A DAS-based method and system for vibration propagation modeling and response prediction of underground structures

Abstract

This invention discloses a method and system for modeling and predicting vibration propagation in underground structures based on DAS (Digital Animation and Sensor) technology, relating to the fields of vibration environment monitoring for rail transit and safety in underground engineering. The method uses an optical cable in the surface soil as the first optical cable and an optical cable inside the tunnel as the second optical cable to form an upper and lower parallel three-dimensional observation system. The spatiotemporal strain records of the two optical cables are recorded synchronously using train passage as the excitation event. The first optical cable record is separated into an upward wave field and a downward wave field. The train-induced upward wave field is inversely extended to a reference surface above the tunnel to reconstruct a virtual downward observation record, which is then combined with the measured record of the second optical cable to construct a virtual downward observation system. Based on the records of this system, propagation parameters are inverted, a vibration propagation model is constructed, and the vibration response is predicted. This invention can obtain the observation constraints of the strata above the tunnel without the need for underground equipment, solving the problems of difficulty in joint modeling and quantitative analysis of propagation laws in parallel DAS observations.

Description

Technical Field

[0001] This application relates to the fields of vibration environment monitoring for rail transit and safety technology for underground engineering, and in particular to a method and system for vibration propagation modeling and response prediction of underground structures based on DAS. Background Technology

[0002] Intercity railways and urban rail transit lines traverse densely built-up areas. Vibrations induced by train operation propagate through tunnel structures and strata to the surface and buildings along the line, impacting residents' quality of life and building safety. Accurately understanding the propagation patterns of vibration within the tunnel structure-strata-surface system, and predicting environmental and structural vibration responses under different operating conditions, is fundamental to vibration reduction and isolation design, effectiveness evaluation of vibration reduction measures, and environmental vibration management. Existing research on subway vibration propagation patterns mainly relies on short-term paired tests at local sections: a small number of point sensors are deployed inside the tunnel and on the surface to simultaneously record vibration signals from several train passes, thereby estimating vibration level differences and transmission characteristics. Such tests involve sparse monitoring points, reflecting only the state of individual sections, and are insufficient to form a systematic understanding of propagation patterns covering different geological conditions, tunnel depths, and operating conditions across the entire line.

[0003] Distributed optical fiber acoustic sensing (DAS) technology uses ordinary communication optical fibers as the sensing and transmission medium, enabling continuous vibration monitoring over distances of tens of kilometers with meter-level spatial resolution. In principle, by utilizing sensing optical cables laid in the shallow subsurface and existing communication optical cables within the tunnel, a parallel three-dimensional observation system can be constructed, using operating trains as repetitive excitation sources to simultaneously obtain paired continuous observations near the vibration source and near the surface. However, these two optical cables are located at the starting point (tunnel) and ending point (surface) of the vibration propagation path, respectively. There are no observation points within the strata above the tunnel through which the vibration actually propagates. The lack of intermediate observation constraints between the two sets of records necessitates a point-based testing approach to statistically analyze the vibration magnitude difference between the surface and the tunnel. It is impossible to integrate the upper and lower sets of observations into a single quantitative framework for joint modeling and analysis of the propagation process within the tunnel structure-strata-surface system. To obtain observation constraints in the strata above the tunnel, current methods rely on drilling and deploying sensors in wells, which is costly, has limited locations, and is difficult to implement in built-up areas, making it unsuitable for continuous DAS observations across the entire line.

[0004] Wavefield separation and wave equation base-plane extension techniques in seismic exploration can transfer records from one observation plane to a base plane at another depth, but their application relies on the ability to distinguish the vertical propagation direction of the wavefield. For DAS optical cables laid horizontally in shallow subsurface layers, the sign of the apparent velocity along the cable only indicates the direction of wave propagation along the line, and cannot directly distinguish between upward waves propagating from the tunnel and downward waves propagating after reflection from the free surface. Furthermore, there is a lack of independent observations that can be used to verify the extension results. Therefore, the above techniques have not yet been combined with parallel DAS observations above and below to reconstruct observation records in strata above tunnels.

[0005] In summary, existing technologies suffer from the technical problem of lacking observational constraints on the strata above the tunnel and the difficulty in jointly modeling parallel DAS observations from above and below, which makes it difficult to quantitatively analyze the propagation law of vibration from the tunnel structure through the strata to the surface. Summary of the Invention

[0006] This invention provides a method and system for modeling and predicting the vibration propagation of underground structures based on DAS. It constructs a parallel DAS three-dimensional observation system using surface optical cables and tunnel optical cables. The train-induced upward wave field separated from the surface optical cable record is retrogradely extended to a reference surface above the tunnel to reconstruct a virtual downward observation record. This record is then combined with the measured record from the tunnel optical cable to construct a virtual downward observation system. This allows for the acquisition of observational constraints on the strata above the tunnel without adding any underground drilling or equipment. By incorporating the two sets of observations into the same quantitative framework for joint modeling, the invention solves the technical problem in existing technologies where the lack of observational constraints on the strata above the tunnel and the difficulty in jointly modeling parallel DAS observations make it difficult to quantitatively analyze the propagation law of vibration from the tunnel structure through the strata to the surface.

[0007] In a first aspect, embodiments of the present invention provide a method for modeling and predicting the vibration propagation of underground structures based on DAS, comprising: using an optical cable laid in the surface soil as a first optical cable and an optical cable laid in a tunnel as a second optical cable, the two optical cables are arranged in parallel vertically along the longitudinal direction of the line; using a distributed optical fiber acoustic wave sensing demodulation device to demodulate the two optical cables synchronously, and synchronizing the time of the detector points of the two optical cables and making them correspond to the line mileage; using the passing of a train as an excitation event, synchronously recording the spatiotemporal strain records of the two optical cables; and separating the spatiotemporal strain record of the first optical cable into an upward wave. The train-induced upgoing wave field is obtained by combining the downgoing wave field with the upgoing wave field. The train-induced upgoing wave field is then extended in the opposite direction of propagation to a set reference plane above the tunnel. The virtual downgoing observation record at the set reference plane is reconstructed, and the virtual downgoing observation record is combined with the measured record of the second optical cable to construct a virtual downgoing observation system covering the strata above the tunnel. Based on the records of the virtual downgoing observation system, the propagation parameters characterizing the variation of vibration with propagation distance and frequency are inverted to construct a vibration propagation model. Based on the vibration propagation model, the vibration response under the set operating conditions is predicted.

[0008] As described above, this embodiment of the invention uses optical cables in the surface soil and optical cables inside the tunnel to form a parallel DAS three-dimensional observation system, achieving continuous paired observation across the entire line. This overcomes the limitations of existing point-based testing and monitoring systems, which have sparse locations and can only reflect the state of individual sections. Addressing the obstacle that the apparent velocity sign along the horizontally laid surface optical cable cannot distinguish between uplink and downlink waves, the first optical cable record is first separated into uplink and downlink wave fields. Then, the train-induced uplink wave field is extended in the opposite direction of propagation to a reference surface above the tunnel to reconstruct a virtual downlink observation record. The measured record of the second optical cable inside the tunnel is used as an independent observation. By combining the two observation systems, a virtual downlink observation system covering the strata above the tunnel was constructed. This allowed for dense virtual observation constraints of the strata above the tunnel without adding any downhole drilling or equipment, realizing the observation reconstruction of "downlink inversion from above the tunnel". This enabled the upper and lower sets of observations to be incorporated into the same quantitative framework for joint modeling. Based on the recording and inversion of the propagation parameters that characterize the changes in vibration with propagation distance and frequency by this virtual downlink observation system, a vibration propagation model was constructed. This elevated the traditional statistical analysis of the vibration level difference between the surface and the tunnel to a quantitative analysis of the propagation law of the tunnel structure-strata-surface system, and based on this, the vibration response under the set working conditions was predicted.

[0009] Preferably, the first optical cable is an armored direct-buried optical cable buried in the surface soil at a depth of 0.2-2m, laid along the tunnel axis in a projection corridor on the surface, or a redundant fiber core of a reused existing communication pipeline optical cable; the second optical cable is a redundant fiber core of an existing communication optical cable in the tunnel, or a dedicated armored vibration sensing optical cable laid longitudinally on the tunnel lining; the horizontal projection distance between the two optical cables in the longitudinal direction of the line is not greater than 1 / 2 of the tunnel burial depth; the two optical cables share the same dual-channel distributed optical fiber acoustic wave sensing demodulation equipment, or are connected to their respective demodulation equipment and synchronized through GNSS time synchronization or PTP network time synchronization, with a time synchronization error not greater than 1ms; the correspondence between the detector points of the two optical cables and the line mileage is achieved by applying fixed-point excitation at a known mileage location and combining it with the real-time position information of the train for spatial mileage calibration, with the spatial alignment error of the detector points of the two optical cables not greater than one spatial sampling interval.

[0010] Preferably, the train is an operating train, and continuous monitoring is performed using the passing of the operating train as a repetitive excitation event. Each passing of the train forms an event record, and the accumulated data forms a repetitive observation dataset covering different train types, speeds, and load conditions. The spatiotemporal strain record is a full-wave field spatiotemporal strain record that includes direct waves, surface waves, interface reflected waves, and tunnel lining guided waves.

[0011] Preferably, separating the spatiotemporal strain record of the first optical cable into an uplink wave field and a downlink wave field includes: transforming the spatiotemporal strain record to the frequency-wavenumber domain or the τ-p domain; distinguishing the train-induced wave field component incident from below and the low-apparent-velocity interference component propagating along the ground surface according to the apparent velocity; constructing a ghost wave operator based on the free surface boundary conditions, the burial depth of the first optical cable, and the near-surface velocity; decomposing the record of the first optical cable into an uplink wave field and a downlink wave field formed by reflection from the free surface in the frequency-wavenumber domain or the τ-p domain; or performing joint wave field decomposition based on the wave equation using the upper and lower double-layer observations formed by the first optical cable and the second optical cable; and verifying the propagation direction of the decomposed wave field by the sequential arrival relationship of the train-induced waves from the two optical cables.

[0012] Preferably, the method further includes: using the train-induced components in the second optical cable synchronous record as a reference signal, using adaptive filtering to estimate and subtract non-train interference components caused by ground vehicles and personnel activities from the record of the first optical cable to obtain a pure train-induced wave field; the reverse extension uses the uplink wave field in the pure train-induced wave field as the extension object, and the inversion of the propagation parameters is also based on the pure train-induced wave field.

[0013] Preferably, the reverse extension employs a phase-shifting method or a finite-difference extension algorithm based on the single-journey wave equation, using the formation velocity model provided by first-arrival travel-time tomography or exploration data as the extension velocity model. The train-induced uplink wave field is extended from the depth of the first optical cable along the reverse propagation direction to a set reference surface above the tunnel arch. Virtual observation points are formed on the set reference surface according to spatial sampling intervals. The separated downlink wave field is discarded as a free surface reflection component, or used to verify the separation results of the uplink and downlink wave fields. The combination of the virtual downlink observation record and the measured record of the second optical cable includes: combining the... The virtual downlink observation record and the measured record of the second optical cable are cross-correlated with the direct wave travel time and waveform. When the comparison residual exceeds a set limit, the extension velocity model is updated and re-extended. Using the virtual downlink observation record or the measured record of the second optical cable as a near-source reference, the spatiotemporal strain record of the first optical cable is subjected to deconvolution interferometry to eliminate the influence of the source time function and obtain an equivalent observation record that reflects the propagation characteristics of the strata above the tunnel between the set reference plane and the ground surface. The virtual observation points and the detector points of the second optical cable are staggered along the longitudinal direction of the line to jointly constitute the virtual downlink observation system.

[0014] Preferably, the method further includes: using each wheelset of the same train as an equivalent repeating vibration source, reconstructing the train-induced wavefield in the spatiotemporal strain record into a common shot gather, and using statistical deconvolution to estimate the equivalent vibration source time function; establishing a forward model of the wave equation including the tunnel structure and the strata, using the equivalent vibration source time function as the forward excitation, constructing an objective function for the difference between the observed wavefield and the forward wavefield, iteratively updating the model parameters, and obtaining the medium parameter field along the line; wherein, the common shot gather is equivalent to a single wheelset passing through the monitoring section as one excitation, and the passing of each wheelset through each receiver point is calculated based on the train speed and wheelset position. At the excitation time of the mileage, the records of each receiver point are time-shifted and aligned according to the excitation time; the statistical deconvolution is as follows: a time window is extracted from the direct wave record, the ensemble average of the autocorrelation of each record is calculated as the estimate of the autocorrelation of the equivalent source wavelet, and then the equivalent source time function is obtained by least squares inverse filtering or spectral whitening deconvolution; the forward model of the wave equation is a forward model of the wave equation of a viscoelastic medium including rail-ballast-tunnel lining-soil, with shear wave velocity, compressive wave velocity, density and quality factor as model parameters; the medium parameter field includes shear wave velocity field, compressive wave velocity field, density field and quality factor field.

[0015] Preferably, the forward modeling wavefield is converted into a synthetic axial strain or strain rate record with the same physical quantity as the observation by the DAS observation operator, and then the objective function is constructed with the observed wavefield. The DAS observation operator projects the synthetic particle velocity or displacement field along the optical cable axis, and performs difference on the axial components at both ends of the gauge length according to the optical cable sensing gauge length and divides by the gauge length. The iterative update of model parameters adopts a multi-scale inversion strategy from low frequency to high frequency, including: dividing the observation data into at least 3 frequency bands according to octave bands, first inverting the large-scale background wave velocity field with the envelope objective function of the lowest frequency band, and then gradually increasing the frequency band and inverting the small-scale parameter perturbation with the waveform phase objective function. The objective function is the weighted sum of the L2 norm of the residuals of the data in each frequency band. The model parameter update adopts the L-BFGS quasi-Newton algorithm. When the relative decrease of the objective function is less than the set threshold or the number of iterations reaches the upper limit, the iteration of the current frequency band is terminated and the next frequency band is entered.

[0016] Preferably, the method further includes: calculating the vibration transfer function from the track reference point to the evaluation point; converting the spatiotemporal strain record into a vibration physical quantity using a pre-calibrated strain-vibration velocity conversion coefficient; and calculating the vibration evaluation quantity of the evaluation point in conjunction with the vibration transfer function; the vibration transfer function is obtained by deconvolution of the spectral ratio of the track reference point and the evaluation point record under the same train excitation, or by forward modeling with unit harmonic excitation applied to the inverted medium parameter field along the track; the strain-vibration velocity conversion coefficient is obtained by comparative calibration with a standard point vibration sensor co-located with the first optical cable or the second optical cable in the monitoring section, with a calibration frequency band covering 1-100Hz, and the conversion is performed according to V(x,f)=β(f)·c app (f)·E(x,f) is realized, where β(f) is the strain-vibration velocity conversion coefficient, c app (f) represents the apparent velocity of the corresponding waveform component, and V(x,f) and E(x,f) represent the spectra of the particle vibration velocity and the optical cable axial strain, respectively. The vibration evaluation quantity is the frequency-weighted Z-level conforming to one-third octave bands as specified in GB10070, or the velocity level, peak particle velocity and its one-third octave band spectrum. The evaluation points include the surface free field point, the foundation point of the building along the line and the tunnel structure point.

[0017] Preferably, the propagation parameters include geometric diffusion parameters, frequency-dependent attenuation characteristics, and dispersion characteristics. The propagation parameters used to invert the vibration variation with propagation distance and frequency are a joint inversion of the geometric diffusion parameters, frequency-dependent attenuation characteristics, and dispersion characteristics, including: performing regression analysis on the attenuation of the amplitude of the train-induced wave field in the spatiotemporal strain record with propagation distance to obtain the geometric diffusion parameters; using the spectral ratio of records at different offsets on the virtual downlink observation system, fitting the amplitude attenuation coefficients of different frequency components, and obtaining the frequency-dependent quality factor Q and attenuation coefficient α(f) according to α(f)=πf / (Q·v), where v is the corresponding... The propagation velocity of the wave type is analyzed; dispersion analysis is performed on the surface wave record to obtain dispersion characteristics and inversely retrieve the distribution of shear wave velocity with depth; the vibration propagation model is a parametric vibration propagation model, whose inputs are vibration source parameters and propagation path parameters, and output is vibration field distribution. The vibration source parameters include vehicle type, train formation, speed, axle load and track state parameters. The propagation path parameters include tunnel burial depth, stratum layering parameters, geometric diffusion parameters, attenuation characteristics and dispersion characteristics. The parametric vibration propagation model is constructed using Gaussian process regression or neural network algorithm, and the calculation results of the semi-analytical or numerical simulation vibration propagation forward calculation model are used as training samples or physical constraints.

[0018] Preferably, the method for predicting the vibration response under the set operating conditions includes: comparing the surface vibration response of different vibration reduction measures in the same train excitation section, and quantitatively evaluating the effect of the vibration reduction measures according to the vibration level difference; predicting the environmental vibration at the location of planned or existing buildings, and comparing the predicted vibration evaluation quantity with the environmental vibration standard limit to determine if it exceeds the limit; predicting the vibration response spectrum of the tunnel lining structure; the method further includes: rolling updates of the vibration propagation model with subsequent monitoring data, wherein the rolling update includes: comparing the train-induced wave field in the spatiotemporal strain record obtained by subsequent monitoring with the prediction result of the vibration propagation model, and when the prediction residual exceeds a set threshold, updating the parameters of the vibration propagation model using newly added monitoring data.

[0019] Secondly, embodiments of the present invention provide a DAS-based underground structure vibration propagation modeling and response prediction system, comprising: a parallel three-dimensional observation subsystem, including a first optical cable laid in the surface soil, a second optical cable laid in the tunnel, and a distributed fiber optic acoustic wave sensing demodulation device for synchronous demodulating the two optical cables. The two optical cables are arranged in parallel vertically along the longitudinal direction of the line, and the detector points of the two optical cables are time-synchronized and correspond to the line mileage, used to synchronously record the spatiotemporal strain records of the two optical cables with train passage as the excitation event; a data transmission subsystem, used to transmit the spatiotemporal strain records to a central processing platform; a central processing platform, including a wavefield separation module, a virtual downlink inversion module, and a propagation modeling and prediction module; the wavefield separation... The first optical cable has a separation module for separating the spatiotemporal strain record into an up-wave field and a down-wave field to obtain a train-induced up-wave field. The second optical cable has a virtual down-wave inversion module for extending the train-induced up-wave field in the opposite direction of propagation to a set reference surface above the tunnel, reconstructing the virtual down-wave observation record at the set reference surface, and combining the virtual down-wave observation record with the measured record of the second optical cable to construct a virtual down-wave observation system covering the strata above the tunnel. The third optical cable has a propagation modeling and prediction module for inverting the propagation parameters that characterize the variation of vibration with propagation distance and frequency based on the records of the virtual down-wave observation system, constructing a vibration propagation model, and predicting the vibration response under a set operating condition based on the vibration propagation model.

[0020] Preferably, the demodulation device is a distributed fiber optic acoustic wave sensing demodulation device, with two optical cables sharing the same dual-channel distributed fiber optic acoustic wave sensing demodulation device; or, the two optical cables are respectively connected to their respective distributed fiber optic acoustic wave sensing demodulation devices. When the two optical cables are respectively connected to their respective distributed fiber optic acoustic wave sensing demodulation devices, the parallel three-dimensional observation subsystem further includes a synchronization timing unit for synchronizing the time of the two distributed fiber optic acoustic wave sensing demodulation devices; the data transmission subsystem is also used to transmit the synchronously accessed train operation information to the central processing platform; the wave field separation module is also used to use the train-induced component in the second optical cable record as a reference signal, and to use adaptive filtering to remove non-train interference components from the record of the first optical cable to obtain a pure train-induced wave field; the virtual downlink inversion module uses an extension algorithm based on the single-journey wave equation to perform the inverse extension, performs cross-correlation comparison between the virtual downlink observation record and the measured record of the second optical cable, and uses the virtual downlink observation record or the measured record of the second optical cable as a near-source reference to compare the first optical cable. The spatiotemporal strain records of the optical cable are subjected to deconvolution interferometry processing. The central processing platform also includes a forward-inversion calculation module, which is used to reorganize the train-induced wave field in the spatiotemporal strain records into a common shot gather using each wheelset of the same train as an equivalent repeating vibration source and estimate the equivalent vibration source time function. A forward model of the viscoelastic medium wave equation including the tunnel structure and the strata is established. The equivalent vibration source time function is used as the forward excitation to perform multi-scale full waveform inversion from low frequency to high frequency segment to obtain the medium parameter field along the line. The central processing platform also includes a vibration transfer calculation module, which is used to calculate the vibration transfer function from the track reference point to the evaluation point, convert the spatiotemporal strain records into vibration physical quantities using the strain-vibration velocity conversion coefficient, and calculate the vibration evaluation quantity of the evaluation point in combination with the vibration transfer function. The propagation parameters include geometric diffusion parameters, frequency-dependent attenuation characteristics, and dispersion characteristics. The vibration propagation model is a parameterized vibration propagation model. The propagation modeling and prediction module is also used to update the vibration propagation model using newly added monitoring data when the prediction residual exceeds a set threshold.

[0021] The beneficial effects of the embodiments of the present invention described above are as follows: The core contribution of this invention lies in addressing the technical obstacles of lacking observational constraints on the strata above the tunnel and the inability of horizontally laid surface optical cables to directly distinguish between uplink and downlink waves in parallel DAS observations. First, the record of the first surface optical cable is separated into uplink and downlink wave fields. Then, the train-induced uplink wave field is inversely extended to a reference surface above the tunnel to reconstruct a virtual downlink observation record. The measured record of the second optical cable inside the tunnel is used as an independent observation to jointly construct a virtual downlink observation system. This achieves dense virtual observations of the strata above the tunnel without adding any underground drilling or equipment, realizing the observation reconstruction of "downlink inversion above the tunnel." This overcomes the technical obstacle of joint modeling in parallel observations, enabling the quantitative analysis of the propagation law of vibration from the tunnel structure through the strata to the surface based on continuous observations of the entire line. Based on this, a vibration propagation model is constructed to predict the vibration response under set operating conditions, realizing the transformation from discrete testing at local sections to continuous quantitative analysis and prediction of the entire line. Meanwhile, a three-dimensional observation system is constructed by using optical cables in the surface soil and optical cables in the tunnel (preferably reusing redundant fiber cores of existing communication optical cables), eliminating the need to enter the track area for operation and significantly reducing the implementation cost and safety risks of three-dimensional observation of the entire line.

[0022] Furthermore, in the preferred embodiment: adaptive interference cancellation is performed using the DAS record of the optical cable inside the tunnel as a reference. Because the optical cable inside the tunnel is close to the vibration source and is not affected by ground traffic, the reference record has a high signal-to-noise ratio, which can effectively suppress strong interference from ground vehicles and personnel activities, solving the problem that the DAS of the ground optical cable can be measured but not distinguished in complex urban environments; by recombining common shot point gathers and statistical deconvolution, the moving train vibration source is transformed into an equivalent fixed source and the equivalent vibration source time function is estimated, breaking through the basic assumption of known vibration source in conventional full waveform inversion, realizing all-weather automated monitoring with the operating train as a maintenance-free repetitive excitation source; quantitative parameter fields of the medium along the line are obtained through multi-scale full waveform inversion, combined with the application of... The variable-vibration velocity calibration conversion and vibration transfer function calculation transform the qualitative records of distributed optical fibers into quantitative evaluation quantities of Z-level vibration, enabling direct alignment of distributed optical fiber monitoring results with current environmental vibration standards such as GB10070. By jointly inverting geometric diffusion parameters, frequency-dependent attenuation characteristics, and dispersion characteristics to construct a parameterized vibration propagation model, the empirical magnitude difference estimation is elevated to a quantitative propagation law driven by both mechanism and data. This model can quickly predict the vibration field distribution under any working condition, directly serving the quantitative comparison of vibration reduction measures under the same excitation, vibration prediction and exceedance determination of the building environment along the route, and vibration response analysis of tunnel structures. Furthermore, it is continuously updated with the accumulation of DAS monitoring data, resulting in continuously improving prediction accuracy. Overall, this invention organically connects three-dimensional observation, wavefield separation, virtual downlink reconstruction, propagation law analysis, and modeling prediction, and can be further expanded into a closed-loop technology chain including equivalent vibration source estimation, full waveform inversion, and parameterized prediction. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating the DAS-based vibration propagation modeling and response prediction method for underground structures provided in this embodiment of the invention.

[0024] Figure 2 This is a schematic diagram of the cross-sectional layout and full-wave field propagation path of the observation system provided in an embodiment of the present invention.

[0025] Figure 3 The diagram below illustrates the signal connection, time synchronization, and data flow of the observation system provided in this embodiment of the invention.

[0026] Figure 4 The diagram illustrates the wavefield separation and interference removal method and the reconstruction principle of the virtual downlink observation system provided in this embodiment of the invention.

[0027] Figure 5 A flowchart of multi-scale full waveform inversion iteration provided for embodiments of the present invention.

[0028] Figure 6 This is a data flow diagram for vibration transmission calculation and quantitative evaluation provided in an embodiment of the present invention.

[0029] Figure 7 The flowchart for propagation law inversion, parameterized modeling, and response prediction provided in the embodiments of the present invention is shown.

[0030] Figure 8 The diagram shows the structure of the DAS-based underground structure vibration propagation modeling and response prediction system provided in this embodiment of the invention. Detailed Implementation

[0031] The following description and accompanying drawings fully illustrate specific embodiments of this application to enable those skilled in the art to practice them. The embodiments represent only possible variations. Individual components and functions are optional unless explicitly required, and the order of operations may vary. Parts and features of some embodiments may be included in or replace parts and features of other embodiments. The scope of embodiments of this application includes the entire scope of the technical solutions and all available equivalents of the technical solutions. In this document, each embodiment may be referred to individually or collectively with the term "invention," which is merely for convenience and, if more than one invention is disclosed, is not intended to automatically limit the scope of the application to any single invention or inventive concept. Relational terms such as "first" and "second" are used herein only to distinguish one entity or operation from another, without requiring or implying any actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed. The various embodiments in this document are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the structures, products, etc., disclosed in the embodiments, since they correspond to the disclosed parts, the descriptions are relatively simple; relevant details can be found in the method section.

[0032] Terminology Explanation Before describing the technical solution in detail, the key terms used in this application will be explained first: Distributed optical fiber acoustic sensing (DAS): Using ordinary communication optical fiber as the sensing and transmission medium, it senses the strain or strain rate along the optical fiber by injecting coherent light pulses into the optical fiber and detecting the phase change of the backscattered Rayleigh signal. It can achieve meter-level spatial resolution and continuous vibration monitoring over distances of tens of kilometers. This invention is used as a sensing technology to construct a surface-tunnel parallel three-dimensional observation system.

[0033] Spatiotemporal strain record: The strain (or strain rate) data matrix output by the DAS demodulation equipment, with time and space (optical cable detector location) as two dimensions, is the original data foundation for all processing and inversion. When this record contains all wave types, including direct waves, surface waves, interface reflected waves, and tunnel lining guided waves, it is called a full-wavelength spatiotemporal strain record. In this document, "spatiotemporal strain record" is a higher-level concept, and "full-wavelength spatiotemporal strain record" is the preferred form when it contains the above-mentioned wave types. The processing described in the steps of the instruction manual for the full-wavelength spatiotemporal strain record also applies to the spatiotemporal strain record.

[0034] Upward and downward wave fields: These are wave field components with different propagation directions in the vertical direction. The upward wave is the wave field that propagates from the tunnel side towards the ground surface, while the downward wave is the wave field that propagates from the upward wave after reflection from the free ground surface towards the tunnel. For horizontally laid sensing optical cables, the apparent velocity sign along the cable only represents the direction of wave propagation along the line and cannot distinguish between upward and downward waves. The separation of the two is achieved through ghost wave operator decomposition based on free ground boundary conditions and optical cable burial depth, or joint wave field decomposition of the upper and lower double-layer optical cables. This separation is a prerequisite for constructing a virtual downlink observation system.

[0035] Virtual Downward Observation System: This system is an equivalent observation system formed by using a wave equation extension algorithm (preferably based on the phase shift method or finite difference extension algorithm) to extend the train-induced upward wave field separated from the surface optical cable record in the reverse direction of propagation to a reference surface above the tunnel to form virtual observation points. This system is combined with the actual measured records inside the tunnel to form a virtual observation system. "Downward" refers to the observation reference surface moving downward from the ground surface. This system is equivalent to setting up dense observation points in the strata above the tunnel without any downhole drilling or equipment, which is the core concept of this invention.

[0036] Common shot point gather: Records excited by the same equivalent vibration source (i.e., the same wheel pair) and received by different detectors are organized into a set of data according to the equivalent vibration source-detector relationship. It is the basic data input unit for full waveform inversion.

[0037] Equivalent vibration source time function: A function characterizing the excitation time characteristics of a single train wheelset. It is estimated from the common shot point ensemble using the statistical deconvolution method and is used as the input for the forward excitation source in the full waveform inversion.

[0038] Multi-scale full waveform inversion: The strategy of dividing the observed data into multiple frequency bands according to octaves and inverting the model parameters segment by segment from low frequency to high frequency. The low frequency band uses the envelope objective function to invert the large-scale background wave velocity field, and the high frequency band uses the waveform phase objective function to invert the small-scale parameter disturbances. The purpose is to alleviate the nonlinear cycle jump problem in the inversion.

[0039] Medium parameter field: The medium physical property parameters spatially distributed along the line from the full waveform inversion output, including the shear wave velocity field V. s Compression wave velocity field V p The density field ρ and the quality factor field Q can be used to calculate the vibration transfer function in forward modeling and can also serve as constraints and verification bases for propagation parameter inversion.

[0040] The strain-vibration velocity conversion coefficient β(f) is a dimensionless frequency correlation coefficient obtained by comparing and calibrating standard point vibration sensors co-located with distributed vibration sensing optical cables within the monitoring section. It characterizes the correction of the plane wave strain-particle velocity theoretical relationship by factors such as optical cable coupling state and demodulation instrument response. The actual conversion is calculated as V(x,f)=β(f)·c app (f)·E(x,f), derived from β(f) and the apparent velocity c of the corresponding waveform component. app (f) Joint implementation for converting strain records measured by DAS optical cables into vibration physical quantities such as particle vibration velocity.

[0041] Vibration transfer function H(f): A frequency domain function that characterizes the amplitude and phase changes of each frequency component during the propagation of vibration from the orbital reference point to the evaluation point. It can be obtained through forward modeling or measured recording of the spectrum deconvolution.

[0042] Z vibration level VL z The vibration acceleration level conforms to the one-third octave band frequency-weighted standard specified in GB10070. It is a quantitative evaluation index specified in China's current environmental vibration standards, with a reference acceleration of 1×10⁻⁶. -6 m / s 2 .

[0043] Vibration propagation model: A model that characterizes the amplitude variation with propagation distance and frequency during the propagation of vibration from the track reference point through the tunnel structure and strata to the evaluation area using propagation parameters obtained by inversion. It is used to predict the vibration response under set working conditions. Its forms include a multi-parameter coupled vibration propagation database classified and statistically analyzed by vehicle type, vehicle speed, axle load, tunnel burial depth, strata conditions and structural working conditions, as well as empirical propagation relationships based on the database, and the following parameterized vibration propagation model.

[0044] Parametric vibration propagation model: A preferred form of vibration propagation model, it is a fast prediction model that takes vibration source parameters and propagation path parameters as inputs and vibration field distribution as output. It is constructed using Gaussian process regression or neural network algorithms, uses forward calculation model results as physical constraints, and uses measured data as calibration targets.

[0045] Geometric diffusion parameter n: A parameter characterizing the amplitude attenuation with propagation distance caused by wavefront area expansion, expressed as A(r) = A0*r -n To describe the relationship between amplitude and distance, n is generally 0.5-1.5 for body waves and 0-0.5 for surface waves.

[0046] Frequency-dependent attenuation coefficient α(f): A parameter characterizing the absorption and attenuation characteristics of a medium for vibrations of different frequencies. Its relationship with the quality factor Q is α(f) = πf / (Q*v), where v is the propagation speed of the corresponding waveform, and high-frequency components attenuate faster.

[0047] Detailed technical solution This invention provides a method for modeling and predicting the vibration propagation and response of underground structures based on DAS. For example... Figure 1 As shown, Figure 1 This is a flowchart illustrating the DAS-based vibration propagation modeling and response prediction method for underground structures provided in this embodiment of the invention. Solid boxes and arrows in the diagram represent essential steps and the main flow of the basic technical solution; dashed boxes and arrows represent preferred steps and paths. The method provided in this embodiment can be executed by a vibration monitoring and prediction system equipped with distributed fiber optic acoustic wave sensing demodulation equipment, a data transmission system, and a central processing platform. This system can be implemented through software and / or hardware. The method includes the following steps: Step 1: Construction of the Surface-Tunnel Parallel Three-Dimensional Observation System like Figure 2 As shown, a first distributed vibration sensing optical cable is laid along the underground pipeline corridor in the surface soil. This cable is laid along the tunnel axis's projection corridor on the surface, buried in the soil beneath green belts, sidewalks, or pedestrian walkways at a depth of 0.2-2m. Armored direct-buried optical cables are used, backfilled with fine sand for dense coupling to ensure coordinated deformation with the strata. In sections with municipal pipeline resources, redundant fiber cores from existing operator communication pipeline optical cables can also be reused as the first distributed vibration sensing optical cable (hereinafter referred to as the first optical cable). When reusing pipeline optical cables, sections with dense pipeline backfill and good coupling between the optical cable and the pipe wall and surrounding soil should be selected. The response characteristics should be verified by comparing with standard point-type vibration sensors deployed at the same site. For sections where the coupling state does not meet the requirements, the records are only used for travel-time analysis or weighted down in inversion to ensure the reliability of strain recording amplitude information.

[0048] Existing communication optical cables or dedicated optical cables within the tunnel are used as the second distributed vibration sensing optical cable (hereinafter referred to as the second optical cable). Redundant fiber cores of the existing communication optical cables are reused preferentially. When existing optical cable resources are insufficient, a dedicated armored vibration sensing optical cable is laid along the tunnel lining and fixed using a fixed-point clamping method. The two optical cables are laid in parallel, vertically, three-dimensional arrangement along the longitudinal direction of the line. The horizontal projection distance along the longitudinal direction should not exceed 1 / 2 of the tunnel burial depth to ensure the coverage correlation of the upper and lower observations for the same vibration source.

[0049] like Figure 3As shown, a distributed fiber optic acoustic wave sensing demodulation device is used to synchronously demodulate two optical cables. The two optical cables can share the same dual-channel distributed fiber optic acoustic wave sensing demodulation device for time synchronization, or they can be connected to their respective demodulation devices and synchronized via GNSS or PTP network time synchronization, with a time synchronization error of no more than 1ms. Spatial mileage calibration is achieved by applying fixed-point tapping excitation at known mileage locations (such as surface maintenance wells or tunnel connecting passage entrances) and combining this with real-time train location information, mapping the detector points of the two optical cables one-to-one with the line mileage, with a spatial alignment error of no more than one spatial sampling interval. The demodulation sampling rate is 1-2kHz, the spatial sampling interval is 2-10m, and the sensing gauge length is 5-20m.

[0050] This step embodies the technical features of the surface-tunnel parallel stereoscopic observation system construction in the first aspect of the technical solution. It achieves continuous stereoscopic observation of the entire line through two parallel DAS optical cables, providing a hardware foundation for subsequent full-field recording and processing.

[0051] Step 2: Full-field synchronous recording Using the passage of a train through a monitored section as the excitation event, preferably the passage of an operating train as the repeated excitation event, a shared dual-channel distributed fiber optic acoustic wave sensing demodulation device, or two demodulation devices connected to two optical cables and synchronized via time synchronization, synchronously records the spatiotemporal strain of the two optical cables. This record is typically a full-wavelength spatiotemporal strain record containing multiple wave types. The train wheelset excitation is transmitted to the tunnel lining via the track bed and then propagates through the strata. The full-wavelength field mainly includes four types of wave types: direct waves propagating directly from the source to the receiver, surface waves propagating along the ground surface, interface reflection waves generated at deep layer interfaces, and tunnel lining guided waves propagating along the circumferential and longitudinal directions of the lining. Each train passage forms an event record, and long-term accumulation constitutes a repeated observation dataset covering different train types, speeds, and load conditions.

[0052] This step embodies the technical feature of the first aspect of the technical solution regarding the synchronous recording of spatiotemporal strain records of two optical cables with the passing of a train as the excitation event; under the preferred method of using an operating train as a repetitive excitation event, the operating train can be used as a maintenance-free repetitive excitation source to achieve all-weather automatic data acquisition.

[0053] Step 3: Wavefield Separation and Interference Removal like Figure 4As shown in (a), wavefield separation and interference removal are performed as follows. First, the synchronous records of the two optical cables are segmented into train events and spatiotemporally aligned (when full waveform inversion is required in subsequent steps 5 and 6, common shot point gather reassembly can be completed at this time). Then, the full wavefield spatiotemporal strain record is transformed to the frequency-wavenumber domain (FK domain) or the τ-p domain. For horizontally laid optical cable arrays, the wavenumber (apparent velocity) sign in the FK domain only represents the propagation direction of the wave along the line and cannot directly distinguish between vertical up and down waves. Therefore, wavefield separation is implemented in the following two levels: The first level is apparent velocity filtering, which distinguishes the train-induced body wave component with higher apparent velocity along the cable from the downward incident wave component and the surface wave and ground interference component with lower apparent velocity propagating along the ground surface based on the apparent velocity. The second level is up and down decomposition, which constructs a ghost wave operator based on the free ground boundary conditions, the burial depth of the first distributed vibration sensing optical cable, and the near-surface velocity obtained from the first arrival travel time or surface wave dispersion. In the FK domain (or correspondingly in the τ-p domain), the first optical cable record is decomposed into an up wavefield and a down wavefield formed by reflection from the free ground surface, or a joint wavefield decomposition based on the wave equation is performed using a double-layer observation consisting of the upper and lower optical cables. The decomposition results are verified by the order of arrival of the same train-induced wave from the two optical cables (the wave propagating from bottom to top arrives at the second optical cable first and then the first optical cable).

[0054] As a preferred method, ground-based optical cable records often contain strong interference from ground vehicles and personnel activities. Further, using the train-induced component from the synchronous record of the second distributed vibration sensing optical cable as a reference signal, adaptive filtering (such as the normalized least mean square algorithm) is employed to estimate and reconstruct the train-induced component from the record of the first distributed vibration sensing optical cable. Residual incoherent components are identified as non-train interference and removed, ultimately obtaining a pure train-induced wave field. Because the optical cable inside the tunnel is close to the vibration source and unaffected by ground traffic interference, its reference record has a high signal-to-noise ratio, resulting in a significantly better cancellation effect than traditional methods based on ground-based reference tracks.

[0055] The clean train-induced wave field after interference removal is used for subsequent inverse continuation and propagation parameter inversion, which can improve the reliability of the continuation and inversion results. In sections with weak surface interference (such as suburbs or nighttime), interference removal can be omitted, and the train-induced uplink wave field obtained after apparent speed filtering and uplink / downlink decomposition can be used directly for subsequent processing.

[0056] The uplink and downlink wave field decomposition in this step reflects the technical feature of separating the spatiotemporal strain record of the first optical cable into uplink and downlink wave fields in the first aspect of the technical solution, which is a prerequisite for implementing subsequent reverse extension. Using the record of the second distributed vibration sensing optical cable as a reference to eliminate non-train interference components is a preferred technical solution, which solves the problem of strong interference suppression of surface optical cable DAS in complex urban environments.

[0057] Step 4: Reconstruction of the Virtual Downlink Observation System like Figure 4 As shown in (b), the train-induced uplink wave field (which is the uplink wave field in the pure train-induced wave field when interference removal is performed) obtained from the first optical cable record separated in step 3 is extended in the reverse direction of propagation from the depth of the first distributed vibration sensing optical cable to a set reference surface above the tunnel arch using the phase-shift method or finite difference extension algorithm based on the one-way wave equation. Virtual observation points are formed on this reference surface according to the spatial sampling interval, and virtual downlink observation records at this reference surface are reconstructed. "Downlink" refers to the observation reference surface migrating downward from the ground surface. The separated downlink wave field is removed as a free surface reflection component, or used to verify the separation results of the uplink and downlink wave fields (such as verifying the correctness of the ghost wave operator construction). The stratigraphic velocity model required for the extension is provided by first-arrival travel-time tomography or exploration data.

[0058] The combination of virtual downlink observation records and second distributed vibration sensing optical cable measured records includes two aspects: First, the virtual downlink observation records and second optical cable measured records are compared by cross-correlation of direct wave travel time and waveform. When the comparison residual exceeds the set limit, the extension velocity model is updated and re-extended, so that the virtual record of the reference plane gradually approaches the real wave field near the tunnel section. This is the embodiment of the inversion meaning in "virtual downlink inversion".

[0059] On the other hand, using verified virtual downlink observation records or measured records from the second optical cable as near-source references, deconvolution interferometry is performed on the surface records of the first optical cable (i.e., the spatiotemporal strain records of the first optical cable) to eliminate the influence of the equivalent source time function (i.e., train excitation time characteristics). This yields equivalent observation records reflecting the propagation characteristics of the strata above the tunnel between the set reference plane and the ground surface, serving as the data basis for subsequent attenuation and dispersion characteristic inversion. This processing does not require prior estimation of the source time function; it can be achieved directly by deconvolution using the near-source reference records.

[0060] Virtual observation points and second optical cable detectors are staggered along the longitudinal direction of the line, together forming a virtual downlink observation system covering the geological space above the tunnel. This observation system is equivalent to deploying dense observation points in the strata above the tunnel, but without any downhole drilling or equipment, realizing the observation reconstruction of downlink inversion above the tunnel and providing spatial observation constraints for propagation law inversion.

[0061] This step embodies the core feature of the first aspect of the technical solution: extending the separated train-induced upward wave field in the opposite direction of propagation to a reference surface above the tunnel to reconstruct the virtual downward observation record, and jointly constructing a virtual downward observation system with the measured record inside the tunnel.

[0062] Step 5: Equivalent source wavelet estimation and common shot point gather formation.

[0063] This is a preferred step and does not affect the handling of the technical issues in this application. When it is necessary to further obtain the quantitative parameter field of the medium along the line through full waveform inversion, perform step 5 and the next step 6.

[0064] The train-induced wave field (preferably the pure train-induced wave field after interference removal in step 3) is preprocessed sequentially with DC removal, trend removal, bandpass filtering (passband of 2-80Hz), and frequency-wavenumber domain filtering. The event unit is a single train passing through a monitoring section. Each wheelset of the train is considered an equivalent pulse excitation. Thus, a train with N cars and M wheelsets passing through once constitutes M equivalent repeated excitations. For the excitation of the j-th wheelset, the excitation time of its passage through each receiver point is calculated based on the train speed and wheelset position. The receiver point records are time-shifted and aligned according to the excitation time, and a unified time window is extracted, reconstructing a common shot point gather with the wheelset as the equivalent vibration source.

[0065] The equivalent vibration source-detector relationship is determined as follows: the equivalent vibration source position of the j-th wheelset is the known motion trajectory of the wheelset along the track (determined by the real-time position of the train, the train speed and the wheel spacing), and its excitation time at any track mileage is known; in the forward modeling simulation of full waveform inversion, the j-th wheelset is applied to the track reference position as a moving point load according to the known trajectory, the excitation time characteristic is taken as the estimated equivalent vibration source time function, and the synthetic record and the observation record are processed according to the same excitation time time shift alignment rule to ensure that the observation data and the synthetic data are completely consistent in the gather organization method.

[0066] As a simplified alternative, a reference mileage x can also be selected. s The wheelset passes through x s When the confocal point is zero, the equivalent vibration source is approximated as being located at x. s For a fixed point source at the orbital elevation, the event window length is taken as the duration corresponding to the source movement distance not exceeding 1 / 4 of the shortest wavelength of the current inversion frequency band. Recording segments exceeding this duration are not included in the waveform fitting of the gather.

[0067] Full waveform inversion requires knowledge of the source time function. The direct wave least affected by the strata is extracted from the receiver ensemble near the tunnel. Time windows are extracted from the direct wave records, and the ensemble average of the autocorrelation of each record is calculated as an estimate of the equivalent source wavelet autocorrelation. Then, through least-squares inverse filtering or spectral whitening deconvolution, the equivalent source time function of the train excitation is obtained. When optical cables are laid both on the surface and inside the tunnel, joint wavelet estimation is performed, primarily using the direct wave records from the tunnel optical cables and secondarily using the surface optical cable records, to improve the robustness of the wavelet estimation.

[0068] This step embodies the technical features of the preferred technical solution, which involves treating each wheelset of the same train as an equivalent repeating vibration source, reorganizing it into a common shot point gather according to the equivalent vibration source-detector relationship, and using the statistical deconvolution method to estimate the time function of the equivalent vibration source. This breaks through the basic assumption of known vibration source in conventional full waveform inversion.

[0069] Step 6: Obtain the medium parameter field along the line through multi-scale full waveform inversion. like Figure 5 As shown, a two-dimensional or three-dimensional forward model of the viscoelastic medium wave equation is established, encompassing rail, track bed, tunnel lining, and strata. The model geometry is determined based on the track design data. The rail, track bed, and lining are discretized according to their actual geometry and material parameters, and the strata are initialized according to the layered structure given in the exploration data. The model boundary uses a perfectly matched layer (PML) absorbing boundary to simulate an infinite domain of strata. The forward modeling employs a finite difference solution of the viscoelastic wave equation in velocity-stress form, with the medium exhibiting a shear wave velocity V0. s Compression wave speed V p Density ρ and quality factor Q are parameterized, and the viscosity effect is introduced using a standard linear solid model. The inversion region is the tunnel and its overlying strata profile along the longitudinal direction of the line. The grid spacing is no greater than 1 / 10 of the shortest wavelength corresponding to the highest inversion frequency (i.e., the ratio of the lowest wave velocity of the model to the highest inversion frequency). The time sampling satisfies the Courant stability condition, that is, the ratio of the product of the maximum wave velocity of the model, the time step, and the grid spacing is no greater than the stability limit of the difference scheme used. For components such as lining segments, rails, and track bed with a thickness less than the grid spacing, local grid refinement or approximation using equivalent medium parameters is adopted.

[0070] For each common shot gather, the estimated equivalent source time function is used as excitation to calculate the synthetic wavefield on the forward model. The synthetic wavefield is then converted into a synthetic record with the same physical quantities as the observation using the DAS observation operator: the synthetic particle velocity (or displacement) field is projected along the optical cable axis to obtain the axial particle velocity (or displacement). Then, the axial particle velocity (or displacement) at both ends of the gauge length is subtracted according to the sensing gauge length of the optical cable and divided by the gauge length to obtain a synthetic axial strain rate (or strain) record equivalent to the average within the gauge length. This observation operator simultaneously reflects the axial direction response of the distributed optical fiber to wavefields with different incident directions and the gauge length smoothing effect. An objective function characterizing the difference between the observed wavefield and the synthetic wavefield is constructed. , Where m is the model parameter vector, s is the equivalent vibration source index, r is the receiver point index, and d is the equivalent vibration source index. obs For axial strain (or strain rate) records observed by DAS, d cal This is the record of the synthesized axial strain (or strain rate) after conversion by the DAS observation operator.

[0071] The gradient of the objective function with respect to the model parameters is calculated using the adjoint state method: the data residuals are used as adjoint sources from the backpropagation of the receiver position, and zero-delay cross-correlation is performed with the forward propagation wavefield to obtain the gradient kernels of each parameter. After applying source illumination preconditions and smoothing constraints to the gradients, the L-BFGS quasi-Newton algorithm is used to update the model parameters, with the step size determined by line search.

[0072] To mitigate the nonlinear cycle jump problem in the inversion, a multi-scale inversion strategy from low to high frequencies is adopted: the observed data is divided into at least three frequency bands (e.g., 2-5Hz, 2-10Hz, 2-20Hz) according to octave bands. First, the large-scale background wave velocity field is inverted in the lowest frequency band using an envelope objective function. Then, the frequency bands are progressively increased, and the small- and medium-scale parameter perturbations are inverted using a waveform phase objective function. Within each frequency band, when the relative decrease in the objective function is less than 1% or the number of iterations reaches the upper limit, the process moves to the next frequency band. Finally, the medium parameter field along the route is obtained, including the shear wave velocity field, compression wave velocity field, density field, and quality factor field.

[0073] This step embodies the technical features of the preferred technical solution regarding establishing a forward model of the viscoelastic medium wave equation, constructing an objective function, calculating the gradient using the adjoint state method, and iteratively updating the model parameters from low frequency to high frequency bands to obtain the medium parameter field along the line, thus transforming the distributed optical fiber record into a quantitative parameter field of wave velocity and attenuation.

[0074] Step 7: Vibration Transmission Calculation and Quantitative Evaluation like Figure 6 As shown, when the medium parameter field has been obtained after step 6, a unit harmonic excitation is applied to the track reference point on the obtained medium parameter field for forward modeling. The steady-state response of each stratum and surface evaluation point is extracted to obtain the vibration transfer function H(f) from the track reference point to each evaluation point. Alternatively, without relying on the medium parameter field, the spectral ratio deconvolution is directly performed on the measured records of the track reference point and evaluation points under the same train excitation to obtain a data-driven transfer function estimate; when both methods are feasible, they are mutually verified.

[0075] The strain recorded by the distributed optical fiber needs to be converted into a vibration physical quantity. A representative location is selected within the monitoring section, and a standard point vibration sensor (force balance accelerometer or velocimeter) is deployed co-located with the distributed vibration sensing optical cable. The sensor is calibrated by comparison within the 1-100Hz frequency band to obtain the strain-vibration velocity conversion coefficient β(f).

[0076] For a given apparent velocity c along the direction of the optical cable app The plane wave component, the particle vibration velocity and the axial strain of the optical cable satisfy V(x,f)=β(f)·c in the frequency domain. app (f)·E(x,f), where V(x,f) and E(x,f) are the spectra of particle vibration velocity and optical cable axial strain, respectively.app (f) represents the apparent velocity of this wave type component, which can be estimated by the travel time of the direct wave or the frequency-wavenumber spectrum of the common shot gather according to the wave type and frequency band; the time domain transformation is performed according to β(f)·c app (f) The corresponding filter and the convolution of the strain record are implemented; for broadband records containing multiple waveforms, they are first separated by waveform in the frequency-wavenumber domain and then converted separately.

[0077] The converted vibration physical quantities are combined with the vibration transfer function to calculate the vibration evaluation quantity at each evaluation point. The vibration evaluation quantity is the frequency-weighted Z-level (VL) conforming to one-third octave bands as specified in GB10070. z =20*lg(a w / a0), where a w The root mean square value of acceleration is calculated using a Z-axis weighted network, with a0 as the reference acceleration of 1×10⁻⁶. -6 m / s 2 Vibration evaluation quantities can also include velocity level, peak mass velocity, and its one-third octave band spectrum. Evaluation points include free field points on the ground surface, foundation points of buildings along the route, and tunnel structural points.

[0078] This step embodies the technical features of the preferred technical solution, namely, calculating the vibration transfer function, converting spatiotemporal strain records into vibration physical quantities using the strain-vibration velocity conversion coefficient, and calculating the vibration evaluation quantity of the evaluation point by combining the vibration transfer function, so that the distributed optical fiber monitoring results can be directly connected with the current environmental vibration standards such as GB10070.

[0079] Step 8: Propagation law inversion and parameterized modeling like Figure 7 As shown, the propagation law inversion and modeling are based on the records of the virtual downlink observation system constructed in step 4 (including the virtual downlink observation records at the reference plane, the measured records of the second optical cable, and the equivalent observation records obtained by deconvolution interferometry processing of the ground records of the first optical cable using one of the two as the near-source reference). It can also incorporate the train-induced wave fields from the records of the two optical cables (such as amplitude regression analysis for geometric diffusion parameters), and does not depend on the medium parameter fields obtained in steps 5 and 6. When the medium parameter fields are obtained, they can be used as constraints and checks for propagation parameter inversion. The propagation law inversion and parametric modeling include the following four aspects: Geometric diffusion parameter inversion: Regression analysis is performed on the amplitude of the train-induced wave field (preferably a pure train-induced wave field after interference removal) as a function of propagation distance r, according to A(r)=A0*r -n The geometric diffusion parameter n is obtained, and the data is fitted to the direct body wave and the surface wave respectively. The n value for the body wave is 0.5-1.5, and the n value for the surface wave is 0-0.5. The inversion results are statistically analyzed according to the section and the working condition.

[0080] Frequency-dependent attenuation characteristic inversion: The quality factor of each frequency component is estimated by using the spectral ratio of records at different offsets on a virtual downlink observation system. The quality factor Q and frequency dependence are inverted from the attenuation coefficient α(f) according to α(f) = πf / (Q*v), where v is the propagation speed of the corresponding waveform. When ln[A(f,r1) / A(f,r2)] has a linear relationship with the frequency f, its slope corresponds to π*(r2-r1) / (Q*v).

[0081] In terms of dispersion characteristics analysis: frequency-wavenumber analysis or multi-channel surface wave analysis is performed on surface wave records to extract phase velocity dispersion curves and invert the distribution of formation shear wave velocity with depth, which serves as the basis for updating formation layering parameters and extension velocity models.

[0082] In terms of guided wave characteristics analysis of the lining: the guided wave components propagating along the lining in the second optical cable record are extracted, and their velocity and attenuation characteristics are analyzed to characterize the coupling state between the tunnel structure and the strata.

[0083] The above propagation parameters are categorized and statistically analyzed according to vehicle type, vehicle speed, axle load, tunnel depth, geological conditions, and structural working conditions to construct a multi-parameter coupled vibration propagation database. This database, along with the segmented and working-condition propagation relationships summarized from it (e.g., according to A(r)=A0*r), -n *e -α(f)r The amplitude-distance-frequency relationship described constitutes the basic form of a vibration propagation model that can be used to predict vibration response.

[0084] As a preferred approach, a parametric vibration propagation model is established by further integrating a semi-analytical or numerical simulation vibration propagation forward calculation model with a data-driven algorithm. The inputs are vibration source parameters (vehicle type, train formation, speed, axle load, and track state parameters) and propagation path parameters (tunnel depth, stratum layering parameters, geometric diffusion parameters, attenuation characteristics, and dispersion characteristics). The output is the vibration field distribution of the evaluation area.

[0085] The model is constructed using Gaussian process regression or neural network algorithms, with forward calculation model results as physical constraints or prior samples and measured data as calibration targets, exhibiting generalization ability and physical consistency.

[0086] As a specific configuration that can be implemented: When using Gaussian process regression, the input vector is composed of normalized source parameters and propagation path parameters. The output is the vibration response level of each center frequency in one-third octave band of the evaluation point. The kernel function is an anisotropic squared exponential kernel determined by automatic correlation. The hyperparameters are determined by maximizing marginal likelihood. The prior mean function is the predicted value of the semi-analytical forward calculation model, so that the regression result regresses to the physical forward calculation result in the sparse data region. When using a neural network, a fully connected structure can be adopted, consisting of an input layer, three hidden layers (each with 64-256 nodes and ReLU activation), and an output layer. The loss function is the weighted sum of the fitting residuals of the measured data and the physical constraint residuals (the deviations between the network prediction and the forward calculation model prediction at the sampling working point). The weight ratio of the two can be 1:0.1 to 1:1. The training samples are composed of the propagation parameter statistics of the measured events and the batch calculation results of the forward calculation model. The training set and the validation set are divided according to the mileage segment to avoid the leakage of spatial information of adjacent detector points.

[0087] In this step, recording and retrieving propagation parameters based on the virtual downlink observation system and constructing a vibration propagation model embodies the technical characteristics of the first aspect of the technical solution; jointly retrieving stratigraphic geometric diffusion parameters, frequency-dependent attenuation characteristics and dispersion characteristics, statistically analyzing propagation parameters under different driving conditions and different site conditions, and constructing a parameterized vibration propagation model are preferred technical solutions.

[0088] Step 9: Vibration Response Prediction and Model Update Vibration response prediction is based on the vibration propagation model (preferably a parametric propagation model) constructed in step 8, including three types of applications.

[0089] (1) Quantitative evaluation of the effect of vibration reduction measures: Compare the surface vibration response of ordinary integral track bed sections and vibration reduction measures sections (such as steel spring floating slab track bed sections) under the same train excitation, according to the vibration level difference ΔVL z The effectiveness of vibration reduction measures was quantitatively evaluated. Since the same vibration source and the same observation system were used, the evaluation results were not affected by differences in train numbers.

[0090] (2) Environmental vibration prediction: For the planned or existing building locations, predict the environmental vibration according to the design driving conditions and make a judgment on whether it exceeds the standard, and support the optimization of vibration reduction design of the line.

[0091] (3) Prediction of vibration response of tunnel structure: Based on the second optical cable observation and propagation model, the vibration response spectrum of tunnel lining structure is predicted to serve the structural safety analysis.

[0092] As a preferred option, a rolling update mechanism for the model can be set up as follows: the train-induced wave field (preferably a pure train-induced wave field) obtained from subsequent monitoring is compared with the prediction results of the parameterized propagation model according to mileage and operating conditions. When the prediction residual exceeds the set threshold (such as vibration level deviation greater than 3dB), the new data is included in the multi-parameter coupled vibration propagation database, the propagation parameters are recalibrated and the model is updated, so that the prediction accuracy continues to improve with the accumulation of monitoring data.

[0093] In this step, predicting the vibration response under the set working conditions based on the vibration propagation model reflects the technical characteristics of the first aspect of the technical solution; using subsequent monitoring data to continuously update the vibration propagation model is the preferred technical solution.

[0094] Example 1 The technical solution of the present invention will be described in detail below through a specific embodiment. This embodiment takes an underground section of an intercity railway as the object. The tunnel is a shield tunnel with an outer diameter of 6.7m and a burial depth of about 25m. The strata from top to bottom are fill and soft soil (0-8m), silty clay and sand (8-20m), strongly weathered rock (20-35m), and moderately weathered rock (below 35m). The total length of the line is about 10km.

[0095] Corresponding to step 1 (Construction of the Surface-Tunnel Parallel Three-Dimensional Observation System): A first distributed vibration sensing optical cable of approximately 10km is laid along the route, buried in the green belt beside the surface projection corridor of the tunnel axis, at a depth of 0.8m. Armored direct-buried optical cables are used, and fine sand is backfilled for dense coupling. The second distributed vibration sensing optical cable reuses redundant fiber cores from existing communication optical cables within the tunnel. The horizontal projection distance between the two optical cables along the longitudinal direction is approximately 8m, less than half of the tunnel's burial depth of 25m (12.5m), meeting the coverage correlation requirements. The two optical cables share a single dual-channel DAS demodulation device, with a demodulation sampling rate set to 1kHz, a spatial sampling interval of 5m, and a sensing gauge length of 10m. At K0+000, K2+500, K5+000, K7+500, and K... 10 Spatial mileage calibration was completed by applying fixed-point tapping excitation at 5 known mileage locations (+000). The detector point alignment error was less than 5m (i.e., 1 spatial sampling interval).

[0096] Corresponding to step 2 (full-field synchronous recording): Continuous monitoring is performed using the passing of operating trains as a recurring excitation event. During the monitoring period, more than 500 train passing events are recorded, covering two types of trains: Type A (6-car formation, speed 120km / h, axle load 16t) and Type B (8-car formation, speed 160km / h, axle load 17t). Each event is recorded for approximately 30 seconds, including the complete process of the train entering, passing through, and leaving the monitoring section. Waveforms such as direct waves, surface waves, interface reflected waves, and lined guided waves can be clearly identified in the full wave field.

[0097] Corresponding to step 3 (wavefield separation and interference removal): The full-wavefield spatiotemporal strain record is subjected to FK domain transformation. First, tilt filtering is performed according to the apparent velocity to distinguish surface waves and ground interference components propagating along the ground surface with apparent velocities of approximately 200-800 m / s from the ground, and train-induced body waves incident from below with apparent velocities greater than 800 m / s along the cable. Then, a free surface ghost wave operator is constructed using the near-surface velocity given by the optical cable burial depth of 0.8 m and first-arrival travel-time tomography to decompose the train-induced wavefield into an up-going wavefield and a down-going wavefield. The propagation direction is verified using the arrival time sequence of the second optical cable synchronous record (the same wave arrives at the second optical cable first, then the first optical cable). Using the train-induced component in the synchronous record of the second distributed vibration sensing optical cable as a reference signal, a normalized minimum mean square adaptive filtering algorithm (step size μ=0.01, filter order 128) is used to remove non-train interference components such as ground vehicles from the record of the first distributed vibration sensing optical cable. After wave field separation and interference removal, the signal-to-noise ratio of the train-induced wave field recorded by the ground optical cable is improved by about 15 dB.

[0098] Corresponding to step 4 (reconstruction of the virtual downlink observation system): Using the phase-shift method based on the one-way wave equation and the stratum velocity model obtained from first-arrival travel-time tomography, the train-induced uplink wave field separated from the first optical cable record is retrograded from a depth of 0.8m in the opposite direction of propagation to a set reference plane 2m above the tunnel arch (i.e., approximately 23m underground). Approximately 2000 virtual observation points are formed on this reference plane at 5m intervals. The direct wave travel-time deviation between the virtual downlink observation record and the measured record of the second distributed vibration sensing optical cable is less than 5%, and the extended velocity model is verified as qualified. Using the verified virtual downlink observation record as a near-source reference, deconvolution interferometry is performed on the first optical cable surface record to obtain an equivalent observation record of the stratum propagation characteristics above the tunnel between the reference plane and the surface.

[0099] Corresponding to step 5 (equivalent source wavelet estimation and common shot gather formation): The pure train-induced wave field is preprocessed by removing DC, removing trend, and applying a 2-80Hz bandpass filter. Taking a Type B train (8 cars, 32 wheelsets) as an example, one pass generates 32 equivalent repeated excitations. Based on a train speed of 160km / h (approximately 44.4m / s) and a wheelset spacing of 2.5m, the excitation time of each wheelset passing through each receiver point is calculated, time-shifted and aligned, and a 1s time window is extracted, recombining them into 32 common shot gathers. Direct waves are extracted from the receiver gathers of adjacent tunnels. After calculating the ensemble average of the autocorrelation of 30 direct wave records, the equivalent source time function is obtained through least squares inverse filtering, with a wavelet dominant frequency of approximately 30Hz. In the forward modeling simulation of full waveform inversion, each wheelset is applied to the track reference position as a moving point load according to its known trajectory determined by the real-time position of the train, the train speed, and the wheelset spacing.

[0100] Corresponding to step 6 (multi-scale full waveform inversion to obtain the medium parameter field along the line): Establish a two-dimensional viscoelastic medium wave equation forward model including rail-ballast-tunnel lining-soil, with a grid spacing of 1m×1m (not greater than 1 / 10 of the shortest wavelength of 10m corresponding to the highest inversion frequency of 20Hz), and a time step of 0.1ms (maximum wave velocity V of the model). p At a speed of 4200 m / s, the Courant number is approximately 0.42, satisfying the stability condition. For components such as lining segments with a thickness less than the grid spacing, equivalent medium parameters are used for approximation, and perfectly matched layers are used for the boundaries. The initial model is set based on the layered structure from the survey data: fill and soft soil layers V p =800m / s, V s =200m / s, ρ=1800kg / m 3 Q=20; Silty clay and sand layers V p =1500m / s, V s =400m / s, ρ=1950kg / m 3 Q=35; Strongly weathered rock strata V p =2300m / s, V s =700m / s, ρ=2100kg / m 3 Q=60; moderately weathered rock strata V p =3500m / s, V s =1200m / s, ρ=2300kg / m 3 Q=100; Lined segment V p =4200m / s, V s =2500m / s, ρ=2500kg / m 3 Q=200.

[0101] The synthetic wavefield is converted into a synthetic axial strain record by the DAS observation operator (projected along the optical cable axis, subtracted at both ends of the 10m gauge length and divided by the gauge length), and then constructed with the observation record to form the objective function.

[0102] The observed data were divided into three frequency bands: 2-5Hz, 2-10Hz, and 2-20Hz, based on octave bands. First, the large-scale background wave velocity field was inverted using the envelope objective function of the 2-5Hz band (maximum 30 iterations per band, convergence threshold 1%). Then, the frequency was progressively increased to 2-10Hz and 2-20Hz, where small- and medium-scale parameter perturbations were inverted using the waveform phase objective function. The L-BFGS algorithm was used to update the parameters. The final shear wave velocity field matched the layered velocity structure given in the exploration data.

[0103] Corresponding to step 7 (Vibration Transfer Calculation and Quantitative Evaluation): On the medium parameter field obtained by inversion, a unit harmonic excitation within the range of 1-80Hz is applied at the track reference point to perform forward simulation, obtaining the vibration transfer function H(f) to the evaluation point on the ground surface. At two representative mileage locations, K3+000 and K7+000, force balance accelerometers co-located with the DAS optical cable are deployed for full-band comparison and calibration from 1-100Hz to obtain the strain-vibration velocity conversion coefficient β(f). Taking the passage of a Type B vehicle as an example, the DAS strain record is calculated as V(x,f)=β(f)·c app (f)·E(x,f) is converted into the particle vibration velocity in the frequency domain (c of the main wave mode component). app The travel time of the direct wave is estimated to be approximately 400 m / s. This is then combined with the vibration transfer function to calculate the Z-level (VL) at the surface evaluation point. z .

[0104] Corresponding to step 8 (propagation law inversion and parameterized modeling): Regression analysis was performed on the amplitude attenuation of the pure train-induced wave field with distance. In this embodiment, the geometric diffusion parameter of the direct body wave is n≈1.0, and that of the surface wave is n≈0.3. The quality factors of each frequency were estimated using the spectral ratio of records within an offset range of 5m to 23m on the virtual downlink observation system. For shallow fill, Q≈20, and for silty clay, Q≈35, consistent with the survey data. Multichannel surface wave analysis was performed on the surface wave records to obtain dispersion curves and invert the shear wave velocity distribution with depth. Propagation parameters were statistically analyzed according to two vehicle types, three vehicle speeds, and five representative sections to construct a multi-parameter coupled vibration propagation database. A parameterized propagation model was established using the Gaussian process regression algorithm with the forward calculation model results as physical constraints.

[0105] Corresponding to step 9 (Vibration Response Prediction and Model Update): The parametric propagation model is used to predict the surface vibration level for 50 independently verified train events (those not involved in model training). The prediction deviation is less than 2.5 dB. A comparative evaluation of the ordinary integral track bed in the K4+000-K5+000 section and the steel spring floating slab track bed in the K5+000-K6+000 section under the same excitation is conducted. The latter shows an average reduction of approximately 11 dB in surface Z-vibration level, consistent with design expectations. A rolling update threshold of 3 dB is set; when the subsequent monitoring prediction residual exceeds this threshold, model parameter updates are automatically triggered.

[0106] This embodiment verifies the complete implementation process of the technical solution in the underground section of the intercity railway. The steps are smoothly connected, and the final results achieved are: a signal-to-noise ratio improvement of 15dB, a travel time deviation of less than 5% between the virtual downlink observation record and the actual measured record in the tunnel, a vibration level prediction deviation of less than 2.5dB, and vibration reduction measures evaluation results consistent with the design expectations.

[0107] Example 2 The application of the present invention's technical solution in shallow-buried sections of urban rail transit (metro) is illustrated below through a second embodiment. This embodiment focuses on a shallow-buried section of a metro line passing through a residential area in a certain city. The tunnel is a shield tunnel with an outer diameter of 6.2m and a burial depth of approximately 12m. The strata are mainly fill (0-3m) and silty clay (3-15m), with dense residential buildings on top, resulting in a high risk of excessive environmental vibration along the line. The monitoring section is approximately 3km long.

[0108] Corresponding to step 1: Approximately 3 km of the first distributed vibration sensing optical cable was laid along the route, buried beneath the sidewalk at a depth of 0.5 m, using armored direct-buried optical cable. Due to insufficient redundant fiber cores in the existing communication optical cable within the tunnel, the second distributed vibration sensing optical cable was a dedicated armored vibration sensing optical cable laid longitudinally along the tunnel lining and fixed at fixed points. The horizontal projection distance between the two optical cables was approximately 5 m, less than half of the tunnel's burial depth of 12 m, i.e., 6 m. The two optical cables were connected to two DAS demodulation devices, achieving synchronization via PTP network time synchronization with a time synchronization error of 0.5 ms. The demodulation sampling rate was 2 kHz, the spatial sampling interval was 2 m, and the sensing gauge length was 5 m. Spatial mileage calibration was completed by applying fixed-point excitation at three known mileage locations.

[0109] Corresponding to step 2: Continuous monitoring was conducted using the passing of subway trains as a recurring excitation event, accumulating over 1000 train passing events. The train type was Type A (6 cars, 24 wheelsets), with an operating speed of 80 km / h and an axle load of 14t. Each event record was approximately 20 seconds long.

[0110] Corresponding to step 3: Perform τ-p domain transformation on the full-field spatiotemporal strain record (in this embodiment, due to the small spatial sampling interval, τ-p domain analysis is suitable). First, distinguish the train-induced wavefield component incident from below and the low-apparent-velocity interference component propagating along the ground surface according to the apparent velocity. Then, construct a ghost wave operator based on the free ground boundary conditions and the 0.5m burial depth of the optical cable to complete the decomposition of the uplink and downlink wavefields. Verify the propagation direction using the arrival time sequence recorded synchronously by the second optical cable. Using the record of the second distributed vibration sensing optical cable as a reference, a normalized minimum mean square adaptive filtering algorithm is used to remove interference from ground public transport vehicles and pedestrian activities. Since this section is located in a busy traffic area, the signal-to-noise ratio is improved by approximately 12dB after interference removal.

[0111] Corresponding to step 4: Using the finite difference extension algorithm and the velocity model provided by the survey data, the train-induced uplink wave field separated from the first optical cable record is extended in the reverse direction from a depth of 0.5m to a set reference surface 1.5m above the tunnel arch (i.e., approximately 10.5m underground). Approximately 1500 virtual observation points are formed on the reference surface at 2m intervals. The extended velocity model is verified by cross-correlation of the virtual downlink observation records with the measured records of the second optical cable using direct wave travel time. Furthermore, deconvolution interferometry is performed on the ground record of the first optical cable using the virtual downlink observation records as a near-source reference to obtain an equivalent observation record.

[0112] Corresponding to step 5: Preprocess the pure train-induced wave field using a 2-80Hz bandpass filter. Taking a type A train (6 cars, 24 wheelsets) as an example, one pass generates 24 equivalent repeated excitations. Based on a train speed of 80km / h (approximately 22.2m / s) and a wheelset spacing of 2.5m, the excitation time is calculated, time-shifted and aligned to extract a 0.8s time window, and reassembled into 24 common shot point gathers. Twenty channels are extracted from the direct-path optical wave record within the tunnel, and autocorrelation set averaging is performed. The equivalent source time function is obtained through spectral whitening and deconvolution, with a wavelet dominant frequency of approximately 25Hz. In the forward modeling simulation, each wheelset is subjected to a moving point load according to a known trajectory.

[0113] Corresponding to step 6: Establish a two-dimensional viscoelastic forward model with a grid spacing of 0.5m × 0.5m (not greater than 1 / 10 of the shortest wavelength of 6.5m corresponding to the highest inversion frequency of 20Hz), and a time step of 0.05ms (the maximum wave velocity V of the model). p At a speed of 4200 m / s, the Courant number is approximately 0.42, satisfying the stability condition. Initial model: Filled with soil (V...). p =500m / s, V s =130m / s, ρ=1750kg / m 3 Q=15; Silty clay V p =1300m / s, V s =350m / s, ρ=1900kg / m 3 Q=30; Lined segment V p =4200m / s, V s =2500m / s, ρ=2500kg / m 3 With Q=200, the tunnel segments are approximated using equivalent medium parameters. The synthesized wavefield is converted into a synthetic axial strain record using the DAS observation operator (projected along the optical cable axis, differentiated at both ends by the 5m gauge length). The observation data is divided into three frequency bands: 2-5Hz, 2-10Hz, and 2-20Hz, for multi-scale inversion, with a maximum of 30 iterations per band. Due to the shallow tunnel depth (12m) in this embodiment, the inversion area is small, resulting in high computational efficiency.

[0114] Corresponding to step 7: Calculate the vibration transfer function in the medium parameter field. Calibrate velocimeters at two representative locations to obtain β(f). Transform the DAS strain record according to the frequency domain relationship V(x,f)=β(f)·c app (f)·E(x,f) is converted into vibration velocity and the Z-level is calculated. Vibration evaluation was conducted on the foundations of 5 residential buildings along the line. The results showed that the Z-level of 2 of the buildings exceeded the limit of GB10070 at night.

[0115] Corresponding to step 8: Regression analysis of the amplitude attenuation of the pure wave field with distance. In this embodiment, due to the tunnel burial depth of only 12m and the stratum being mainly soft soil, the surface wave energy accounts for a relatively high proportion. The surface wave geometric diffusion parameter n≈0.4, and the shallow quality factor Q≈15-30, the attenuation characteristics are significantly stronger than those of the deep-buried section in Example 1. The shear wave velocity distribution with depth is obtained by surface wave dispersion analysis. A parameterized propagation model is constructed and a neural network is trained using the forward calculation results as constraints. The network adopts a fully connected structure of input layer - 3 hidden layers (64-256 nodes per layer, ReLU activation) - output layer. The loss function is the weighted sum of the measured data fitting residual and the physical constraint residual. The training set and validation set are divided according to the mileage section.

[0116] Corresponding to step 9: Using a parametric propagation model, predict the vibration response at each building location along the route after the installation of the designed vibration reduction measures (floating slab track bed). The prediction results show that the Z-vibration level of the two substandard buildings will be reduced by approximately 10-12 dB after installation, meeting the standard requirements. Set a rolling update threshold of 3 dB, and continuously monitor and verify the prediction results and update the model after the vibration reduction measures are installed.

[0117] This embodiment verifies the applicability of the technical solution in shallow-buried subway sections, demonstrating that the technical solution can still work effectively under conditions of shallow tunnel burial depth, strong stratum attenuation, and complex surface interference. It has been successfully applied to the decision support for environmental vibration exceeding the standard and vibration reduction measures design. It forms a comparative verification with Embodiment 1 for deep burial and shallow burial, intercity railway and urban subway.

[0118] like Figure 8 As shown in the figure, this invention also provides a DAS-based system for modeling and predicting the vibration propagation of underground structures, which includes: The parallel three-dimensional observation subsystem includes a first distributed vibration sensing optical cable (a newly built armored direct-buried optical cable or a reused redundant fiber core of an existing communication pipeline optical cable) laid in the surface soil, an existing communication optical cable or a dedicated optical cable in the tunnel that serves as the second distributed vibration sensing optical cable, a distributed fiber optic acoustic wave sensing demodulation device, and a synchronous timing unit, used to synchronously record the full-wave field spatiotemporal strain record excited by the train. The data transmission subsystem is used to transmit the demodulated full-wave field spatiotemporal strain records and synchronously accessed train operation information to the central processing platform. The data is transmitted through the data transmission network after train event marking, sampling data segmentation and compression by edge computing nodes. The central processing platform includes a wavefield separation module, a virtual downlink inversion module, and a propagation modeling and prediction module. Preferably, it also includes a forward-inversion calculation module and a vibration transmission calculation module. The wave field separation module is used to transform the full-wave field spatiotemporal strain record to the frequency-wavenumber domain or τ-p domain to separate the up-going wave field from the down-going wave field, and to use the record of the second distributed vibration sensing optical cable as a reference to adopt adaptive filtering to remove non-train interference components and obtain a pure train-induced wave field. The virtual downlink inversion module is used to extend the train-induced uplink wave field separated from the first distributed vibration sensing optical cable record in the reverse direction of propagation to a reference surface above the tunnel using an extension algorithm based on the single-path wave equation, forming a virtual downlink observation record. It is then cross-correlated and compared with the measured record of the second distributed vibration sensing optical cable and deconvolution interferometry is performed to construct a virtual downlink observation system. The forward-inverse calculation module is used to reconstruct the common shot point gather and estimate the equivalent vibration source time function of the pure train-induced wave field, establish a forward model of the viscoelastic medium wave equation, and perform multi-scale full waveform inversion to obtain the medium parameter field along the line. The vibration transfer calculation module is used to calculate the vibration transfer function in the medium parameter field. It uses the strain-vibration velocity conversion coefficient to convert the spatiotemporal strain record into vibration physical quantities, and combines the vibration transfer function to calculate vibration evaluation quantities such as the Z-level of the evaluation point. The propagation modeling and prediction module is used to invert and characterize the propagation parameters that represent the variation law of vibration with propagation distance and frequency based on the records of the virtual downlink observation system, construct a vibration propagation model, and predict the vibration response under a set working condition. Preferably, the propagation parameters include formation geometric diffusion parameters, frequency-dependent attenuation characteristics, and dispersion characteristics. The vibration propagation model is a parameterized vibration propagation model, and the module triggers a rolling update of the model when the prediction residual exceeds a threshold.

[0119] The specific functions and implementation methods of the above modules correspond to the corresponding steps in the aforementioned method embodiments, and will not be repeated here.

Claims

1. A method for modeling and predicting the vibration propagation and response of underground structures based on DAS, characterized in that, include: The optical cable laid in the surface soil is the first optical cable, and the optical cable laid in the tunnel is the second optical cable. The two optical cables are laid in parallel vertically along the line. Demodulation equipment is used to demodulate the two optical cables synchronously, and the detection point time of the two optical cables is synchronized and corresponds to the line mileage. Using the passing of a train as the excitation event, the spatiotemporal strain records of the two optical cables are recorded simultaneously; the spatiotemporal strain record of the first optical cable is separated into an uplink wave field and a downlink wave field to obtain the train-induced uplink wave field; The train-induced up-going wave field is extended in the opposite direction of propagation to a set reference plane above the tunnel. The virtual down-going observation record at the set reference plane is reconstructed, and the virtual down-going observation record is combined with the measured record of the second optical cable to construct a virtual down-going observation system covering the strata above the tunnel. Based on the records of the virtual downlink observation system, propagation parameters that characterize the variation of vibration with propagation distance and frequency are inverted, a vibration propagation model is constructed, and the vibration response under the set working conditions is predicted based on the vibration propagation model.

2. The method according to claim 1, characterized in that, The first optical cable is an armored direct-buried optical cable buried in the surface soil at a depth of 0.2-2m, laid along the tunnel axis in a projection corridor on the surface; the second optical cable is a redundant fiber core of an existing communication optical cable in the tunnel, or a dedicated armored vibration sensing optical cable laid longitudinally on the tunnel lining; the horizontal projection distance between the two optical cables in the longitudinal direction of the line is no greater than 1 / 2 of the tunnel burial depth; the demodulation equipment is a distributed fiber optic acoustic wave sensing demodulation equipment, with the two optical cables sharing the same dual-channel distributed fiber optic acoustic wave sensing demodulation equipment, or connected to their respective demodulation equipment and synchronized through GNSS or PTP network timing, with a time synchronization error of no more than 1ms; the correspondence between the detector points of the two optical cables and the line mileage is achieved by applying fixed-point excitation at a known mileage location and combining it with the real-time position information of the train for spatial mileage calibration, with the spatial alignment error of the detector points of the two optical cables no greater than one spatial sampling interval.

3. The method according to claim 1, characterized in that, The train is an operational train, and continuous monitoring is performed using the passing of the operational train as a repetitive excitation event. Each passing of the train forms an event record, which is accumulated to form a repetitive observation dataset covering different train types, speeds, and load conditions. The spatiotemporal strain record is a full-wave field spatiotemporal strain record that includes direct waves, surface waves, interface reflected waves, and tunnel lining guided waves.

4. The method according to claim 1, characterized in that, The step of separating the spatiotemporal strain record of the first optical cable into an uplink wave field and a downlink wave field includes: transforming the spatiotemporal strain record to the frequency-wavenumber domain or the τ-p domain; distinguishing the train-induced wave field component incident from below and the low-apparent-velocity interference component propagating along the ground surface according to the apparent velocity; constructing a ghost wave operator based on the free ground surface boundary conditions, the burial depth of the first optical cable, and the near-surface velocity; decomposing the record of the first optical cable into an uplink wave field and a downlink wave field formed by reflection from the free ground surface in the frequency-wavenumber domain or the τ-p domain; or performing joint wave field decomposition based on the wave equation using the upper and lower double-layer observations formed by the first optical cable and the second optical cable; and verifying the propagation direction of the decomposed wave field by the sequential arrival relationship of the train-induced waves from the two optical cables.

5. The method according to claim 1, characterized in that, Also includes: Using the train-induced components in the second optical cable synchronous record as a reference signal, adaptive filtering is used to estimate and subtract non-train interference components caused by ground vehicles and personnel activities from the record of the first optical cable to obtain a pure train-induced wave field; the reverse extension uses the uplink wave field in the pure train-induced wave field as the extension object, and the inversion of the propagation parameters is also based on the pure train-induced wave field.

6. The method according to claim 1, characterized in that, The reverse extension employs a phase-shift method or finite-difference extension algorithm based on the single-journey wave equation, using the formation velocity model provided by first-arrival travel-time tomography or exploration data as the extension velocity model. The train-induced uplink wave field is extended from the depth of the first optical cable along the reverse propagation direction to a set reference surface above the tunnel arch. Virtual observation points are formed on this set reference surface at spatial sampling intervals. The separated downlink wave field is discarded as a free surface reflection component, or used to verify the separation results of the uplink and downlink wave fields. The combination of the virtual downlink observation record with the measured record of the second optical cable includes: combining the virtual downlink observation record with the measured record of the second optical cable. The virtual downlink observation record and the measured record of the second optical cable are cross-correlated with the direct wave travel time and waveform. When the comparison residual exceeds the set limit, the extension velocity model is updated and re-extended. Using the virtual downlink observation record or the measured record of the second optical cable as the near source reference, the spatiotemporal strain record of the first optical cable is subjected to deconvolution interferometry to eliminate the influence of the source time function and obtain an equivalent observation record that reflects the propagation characteristics of the strata above the tunnel between the set reference plane and the ground surface. The virtual observation points and the detector points of the second optical cable are staggered along the longitudinal direction of the line to jointly constitute the virtual downlink observation system.

7. The method according to claim 1, characterized in that, Also includes: Using each wheel pair of the same train as an equivalent repeating vibration source, the train-induced wave field in the spatiotemporal strain record is reconstructed into a common shot gather, and the equivalent vibration source time function is estimated using statistical deconvolution. A forward model of the wave equation, including the tunnel structure and strata, is established. Using the equivalent vibration source time function as the forward excitation, an objective function is constructed to differentiate the observed wave field from the forward modeled wave field. The model parameters are iteratively updated to obtain the medium parameter field along the line. The common shot gather is defined as an equivalent excitation when a single wheel pair passes through the monitoring section. The excitation time of each wheel pair passing through each receiver point is calculated based on the train speed and wheel pair position. At each moment, the records of each receiver point are time-shifted and aligned according to the excitation time; the statistical deconvolution is as follows: the time window of the direct wave record is extracted, the ensemble average of the autocorrelation of each record is calculated as the estimate of the autocorrelation of the equivalent source wavelet, and then the equivalent source time function is obtained by least squares inverse filtering or spectral whitening deconvolution; the forward model of the wave equation is a forward model of the wave equation of a viscoelastic medium including rail-ballast-tunnel lining-soil, with shear wave velocity, compression wave velocity, density and quality factor as model parameters; the medium parameter field includes shear wave velocity field, compression wave velocity field, density field and quality factor field.

8. The method according to claim 7, characterized in that, The forward-modeled wavefield is converted into a synthetic axial strain or strain rate record by the DAS observation operator and then used to construct the objective function with the observed wavefield. The DAS observation operator projects the synthetic particle velocity or displacement field along the optical cable axis and performs differential calculations on the axial components at both ends of the gauge length according to the optical cable sensing gauge length, and divides by the gauge length. The iterative update of model parameters adopts a multi-scale inversion strategy from low frequency to high frequency, including: dividing the observed data into at least 3 frequency bands according to octave bands; first, inverting the large-scale background wave velocity field with the envelope objective function of the lowest frequency band; then, gradually increasing the frequency band and inverting the small-scale parameter perturbations with the waveform phase objective function. The objective function is a weighted sum of the L2 norms of the residuals of the data in each frequency band. The model parameter update adopts the L-BFGS quasi-Newton algorithm. When the relative decrease of the objective function is less than a set threshold or the number of iterations reaches the upper limit, the iteration of the current frequency band is terminated and the process moves to the next frequency band.

9. The method according to claim 7, characterized in that, Also includes: The vibration transfer function from the track reference point to the evaluation point is calculated. A pre-calibrated strain-velocity conversion coefficient is used to convert the spatiotemporal strain record into a vibration physical quantity. The vibration evaluation quantity at the evaluation point is then calculated based on the vibration transfer function. The vibration transfer function is obtained by deconvolution of the spectral ratio of the track reference point and the evaluation point record under the same train excitation, or by forward modeling with unit harmonic excitation applied to the inverted medium parameter field along the track. The strain-velocity conversion coefficient is obtained by calibrating a standard point-type vibration sensor co-located with the first or second optical cable within the monitoring section, with a calibration frequency band covering 1-100Hz. The vibration evaluation quantity is a frequency-weighted Z-level conforming to one-third octave band frequency as specified in GB10070, or a velocity level, peak mass velocity, and its one-third octave band spectrum. The evaluation points include surface free field points, foundation points of buildings along the track, and tunnel structure points.

10. The method according to claim 1, characterized in that, The propagation parameters include geometric diffusion parameters, frequency-dependent attenuation characteristics, and dispersion characteristics. The propagation parameters characterizing the variation of vibration with propagation distance and frequency are obtained through a joint inversion of the geometric diffusion parameters, frequency-dependent attenuation characteristics, and dispersion characteristics. This includes: performing regression analysis on the attenuation of the amplitude of the train-induced wave field in the spatiotemporal strain record with propagation distance to obtain the geometric diffusion parameters; using the spectral ratio of records at different offsets on the virtual downlink observation system, fitting the amplitude attenuation coefficients of different frequency components, and obtaining the frequency-dependent quality factor Q and attenuation coefficient α(f) according to α(f)=πf / (Q·v), where v is the corresponding wave type. The propagation speed is determined; dispersion analysis is performed on the surface wave record to obtain dispersion characteristics and inversely retrieve the distribution of shear wave velocity with depth; the vibration propagation model is a parametric vibration propagation model, whose inputs are source parameters and propagation path parameters, and output is the vibration field distribution. The source parameters include vehicle type, train formation, vehicle speed, axle load and track state parameters. The propagation path parameters include tunnel burial depth, stratum layering parameters, geometric diffusion parameters, attenuation characteristics and dispersion characteristics. The parametric vibration propagation model is constructed using Gaussian process regression or neural network algorithm, and the calculation results of the semi-analytical or numerical simulation vibration propagation forward calculation model are used as training samples or physical constraints.

11. The method according to claim 9, characterized in that, The method for predicting vibration response under the set operating conditions includes: comparing the surface vibration response of different vibration reduction measures in the same train excitation section, and quantitatively evaluating the effectiveness of vibration reduction measures according to the vibration level difference; predicting the environmental vibration at the location of planned or existing buildings, and comparing the predicted vibration evaluation quantity with the environmental vibration standard limit to determine if it exceeds the limit; predicting the vibration response spectrum of the tunnel lining structure; the method also includes: rolling updates of the vibration propagation model with subsequent monitoring data, wherein the rolling update includes: comparing the train-induced wave field in the spatiotemporal strain record obtained by subsequent monitoring with the prediction results of the vibration propagation model, and when the prediction residual exceeds a set threshold, updating the parameters of the vibration propagation model using newly added monitoring data.

12. A DAS-based system for modeling and predicting the vibration propagation of underground structures, characterized in that, For implementing the method as described in any one of claims 1-11, comprising: The parallel three-dimensional observation subsystem includes a first optical cable laid in the surface soil, a second optical cable laid in the tunnel, and demodulation equipment for synchronous demodulation of the two optical cables. The two optical cables are laid in parallel three-dimensional arrangement along the longitudinal direction of the line, and the detection points of the two optical cables are time-synchronized and correspond to the line mileage. It is used to synchronously record the spatiotemporal strain records of the two optical cables with the passing of a train as the excitation event. A data transmission subsystem is used to transmit the spatiotemporal strain records to the central processing platform; The central processing platform includes a wavefield separation module, a virtual downlink inversion module, and a propagation modeling and prediction module; The wave field separation module is used to separate the spatiotemporal strain record of the first optical cable into an uplink wave field and a downlink wave field to obtain the train-induced uplink wave field. The virtual downlink inversion module is used to extend the train-induced uplink wave field in the opposite direction of propagation to a set reference plane above the tunnel, reconstruct the virtual downlink observation record at the set reference plane, and combine the virtual downlink observation record with the measured record of the second optical cable to construct a virtual downlink observation system covering the strata above the tunnel. The propagation modeling and prediction module is used to invert the propagation parameters that characterize the variation of vibration with propagation distance and frequency based on the records of the virtual downlink observation system, construct a vibration propagation model, and predict the vibration response under a set working condition based on the vibration propagation model.

13. The system according to claim 12, characterized in that, The demodulation device is a distributed fiber optic acoustic wave sensing demodulation device, with two optical cables sharing the same dual-channel distributed fiber optic acoustic wave sensing demodulation device; alternatively, the two optical cables are each connected to their respective distributed fiber optic acoustic wave sensing demodulation devices. When the two optical cables are connected to their respective distributed fiber optic acoustic wave sensing demodulation devices, the parallel three-dimensional observation subsystem further includes a synchronization timing unit for synchronizing the time of the two distributed fiber optic acoustic wave sensing demodulation devices. The data transmission subsystem is also used to transmit the synchronously accessed train operation information to the central processing platform. The wave field separation module is further used to use the train-induced components in the second optical cable record as a reference signal, employing adaptive filtering to remove non-train interference components from the first optical cable record, obtaining a clean train-induced wave field. The virtual downlink inversion module uses an extension algorithm based on the one-way wave equation for the inverse extension, performs cross-correlation comparison between the virtual downlink observation record and the measured record of the second optical cable, and uses either the virtual downlink observation record or the measured record of the second optical cable as a near-source reference for the first optical cable. The spatiotemporal strain records are subjected to deconvolution interferometry processing. The central processing platform also includes a forward-inversion calculation module, which is used to reorganize the train-induced wave field in the spatiotemporal strain records into a common shot gather using each wheelset of the same train as an equivalent repeating vibration source and estimate the equivalent vibration source time function. A forward model of the viscoelastic medium wave equation including the tunnel structure and the strata is established. The equivalent vibration source time function is used as the forward excitation to perform multi-scale full waveform inversion from low frequency to high frequency segment to obtain the medium parameter field along the line. The central processing platform also includes a vibration transfer calculation module, which is used to calculate the vibration transfer function from the track reference point to the evaluation point, convert the spatiotemporal strain records into vibration physical quantities using the strain-vibration velocity conversion coefficient, and calculate the vibration evaluation quantity of the evaluation point in combination with the vibration transfer function. The propagation parameters include geometric diffusion parameters, frequency-dependent attenuation characteristics, and dispersion characteristics. The vibration propagation model is a parameterized vibration propagation model. The propagation modeling and prediction module is also used to update the vibration propagation model using newly added monitoring data when the prediction residual exceeds a set threshold.

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