A highway time-series insar deformation estimation method in soft soil area considering cyclic loading

Abstract

The application provides a kind of soft soil area highway time series InSAR deformation estimation method considering cyclic load.The method is for the deformation monitoring of soft soil area highway under the influence of long-term cyclic load of vehicle, based on multi-temporal InSAR technology, respectively carries out time series deformation modeling and model parameter solution, finally estimates the time series deformation of soft soil area highway by the obtained deformation parameter solution.The cyclic load plastic strain model component is introduced into the InSAR deformation model in the time series InSAR modeling link, and a kind of soft soil area highway time series InSAR deformation model considering the influence of vehicle cyclic load is established.The method overcomes the defect that the influence of vehicle load is ignored in the traditional InSAR monitoring method, can accurately estimate the time series deformation of soft soil area highway under the influence of long-term vehicle cyclic load, widens the application field of InSAR technology, and can also provide reference for highway deformation analysis interpretation and deformation prediction warning under the influence of vehicle load.

Description

Technical Field

[0001] This invention relates to the field of highway deformation monitoring and early warning, and specifically to a time-series InSAR deformation estimation method for highways in soft soil areas that takes into account cyclic loads. Background Technology

[0002] Due to the inherent characteristics of soft soil, such as high natural water content, high compressibility, low strength, and poor structure, it is more prone to settlement and other defects under vehicle loads. Especially when vehicles are overloaded, the loads far exceed the road's design load, leading to pavement damage, bridge fractures, and a significantly shortened service life. Therefore, long-term settlement monitoring of roads in soft soil areas under continuous cyclic vehicle loads is urgently needed.

[0003] Traditional deformation monitoring methods, such as precision leveling and global navigation satellite systems, can meet the accuracy requirements of highway monitoring, but their low spatial resolution, high manpower and material consumption, and difficulty in protecting on-site instruments and equipment limit their application in large-scale deformation monitoring. Differential Interferometric Synthetic Aperture Radar (D-InSAR), as an emerging space-based Earth observation technology, offers advantages such as wide monitoring range, high spatial resolution, non-contact measurement, strong penetration through clouds and fog, and sensitivity to minute deformations. It significantly compensates for the shortcomings of traditional measurement methods, providing a new opportunity for monitoring the overall deformation of road networks in large-scale soft soil areas. However, spatiotemporal decorrelation and atmospheric delay limit the monitoring accuracy of D-InSAR technology. Therefore, multi-temporal interferometry synthesized aperture radar (MT-InSAR) technology was proposed by scholars. This technology mainly uses advanced InSAR techniques such as permanent scatterer (PS) and small baseline subset (SBAS) as representatives. It has been proven to have greater application potential in monitoring large-area urban surface deformation and the settlement of large linear facilities, and has achieved many advanced application results at home and abroad.

[0004] In the processing of time-series InSAR data, the establishment of the deformation model is a crucial step, directly affecting the accuracy of deformation estimation and influencing the solution of deformation parameters, the optimization selection of high-coherence points, and phase unwrapping. Furthermore, it provides a reference for the subsequent interpretation of deformation results. Currently, the InSAR models used in highway deformation monitoring are mostly combinations of one or more mathematical functions. The model parameters are often mathematical coefficients with unclear physical meanings, and the contribution of cyclic vehicle loads to settlement is rarely included in the deformation model. For highways in soft soil areas, they bear not only the static load of the highway structure's weight but also the cyclic dynamic load from repeated vehicle movements. The former is a static load on the roadbed, the magnitude of which depends on the type of the highway superstructure, while the latter is a dynamic stress that repeatedly changes with the movement of wheel axles. Post-construction settlement of highways in soft soil areas mainly includes settlement caused by additional dynamic stress induced by cyclic dynamic loads in the foundation and settlement caused by long-term rheological effects of soft soil. Among these, the additional impact of cyclic loads on foundation deformation has been proven to be significant, with plastic deformation typically accounting for more than 70% of the total foundation deformation. Therefore, providing a method for accurately estimating highway deformation in soft soil areas is of great importance. Summary of the Invention

[0005] The purpose of this invention is to provide a time-series InSAR deformation estimation method for highways in soft soil areas that takes into account cyclic loading. This method is geared towards monitoring the deformation of highways in soft soil areas under the influence of long-term cyclic vehicle loads. Based on multi-temporal InSAR technology, it performs time-series deformation modeling and model parameter calculation separately, and finally estimates the time-series deformation of highways in soft soil areas through the obtained deformation parameter solutions. In the time-series InSAR modeling stage, the Maxwell settlement model in rheology theory is used as the basic model for InSAR soft soil deformation. Then, the plastic strain model components of cyclic loading are introduced into the InSAR deformation model to establish a time-series InSAR deformation model for highways in soft soil areas that takes into account the influence of cyclic vehicle loads. The model parameter solution is performed using a sequential method (GALM) of Genetic Algorithm (GA) and Levenberg-Marquardt Algorithm (LM). This method overcomes the shortcomings of traditional InSAR monitoring methods that ignore the influence of vehicle loads. It can accurately estimate the temporal deformation of highways in soft soil areas under the influence of long-term cyclic vehicle loads, broaden the application field of InSAR technology, and provide a reference for the analysis, interpretation and prediction of highway deformation under the influence of vehicle loads.

[0006] The technical solution adopted in this invention is as follows:

[0007] A time-series InSAR deformation estimation method for highways in soft soil areas considering cyclic loading includes the following steps:

[0008] Step 1, InSAR differential interferometric phase acquisition, specifically: generating time-series InSAR differential interferograms based on high coherence points; using time-series InSAR technology to obtain unwrapped differential interferograms of soft soil regions, and using a double threshold method to filter high coherence points, generating the unwrapped phase difference matrix of the high coherence point targets in the filtered interferograms, thus obtaining the InSAR differential interferometric phase;

[0009] Step 2: Based on the InSAR differential interferometric phase obtained in Step 1, construct a time-series InSAR model for highways in soft soil areas that takes into account cyclic loads.

[0010] Step 3: Parameter estimation of InSAR soft soil area highway deformation model considering cyclic load. Specifically, the GALM algorithm is used to solve the parameters. First, the genetic algorithm is used to search for the approximate optimal solution of the parameters of the time series function model obtained in Step 2, and this solution is used as the initial value of the Levenberg-Marquardt method for iterative optimization to obtain the optimal solution of the parameters.

[0011] Step 4: Estimating the temporal deformation of roads in soft soil areas based on the InSAR road deformation model considering cyclic loads. Specifically, the optimal solution of parameters obtained in Step 3 is used to estimate the temporal deformation of roads in soft soil areas during the InSAR image interferometric period, generating the temporal deformation field of roads in soft soil areas.

[0012] Step one includes the following steps:

[0013] Step 1.1: Based on N+1 SAR images and external DEM data, perform image registration, multi-view processing and resampling on the N+1 SAR data. Select interferometric combinations through spatiotemporal baseline thresholding to generate image intensity map, interferogram and coherence coefficient map.

[0014] Step 1.2: Perform orbital error removal, flat phase removal, and terrain phase removal on the interferogram from Step 1.1 to generate a differential interferogram;

[0015] Step 1.3: Perform phase unwrapping on the differential interferogram from Step 1.2 to obtain the unwrapped differential interferogram;

[0016] Step 1.4: Using the coherence coefficient map and image intensity map generated in Step 1.1, set dual thresholds for coherence and amplitude deviation values, extract high coherence points from the unwrapped differential interferogram obtained in Step 1.3, and generate the unwrapped phase difference matrix of the high coherence point targets in the selected interferogram, thus obtaining the InSAR differential interferometric phase.

[0017] Step two specifically involves:

[0018] Step 2.1: Establish the time-series functional relationship between viscous strain in Maxwell's rheological equations and cumulative plastic strain and cumulative deformation in the Li Dingqing cyclic dynamic stress model; the cumulative viscous strain in Maxwell's rheological equations of state is expressed as:

[0019]

[0020] In equation (1), ε rhe For the cumulative viscous strain of highways in soft soil areas, σ c η is the static load of the overlying structure, E is the elastic modulus of the soft soil, η1 is the viscosity coefficient of the soft soil, and t is the loading time of the load, which is taken as the image time.

[0021] In LiDingqing's cyclic dynamic stress model, the cumulative plastic strain under load is expressed as:

[0022]

[0023] In equation (2), ε tra Let be the cumulative plastic strain caused by cyclic loading, a, m, and b be material parameters, β be the ratio of dynamic deviatoric stress to soil static strength, and N be the total strain. per The total number of cycles between the reference time and time t is the loading time of the load, which is the image time.

[0024] The relationship between cumulative strain ε and cumulative deformation d on the highway surface is expressed as:

[0025]

[0026] In equation (3), ε = ε rhe +ε tra h is the depth below the foundation surface where strain occurs;

[0027] Combining equations (1), (2), and (3), the cumulative deformation d of highways in soft soil areas is expressed as viscous deformation d. rhe With cyclic load deformation d tra The summation yields t. A -t B Cumulative deformation Δd(t) of soft soil over a period of time A ,t B ) is represented as:

[0028]

[0029] Step 2.2: Single-point modeling of the InSAR differential interferometric phase, constructing the temporal relationship between viscous strain and cumulative deformation under cyclic loading and the InSAR interferometric phase during the interferometric period; k-th interferogram. The unwrapping phase difference of pixel i is expressed as:

[0030]

[0031] In equation (5), To untangle the phase difference, For deformation phase difference, For the residual phase difference of the terrain, For atmospheric delay phase difference, For noise phase difference, This represents the residual high-pass deformation phase difference;

[0032] Deformation phase difference Further expressed as:

[0033]

[0034] In equation (6), λ is the wavelength and θ is the incident angle of the radar sensor;

[0035] Terrain residual phase difference Further expressed as:

[0036]

[0037] In equation (7), R is the slant range from the radar sensor to the observed target. Let δH be the vertical spatial baseline of the k-th interferogram, and let δH be the elevation correction value.

[0038] Combining equations (4), (5), (6), and (7), the temporal relationship between viscous strain and cumulative deformation caused by cyclic loading during the interference period and the InSAR interferometric phase is obtained, thus yielding the temporal InSAR phase model for highways in soft soil areas considering cyclic loading:

[0039]

[0040] In equation (8), the unknown parameters of the model are β i δH i When the number of equations is ≥3, the optimal solution of the unknown parameters can be estimated, and the low-pass deformation component can be calculated from the parameters; The atmospheric delay phase difference can be separated from the model residual phase through spatiotemporal filtering. Phase difference with noise Obtain the residual high-pass deformation phase difference

[0041] Step three specifically involves:

[0042] Step 3.1: Estimate the initial solution of the InSAR deformation model parameters using a genetic algorithm, including the following steps:

[0043] Step 3.1.1: Construct the fitness function: Taking pixel i as an example, construct the objective function f based on the principle of minimizing the sum of squared residuals of the model on M interferograms. i Represented as:

[0044]

[0045] Step 3.1.2: Generate the initial population: Set the population size, number of iterations, and range of chromosome values ​​to generate random initial individuals, each representing the genotype of a chromosome;

[0046] Step 3.1.3: Calculate fitness: Calculate the target fitness function for each individual and determine whether it meets the optimization criteria; if it does, output the chromosome genotype and fitness of the individual with the best fitness; if it does not, proceed to the next step.

[0047] Step 3.1.4: Selection, Crossover, and Mutation: Select the two individuals with the best fitness among all current individuals as the father and mother; extract chromosomes from both parents according to a certain crossover probability and crossover method to generate offspring individuals; mutate some offspring individuals according to a certain mutation probability.

[0048] Step 3.1.5 Iterative Update: The new generation of population generated by crossover and mutation returns to step 3.1.3 until the optimization criteria are met. The chromosome genotype and optimal fitness of the best individual are output. This genotype is the approximate optimal solution and is used as the initial value for the Levenberg-Marquardt method for secondary optimization.

[0049] Step 3.2: Using the initial values ​​obtained by the genetic algorithm in step 3.1.5 as initial values, solve for the unknown parameters of the model using the Levenberg-Marquardt method;

[0050] Step 3.2.1: Construct the target residual function: Taking pixel i as an example, establish the residual phase function for M interferograms according to the model of equation (8):

[0051]

[0052] in, Let be the parameter vector to be optimized. The residual phase corresponding to each interferogram is expressed as:

[0053]

[0054] Step 3.2.2: Calculate the initial value of the function and determine whether the initial residual is less than the threshold: Set the initial damping coefficient α. (0) (α>0), the parameter estimation results of the genetic algorithm are used as the initial parameter values ​​x for the Levenberg-Marquardt method. (0)Substitute into equation (10) to calculate the initial value r(x) of the residual function. (0) If ||r(x) (0) If ||2≤tol, where tol is the residual threshold, then the output x is... opti =x (0) r opti (x)=r(x (0) If the result is the optimal one, proceed to the next step; otherwise, continue to the next step.

[0055] Step 3.2.3, Calculate the parameter increment: Assume the current parameter value is x = x (n) The contemporary damping coefficient is α = α (n) Calculate the function value r(x) = r(x) according to equation (10). (n) The Jacobian matrix J of equation (11), i.e., the first-order partial derivatives of the model with respect to the unknown parameters, is expressed as:

[0056]

[0057] The formula for calculating the parameter increment is as follows:

[0058] Δx=-(J T J+αI) -1 J T r(x) (13);

[0059] Where: I is the identity matrix; then the next generation parameter value is expressed as:

[0060] x (n+1) =x (n) +Δx (14);

[0061] Step 3.2.4: Adjust the damping coefficient and determine if the new residual is less than the threshold: If the new residual is less than the previous generation residual, i.e., ||r(x) (n+1) )||2<||r(x (n) If ||2, then the damping coefficient is adjusted to α = α (n) / q, where q is the step size, output x = x (n+1) r(x) = r(x) (n+1) ), J = J(x (n+1) Then proceed to the next step; otherwise, adjust the damping coefficient to α = α (n) ·q, and return to step 3.2.3 to recalculate the parameter increment;

[0062] Step 3.2.5, Iteration Termination Condition Judgment: If ||r(x)||2≤tol, then terminate the iteration and output x. opti =x, r opti If r(x) = r(x) is the optimal solution for the parameter, then return to step 3.2.3 to recalculate the parameter increment.

[0063] Step four specifically involves:

[0064] Step 4.1: Utilize the optimal solution set x of all unknown parameters for highly coherent points obtained in Step 3. opti =[η1,β,δH], calculate the cumulative deformation at any image time t according to equation (15) (i.e., parameter back-substitution model), and obtain the low-pass deformation time series D generated by the model. low :

[0065]

[0066] D low =[D low (t0),D low (t1),…D low (t N (16)

[0067] Step 4.2: For the model residual phase obtained in Step 3

[0068] r opti (x)=[r 1 (x),r 2 (x),…,r M (x)], the residual phase time series is obtained by applying singular value decomposition; based on the characteristics of atmospheric delay phase and noise phase in the spatiotemporal domain, the residual phase time series is subjected to high-pass filtering in the time dimension and low-pass filtering in the spatial dimension to extract the residual high-pass deformation time series D in the residual phase. high The low-pass deformation time series D obtained in step 4.1 low The complete temporal deformation D:

[0069] D = D low +D high (17);

[0070] Step 4.3: Convert the temporal deformation D generated in Step 4.2 from line-of-sight deformation to vertical deformation and perform geocoding to generate the temporal deformation field of highways in soft soil areas.

[0071] The application of the technical solution of the present invention has the following beneficial effects:

[0072] This invention introduces the LiDingqing cyclic load cumulative plastic strain model into time-series InSAR deformation modeling for highways in soft soil areas, overcoming the deficiency of traditional highway InSAR deformation models that neglect the additional deformation caused by cyclic vehicle dynamic loads. Furthermore, a serial nonlinear parameter estimation algorithm combining a genetic algorithm (GA) and the Levenberg-Marquardt method (LM) is proposed for the new model, overcoming the time-consuming and inaccurate limitations of traditional genetic algorithms. This invention can improve the accuracy of long-term post-construction deformation monitoring of highways in soft soil areas under vehicle loads using InSAR technology, and can also provide a reference for the analysis, interpretation, prediction, and early warning of highway deformation under vehicle load influence.

[0073] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0074] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0075] Figure 1 This is a flowchart of a time-series InSAR deformation estimation method for highways in soft soil areas that takes into account cyclic loads, as described in an embodiment of the present invention.

[0076] Figure 2 The following are the distribution diagrams of the simulated model parameters, where: (a) is the distribution diagram of viscosity coefficient η1; (b) is the distribution diagram of the ratio of dynamic deviatoric stress to soil static strength β; and (c) is the distribution diagram of elevation correction δH.

[0077] Figure 3 The following are schematic diagrams of the simulated time-series deformation field, where (a)-(f) are schematic diagrams of the time-series deformation field on day 0, day 66, day 275, day 517, day 605, and day 715, respectively.

[0078] Figure 4 The figures are comparisons between the parameter estimates and the simulated actual values ​​based on the method of the present invention, wherein (a) is a comparison between the estimated value of the viscosity coefficient η1 and the simulated actual value; (b) is a comparison between the estimated value of the ratio of dynamic deviatoric stress to soil static strength β and the simulated actual value; and (c) is a comparison between the estimated value of the elevation correction δH and the simulated actual value. Detailed Implementation

[0079] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, the present invention can be implemented in many different ways as defined and covered by the claims.

[0080] Example

[0081] See Figure 1 This embodiment provides a time-series InSAR deformation estimation method for highways in soft soil areas that takes into account cyclic loading, including the following steps:

[0082] Step 1, InSAR differential interferometric phase acquisition, specifically: generating time-series InSAR differential interferograms based on high coherence points; using time-series InSAR technology to obtain unwrapped differential interferograms of soft soil regions, and using a double threshold method to filter high coherence points, generating the unwrapped phase difference matrix of the high coherence point targets in the filtered interferograms, thus obtaining the InSAR differential interferometric phase;

[0083] Step 2: Based on the InSAR differential interferometric phase obtained in Step 1, construct a time-series InSAR model of highways in soft soil areas that takes into account cyclic loads (i.e., the time-series InSAR modeling step of highways in soft soil areas that takes into account cyclic loads).

[0084] Step 3: Estimating the deformation parameters of highways in soft soil areas considering cyclic loads. Specifically, the GALM algorithm is used to solve the parameters. First, the genetic algorithm is used to search for the approximate optimal solution of the parameters of the time series function model obtained in Step 2, and this solution is used as the initial value of the Levenberg-Marquardt method for iterative optimization to obtain the optimal solution of the parameters.

[0085] Step 4: Estimation of temporal deformation of roads in soft soil areas based on InSAR deformation model considering cyclic load (i.e., the step of estimating temporal deformation of roads in soft soil areas considering cyclic load). Specifically, the optimal solution of parameters obtained in Step 3 is used to estimate the temporal deformation of roads in soft soil areas during the InSAR image interferometric period, and the temporal deformation field of roads in soft soil areas is generated.

[0086] Step one includes the following steps:

[0087] Step 1.1: Based on N+1 SAR images and external DEM data, perform image registration, multi-view processing and resampling on the N+1 SAR data. Select interferometric combinations through spatiotemporal baseline thresholding to generate image intensity map, interferogram and coherence coefficient map.

[0088] Step 1.2: Perform orbital error removal, flat phase removal, and terrain phase removal on the interferogram from Step 1.1 to generate a differential interferogram;

[0089] Step 1.3: Perform phase unwrapping on the differential interferogram from Step 1.2 to obtain the unwrapped differential interferogram;

[0090] Step 1.4: Using the coherence coefficient map and image intensity map generated in Step 1.1, set dual thresholds for coherence and amplitude deviation values, extract high coherence points from the unwrapped differential interferogram obtained in Step 1.3, and generate the unwrapped phase difference matrix of the high coherence point targets in the selected interferogram, thus obtaining the InSAR differential interferometric phase.

[0091] Step two specifically involves:

[0092] Step 2.1: Establish the time-series functional relationship between viscous strain in Maxwell's rheological equations and cumulative plastic strain and cumulative deformation in the Li Dingqing cyclic dynamic stress model; the cumulative viscous strain in Maxwell's rheological equations of state is expressed as:

[0093]

[0094] In equation (1), ε rhe For the cumulative viscous strain of highways in soft soil areas, σ c η is the static load of the overlying structure, E is the elastic modulus of the soft soil, η1 is the viscosity coefficient of the soft soil, and t is the loading time of the load, which is taken as the image time.

[0095] In LiDingqing's cyclic dynamic stress model, the cumulative plastic strain under load is expressed as:

[0096]

[0097] In equation (2), ε tra Let be the cumulative plastic strain caused by cyclic loading, a, m, and b be material parameters, β be the ratio of dynamic deviatoric stress to soil static strength, and N be the total strain. per The total number of cycles between the reference time and time t is the loading time of the load, which is the image time.

[0098] The relationship between cumulative strain ε and cumulative deformation d on the highway surface is expressed as:

[0099]

[0100] In equation (3), ε = ε rhe +ε tra h is the depth below the foundation surface where strain occurs;

[0101] Combining equations (1), (2), and (3), the cumulative deformation d of highways in soft soil areas is expressed as viscous deformation d. rhe With cyclic load deformation d tra The summation yields t. A -t B Cumulative deformation Δd(t) of soft soil over a period of time A ,t B ) is represented as:

[0102]

[0103] Step 2.2: Single-point modeling of the InSAR differential interferometric phase, constructing the temporal relationship between viscous strain and cumulative deformation under cyclic loading and the InSAR interferometric phase during the interferometric period; k-th interferogram. The unwrapping phase difference of pixel i is expressed as:

[0104]

[0105] In equation (5), To untangle the phase difference, For deformation phase difference, For the residual phase difference of the terrain, For atmospheric delay phase difference, For noise phase difference, This represents the residual high-pass deformation phase difference;

[0106] Deformation phase difference Further expressed as:

[0107]

[0108] In equation (6), λ is the wavelength and θ is the incident angle of the radar sensor;

[0109] Terrain residual phase difference Further expressed as:

[0110]

[0111] In equation (7), R is the slant range from the radar sensor to the observed target. Let δH be the vertical spatial baseline of the k-th interferogram, and let δH be the elevation correction value.

[0112] Combining equations (4), (5), (6), and (7), the temporal relationship between viscous strain and cumulative deformation caused by cyclic loading during the interference period and the InSAR interferometric phase is obtained, thus yielding the temporal InSAR phase model for highways in soft soil areas considering cyclic loading:

[0113]

[0114] In equation (8), the unknown parameters of the model are β i δH i When the number of equations is ≥3, the optimal solution of the unknown parameters can be estimated, and the low-pass deformation component can be calculated from the parameters; The atmospheric delay phase difference can be separated from the model residual phase through spatiotemporal filtering. Phase difference with noise Obtain the residual high-pass deformation phase difference

[0115] Step three specifically involves:

[0116] Step 3.1: Estimate the initial solution of the InSAR deformation model parameters using a genetic algorithm, including the following steps:

[0117] Step 3.1.1: Construct the fitness function: Taking pixel i as an example, construct the objective function f based on the principle of minimizing the sum of squared residuals of the model on M interferograms. i Represented as:

[0118]

[0119] Step 3.1.2: Generate the initial population: Set the population size, number of iterations, and range of chromosome values ​​to generate random initial individuals, each representing the genotype of a chromosome;

[0120] Step 3.1.3: Calculate fitness: Calculate the target fitness function for each individual and determine whether it meets the optimization criteria; if it does, output the chromosome genotype and fitness of the individual with the best fitness; if it does not, proceed to the next step.

[0121] Step 3.1.4: Selection, Crossover, and Mutation: Select the two individuals with the best fitness among all current individuals as the father and mother; extract chromosomes from both parents according to a certain crossover probability and crossover method to generate offspring individuals; mutate some offspring individuals according to a certain mutation probability.

[0122] Step 3.1.5 Iterative Update: The new generation of population generated by crossover and mutation returns to step 3.1.3 until the optimization criteria are met. The chromosome genotype and optimal fitness of the best individual are output. This genotype is the approximate optimal solution and is used as the initial value for the Levenberg-Marquardt method for secondary optimization.

[0123] Step 3.2: Using the initial values ​​obtained by the genetic algorithm in step 3.1.5 as initial values, solve for the unknown parameters of the model using the Levenberg-Marquardt method;

[0124] Step 3.2.1: Construct the target residual function: Taking pixel i as an example, establish the residual phase function for M interferograms according to the model of equation (8):

[0125]

[0126] in, Let be the parameter vector to be optimized. The residual phase corresponding to each interferogram is expressed as:

[0127]

[0128] Step 3.2.2: Calculate the initial value of the function and determine whether the initial residual is less than the threshold: Set the initial damping coefficient α. (0) (α>0), the parameter estimation results of the genetic algorithm are used as the initial parameter values ​​x for the Levenberg-Marquardt method. (0) Substitute into equation (10) to calculate the initial value r(x) of the residual function. (0) If ||r(x) (0) If ||2≤tol, where tol is the residual threshold, then the output x is... opti =x(0), r opti (x)=r(x (0) If the result is the optimal one, proceed to the next step; otherwise, continue to the next step.

[0129] Step 3.2.3, Calculate the parameter increment: Assume the current parameter value is x = x (n) The contemporary damping coefficient is α = α (n) Calculate the function value r(x) = r(x) according to equation (10). (n) The Jacobian matrix J of equation (11), i.e., the first-order partial derivatives of the model with respect to the unknown parameters, is expressed as:

[0130]

[0131] The formula for calculating the parameter increment is as follows:

[0132] Δx=-(J T J+αI) -1 J T r(x) (13);

[0133] Where: I is the identity matrix; then the next generation parameter value is expressed as:

[0134] x (n+1) =x (n) +Δx (14);

[0135] Step 3.2.4: Adjust the damping coefficient and determine if the new residual is less than the threshold: If the new residual is less than the previous generation residual, i.e., ||r(x) (n+1) )||2<||r(x (n) If ||2, then the damping coefficient is adjusted to α = α (n) / q, where q is the step size, output x = x (n+1) r(x) = r(x) (n+1) ), J = J(x (n+1) Then proceed to the next step; otherwise, adjust the damping coefficient to α = α (n) ·q, and return to step 3.2.3 to recalculate the parameter increment;

[0136] Step 3.2.5, Iteration Termination Condition Judgment: If ||r(x)||2≤tol, then terminate the iteration and output x. opti =x, r opti If r(x) = r(x) is the optimal solution for the parameter, then return to step 3.2.3 to recalculate the parameter increment.

[0137] Step four specifically involves:

[0138] Step 4.1: Utilize the optimal solution set x of all unknown parameters for highly coherent points obtained in Step 3. opti =[η1,β,δH], calculate the cumulative deformation at any image time t according to equation (15) (i.e., parameter back-substitution model), and obtain the low-pass deformation time series D generated by the model. low As shown in equation (16):

[0139]

[0140] D low =[D low (t0),D low (t1),…D low (t N (16)

[0141] Step 4.2: For the model residual phase obtained in Step 3

[0142] r opti (x)=[r 1 (x),r 2 (x),…,r M (x)], the residual phase time series is obtained by applying singular value decomposition; based on the characteristics of atmospheric delay phase and noise phase in the spatiotemporal domain, the residual phase time series is subjected to high-pass filtering in the time dimension and low-pass filtering in the spatial dimension to extract the residual high-pass deformation time series D in the residual phase. high The low-pass deformation time series D obtained in step 4.1 low The complete temporal deformation D:

[0143] D = D low +D high (17);

[0144] Step 4.3: Convert the temporal deformation D generated in Step 4.2 from line-of-sight deformation to vertical deformation and perform geocoding to generate the temporal deformation field of highways in soft soil areas.

[0145] The simulation experiment was conducted using the time-series InSAR deformation estimation method for highways in soft soil areas that takes into account cyclic loading, as detailed below:

[0146] Step 1: Simulate InSAR differential interferometric phase. Set a simulated survey area of ​​100×100 pixels. Based on the soft soil characteristics and average annual traffic volume of the test area, set the range and spatial distribution of simulation parameters, such as... Figure 2 (a)-(c). The viscosity coefficient η1 is set to a range of (0, 3 × 10⁻⁶). 8 The dynamic deviatoric stress to soil static strength ratio β ranges from [0.01, 0.1] MPa.s, the elevation correction δH is [-20, 20] m, the strain depth below the foundation surface is within 5 m, and other known parameter settings are shown in Table 1. The SAR sensor parameters were set using real radar parameters from 19 TerraSAR-X satellite Stripap mode ascending-orbit SAR images covering a soft soil area. A time-series deformation field was simulated using the model parameters and the designed known parameters. (See [reference needed]). Figure 3 , Figure 3 (a)-(f) show the temporal deformation fields for day 0, day 66, day 275, day 517, day 605, and day 715, respectively.

[0147] Step 2: Construct a time series function model of the simulated interferometric phase and the viscous and plastic strain of highways in soft soil areas. Twenty-eight simulated unwrapped differential interferograms are formed by arbitrarily combining 19 images. The unwrapped phase differences of 100 highly coherent point targets are randomly extracted from the simulated interferograms. Based on the new model proposed in this invention, a set of target residual equations is established point by point.

[0148] Step 3: Model Parameter Estimation and Accuracy Evaluation. A genetic algorithm is used to search for the approximate optimal solution of the parameters of the time series function model obtained in Step 2. This solution is then used as the initial value for the Levenberg-Marquardt method for iterative optimization to obtain the optimal parameter solution. To evaluate the stability of the algorithm, five levels of random noise (from -0.1, 0.1] rad to [-0.5, 0.5] rad) are added to the unwrapped phase difference, and parameter estimation is performed at different noise levels. See Table 2. The root mean square error (RMSE) of the parameter estimates compared to the simulated true values ​​at each noise level is shown in Table 2. It can be seen that in the absence of noise estimation, the percentage of the RMSE to the maximum parameter value is less than 0.1%. As the noise level increases, the RMSE gradually increases. When the noise level is increased to ±0.5 rad, the percentages of the RMSE to the maximum parameter value for the three parameters are 3.82%, 2.30%, and 1.07%, respectively, all below 5%, indicating that the GA+LM serial parameter estimation algorithm has good stability. Figure 4Figures (a)-(c) show a comparison between the simulated true values ​​of the three unknown parameters and the noise-free and noisy (±0.5 rad) estimates. Even under the highest level of noise interference, the parameter estimates still show good consistency with the simulated true values.

[0149] Step 4: Temporal Deformation Estimation. Based on the parameters obtained in Step 3, the temporal deformation field of highways in soft soil areas is generated.

[0150] Table 1. Design values ​​of known parameters for the simulation experiment.

[0151] numerical values 9.6 1.2 2.4 0.18 400

[0152] Table 2 shows the root mean square error between the parameter estimates and the simulated values.

[0153]

[0154]

[0155] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A time-series InSAR deformation estimation method for highways in soft soil areas considering cyclic loading, characterized in that, Includes the following steps: Step 1, InSAR differential interferometric phase acquisition, specifically: generating time-series InSAR differential interferograms based on high coherence points; using time-series InSAR technology to obtain unwrapped differential interferograms of soft soil regions, and using a double threshold method to filter high coherence points, generating the unwrapped phase difference matrix of the high coherence point targets in the filtered interferograms, thus obtaining the InSAR differential interferometric phase; Step 2: Based on the InSAR differential interferometric phase obtained in Step 1, construct a time-series InSAR model for highways in soft soil areas that takes into account cyclic loads. Specifically: Step 2.1: Establish the time-series functional relationship between viscous strain in Maxwell's rheological equations and cumulative plastic strain and cumulative deformation in Li Dingqing's cyclic dynamic stress model; In Maxwell's rheological equation of state, the cumulative viscous strain is expressed as: （1）； In equation (1), For the cumulative viscous strain of highways in soft soil areas, For the static load of the overlying structure on the foundation, The elastic modulus of soft soil. Let be the viscosity coefficient of soft soil. The value represents the loading time of the load, and is taken as the image time. In Li Dingqing's cyclic dynamic stress model, the cumulative plastic strain under load is expressed as: （2）； In equation (2), The cumulative plastic strain caused by cyclic loading For material parameters, This is the ratio of dynamic deviatoric stress to soil static strength. For reference time and Total number of loops over time The value represents the loading time of the load, and is taken as the image time. Accumulated strain on highway surface With cumulative deformation The relationship is represented as: （3）； In equation (3), = + , The depth at which strain occurs below the surface of the foundation; Combining equations (1), (2), and (3), cumulative deformation of highways in soft soil areas Represented as viscous deformation With cyclic load deformation The summation yields - Cumulative deformation of soft soil over a period of time Represented as: （4）； Step 2.2: Perform single-point modeling of the InSAR differential interferometric phase, and construct the temporal relationship between viscous strain and cumulative deformation under cyclic loading and the InSAR interferometric phase during the interferometric period; Aspect Interference Diagram ( - ) in pixels The untangling phase difference is expressed as: （5）； In equation (5), To untangle the phase difference, For deformation phase difference, For the residual phase difference of the terrain, For atmospheric delay phase difference, For noise phase difference, This represents the residual high-pass deformation phase difference; Deformation phase difference Further expressed as: （6）； In equation (6), For wavelength, The incident angle of the radar sensor; Terrain residual phase difference Further expressed as: （7）； In equation (7), The slant range from the radar sensor to the observed target. For the first The vertical spatial baseline of the amplitude interferogram. This is the elevation correction value; Combining equations (4), (5), (6), and (7), we obtain the temporal relationship between viscous strain and cumulative deformation caused by cyclic loading during the interference period and the InSAR interferometric phase, thus obtaining the temporal InSAR phase model for highways in soft soil areas considering cyclic loading as follows: （8）； In equation (8), the unknown parameters of the model are , , When the number of equations is ≥3, the optimal solution of the unknown parameters can be estimated, and the low-pass deformation component can be calculated from the parameters; The atmospheric delay phase difference can be separated from the model residual phase through spatiotemporal filtering. Phase difference with noise The residual high-pass deformation phase difference was obtained. ; Step 3: Parameter estimation of InSAR road deformation model in soft soil area considering cyclic load. Specifically, the GALM algorithm is used to solve the parameters. First, the genetic algorithm is used to search for the approximate optimal solution of the parameters of the time series InSAR model of road in soft soil area considering cyclic load obtained in Step 2. This solution is then used as the initial value of the Levenberg-Marquardt method for iterative optimization to obtain the optimal solution of the parameters. Step 4: Estimating the temporal deformation of roads in soft soil areas based on the InSAR road deformation model considering cyclic loads. Specifically, the optimal solution of parameters obtained in Step 3 is used to estimate the temporal deformation of roads in soft soil areas during the InSAR image interferometric period, generating the temporal deformation field of roads in soft soil areas.

2. The method for estimating time-series InSAR deformation of highways in soft soil areas considering cyclic loads as described in claim 1, characterized in that, Step one includes the following steps: Step 1.1: Based on N+1 SAR images and external DEM data, perform image registration, multi-view processing and resampling on the N+1 SAR data. Select interferometric combinations through spatiotemporal baseline thresholding to generate image intensity map, interferogram and coherence coefficient map. Step 1.2: Perform orbital error removal, flat phase removal, and terrain phase removal on the interferogram from Step 1.1 to generate a differential interferogram; Step 1.3: Perform phase unwrapping on the differential interferogram from Step 1.2 to obtain the unwrapped differential interferogram; Step 1.4: Using the coherence coefficient map and image intensity map generated in Step 1.1, set dual thresholds for coherence and amplitude deviation values, extract high coherence points from the unwrapped differential interferogram obtained in Step 1.3, and generate the unwrapped phase difference matrix of the high coherence point targets in the selected interferogram, thus obtaining the InSAR differential interferometric phase.

3. The method for estimating time-series InSAR deformation of highways in soft soil areas considering cyclic loads as described in claim 1, characterized in that, Step three specifically involves: Step 3.1: Estimate the initial solution of the InSAR deformation model parameters using a genetic algorithm, including the following steps: Step 3.1.1: Construct the fitness function: using pixels For example, based on its The objective function is constructed based on the principle of minimizing the sum of squared residuals of the model on each interferogram. Represented as: （9）； Step 3.1.2: Generate the initial population: Set the population size, number of iterations, and range of chromosome values ​​to generate random initial individuals, each representing the genotype of a chromosome; Step 3.1.3: Calculate fitness: Calculate the target fitness function for each individual and determine whether it meets the optimization criteria; if it does, output the chromosome genotype and fitness of the individual with the best fitness; if it does not, proceed to the next step. Step 3.1.4: Selection, Crossover, and Mutation: Select the two individuals with the best fitness among all current individuals as the father and mother; extract chromosomes from both parents according to a certain crossover probability and crossover method to generate offspring individuals; mutate some offspring individuals according to a certain mutation probability. Step 3.1.5 Iterative Update: The new generation of population generated by crossover and mutation returns to step 3.1.3 until the optimization criteria are met. The chromosome genotype and optimal fitness of the best individual are output. This genotype is the approximate optimal solution and is used as the initial value for the Levenberg-Marquardt method for secondary optimization. Step 3.2: Using the initial values ​​obtained by the genetic algorithm in step 3.1.5 as initial values, solve for the unknown parameters of the model using the Levenberg-Marquardt method; Step 3.2.1: Construct the target residual function: using pixels For example, based on the model of equation (8) Establish the residual phase function using interferograms: （10）； in, Let be the parameter vector to be optimized. The residual phase corresponding to each interferogram is expressed as: （11）； Step 3.2.2: Calculate the initial value of the function and determine whether the initial residual is less than the threshold: Set the initial damping coefficient. The results of the genetic algorithm parameter estimation are used as the initial values ​​of the parameters for the Levenberg-Marquardt method. Substitute into equation (10) to calculate the initial value of the residual function. ,like ,in, If the residual threshold is used, then the output will be... , This is the optimal result; otherwise, proceed to the next step. Step 3.2.3, Calculate the parameter increment: Assume the current parameter value is The contemporary damping coefficient is Calculate the function value according to equation (10). Jacobian matrix of equation (11) That is, the first-order partial derivatives of the model with respect to the unknown parameters are expressed as: （12）； The formula for calculating the parameter increment is as follows: （13）； in: If the identity matrix is ​​denoted by , then the next generation parameter values ​​are expressed as: （14）； Step 3.2.4: Adjust the damping coefficient and determine if the new residual is less than the threshold: If the new residual is less than the previous generation residual, i.e. Then the damping coefficient is adjusted to be ,in, The step size is the output. , , Proceed to the next step; otherwise, adjust the damping coefficient to... Then return to step 3.2.3 to recalculate the parameter increment; Step 3.2.5, Iteration Termination Condition Judgment: If Then terminate the iteration and output. , If the parameter is the optimal solution, then return to step 3.2.3 to recalculate the parameter increment.

4. The method for estimating time-series InSAR deformation of highways in soft soil areas considering cyclic loads as described in claim 3, characterized in that, Step four specifically involves: Step 4.1: Utilize the optimal solution set of all unknown parameters for highly coherent points obtained in Step 3. Calculate any image time according to equation (15) The cumulative deformation is used to obtain the low-pass deformation time series generated by the model. For example, expression (16): （15）； （16）； Step 4.2: For the model residual phase obtained in Step 3 The residual phase time series was obtained by applying singular value decomposition. Based on the spatiotemporal characteristics of atmospheric delay phase and noise phase, the residual phase time series was subjected to high-pass filtering in the time dimension and low-pass filtering in the spatial dimension to extract the residual high-pass deformation time series in the residual phase. Compared with the low-pass deformation time series obtained in step 4.1 Composing a complete time-series deformation : (17); Step 4.3: Apply the timing deformation generated in step 4.2 The deformation field of highways in soft soil areas is generated by converting the line-of-sight deformation into vertical deformation and performing geocoding.

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