Physical-data hybrid method for predicting temperature-induced deformation and irregularity of ballastless track slab

Abstract

The application discloses a physical-data mixed ballastless track slab temperature-induced deformation and unevenness prediction method, relates to the field of railway traffic infrastructure structure health monitoring and intelligent operation and maintenance, and comprises the following steps: a three-dimensional thermal-mechanical coupling finite element model is established and equivalent air temperature is calculated; based on the finite element data, a discrete Fourier series is used to fit the harmonic coefficient to extract the amplitude and phase, the amplitude attenuation and phase lag coefficients are calculated as the transferable physical priori; the historical equivalent air temperature harmonic coefficient is extrapolated to predict the period coefficient, and the physical information is traced back to the slab temperature coefficient, the ridge regression is used to correct the linear residual of the harmonic coefficient; after the temperature sequence is reconstructed, the prediction residual is taken as the LSTM input to correct the nonlinear residual to obtain the final slab temperature prediction value; based on the predicted slab temperature, the gradient temperature is calculated to construct the shape function to predict the temperature-induced deformation; the deformation is superimposed to the original unevenness, and the LSTM is used to predict the track unevenness spectrum. The application realizes real-time and accurate prediction of meteorological data-deformation-unevenness spectrum under small samples.

Description

Technical Field

[0001] This application relates to the field of structural health monitoring and intelligent operation and maintenance technology for railway transportation infrastructure, and in particular to a physical-data hybrid method for predicting temperature-induced deformation and irregularities of ballastless track slabs. Background Technology

[0002] Ballastless track slabs are subjected to complex environments such as solar radiation, atmospheric temperature, and wind speed over long periods. Non-uniform temperature fields and vertical temperature gradients form between the top and bottom surfaces, and between shallow and deep layers of the track slab. Under thermal expansion constraints and support boundary conditions, this easily induces defects such as track slab arching, end separation, mortar layer delamination, and joint width deformation. Under extreme weather conditions, excessive temperature-induced deformation can alter the geometry of the rail top surface, affecting wheel-rail contact and vehicle dynamic response, threatening driving safety and passenger comfort. Therefore, it is necessary not only to understand the evolution of the multi-depth temperature field within the slab but also to predict track slab deformation based on temperature, further assessing its impact on driving safety. This comprehensive assessment, from environmental monitoring to structural response and driving risk evaluation, provides a real-time evaluation method for the service performance and driving safety of track slabs under long-term environmental conditions.

[0003] Currently, existing research has established thermo-mechanical coupled finite element models of track slabs to solve for the temperature and deformation fields within the slabs. These models can characterize the temperature transfer and temperature-induced deformation mechanisms in the depth direction under relatively complete meteorological excitation and structural stratification conditions, providing a reliable numerical basis for physical priors. However, finite element calculations are mostly geared towards representative working conditions or offline simulations, while field monitoring sequences are often short-term and limited in the number of measurement points. The two differ in data scale and application objectives, making it difficult to directly replace field assessments with finite element results and form a forecast chain that can be linked to monitoring data in real time and is oriented towards engineering deployment. Pure data-driven methods (such as artificial neural networks and LSTM) have a certain fitting ability for nonlinear time-varying sequences, but they are sensitive to the number and distribution of training samples, have weak physical interpretability, and lack the ability to generalize to sudden weather changes. Existing hybrid-driven schemes mostly focus on temperature prediction or local deformation monitoring, lacking a temperature prediction framework that combines the equivalent air temperature heat transfer mechanism, depth-direction physical information transfer, and data-driven learning residual correction. Furthermore, there is a lack of a method for the whole-process evaluation of train operation safety performance, which involves calculating the vertical deformation field from the predicted slab temperature and further superimposing it onto track irregularities. Summary of the Invention

[0004] The purpose of this application is to provide a physical-data hybrid method for predicting temperature-induced deformation and irregularities of ballastless track slabs, so as to achieve a forward-looking assessment of the service status and driving safety of ballastless track slabs under normal and extreme weather conditions.

[0005] To achieve the above objectives, this application provides a physical-data hybrid method for predicting temperature-induced deformation and irregularities of ballastless track slabs, comprising the following steps: S1. Establish a three-dimensional thermo-mechanical coupled finite element model of the ballastless track slab, perform sliding window processing on meteorological conditions and finite element multi-depth track slab temperature samples, and calculate the equivalent air temperature representing the meteorological conditions based on the heat exchange mechanism of the ballastless track and the environment. S2. Based on the least squares method, discrete Fourier series fitting is performed on the finite element temperature and equivalent air temperature data of each sliding window to obtain the harmonic coefficients and extract the amplitude and phase. The amplitude attenuation coefficient and phase lag coefficient of the equivalent air temperature relative to the finite element track plate temperature are calculated as transferable physical prior information. S3. Transfer the above physical prior information to the actual structure prediction, extrapolate the equivalent temperature harmonic coefficient of the predicted time period by the equivalent temperature harmonic coefficient of the historical time period, and backtrack the actual structural plate temperature harmonic coefficient by the transferred physical prior information. S4. The Ridge method is used to correct the linear residuals of the harmonic coefficients. S5. Perform inverse Fourier transform on the predicted harmonic coefficients to the time-domain temperature sequence. Use the residual sequence predicted by each sliding window data as the input of the LSTM neural network to correct the nonlinear residuals and obtain the final plate temperature prediction value. S6. Calculate the maximum gradient temperature based on the predicted plate temperature, construct a normalized shape function for the reference simulation data, and predict the temperature-induced deformation of the track slab. S7. The temperature-induced deformation is converted into an additional track irregularity excitation and superimposed on the original track irregularity. An LSTM neural network is used to predict the track irregularity spectrum caused by temperature-induced deformation.

[0006] Preferably, S1 specifically includes: S11. The measured meteorological elements of solar radiation, atmospheric temperature and wind speed are applied as time-varying boundary conditions to the surface of the track slab structure to establish a three-dimensional thermo-mechanical coupled finite element model of the ballastless track slab. Transient thermal analysis is carried out to obtain multi-depth temperature fields, and thermal expansion and warping deformation are driven by the vertical temperature gradient.

[0007] S12. Perform sliding window processing on the meteorological conditions data of solar radiation, atmospheric temperature and wind speed, divide the dataset, the data sampling frequency is 30 minutes, the length of each sliding window dataset is 24 hours, that is, 48 ​​data points, the prediction dataset and the overlap length is 2 hours, that is, 4 data points, and so on for rolling prediction. S13. Calculate the average air temperature, convective heat transfer coefficient, and equivalent air temperature for each sliding window; The average temperature per sliding window is expressed as: ; in, The average atmospheric temperature of the sliding window is used for calculating the heat transfer coefficient; N represents the number of sampling points in the sliding window. This represents the measured temperature at time n; n represents time. The convective heat transfer coefficient is expressed as: ; Where v is the wind speed; The equivalent temperature is expressed as: ; in, The solar radiation absorption coefficient of the track slab surface. for Total heat flux density at time t, is the convective heat transfer coefficient.

[0008] Preferably, S2 specifically includes: S21. Perform discrete Fourier series transformation on the equivalent air temperature and the finite element temperature of the track slab at different depths. For any scalar sequence, the K-order harmonic model is calculated using the following formula: ; Where t is time; T is the fundamental frequency period; and K is the harmonic fundamental number; The constant term represents the zero-frequency component; and These are the coefficients of the cosine term of the kth harmonic and the sine term of the kth harmonic, respectively; Let the harmonic coefficient vector be... ; S22, at discrete time Each basis function in The vector representation of the values ​​at each time step is: ; For y(t) and harmonic coefficients Construct a matrix, represented as: ; ; S23. The harmonic coefficients are estimated using the least squares method, expressed as follows: ; After obtaining the harmonic coefficients, the sequence values ​​at any time t are reconstructed, as follows: ; in, At discrete time The equivalent temperature, The constant term obtained from the fitting, To obtain the cosine coefficients of the k-th harmonic obtained by fitting, The coefficients of the sinusoidal term of the k-th harmonic obtained by fitting; S24. Perform K=2nd harmonic fitting on the data within each sliding window, and extract the amplitude and phase of the Kth harmonic component: Define the amplitude attenuation coefficient and the phase lag coefficient: ; in, Let be the equivalent air temperature amplitude of the k-th harmonic. The track slab temperature amplitude of the k-th harmonic. , The cosine and sine coefficients obtained from the temperature fitting of the track slab. The phase of the kth harmonic of the equivalent temperature. Let be the phase of the k-th harmonic of the track slab temperature. This is the amplitude attenuation coefficient. This is the phase lag coefficient; S25. Fit the amplitude attenuation coefficients calculated at different depths over the entire time period using finite element simulation to obtain physical prior information about the relationship between depth and amplitude attenuation. Simultaneously, average the amplitude attenuation coefficients of the observation data calculated from different blocks of data in the training set to obtain the amplitude attenuation coefficients of the observation data. Calculate the solar wave depth and amplitude attenuation coefficients under hybrid drive with a weight of 50% for both physical prior information and observation data. The half-sunwave coefficient is taken as 0.5 of the solar wave value, expressed as: Where, in the formula The amplitude attenuation coefficient of the observation data at depth z; M is the number of data blocks; For data block index, z is the depth; Let z be the amplitude attenuation coefficient of the observed data calculated at depth z for the b-th data block. This is the diurnal amplitude coefficient; D is the amplitude coefficient for the semi-diurnal wave; D and B are the exponential relationship coefficients between amplitude and depth fitted over the entire time period.

[0009] Preferably, S3 specifically includes: In the prediction phase, the harmonic coefficient is set to K=1. The harmonic coefficient of the equivalent temperature over the extrapolated time period is calculated. And through depth transfer transformation, the plate temperature harmonic coefficients at different depths are obtained, expressed as: ; in, The plate temperature harmonic coefficient at depth z; The phase of the Kth harmonic of the equivalent temperature. Let z be the phase of the Kth harmonic at depth z; Calculate the harmonic coefficient vector at different depths Multiple depths together construct the total vector of physical information harmonic coefficients. Harmonic reconstruction is performed according to the following formula to obtain the temperature sequence based on physical information. The calculation formula is as follows: ; ; in, Let z be the harmonic coefficient vector at depth z. , , For the constant term, first-order cosine harmonic coefficient, and first-order sine harmonic coefficient of the discrete Fourier series; The obtained physical prior information is transferred to the actual track slab structure, and the temperature of the actual track slab structure is predicted using the measured meteorological conditions and the transferred physical prior information.

[0010] Preferably, S4 specifically includes: In the harmonic coefficient space, the Ridge linear model is used to correct the systematic deviation between physical information and actual measurements. The linear components that the physical model cannot explain are corrected, expressed as: ; ; in, The vector of ridge regression coefficients; The measured harmonic coefficient of the plate temperature; The harmonic coefficients are physical information. The corrected harmonic coefficients, Design matrix for ridge regression.

[0011] Preferably, S5 specifically includes: The predicted harmonic coefficients are subjected to an inverse Fourier transform to a time-domain temperature sequence. The residuals predicted from each sliding window data point are used as input to the LSTM neural network to correct the nonlinear residuals, yielding the final plate temperature prediction. The temperature residuals are expressed as follows: ; in, This represents the residual between the measured temperature and the baseline temperature. This is the measured temperature; Baseline temperature; ; ; in, The final predicted temperature; The residuals predicted by LSTM; For historical window count; For the past The residual sequence of each prediction window.

[0012] Preferably, S6 specifically includes: S61. Based on the temperature data predicted in S5, calculate the vertical temperature gradient of the track slab, expressed as: ; in, Predicting temperature for shallow layers; For deep temperature prediction; This is the shallow depth; For deep depth; The predicted vertical temperature gradient; S62. Normalize the reference finite element deformation data and construct shape functions. , represented as: ; in, For reference, the vertical deformation value at time t along the plate width coordinate x is simulated. Vertical deformation value at the center point at time t. For coordinates along the width of the plate, The reference center point in the width direction of the plate is the coordinate of the plate width at the point where the upper arch deformation is the maximum. It is usually taken as the center point of the plate width. S63. The vertical deformation value calculated based on the predicted temperature is expressed as follows: ; in, Sensitivity is the ratio of the deformation at the reference center to the reference temperature gradient. This represents the predicted temperature gradient.

[0013] Preferably, S7 specifically includes: The temperature-induced deformation value of the track slab under the daily maximum temperature gradient calculated in S6 is superimposed on the original track irregularity as an additional track irregularity, forming a sequence of track irregularities with temperature-induced additional excitation. The LSTM neural network is used again to predict the track irregularities caused by temperature-induced deformation, thereby realizing real-time early warning and assessment of temperature deformation and track irregularities of ballastless track.

[0014] Therefore, the above-mentioned physical-data hybrid method for predicting temperature-induced deformation and irregularities of ballastless track slabs has the following beneficial effects: (1) This application constructs physical prior information in the frequency domain based on the equivalent air temperature heat transfer mechanism and the plate temperature depth transfer law, and then uses ridge regression and LSTM to correct the linear and nonlinear residuals in layers to form a physical-data hybrid temperature prediction method. This method overcomes the problems of strong sample dependence and weak physical interpretability of traditional pure data-driven methods, and ensures the physical consistency and numerical stability of prediction results under limited sample and extreme weather conditions, thereby improving the interpretability and generalization of the model.

[0015] (2) This application uses physical laws and data fusion to predict the temperature deformation data of the track slab 2 hours after 24 hours of meteorological data. It does not require online calling of high-fidelity finite element model, and can realize rapid rolling update of temperature deformation of track slab at multiple depths, which significantly reduces calculation time and cost and is suitable for on-site real-time monitoring and early warning.

[0016] (3) This application provides reliable technical support for core tasks related to track structure health monitoring and intelligent operation and maintenance. It can accurately predict the temperature-induced deformation of the track slab through meteorological data, and convert the temperature-induced deformation into additional track irregularity excitations superimposed on the original track irregularities. The LSTM neural network is used to predict the track irregularity spectrum caused by temperature-induced deformation. This lays the foundation for subsequent track structure damage identification, remaining life prediction, and train operation safety assessment, and helps track structure operation and maintenance to conduct real-time assessments from meteorological conditions to temperature-induced deformation to track irregularities.

[0017] The technical solution of this application will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1 A three-dimensional thermo-mechanical coupled finite element model of the ballastless track slab was established; Figure 2 This is a flowchart of a physical-data hybrid method for predicting temperature-induced deformation and irregularities in ballastless tracks, as described in this application. Figure 3 This is a schematic diagram of the sliding prediction in this application; Figure 4 The spectrum diagrams of equivalent air temperature and temperature at different depths of the track slab in the embodiments of this application are shown. Figure 5 This is a schematic diagram of temperature prediction results for the period from July 21 to August 19, 2016, in an embodiment of this application; wherein, (a) is a schematic diagram of temperature prediction results at a depth of 50 mm during the period from July 21 to August 19, 2016, (b) is a schematic diagram of temperature prediction results at a depth of 100 mm during the period from July 21 to August 19, 2016, (c) is a schematic diagram of temperature prediction results at a depth of 180 mm during the period from July 21 to August 19, 2016, (d) is a schematic diagram of temperature prediction results at a depth of 215 mm during the period from July 21 to August 19, 2016, and (e) is a schematic diagram of temperature prediction results at a depth of 260 mm during the period from July 21 to August 19, 2016. Figure 6This is a schematic diagram of temperature prediction results for the period from October 21 to November 19, 2016, in an embodiment of this application; wherein, (a) is a schematic diagram of temperature prediction results at a depth of 50 mm during the period from October 21 to November 19, 2016, (b) is a schematic diagram of temperature prediction results at a depth of 100 mm during the period from October 21 to November 19, 2016, (c) is a schematic diagram of temperature prediction results at a depth of 180 mm during the period from October 21 to November 19, 2016, (d) is a schematic diagram of temperature prediction results at a depth of 215 mm during the period from October 21 to November 19, 2016, and (e) is a schematic diagram of temperature prediction results at a depth of 260 mm during the period from October 21 to November 19, 2016. Figure 7 This is a schematic diagram of temperature prediction results for the period from January 21 to February 19, 2017, in an embodiment of this application; wherein, (a) is a schematic diagram of temperature prediction results at a depth of 50 mm during the period from January 21 to February 19, 2017, (b) is a schematic diagram of temperature prediction results at a depth of 100 mm during the period from January 21 to February 19, 2017, (c) is a schematic diagram of temperature prediction results at a depth of 180 mm during the period from January 21 to February 19, 2017, (d) is a schematic diagram of temperature prediction results at a depth of 215 mm during the period from January 21 to February 19, 2017, and (e) is a schematic diagram of temperature prediction results at a depth of 260 mm during the period from January 21 to February 19, 2017. Figure 8 This is a schematic diagram of temperature prediction results for the period from April 21 to May 19, 2017, in an embodiment of this application; wherein, (a) is a schematic diagram of temperature prediction results at a depth of 50 mm during the period from April 21 to May 19, 2017, (b) is a schematic diagram of temperature prediction results at a depth of 100 mm during the period from April 21 to May 19, 2017, (c) is a schematic diagram of temperature prediction results at a depth of 180 mm during the period from April 21 to May 19, 2017, (d) is a schematic diagram of temperature prediction results at a depth of 215 mm during the period from April 21 to May 19, 2017, and (e) is a schematic diagram of temperature prediction results at a depth of 260 mm during the period from April 21 to May 19, 2017. Figure 9 The above are comparison diagrams of the predicted and actual results of temperature-induced deformation in the embodiments of this application; wherein, (a) is a comparison diagram of temperature-induced deformation when the temperature gradient reaches 90℃ / m under extreme weather conditions, and (b) is a comparison diagram of temperature-induced deformation when the temperature gradient is 67.6℃ / m under non-extreme weather conditions (August 13, 2016). Figure 10The following diagrams illustrate the error distribution between predicted and actual results in the embodiments of this application: (a) is a diagram showing the error distribution between predicted and actual results from July 21 to August 19, 2016; (b) is a diagram showing the error distribution between predicted and actual results from October 21 to November 19, 2016; (c) is a diagram showing the error distribution between predicted and actual results from January 21 to February 19, 2017; and (d) is a diagram showing the error distribution between predicted and actual results from April 21 to May 19, 2017. Figure 11 The following are correlation diagrams between predicted and actual results in the embodiments of this application: (a) is a correlation diagram between predicted and actual results from July 21 to August 19, 2016; (b) is a correlation diagram between predicted and actual results from October 21 to November 19, 2016; (c) is a correlation diagram between predicted and actual results from January 21 to February 19, 2017; and (d) is a correlation diagram between predicted and actual results from April 21 to May 19, 2017. Figure 12 This is a comparison diagram of the original track irregularity and the track irregularity spectrum after superimposed temperature-induced deformation in the embodiments of this application; Figure 13 This is a comparison chart of the predicted orbital irregularity spectrum and the actual orbital irregularity spectrum in the embodiments of this application. Detailed Implementation

[0019] The following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0020] Unless otherwise defined, the technical or scientific terms used in this application shall have the ordinary meaning as understood by a person of ordinary skill in the art to which this application pertains.

[0021] The terms "comprising" or "including," as used in this application, mean that the element preceding the term encompasses the element listed after the term, and do not exclude the possibility of encompassing other elements as well. The terms "inner," "outer," "upper," and "lower," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application. When the absolute position of the described object changes, the relative positional relationship may also change accordingly. In this application, unless otherwise expressly specified and limited, the term "attached," etc., should be interpreted broadly. For example, it can refer to a fixed connection, a detachable connection, or an integral part; it can refer to a direct connection or an indirect connection through an intermediate medium; it can refer to the internal communication of two elements or the interaction relationship between two elements. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0022] Example 1: A physical-data hybrid method for predicting temperature-induced deformation and irregularities in ballastless track slabs, such as... Figure 2 As shown, it includes the following steps: S1. Establish a three-dimensional thermo-mechanical coupled finite element model of the ballastless track slab, perform sliding window processing on meteorological conditions and finite element multi-depth track slab temperature samples, and calculate the equivalent air temperature representing the meteorological conditions based on the heat exchange mechanism of the ballastless track and the environment. S1 specifically includes: S11. Measured meteorological elements such as solar radiation, atmospheric temperature, and wind speed are applied as time-varying boundary conditions to the surface of the track slab structure to establish a three-dimensional thermo-mechanical coupled finite element model of the ballastless track slab, such as... Figure 1 As shown, transient thermal analysis is carried out to obtain a multi-depth temperature field, and thermal expansion and warping deformation are driven by the vertical temperature gradient.

[0023] S12. Perform sliding window processing on the meteorological data of solar radiation, atmospheric temperature, and wind speed, dividing the data into datasets. The data sampling frequency is 30 minutes, and each sliding window dataset is 24 hours long, i.e., 48 data points. The prediction dataset and overlap length are 2 hours, i.e., 4 data points, and so on, rolling the prediction. Figure 3 As shown; S13. Calculate the average air temperature, convective heat transfer coefficient, and equivalent air temperature for each sliding window; The average temperature per sliding window is expressed as: ; in, The average atmospheric temperature of the sliding window is used for calculating the heat transfer coefficient; N represents the number of sampling points in the sliding window. This represents the measured temperature at time n; n represents time. The convective heat transfer coefficient is expressed as: ; Where v is the wind speed; The equivalent temperature is expressed as: ; in, The solar radiation absorption coefficient of the track slab surface. for Total heat flux density at any given time.

[0024] S2. Based on the least squares discrete Fourier series, harmonic coefficients are fitted to each sliding window data block, the amplitude and phase are extracted, and the amplitude attenuation coefficient and phase lag coefficient of the equivalent air temperature relative to the track slab temperature are calculated as physical prior information. S2 specifically includes: S21. Perform discrete Fourier series transformation on the equivalent air temperature and the finite element temperature of the track slab at different depths. For any scalar sequence, the K-order harmonic model is calculated using the following formula: ; Where t is time; T is the fundamental frequency period; and K is the harmonic fundamental number; The constant term represents the zero-frequency component; and These are the coefficients of the cosine term of the kth harmonic and the sine term of the kth harmonic, respectively; Let the harmonic coefficient vector be... ; S22, at discrete time Each basis function in The vector representation of the values ​​at each time step is: ; in Let be the harmonic coefficient vector at time ti; For y(t) and harmonic coefficients Construct a matrix, represented as: ; ; S23. The harmonic coefficients are estimated using the least squares method, expressed as follows: ; After obtaining the harmonic coefficients, the sequence values ​​at any time t are reconstructed, as follows: ; in, At discrete time The equivalent temperature, The constant term obtained from the fitting, To obtain the cosine coefficients of the k-th harmonic obtained by fitting, The coefficients of the sinusoidal term of the k-th harmonic obtained by fitting; S24. Perform K=2nd harmonic fitting on the data within each sliding window, and extract the amplitude and phase of the Kth harmonic component: Define the amplitude attenuation coefficient and the phase lag coefficient: ; in, Let be the equivalent air temperature amplitude of the k-th harmonic. The track slab temperature amplitude of the k-th harmonic. , The cosine and sine coefficients obtained from the temperature fitting of the track slab. The phase of the kth harmonic of the equivalent temperature. Let be the phase of the k-th harmonic of the track slab temperature. This is the amplitude attenuation coefficient. This is the phase lag coefficient; S25, such as Figure 4 The figure shows the spectrum of equivalent air temperature and temperature at different depths of the track slab in an embodiment of the present invention. The amplitude attenuation coefficients calculated at different depths over a whole time period using finite element simulation are fitted to obtain the physical prior information of the depth and amplitude attenuation law. Simultaneously, the amplitude attenuation coefficients of the observation data calculated from different blocks of data in the training set are averaged to obtain the amplitude attenuation coefficient of the observation data. The solar wave depth and amplitude attenuation coefficients under hybrid drive are calculated with a weight of 50% for both the physical prior information and the observation data. The half-sunwave coefficient is taken as 0.5 of the solar wave value, expressed as: Where, in the formula The amplitude attenuation coefficient of the observation data at depth z; M is the number of data blocks; For data block index, z is the depth; Let z be the amplitude attenuation coefficient of the observed data calculated at depth z for the b-th data block. This is the diurnal amplitude coefficient; D is the amplitude coefficient for the semi-diurnal wave; D and B are the exponential relationship coefficients between amplitude and depth fitted over the entire time period.

[0025] S3. Transfer the above-mentioned physical prior information to the actual structure prediction, extrapolate the equivalent temperature harmonic coefficient of the time period through the equivalent temperature harmonic coefficient of the historical time period, and backtrack the plate temperature harmonic coefficient through physical information. S3 specifically includes: Temperature frequency domain analysis shows that the predicted time period still conforms to the physical laws of diurnal and semi-diurnal waves. To meet the prediction accuracy requirements, the prediction time length usually cannot be too long. Therefore, the harmonic coefficient in the prediction stage is taken as K=1. The harmonic coefficients of the equivalent air temperature for the extrapolated time period are then calculated. And through depth transfer transformation, the plate temperature harmonic coefficients at different depths are obtained, expressed as: ; in, The plate temperature harmonic coefficient at depth z; The phase of the Kth harmonic of the equivalent temperature. The phase (lag phase) of the Kth harmonic at depth z. Calculate the harmonic coefficient vector at different depths Multiple depths together construct the total vector of physical information harmonic coefficients. Harmonic reconstruction is performed according to the following formula to obtain the temperature sequence based on physical information. The calculation formula is as follows: ; ; in, Let z be the harmonic coefficient vector at depth z. , , For the constant term, first-order cosine harmonic coefficient, and first-order sine harmonic coefficient of the discrete Fourier series; The obtained physical prior information is transferred to the actual track slab structure, and the temperature of the actual track slab structure is predicted using the measured meteorological conditions and the transferred physical prior information.

[0026] S4. The Ridge method is used to correct the linear residuals of the harmonic coefficients. S4 specifically includes: In the harmonic coefficient space, the Ridge linear model is used to correct the systematic deviation between physical information and actual measurements. The linear components that the physical model cannot explain are corrected, expressed as: ; ; in, The vector of ridge regression coefficients; The measured harmonic coefficient of the plate temperature; The harmonic coefficients are physical information. The corrected harmonic coefficients, Design matrix for ridge regression.

[0027] S5. Perform inverse Fourier transform on the predicted harmonic coefficients to the time-domain temperature sequence. Use the residuals predicted by each sliding window data block as the input of the LSTM neural network to correct the nonlinear residuals and obtain the final plate temperature prediction value. S5 specifically includes: The predicted harmonic coefficients are subjected to an inverse Fourier transform to a time-domain temperature sequence. The residuals predicted from each sliding window data point are used as input to the LSTM neural network to correct the nonlinear residuals, yielding the final plate temperature prediction. The temperature residuals are expressed as follows: ; in, This represents the residual between the measured temperature and the baseline temperature. This is the measured temperature; Baseline temperature; ; ; in, The final predicted temperature; The residuals predicted by LSTM; For historical window count; For the past The residual sequence of each prediction window.

[0028] like Figures 5-8 The diagram shows the temperature prediction results in an embodiment of this application. The four figures are comparative temperature prediction results for four months: July 21-August 19, 2016 (summer); October 21-November 19, 2016 (autumn); January 21-February 19, 2017 (winter); and April 21-May 19, 2017 (spring). One month from each season was selected as a typical prediction. As can be seen from the figures, the method of this application can fit the measured temperature change trend well in all four seasons, and the predicted values ​​match the actual values ​​well.

[0029] S6. Calculate the maximum gradient temperature based on the predicted plate temperature, construct the shape function of the measured data, and predict the temperature-induced deformation of the track slab. S6 specifically includes: S61. Based on the temperature data predicted in S5, calculate the vertical temperature gradient of the track slab, expressed as: ; in, Predicting temperature for shallow layers; For deep temperature prediction; This is the shallow depth; For deep depth; The predicted vertical temperature gradient; S62. Normalize the deformation data of the reference finite element and construct the shape function. , represented as: ; in, For reference, the vertical deformation value at time t along the plate width coordinate x is simulated. Vertical deformation value at the center point at time t. For coordinates along the width of the plate, The reference center point in the width direction of the plate is the coordinate of the plate width at the point where the upper arch deformation is the maximum. It is usually taken as the center point of the plate width. S63. The vertical deformation value calculated based on the predicted temperature is expressed as follows: ; in, Sensitivity is the ratio of the deformation at the reference center to the reference temperature gradient. This represents the predicted temperature gradient.

[0030] like Figures 9-11 The comparison between the predicted and actual results of temperature-induced deformation, the error between the predicted and actual results, and the correlation between the predicted and actual results are presented respectively. It can be seen that the temperature-induced deformation predicted by the method of this application is highly consistent with the actual deformation trend, the error distribution is concentrated, and the correlation coefficient is high.

[0031] S7. The temperature-induced deformation is converted into an additional track irregularity excitation and superimposed on the original track irregularity. An LSTM neural network is used to predict the track irregularity spectrum caused by temperature-induced deformation.

[0032] S7 specifically includes: The temperature-induced deformation value of the track slab under the daily maximum temperature gradient calculated in S6 is superimposed on the original track irregularity as an additional track irregularity, forming a sequence of track irregularities with temperature-induced additional excitation. The LSTM neural network is used again to predict the track irregularities caused by temperature-induced deformation, thereby realizing real-time early warning and assessment of temperature deformation and track irregularities of ballastless track.

[0033] like Figure 12 The figure shows a comparison of the original track irregularity spectrum and the track irregularity spectrum after superimposed temperature-induced deformation in an embodiment of this application. As can be seen from the figure, after the temperature-induced deformation is superimposed, the amplitude of the track irregularity spectrum increases significantly in the mid-to-long wavelength range, indicating that the temperature-induced deformation has a significant impact on the track geometry.

[0034] The LSTM neural network is used again to predict track irregularities caused by temperature-induced deformation, such as... Figure 13The figure shows a comparison between the predicted track irregularity spectrum and the actual track irregularity spectrum in an embodiment of this application. As can be seen from the figure, the track irregularity spectrum predicted by the method of this application matches the actual spectrum well, thereby achieving real-time early warning and assessment of temperature deformation and track irregularity in ballastless tracks.

[0035] Therefore, this application adopts the above-mentioned physical-data hybrid method for predicting temperature-induced deformation and irregularities of ballastless track slabs. Based on the hybrid driving of physical prior information and monitoring data, it uses a long short-term memory neural network to learn nonlinear residuals, so as to realize real-time and accurate prediction of meteorological conditions-temperature-induced deformation-track irregularity spectrum under small sample data. It is suitable for real-time evaluation of the service performance and traffic safety performance of ballastless track slabs under extreme weather conditions.

[0036] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and not to limit them. Although this application has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of this application, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of this application.

Claims

1. A physical-data hybrid method for predicting temperature-induced deformation and irregularities of ballastless track slabs, characterized in that, Includes the following steps: S1. Establish a three-dimensional thermo-mechanical coupled finite element model of the ballastless track slab, perform sliding window processing on meteorological conditions and finite element multi-depth track slab temperature samples, and calculate the equivalent air temperature representing the meteorological conditions based on the heat exchange mechanism of the ballastless track and the environment. S2. Based on the least squares method, discrete Fourier series fitting is performed on the finite element temperature and equivalent air temperature data of each sliding window to obtain the harmonic coefficients and extract the amplitude and phase. The amplitude attenuation coefficient and phase lag coefficient of the equivalent air temperature relative to the finite element track plate temperature are calculated as transferable physical prior information. S3. Transfer the above physical prior information to the actual structure prediction, extrapolate the equivalent temperature harmonic coefficient of the predicted time period by the equivalent temperature harmonic coefficient of the historical time period, and backtrack the actual structural plate temperature harmonic coefficient by the transferred physical prior information. S4. The Ridge method is used to correct the linear residuals of the harmonic coefficients. S5. Perform inverse Fourier transform on the predicted harmonic coefficients to the time-domain temperature sequence. Use the residual sequence predicted by each sliding window data as the input of the LSTM neural network to correct the nonlinear residuals and obtain the final plate temperature prediction value. S6. Calculate the maximum gradient temperature based on the predicted plate temperature, construct a normalized shape function for the reference simulation data, and predict the temperature-induced deformation of the track slab. S7. The temperature-induced deformation is converted into an additional track irregularity excitation and superimposed on the original track irregularity. An LSTM neural network is used to predict the track irregularity spectrum caused by temperature-induced deformation.

2. The method for predicting temperature-induced deformation and irregularities of ballastless track slabs using a physical-data hybrid approach as described in claim 1, characterized in that, S1 specifically includes: S11. Apply the measured meteorological elements of solar radiation, atmospheric temperature and wind speed as time-varying boundary conditions to the surface of the track slab structure, establish a three-dimensional thermo-mechanical coupled finite element model of the ballastless track slab, carry out transient thermal analysis, obtain multi-depth temperature fields, and drive thermal expansion and warping deformation by the vertical temperature gradient. S12. Perform sliding window processing on the meteorological conditions data of solar radiation, atmospheric temperature and wind speed, divide the dataset, the data sampling frequency is 30 minutes, the length of each sliding window dataset is 24 hours, that is, 48 ​​data points, the prediction dataset and the overlap length is 2 hours, that is, 4 data points, and so on for rolling prediction. S13. Calculate the average air temperature, convective heat transfer coefficient, and equivalent air temperature for each sliding window; The average temperature per sliding window is expressed as: ； in, The average atmospheric temperature of the sliding window is used for calculating the heat transfer coefficient; N represents the number of sampling points in the sliding window. This represents the measured temperature at time n; n represents time. The convective heat transfer coefficient is expressed as: ； Where v is the wind speed; The equivalent temperature is expressed as: ； in, The solar radiation absorption coefficient of the track slab surface. for Total heat flux density at time t, is the convective heat transfer coefficient.

3. The method for predicting temperature-induced deformation and irregularities of ballastless track slabs using a physical-data hybrid approach as described in claim 2, characterized in that... S2 specifically includes: S21. Perform discrete Fourier series transformation on the equivalent air temperature and the finite element temperature of the track slab at different depths. For any scalar sequence, the K-order harmonic model is calculated using the following formula: ； Where t is time; T is the fundamental frequency period; and K is the harmonic fundamental number; The constant term represents the zero-frequency component; and These are the coefficients of the cosine term of the kth harmonic and the sine term of the kth harmonic, respectively; Let the harmonic coefficient vector be... ; S22, at discrete time Each basis function in The vector representation of the values ​​at each time step is: ； For y(t) and harmonic coefficients Construct a matrix, represented as: ； ； S23. The harmonic coefficients are estimated using the least squares method, expressed as follows: ； After obtaining the harmonic coefficients, the sequence values ​​at any time t are reconstructed, as follows: ； in, At discrete time The equivalent temperature, The constant term obtained from the fitting, To obtain the cosine coefficients of the k-th harmonic obtained by fitting, The coefficients of the sinusoidal term of the k-th harmonic obtained by fitting; S24. Perform K=2nd harmonic fitting on the data within each sliding window, and extract the amplitude and phase of the Kth harmonic component: Define the amplitude attenuation coefficient and the phase lag coefficient: ； in, Let be the equivalent air temperature amplitude of the k-th harmonic. The track slab temperature amplitude of the k-th harmonic. , The cosine and sine coefficients obtained from the temperature fitting of the track slab. The phase of the kth harmonic of the equivalent temperature. Let be the phase of the k-th harmonic of the track slab temperature. This is the amplitude attenuation coefficient. This is the phase lag coefficient; S25. Fit the amplitude attenuation coefficients calculated at different depths over the entire time period using finite element simulation to obtain physical prior information about the relationship between depth and amplitude attenuation. Simultaneously, average the amplitude attenuation coefficients of the observation data calculated from different blocks of data in the training set to obtain the amplitude attenuation coefficients of the observation data. Calculate the solar wave depth and amplitude attenuation coefficients under hybrid drive with a weight of 50% for both physical prior information and observation data. The half-sunwave coefficient is taken as 0.5 of the solar wave value, expressed as: Where, in the formula The amplitude attenuation coefficient of the observation data at depth z; M is the number of data blocks; For data block index, z is the depth; Let z be the amplitude attenuation coefficient of the observed data calculated at depth z for the b-th data block. This is the diurnal amplitude coefficient; D is the amplitude coefficient for the semi-diurnal wave; D and B are the exponential relationship coefficients between amplitude and depth fitted over the entire time period.

4. The method for predicting temperature-induced deformation and irregularities of ballastless track slabs using a physical-data hybrid approach as described in claim 3, characterized in that... S3 specifically includes: In the prediction phase, the harmonic coefficient is set to K=1. The harmonic coefficient of the equivalent temperature over the extrapolated time period is calculated. And through depth transfer transformation, the plate temperature harmonic coefficients at different depths are obtained, expressed as: ； in, The plate temperature harmonic coefficient at depth z; The phase of the Kth harmonic of the equivalent temperature. Let z be the phase of the Kth harmonic at depth z; Calculate the harmonic coefficient vector at different depths Multiple depths together construct the total vector of physical information harmonic coefficients. Harmonic reconstruction is performed according to the following formula to obtain the temperature sequence based on physical information. The calculation formula is as follows: ； ； in, Let z be the harmonic coefficient vector at depth z. , , For the constant term, first-order cosine harmonic coefficient, and first-order sine harmonic coefficient of the discrete Fourier series; The obtained physical prior information is transferred to the actual track slab structure, and the temperature of the actual track slab structure is predicted using the measured meteorological conditions and the transferred physical prior information.

5. The method for predicting temperature-induced deformation and irregularities of ballastless track slabs using a physical-data hybrid approach as described in claim 4, characterized in that... S4 specifically includes: In the harmonic coefficient space, the Ridge linear model is used to correct the systematic deviation between physical information and actual measurements. The linear components that the physical model cannot explain are corrected, expressed as: ； ； in, The vector of ridge regression coefficients; The measured harmonic coefficient of the plate temperature; The harmonic coefficients are physical information. The corrected harmonic coefficients, Design matrix for ridge regression.

6. The method for predicting temperature-induced deformation and irregularities of ballastless track slabs using a physical-data hybrid approach as described in claim 2, characterized in that, S5 specifically includes: The predicted harmonic coefficients are subjected to an inverse Fourier transform to a time-domain temperature sequence. The residuals predicted from each sliding window data point are used as input to the LSTM neural network to correct the nonlinear residuals, yielding the final plate temperature prediction. The temperature residuals are expressed as follows: ； in, This represents the residual between the measured temperature and the baseline temperature. This is the measured temperature; Baseline temperature; ； ； in, The final predicted temperature; The residuals predicted by LSTM; For historical window count; For the past The residual sequence of each prediction window.

7. The method for predicting temperature-induced deformation and irregularities of ballastless track slabs using a physical-data hybrid approach as described in claim 6, characterized in that... S6 specifically includes: S61. Based on the temperature data predicted in S5, calculate the vertical temperature gradient of the track slab, expressed as: ； in, Predicting temperature for shallow layers; For deep temperature prediction; This is the shallow depth; For deep depth; The predicted vertical temperature gradient; S62. Normalize the reference finite element deformation data and construct shape functions. , represented as: ； ； in, For reference, the vertical deformation value at time t along the plate width coordinate x is simulated. Let be the vertical deformation value at the center point at time t. For coordinates along the width of the plate, The reference center point in the width direction of the plate is the coordinate of the plate width at the point where the upper arch deformation is the maximum. It is usually taken as the center point of the plate width. S63. The vertical deformation value calculated based on the predicted temperature is expressed as follows: ； in, Sensitivity is the ratio of the deformation at the reference center to the reference temperature gradient. This represents the predicted temperature gradient.

8. The method for predicting temperature-induced deformation and irregularities of ballastless track slabs using a physical-data hybrid approach as described in claim 7, characterized in that... S7 specifically includes: The temperature-induced deformation value of the track slab under the daily maximum temperature gradient calculated in S6 is superimposed on the original track irregularity as an additional track irregularity, forming a sequence of track irregularities with temperature-induced additional excitation. The LSTM neural network is used again to predict the track irregularities caused by temperature-induced deformation, thereby realizing real-time early warning and assessment of temperature deformation and track irregularities of ballastless track.

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