Method for extracting temperature-sensitive components of track vertical deviation of long-span bridge in multi-dimensional space

Abstract

The present application relates to a long-span bridge track vertical deviation temperature-sensitive component extraction method in multi-dimensional space, comprising: integrating the long-span bridge track vertical deviation three-dimensional historical data with additional environmental temperature labels; using empirical wavelet transform to construct a four-dimensional data set containing temperature labels and wavelength labels; after resampling in the mileage dimension, projecting the data to the amplitude-wavelength space, drawing the accumulated amplitude growth curve, identifying the amplitude-wavelength curve type and determining the boundary wavelength of the bridge deformation and track irregularity; then projecting the data to the amplitude-temperature space to identify the amplitude curve and temperature sensitivity; combining the boundary wavelength and temperature sensitivity to extract the temperature-sensitive component of the track irregularity and the construction deviation component in the actual bridge deformation. The method of the present application can realize the synchronous identification and extraction of the temperature-sensitive component in the track vertical deviation and the bridge construction deviation component, and provide quantitative basis for the accurate maintenance and repair of long-span railway bridges.

Description

Technical Field

[0001] This invention relates to the field of track data processing technology, specifically to a method for extracting temperature-sensitive components of vertical deviation in long-span bridge tracks in multidimensional space. Background Technology

[0002] Long-span high-speed railway bridges, due to their complex structural systems and continuous exposure to the natural environment during long-term operation, are susceptible to the combined effects of multiple factors such as temperature changes, wind loads, and pier settlement. This results in significant and periodic bridge deformation, which in turn leads to the deterioration of the track geometry. Taking a kilometer-class suspension bridge as an example, the annual variation in its mid-span elevation can exceed 1000 mm, far exceeding the adjustment capacity of the track structure itself. Currently, it is generally believed in the industry that the dominant wavelength of the vertical deviation of the track caused by bridge deformation is basically consistent with the main span of the bridge, and when this wavelength is much larger than the wavelength sensitive to train operation, its impact on the comfort and safety of high-speed train operation is limited. Therefore, accurately separating the temperature-sensitive long-wave deformation component of the track vertical deviation is a critical issue that urgently needs to be addressed in order to scientifically formulate maintenance strategies for long-span bridge lines.

[0003] Currently, the time-frequency decomposition and analysis methods for track irregularities in long-span bridges still rely primarily on signal decomposition techniques. However, existing technologies have significant limitations: on the one hand, decomposition methods based on basis functions, such as short-time Fourier transform, are constrained by the fixed characteristics of these basis functions and cannot meet the requirements for high-precision analysis. On the other hand, data-driven decomposition methods, such as empirical mode decomposition and variational mode decomposition, cannot guarantee the consistency of the number and frequency homogeneity of track irregularity decomposition modes under different temperature conditions. These shortcomings make it difficult for existing technologies to accurately characterize the time-frequency distribution features of track irregularities, especially to achieve a fine-grained "mile-by-mile-by-wavelength" characterization of the temperature sensitivity of long-wavelength irregularities, thus hindering the precise formulation of track maintenance strategies. Summary of the Invention

[0004] This invention addresses the problems of insufficient accuracy, inconsistent modes, and difficulty in accurately characterizing the temperature sensitivity of track irregularities in existing methods. It provides a multi-dimensional spatial method for extracting temperature-sensitive components of vertical deviations in long-span bridge tracks, achieving separation of bridge deformation and track irregularities and identification of temperature-sensitive components, thus significantly improving the accuracy of maintenance strategies.

[0005] A method for extracting temperature-sensitive components of vertical deviation of track in a long-span bridge in multidimensional space, the method comprising the following steps:

[0006] S1. Three-dimensional historical detection data of static track vertical deviation of long-span bridges with added ambient temperature labels;

[0007] S2. Perform empirical wavelet transform processing on the three-dimensional historical detection data with different cutoff wavelengths to construct a four-dimensional dataset of MRA components with additional temperature and wavelength labels.

[0008] S3. Resample the four-dimensional dataset in the mileage dimension to obtain the resampled dataset;

[0009] S4. Project the resampled dataset onto the amplitude-wavelength two-dimensional space, continuously add the corresponding wavelength MRA component as the wavelength increases, plot the cumulative amplitude growth curve with wavelength, and determine the corresponding amplitude-wavelength curve type in the mileage dimension and wavelength dimension respectively to obtain the amplitude-wavelength curve type determination result.

[0010] S5. Based on the discrimination result of the amplitude-wavelength curve type, piecewise fitting is used to obtain the boundary wavelength between bridge deformation and track irregularity.

[0011] S6. Project the resampled dataset onto the amplitude-temperature two-dimensional space, and determine the corresponding amplitude curve and temperature sensitivity in the mileage dimension and wavelength dimension, respectively, to obtain the determination results of amplitude curve and temperature sensitivity;

[0012] S7. Based on the discrimination results of the boundary wavelength and temperature sensitivity, extract the temperature-sensitive components in the actual track irregularities and the construction deviation components in the actual bridge deformation.

[0013] Furthermore, the three-dimensional historical detection data mentioned in step S1 is the amplitude-mileage curve data obtained by subtracting the original design rail surface elevation from the absolute rail surface elevation obtained by the measuring trolley; the ambient temperature label is obtained through an ambient temperature sensor.

[0014] Furthermore, S2 specifically includes:

[0015] S21. Perform a Fourier transform on the three-dimensional historical detection data to obtain the spatial frequency range [0, fs / 2] of the single-sided spectrum containing actual physical information, where fs is the sampling frequency;

[0016] S22. Divide the spatial frequency range into multiple consecutive small intervals, starting from the initial wavelength and ending at the upper limit wavelength, with each interval being 1m. With wavelength The conversion relationship is ,according to【 , , Set boundary points in sequence ,in The starting wavelength;

[0017] S23. Convert the spatial frequency boundary to a normalized frequency boundary. The conversion formula is as follows:

[0018]

[0019] In the formula, The boundary point of the normalized frequency; fs is the sampling frequency;

[0020] S24. The three-dimensional historical detection data is sequentially input into the Empirical Wavelet Transform (EWT) algorithm, combined with the normalized frequency boundary sequence. Construct detail coefficients and scaling coefficients for any given period of data; perform convolution operations between detail coefficients and wavelet functions, and between scaling coefficients and scaling functions to obtain multiple MRA component amplitude-mileage curves corresponding to the center wavelength labels, and combine them with temperature labels to form a four-dimensional dataset.

[0021] Furthermore, the resampling in step S3 specifically includes:

[0022] The mileage dimension is divided into segments at 10m intervals. Within each segment, the data point with the largest absolute amplitude value is selected for sampling. The original value of the data point with the largest absolute amplitude value is used as the representative amplitude value of the corresponding segment, and the midpoint mileage of each segment is used as the representative mileage of the corresponding segment.

[0023] Furthermore, the amplitude-wavelength curve types mentioned in step S4 are classified into reverse bending type, transition type and upward arch type according to the variation law.

[0024] Furthermore, the variation law of the inverted amplitude-wavelength curve is as follows: as the wavelength increases, the amplitude remains basically unchanged at first, and after reaching the abrupt wavelength, the amplitude begins to rapidly increase negatively;

[0025] The transitional amplitude-wavelength curve follows this pattern: as the wavelength increases, the amplitude remains essentially constant at first, followed by a wavelength with a sudden slope change and an extreme wavelength.

[0026] The variation pattern of the upward-arched amplitude-wavelength curve is as follows: as the wavelength increases, the amplitude initially remains basically constant. After reaching the wavelength where the slope abruptly changes, the amplitude begins to increase rapidly.

[0027] Furthermore, the piecewise fitting described in step S5 specifically includes:

[0028] The Levenberg-Marquardt algorithm is used to solve for the piecewise points, where:

[0029] The slope abrupt change point is solved by straight-line fitting of the inverted amplitude-wavelength curve.

[0030] The transitional amplitude-wavelength curve is solved by using a straight-line-curve-curve fitting method to find the slope abrupt change points and extreme points.

[0031] The slope abrupt change point is solved by straight-line fitting of the upward-arched amplitude-wavelength curve.

[0032] Furthermore, the piecewise function formula for the line-line fitting is:

[0033]

[0034] In the formula, ~ These are the fitting coefficients; , These are the filter wavelength and the corresponding filter amplitude, respectively. This represents the point of abrupt slope change corresponding to a line-to-line fit.

[0035] The piecewise function formula for the line-curve-curve fitting is:

[0036]

[0037] In the formula, ~ These are the fitting coefficients; , These are the filter wavelength and the corresponding filter amplitude, respectively. , These represent the wavelengths corresponding to the slope abrupt change points and extreme points of the straight-curve-curve fitting, respectively.

[0038] Furthermore, S6 specifically includes:

[0039] The resampled dataset is projected into an amplitude-temperature two-dimensional space to form amplitude-temperature curves corresponding to different mileage and wavelength labels. The Pearson correlation coefficient and significance coefficient between amplitude and temperature in the amplitude-temperature curve are calculated, and the discrimination value of the significance coefficient is 0.05.

[0040] Furthermore, S7 specifically includes:

[0041] S71. Based on the boundary wavelength, data with wavelength labels smaller than the boundary wavelength are classified as actual track irregularities, and data with wavelength labels larger than the boundary wavelength are classified as actual bridge deformations.

[0042] S72. Based on the significance coefficient, determine the wavelength and mileage information of the temperature-sensitive component in the actual track irregularity and the construction deviation component in the actual bridge deformation. The component with a significance coefficient less than 0.05 is determined to be a temperature-sensitive component, and the component with a significance coefficient greater than 0.05 is determined to be a construction deviation component of the bridge deformation.

[0043] S73. Reconstruct the construction deviation components using the following formula:

[0044]

[0045] In the formula, The center mileage is The construction deviation amplitude within a 10m interval; n is the corresponding temperature label; K is the total number of wavelength labels for insensitive components within the interval; Wavelength labeling for insensitive components; MRA for multi-resolution analysis; For the central mileage is Within a 10m interval, the corresponding characteristic wavelength is The k One MRA component;

[0046] By splicing together the construction deviation amplitudes corresponding to each interval, the linear shape of the construction deviation across the entire bridge at any temperature can be obtained. .

[0047] The technical solution of this invention can achieve the following beneficial effects:

[0048] (1) An adaptive signal processing algorithm is introduced to achieve efficient and refined spectral decomposition driven by data. By adopting the empirical wavelet transform (EWT) method and constructing an adaptive spectral segmentation scheme with a fixed wavelength interval, a four-dimensional dataset of multi-resolution analysis (MRA) components containing temperature and wavelength labels is generated in one go. Compared with the traditional fixed filter bank method, this scheme avoids multiple filtering calculations, significantly improves computational efficiency, and can more accurately match the actual spectral characteristics of track geometry irregularities, providing a higher quality data foundation for subsequent component identification;

[0049] (2) Accurately identify the boundary characteristics between bridge deformation and track irregularities. By analyzing the cumulative amplitude growth curve with wavelength and the classification of amplitude-wavelength curve types, a targeted piecewise fitting algorithm is used to solve the boundary wavelength, realizing the quantitative separation of bridge deformation and track irregularities, and solving the technical problem that traditional methods cannot clearly define the boundary between the two;

[0050] (3) Precisely locate temperature-sensitive components and analyze construction deviations. By projecting the dataset onto the amplitude-temperature two-dimensional space for correlation analysis, it is possible not only to locate the temperature-sensitive wavelengths and mileage ranges in track irregularities, but also to separate temperature-insensitive construction deviation components from bridge deformation. This achieves simultaneous and refined identification and extraction of temperature-sensitive sources of track irregularities and inherent construction deviations of bridges;

[0051] (4) The method is universal and easy to operate, and has practical application value. This invention does not rely on the specific structural parameters of the bridge. It can complete the analysis only through detection data and algorithms, and is highly operable. Its analysis results can directly provide a quantitative basis for the formulation of maintenance and repair strategies for long-span railway bridges, effectively avoid track geometry deterioration caused by blind adjustments, and improve maintenance efficiency and accuracy. Attached Figure Description

[0052] Figure 1 This is a flowchart of a method for extracting temperature-sensitive components of vertical deviation of track in a long-span bridge in multidimensional space, provided by the present invention.

[0053] Figure 2 This is a diagram showing the multi-stage static track vertical deviation detection results of a large-span high-speed railway bridge obtained by a measuring trolley in an embodiment of the present invention;

[0054] Figure 3 This is a schematic diagram of the spectrum cutting scheme in an embodiment of the present invention;

[0055] Figure 4 This is a four-dimensional dataset of MRA components with added temperature and wavelength labels in an embodiment of the present invention;

[0056] Figure 5 This is a diagram showing the calculated boundary wavelength between bridge deformation and track irregularities in an embodiment of the present invention.

[0057] Figure 6 This is a heatmap showing the significant coefficients of the correlation between the vertical deviation of the static track and temperature in an embodiment of the present invention.

[0058] Figure 7 This refers to the construction deviation line shape in the embodiments of the present invention. Detailed Implementation

[0059] The technical solutions of the embodiments of the present invention will now be described in detail and completely with reference to the accompanying drawings. It should be noted that the described embodiments are merely some examples of the present invention and do not represent all possible implementations of the present invention. Any other implementations obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0060] Example 1

[0061] Figure 1 The flowchart illustrates a method for extracting temperature-sensitive components of vertical deviation in the track of a long-span bridge in multidimensional space, as provided by this invention.

[0062] The method flow steps of the embodiments in this specification are as follows:

[0063] S1. Three-dimensional historical detection data of static track vertical deviation of long-span bridges with added ambient temperature labels;

[0064] S2. Perform empirical wavelet transform processing on the three-dimensional historical detection data with different cutoff wavelengths to construct a four-dimensional dataset of MRA components with additional temperature and wavelength labels.

[0065] S3. Resample the four-dimensional dataset in the mileage dimension to obtain the resampled dataset;

[0066] S4. Project the resampled dataset onto the amplitude-wavelength two-dimensional space, continuously add the corresponding wavelength MRA component as the wavelength increases, plot the cumulative amplitude growth curve with wavelength, and determine the corresponding amplitude-wavelength curve type in the mileage dimension and wavelength dimension respectively to obtain the amplitude-wavelength curve type determination result.

[0067] S5. Based on the discrimination result of the amplitude-wavelength curve type, piecewise fitting is used to obtain the boundary wavelength between bridge deformation and track irregularity.

[0068] S6. Project the resampled dataset onto the amplitude-temperature two-dimensional space, and determine the corresponding amplitude curve and temperature sensitivity in the mileage dimension and wavelength dimension, respectively, to obtain the determination results of amplitude curve and temperature sensitivity;

[0069] S7. Based on the discrimination results of the boundary wavelength and temperature sensitivity, extract the temperature-sensitive components in the actual track irregularities and the construction deviation components in the actual bridge deformation.

[0070] Specifically, let's take the measured static track vertical deviation of a long-span high-speed railway bridge as an example.

[0071] Step S1 specifically includes:

[0072] Historical static monitoring data of track vertical deviation collected by the measuring trolley, along with the corresponding temperatures synchronously measured by the temperature sensors, are extracted to form three-dimensional historical detection data of static track vertical deviation with temperature labels, such as... Figure 2 As shown.

[0073] in, Figure 2 The horizontal axis represents the measured mileage, with a sampling interval of 1m; the vertical axis represents the static track vertical deviation at different temperatures at each mileage of the bridge. Within the ambient temperature range of 0.2~31.5℃, the amplitude of track unevenness caused by bridge deformation exceeds 1000mm, a value far exceeding the adjustment capacity of the existing track structure.

[0074] Step S2 specifically includes:

[0075] S21. Perform a Fourier transform on the three-dimensional historical detection data to obtain the spatial frequency range [0, fs / 2] of the single-sided spectrum containing actual physical information, where fs is the sampling frequency.

[0076] S22. Divide the spatial frequency range into multiple consecutive small intervals, starting from the initial wavelength and ending at the upper limit wavelength, with each interval being 1m. With wavelength The conversion relationship is ,according to【 , , Set boundary points in sequence ,in The starting wavelength is shown in the diagram below. A schematic of the refined spectrum cutting scheme is also shown. Figure 3 As shown.

[0077] S23. Convert the spatial frequency boundary obtained above into a normalized frequency boundary. The conversion formula is as follows:

[0078]

[0079] In the formula, is the boundary point of the normalized frequency; fs is the sampling frequency.

[0080] S24. Input the three-dimensional historical detection data into the EWT algorithm sequentially, and combine it with the normalized frequency boundary sequence constructed above. It can adaptively construct detail coefficients and scaling coefficients corresponding to any period of data. By convolving the detail coefficients with the wavelet function, scaling coefficients, and scaling function, multiple MRA component amplitude-otter curves corresponding to the center wavelength label can be obtained. Combining these with temperature labels forms a four-dimensional dataset. A schematic diagram of the resulting four-dimensional dataset structure including temperature and wavelength labels is shown below. Figure 4 As shown.

[0081] Step S3 specifically includes:

[0082] All amplitude-wavelength curves are divided into several segments at 10m intervals along the mileage dimension. Within each segment, the data point with the largest absolute amplitude value is selected for resampling. The original amplitude of this data point is used as the representative amplitude value of the segment, and the mileage of the midpoint of the segment is used as the representative mileage of the segment.

[0083] Step S4 specifically includes:

[0084] For each data point in the resampled dataset with a specific mileage and temperature label, the MRA component amplitudes of the corresponding wavelengths are accumulated sequentially in ascending order of wavelength, and a growth curve of the accumulated amplitude as the wavelength increases is plotted.

[0085] Based on the changing patterns of the accumulated amplitude-wavelength growth curves, the amplitude-wavelength curve types with different mileage and temperature labels are classified.

[0086] Amplitude-wavelength curves are classified into three types based on their variation patterns: inverted curve, transition curve, and upward arch curve.

[0087] The variation law of the inverted amplitude-wavelength curve is as follows: as the wavelength increases, the amplitude remains basically unchanged at first, and after reaching the abrupt wavelength, the amplitude begins to rapidly increase negatively;

[0088] The transitional amplitude-wavelength curve follows this pattern: as the wavelength increases, the amplitude remains essentially constant at first, followed by a wavelength with a sudden slope change and an extreme wavelength.

[0089] The variation pattern of the upward-arched amplitude-wavelength curve is as follows: as the wavelength increases, the amplitude initially remains basically constant. After reaching the wavelength where the slope abruptly changes, the amplitude begins to increase rapidly.

[0090] Step S5 specifically includes:

[0091] Based on the amplitude-wavelength curve type classification results, corresponding piecewise functions are selected for different types of curves, and the Levenberg-Marquardt algorithm is used to fit the amplitude-wavelength curves piecewise, where:

[0092] The slope abrupt change point is solved by straight-line fitting of the inverted amplitude-wavelength curve.

[0093] The transitional amplitude-wavelength curve is solved by using a straight-line-curve-curve fitting method to find the slope abrupt change points and extreme points.

[0094] The slope abrupt change point is solved by straight-line fitting of the upward-arched amplitude-wavelength curve.

[0095] The piecewise function formula for line-to-line fitting is:

[0096]

[0097] In the formula, ~ These are the fitting coefficients; , These are the filter wavelength and the corresponding filter amplitude, respectively. This represents the point of abrupt slope change corresponding to a line-to-line fit.

[0098] The piecewise function formula for line-curve-curve fitting is:

[0099]

[0100] In the formula, ~ These are the fitting coefficients; , These are the filter wavelength and the corresponding filter amplitude, respectively. , These represent the wavelengths corresponding to the slope abrupt change points and extreme points of the straight-curve-curve fitting, respectively.

[0101] Examples of calculation results for the wavelengths corresponding to slope abrupt changes and extreme points for different mileage and temperature tags are shown below. Figure 4 As shown. From Figure 5 It can be observed that the distribution of the dividing wavelength between bridge deformation and track irregularities in the mileage domain is basically unaffected by temperature changes.

[0102] Step S6 specifically includes:

[0103] The resampled dataset is projected onto the amplitude-temperature space to form amplitude-temperature curves corresponding to different mileage and wavelength labels. The Pearson correlation coefficient and significance coefficient between amplitude and temperature in the amplitude-temperature curve are calculated. A significance coefficient of less than 0.05 is used as the discrimination index to determine whether the amplitude and temperature in the curve are significantly correlated.

[0104] The temperature-sensitive wavelengths of track irregularities at each mileage calculated using the above method are as follows: Figure 5 As shown. By Figure 5 It is evident that as the mileage approaches the midpoint, the temperature-sensitive wavelength gradually increases, reaching 140m at the midpoint. Combined with... Figure 4 As can be seen, the dividing wavelength is located in the dark blue region, which indicates that the wavelength component corresponding to bridge deformation is significantly sensitive to temperature changes.

[0105] Step S7 specifically includes:

[0106] S71. First, classify the actual track irregularities based on the boundary wavelengths obtained in step S5. Then, combine the significance coefficient distribution obtained in step S6 to determine the wavelength and mileage information of the temperature-sensitive components in the actual track irregularities and the construction deviation components in the actual bridge deformation.

[0107] Based on the defined wavelength, data with wavelength labels smaller than the defined wavelength are classified as actual track irregularities; data with wavelength labels larger than the defined wavelength are classified as actual bridge deformations.

[0108] S72. Based on the significance coefficient, determine the wavelength and mileage information of the temperature-sensitive component in the actual track irregularity and the construction deviation component in the actual bridge deformation. The component with a significance coefficient less than 0.05 is determined to be the temperature-sensitive component of the track irregularity, and the component with a significance coefficient greater than 0.05 is determined to be the construction deviation component of the bridge deformation.

[0109] S73. To obtain the construction deviation alignment across the entire bridge, the extracted construction deviation components are reconstructed. The reconstruction is performed on the four-dimensional dataset before resampling, according to the following formula:

[0110]

[0111] In the formula, The center mileage is The construction deviation amplitude within a 10m interval; n is the corresponding temperature label; K is the total number of wavelength labels for insensitive components within the interval; Wavelength labeling for insensitive components; MRA for multi-resolution analysis; For the central mileage is Within a 10m interval, the corresponding characteristic wavelength is The k MRA components.

[0112] By splicing together the construction deviation amplitudes corresponding to each interval, the construction deviation linearity across the entire bridge at any temperature can be obtained. .

[0113] Figure 6 The results show that the 50-80m band in actual track irregularities exhibits a discontinuous correlation with temperature in the mileage domain.

[0114] The construction deviation line shape extracted based on the above-mentioned boundary wavelength and significance coefficient discrimination results is as follows: Figure 7 As shown.

[0115] Based on the calculation results of the embodiments, the multi-dimensional spatial long-span bridge track vertical deviation temperature-sensitive component extraction method provided by the present invention can identify and finely characterize the temperature-sensitive components of bridge deformation and track irregularities in static track vertical deviation. This method can effectively distinguish between bridge deformation and actual track irregularities from static track vertical deviation, and accurately identify the temperature-sensitive wavelengths of track irregularities at different bridge mileages, as well as deviation components reflecting inherent construction quality. This provides support for the formulation of long-span railway bridge line adjustment schemes and effectively avoids track geometry deterioration caused by blind adjustments.

[0116] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on describing the differences from other embodiments. In particular, the method and system embodiments are basically similar to the method embodiments, so the descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0117] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0118] The above description is merely one or more embodiments of this specification and is not intended to limit this specification. Various modifications and variations can be made to the one or more embodiments of this specification by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of one or more embodiments of this specification should be included within the scope of the claims of this specification.

Claims

1. A method for extracting temperature-sensitive components of vertical deviation of track in a long-span bridge in multidimensional space, characterized in that, Includes the following steps: S1. Three-dimensional historical detection data of static track vertical deviation of long-span bridges with added ambient temperature labels; S2. Perform empirical wavelet transform processing on the three-dimensional historical detection data with different cutoff wavelengths to construct a four-dimensional dataset of MRA components with additional temperature and wavelength labels. S3. Resample the four-dimensional dataset in the mileage dimension to obtain the resampled dataset; S4. Project the resampled dataset onto the amplitude-wavelength two-dimensional space, continuously add the corresponding wavelength MRA component as the wavelength increases, plot the cumulative amplitude growth curve with wavelength, and determine the corresponding amplitude-wavelength curve type in the mileage dimension and wavelength dimension respectively to obtain the amplitude-wavelength curve type determination result. S5. Based on the discrimination result of the amplitude-wavelength curve type, piecewise fitting is used to obtain the boundary wavelength between bridge deformation and track irregularity. S6. Project the resampled dataset onto the amplitude-temperature two-dimensional space, and determine the corresponding amplitude curve and temperature sensitivity in the mileage dimension and wavelength dimension, respectively, to obtain the determination results of amplitude curve and temperature sensitivity; S7. Based on the discrimination results of the boundary wavelength and temperature sensitivity, extract the temperature-sensitive components in the actual track irregularities and the construction deviation components in the actual bridge deformation.

2. The method for extracting temperature-sensitive components of vertical deviation of track in a multi-dimensional long-span bridge according to claim 1, characterized in that, The three-dimensional historical detection data mentioned in step S1 is the amplitude-mileage curve data obtained by subtracting the original design rail surface elevation from the absolute rail surface elevation obtained by the measuring trolley; the ambient temperature label is obtained through an ambient temperature sensor.

3. The method for extracting temperature-sensitive components of vertical deviation of track in a multi-dimensional long-span bridge according to claim 1, characterized in that, S2 specifically includes: S21. Perform a Fourier transform on the three-dimensional historical detection data to obtain the spatial frequency range [0, fs / 2] of the single-sided spectrum containing actual physical information, where fs is the sampling frequency; S22. Divide the spatial frequency range into multiple consecutive small intervals, starting from the initial wavelength and ending at the upper limit wavelength, with each interval being 1m. With wavelength The conversion relationship is ,according to【 , , Set boundary points in the order of 】 ,in The starting wavelength; S23. Convert the spatial frequency boundary to a normalized frequency boundary. The conversion formula is as follows: In the formula, The boundary point of the normalized frequency; fs is the sampling frequency; S24. The three-dimensional historical detection data is sequentially input into the Empirical Wavelet Transform (EWT) algorithm, combined with the normalized frequency boundary sequence. Construct detail coefficients and scaling coefficients for any given period of data; perform convolution operations between detail coefficients and wavelet functions, and between scaling coefficients and scaling functions to obtain multiple MRA component amplitude-mileage curves corresponding to the center wavelength labels, and combine them with temperature labels to form a four-dimensional dataset.

4. The method for extracting temperature-sensitive components of vertical deviation of track in a multi-dimensional long-span bridge according to claim 1, characterized in that, The resampling in step S3 specifically includes: The mileage dimension is divided into segments at 10m intervals. Within each segment, the data point with the largest absolute amplitude value is selected for sampling. The original value of the data point with the largest absolute amplitude value is used as the representative amplitude value of the corresponding segment, and the midpoint mileage of each segment is used as the representative mileage of the corresponding segment.

5. The method for extracting temperature-sensitive components of vertical deviation of track in a multi-dimensional long-span bridge according to claim 1, characterized in that, The amplitude-wavelength curve types mentioned in step S4 are classified into inverted curve type, transition type and upward arch type according to the variation law.

6. The method for extracting temperature-sensitive components of vertical deviation of track in a multi-dimensional long-span bridge according to claim 5, characterized in that, The piecewise fitting in step S5 specifically includes: The Levenberg-Marquardt algorithm is used to solve for the piecewise points, where: The slope abrupt change point is solved by straight-line fitting of the inverted amplitude-wavelength curve. The transitional amplitude-wavelength curve is solved by using a straight-line-curve-curve fitting method to find the slope abrupt change points and extreme points. The slope abrupt change point is solved by straight-line fitting of the upward-arched amplitude-wavelength curve.

7. The method for extracting temperature-sensitive components of vertical deviation of track in a multi-dimensional long-span bridge according to claim 6, characterized in that, The piecewise function formula for the line-line fitting is: In the formula, ~ These are the fitting coefficients; , These are the filter wavelength and the corresponding filter amplitude, respectively. This represents the point of abrupt slope change corresponding to a line-to-line fit. The piecewise function formula for the line-curve-curve fitting is: In the formula, ~ These are the fitting coefficients; , These are the filter wavelength and the corresponding filter amplitude, respectively. , These represent the wavelengths corresponding to the slope abrupt change points and extreme points of the straight-curve-curve fitting, respectively.

8. The method for extracting temperature-sensitive components of vertical deviation of track in a multi-dimensional long-span bridge according to claim 1, characterized in that, S6 specifically includes: The resampled dataset is projected into an amplitude-temperature two-dimensional space to form amplitude-temperature curves corresponding to different mileage and wavelength labels. The Pearson correlation coefficient and significance coefficient between amplitude and temperature in the amplitude-temperature curve are calculated, and the discrimination value of the significance coefficient is 0.

05.

9. The method for extracting temperature-sensitive components of vertical deviation of track in a multi-dimensional long-span bridge according to claim 8, characterized in that, Specifically, S7 includes: S71. Based on the boundary wavelength, data with wavelength labels smaller than the boundary wavelength are classified as actual track irregularities, and data with wavelength labels larger than the boundary wavelength are classified as actual bridge deformations. S72. Based on the significance coefficient, determine the wavelength and mileage information of the temperature-sensitive component in the actual track irregularity and the construction deviation component in the actual bridge deformation. The component with a significance coefficient less than 0.05 is determined to be a temperature-sensitive component, and the component with a significance coefficient greater than 0.05 is determined to be a construction deviation component of the bridge deformation. S73. Reconstruct the construction deviation components using the following formula: In the formula, The center mileage is The construction deviation amplitude within a 10m interval; n is the corresponding temperature label; K is the total number of wavelength labels for insensitive components within the interval; Wavelength labeling for insensitive components; MRA for multi-resolution analysis; For the central mileage is Within a 10m interval, the corresponding characteristic wavelength is The k One MRA component; By splicing together the construction deviation amplitudes corresponding to each interval, the linear shape of the construction deviation across the entire bridge at any temperature can be obtained. .

Images