, the Newmark algorithm is used to numerically calculate the equations, yielding the vertical acceleration of the train body. S2. Perform Hilbert-Huang transform on the vertical acceleration of the vehicle body to obtain the Hilbert-Huang transform spectrum of the decomposition curves imf1 to imf6, and use the color scale values ​​of the curves to represent the magnitude of the energy value. S3. Determine whether local voiding exists in the overall track bed and the location of the voiding area based on the energy change of the Hilbert-Huang transform spectrum of the car body in the non-voiding condition; compare the Hilbert-Huang transform spectrum of the car body vertical acceleration from IMF1 to IMF6 with the data from the non-voiding condition. Under voiding conditions, the frequency value curve of the Hilbert-Huang transform spectrum of the IMF2 decomposition curve changes with time. Before reaching the voiding area, the frequency in the IMF2 curve oscillates periodically; when approaching the voiding area, the frequency curve of IMF2 fluctuates, showing a minimum value point where the frequency value increases for a short time and then decreases by more than 15%. The time corresponding to the minimum value point is when the center of the front bogie of the first car reaches the voiding point. The coordinates of the starting point of the vacant area can be obtained by calculating the center position of the bogie of the first car at the starting time of the vacant area. The color mark value of the curve imf2 decreases as the length of the vacant area increases, and the decreasing trend of the color mark value of imf2 in the non-vacant area is greater than that in the vacant area. According to the changes of the color mark value of the curve imf2 in different time periods, if the absolute value of the color mark value outside a certain time period decreases by more than 15%, it is determined that there is a vacant situation in the ballast section passed by the train in that time period. The starting position of the vacant area of ​​the ballast can be calculated based on the nearest minimum value point with a decrease of more than 15% and the train speed.

2. The theoretical detection method for determining local voids in the overall track bed according to claim 1, characterized in that, In step S1: The rail is simulated by a Euler beam simply supported at both ends, and its governing equation is: In the formula: The bending stiffness of the rail is expressed in N·m. 2 ; This represents the vertical displacement of the rail, with the unit symbol being meters (m). For the first j The location of each fastener is indicated by the unit symbol (m). The mass distributed along the rails is expressed in kg / m. For the number of fasteners; For the first i Wheels t Location at any given time; This refers to the number of train formations. For the first j The fastening force of each fastener is calculated using the following formula: in, The stiffness of the fastener is expressed in N / m. For fastener damping, the unit symbol is N·s / m; For the first a Car i The wheel-rail contact force of the wheelset is calculated using the following formula: in This refers to the wheel-rail contact stiffness, with the unit symbol N / m; For the first a Car i Vertical displacement of wheelset, with the unit symbol m; .

3. The theoretical detection method for determining local voids in the overall track bed according to claim 1, characterized in that, In step S1: the track bed is simulated using a Timoshenko beam with simply supported ends, and its governing equation is: In the formula: The shear stiffness of the overall track bed is expressed in N. The vertical external force acting on the entire track bed is represented by the symbol N; The external bending moment applied to the entire track bed, with the unit symbol N·m; The density of the entire track bed is expressed in kg / m³. 3 ; The total mass of the track bed is expressed in kg / m. The moment of inertia of the integral track bed section is expressed in meters (m). 4 ; The overall flexural stiffness of the track bed is expressed in N·m. 2 ; The vertical displacement of the entire track bed is expressed in meters (m). This represents the angular displacement of the entire track bed, with the unit symbol being rad.

4. The theoretical detection method for determining local voids in the overall track bed according to claim 3, characterized in that, In step S1: The lining is also simulated using a Timoshenko beam with simple support at both ends. Its governing equation is the same as that of the overall track bed, except that the subscript in the formula and variables changes from h to t.

5. The theoretical detection method for determining local voids in the overall track bed according to claim 1, characterized in that, In step S2: In the Hilbert-Huang transform spectrum of the vehicle body's vertical acceleration, from top to bottom are the Hilbert-Huang transform spectra of the IMF1 to IMF6 decomposition curves. The color scale values ​​of each curve are negative, and the absolute value of the color scale value is negatively correlated with the energy value. The smaller the absolute value of the color scale value, the greater the energy value.

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