A Method and System for Diagnosing the Equivalent Stiffness of Dams Based on InSAR Residual Inversion

Abstract

This application provides a method and system for diagnosing the equivalent stiffness of a dam body based on InSAR residual inversion, relating to the field of synthetic aperture radar interferometry technology. After acquiring multi-source data, the method constructs a physical forward model and generates forward prediction results based on the multi-source data using this model. Then, it solves for the parameter field of the residual inversion based on the forward prediction results to obtain spatial distribution information, and finally generates diagnostic results based on this spatial distribution information. The method constructs a closed-loop processing framework for physical forward modeling and residual inversion. During the residual inversion process, it uses the InSAR observation line-of-sight deformation time series as the target value and the physical forward model as the forward operator. By minimizing the residual between the theoretical line-of-sight displacement and the InSAR observation line-of-sight deformation, it inverts the spatial distribution of the dam body's equivalent elastic modulus and the reservoir bank's equivalent permeability coefficient, transforming InSAR monitoring from deformation response description to structural stiffness diagnosis, thus improving the accuracy of the diagnostic results.

Description

Technical Field

[0001] This application relates to the field of synthetic aperture radar interferometry technology, and in particular to a method and system for diagnosing the equivalent stiffness of dams based on InSAR residual inversion. Background Technology

[0002] Interferometric Synthetic Aperture Radar (InSAR) is a method that uses two or more synthetic aperture radar (SAR) images of the same target area acquired at different times and locations by remote sensing objects such as radar satellites. By analyzing the phase difference of each pixel in the SAR images, an interferogram is generated to monitor the terrain and deformation information of the monitored area.

[0003] For example, time-series InSAR techniques such as Small Baseline Subset (SBAS) and Permanent Scatterer (PS-InSAR) can be applied to the monitoring of deformation of reservoir dams and banks. Time-series InSAR is used to obtain line-of-sight (LOS) deformation rates and cumulative displacement maps of the dam body and banks. Abnormal deformation zones can be identified through visual interpretation or threshold setting. Alternatively, the displacement field of the dam body under specific water level conditions can be calculated using finite element method (FEM) numerical simulation, and qualitative comparisons can be made with InSAR observations for verification.

[0004] While the aforementioned time-series InSAR technology facilitates the conversion from deformation observation to structural health diagnosis, the water level-deformation analysis process can be statistically described or extracted at the response parameter level, using methods such as global cross-correlation analysis, cross wavelet transform, or linear regression to output water level-deformation correlation coefficients or regression slopes. However, these analytical methods lack a physical mapping mechanism from deformation response to structural mechanical parameters, failing to decompose the observed deformation into components with clear physical meaning. Furthermore, the output of these analytical methods essentially represents response parameters at the deformation level, rather than the structural mechanical parameters themselves. Changes in response parameters may be the result of multiple coupled factors such as water level fluctuations and structural stiffness degradation, making them difficult to directly use for quantitative diagnosis of structural health status and reducing the accuracy of diagnostic results. Summary of the Invention

[0005] In view of this, embodiments of this application provide a method and system for diagnosing the equivalent stiffness of dam bodies based on InSAR residual inversion, in order to solve the problem of low accuracy of diagnostic results of time-series InSAR methods.

[0006] According to a first aspect of this application, a method for diagnosing the equivalent stiffness of a dam body based on InSAR residual inversion is provided, the method comprising: Acquire multi-source data, including InSAR observation line-of-sight deformation time series, water level process line, dam body geometric parameters, and digital elevation model of the target dam area; A physical forward model is constructed, and forward prediction results are generated based on the multi-source data using the physical forward model; the physical forward model is used to perform forward prediction on multiple physical processes with the water level process line, the dam body geometric parameters and the digital elevation model as input; the forward prediction results include the theoretical line-of-sight displacement of each pixel; Based on the theoretical line-of-sight displacement, the parameter field is solved by residual inversion to obtain spatial distribution information. The residual inversion is used to take the InSAR observation line-of-sight deformation time series as the target value and the physical forward model as the forward operator. By minimizing the residual between the theoretical line-of-sight displacement and the InSAR observation line-of-sight deformation, the spatial distribution of the dam body's equivalent elastic modulus and the reservoir bank's equivalent permeability coefficient is inverted pixel by pixel. Diagnostic results are generated based on the spatial distribution information.

[0007] In some embodiments, acquiring multi-source data includes: Acquire InSAR observation data for the target dam area, wherein the InSAR observation data includes a single-track time-series SAR image sequence covering the target dam area; the time span of the InSAR observation data covers at least one complete water level regulation cycle of the reservoir corresponding to the target dam area. Select the master image and slave image from the InSAR observation data; By registration and resampling, the image is aligned to the slant range azimuth coordinate system of the main image; The interference pair is determined based on the registered and resampled master image and slave image; Based on the unwrapped phase of the interferometric pair, the minimum norm solution is obtained by singular value decomposition, and the cumulative line-of-sight deformation value at each SAR imaging time is obtained by integration. The InSAR observation line-of-sight deformation time series is generated based on the accumulated line-of-sight deformation value.

[0008] In some embodiments, acquiring multi-source data includes: Acquire reservoir water level data, optical remote sensing images, and digital elevation models for the target dam area. The reservoir water level data is a scheduling record that is consistent with the time range covered by the SAR observation data. Align the reservoir water level data to the imaging time of the SAR observation data; The water level process line is generated based on the aligned reservoir water level data; The crest length and outline of the target dam area are measured by visually interpreting the optical remote sensing images. The dam height information is extracted from the digital elevation model to obtain the geometric parameters of the dam body.

[0009] In some embodiments, the physical forward model includes a crustal elastic load forward model layer, a dam static response forward model layer, and a reservoir bank unsaturated seepage forward model layer; the physical forward model generates the theoretical line-of-sight displacement for each pixel based on the multi-source data, including: A three-dimensional displacement field is obtained, which includes a first displacement field output by the crustal elastic load forward modeling layer, a second displacement field output by the dam body static response forward modeling layer, and a third displacement field output by the reservoir bank unsaturated seepage forward modeling layer. By superimposing the first displacement field, the second displacement field, and the third displacement field, a total three-dimensional displacement vector is obtained; The total three-dimensional displacement vector is projected onto the line of sight of the InSAR satellite to obtain the theoretical line-of-sight displacement.

[0010] In some embodiments, the crustal elastic load forward modeling layer is used to calculate the crustal surface elastic displacement field caused by reservoir water load changes based on elastic load theory; obtaining the three-dimensional displacement field includes: Based on the dam's geometric parameters, the reservoir's water surface is discretized into multiple grid units; For each of the aforementioned grid cells, the crustal surface displacement response caused by a unit point load is calculated using the Green's function; The first displacement field is obtained by superimposing the crustal surface displacement responses of all the grid cells. The first displacement field is used to characterize the crustal elastic displacement field of the entire reservoir area.

[0011] In some embodiments, the dam static response forward modeling layer is used to calculate the static flexural displacement of the dam body under water pressure based on structural mechanics; and to obtain a three-dimensional displacement field, including: Extract the spatial location of the dam surface from the digital elevation model and the dam geometric parameters; Determine the height coordinates of each pixel on the dam surface based on the spatial location; The dam type category is extracted from the dam body geometric parameters, and a closed analytical model is called according to the dam type category. When the dam type category is a gravity dam, the closed analytical model adopts a cantilever beam model; when the dam type category is an arch dam, the closed analytical model adopts a thin shell analytical model or a simplified model of the arch beam load distribution method. Based on the closed analytical model, the displacement component along the river is calculated by combining the height coordinates, the current water level, and the equivalent elastic modulus of the dam body. Based on the Poisson effect, the lateral and vertical displacement components are estimated from the downstream displacement components. The downstream displacement component, the lateral displacement component, and the vertical displacement component are combined into a three-dimensional displacement vector to obtain the second displacement field.

[0012] In some embodiments, the unsaturated seepage forward modeling layer on the reservoir bank is used to calculate the shallow deformation of the reservoir bank caused by the rise and fall of the reservoir water level based on the unsaturated seepage theory; and to obtain the three-dimensional displacement field, including: The reservoir bank parameters are calculated based on the dam body geometric parameters and the digital elevation model. The reservoir bank parameters include the distance and elevation of each pixel in the reservoir bank area to the reservoir bank. An unsaturated seepage model is established based on the reservoir bank parameters and the water level process line. The unsaturated seepage model is used to describe the relationship between the groundwater level and the reservoir water level. According to the unsaturated seepage model, the change in saturated zone thickness caused by water level change is calculated using soil-water characteristic curves and permeability coefficient functions. The shallow displacement is calculated based on the effective stress principle and the change in the thickness of the saturated zone, and the third displacement field is obtained.

[0013] In some embodiments, the parameter field solution is obtained by performing residual inversion based on the theoretical line-of-sight displacement to obtain spatial distribution information, including: Define an objective function, which is the sum of squared residuals between the InSAR observation line-of-sight deformation and the theoretical line-of-sight displacement over the entire monitoring period, plus a spatial smoothing regularization term; The gradient of the objective function with respect to the equivalent elastic modulus of the dam body and the equivalent permeability coefficient of the reservoir bank is calculated analytically using the chain rule. Iterative optimization and inversion are performed based on the gradient to output the spatial distribution information; the spatial distribution information includes a spatial distribution map of the dam body's equivalent elastic modulus and a spatial distribution map of the reservoir bank's equivalent permeability coefficient.

[0014] In some embodiments, generating a diagnostic result based on the spatial distribution information includes: Obtain the InSAR raster information corresponding to the deformation time sequence of the InSAR observation line; An output format is defined based on the InSAR raster information, and the output format includes the same spatial range and resolution as the InSAR raster information. The spatial distribution information is converted into an output product according to the output format, and the output product includes the spatial distribution information and the transfer gain drift rate. A hierarchical early warning mechanism is constructed based on the transfer gain drift rate, and the diagnostic results are generated according to the hierarchical early warning mechanism.

[0015] According to a second aspect of this application, a dam equivalent stiffness diagnosis system based on InSAR residual inversion is provided, the system comprising: The data acquisition module is used to acquire multi-source data, including the InSAR observation line deformation time series, water level process line, dam body geometric parameters, and digital elevation model of the target dam area; The physical forward modeling module is used to construct a physical forward modeling model and generate forward prediction results based on the multi-source data using the physical forward modeling model; the physical forward modeling model is used to perform forward prediction on multiple physical processes using the water level process line, the dam body geometric parameters, and the digital elevation model as inputs; the forward prediction results include the theoretical line-of-sight displacement of each pixel; The residual inversion module is used to solve the parameter field based on the theoretical line-of-sight displacement to obtain spatial distribution information. The residual inversion is used to take the InSAR observation line-of-sight deformation time series as the target value and the physical forward model as the forward operator, and to invert the spatial distribution of the dam body equivalent elastic modulus and the reservoir bank equivalent permeability coefficient pixel by pixel by minimizing the residual between the theoretical line-of-sight displacement and the InSAR observation line-of-sight deformation. The result output module is used to generate diagnostic results based on the spatial distribution information.

[0016] Using the above technical solutions, embodiments of this application provide a method and system for diagnosing the equivalent stiffness of a dam body based on InSAR residual inversion. After acquiring multi-source data, the method can construct a physical forward model and generate forward prediction results based on the multi-source data using the physical forward model. Then, based on the theoretical line-of-sight displacement in the forward prediction results, the parameter field of the residual inversion is solved to obtain spatial distribution information, and then a diagnostic result is generated based on the spatial distribution information. The method described above can construct a closed-loop processing framework of physical forward modeling and residual inversion, encapsulating the classical mechanical model into multiple forward modeling layers, which are then superimposed and projected onto the InSAR line of sight to form a differentiable forward modeling operator. This decomposes the LOS deformation observed by InSAR into multiple components with clear physical meaning. In the residual inversion process, the deformation time series along the InSAR line of sight is used as the target value, and the physical forward model is used as the forward operator. By minimizing the residual between the theoretical line of sight displacement and the InSAR line of sight deformation, the spatial distribution of the dam's equivalent elastic modulus and the reservoir bank's equivalent permeability coefficient is inverted pixel by pixel. This transforms InSAR monitoring from deformation response description to structural stiffness diagnosis, improving the accuracy of the diagnostic results.

[0017] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 Flowchart of the dam equivalent stiffness diagnosis method based on InSAR residual inversion provided in the embodiments of this application; Figure 2 This is an overall flowchart of the dam equivalent stiffness diagnosis provided in the embodiments of this application; Figure 3 A flowchart of data acquisition and preprocessing provided for embodiments of this application; Figure 4 A flowchart of a three-layer coupled physical forward model provided in an embodiment of this application; Figure 5 A flowchart of the parameter field solution based on residual inversion provided for embodiments of this application; Figure 6 A flowchart for generating diagnostic results based on spatial distribution information is provided in this embodiment of the application. Figure 7 A flowchart illustrating the hierarchical early warning logic provided in this application embodiment; Figure 8 The diagram shows the structure of the dam equivalent stiffness diagnostic system based on InSAR residual inversion provided in this application embodiment. Detailed Implementation

[0019] The present application will be described in detail below with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in the embodiments of the present application can be combined with each other.

[0020] In the embodiments of this application, Synthetic Aperture Radar (SAR) is an active microwave remote sensing imaging device that transmits electromagnetic waves to the monitoring area and receives the echoes reflected from the ground. Then, through coherent processing, it focuses the weak echo energy dispersed in space and time to obtain high-resolution remote sensing images.

[0021] Interferometric Synthetic Aperture Radar (InSAR) is a method that uses two or more synthetic aperture radar (SAR) images of the same target area acquired at different times and locations by remote sensing objects such as radar satellites. By analyzing the phase difference of each pixel in the SAR images, an interferogram is generated to monitor the terrain and deformation information of the monitored area.

[0022] In some embodiments, synthetic aperture radar interferometry may include temporal InSAR, such as Small Baseline Subset (SBAS) and Permanent Scatterer (PS-InSAR). Temporal InSAR technology can be applied to the monitoring of deformation of reservoir dams and reservoir banks. Specifically, temporal InSAR is used to obtain the line-of-sight (LOS) deformation rate and cumulative displacement map of the dam body and reservoir banks. Abnormal deformation areas can be identified by visual interpretation or threshold setting, or the displacement field of the dam body under specific water level conditions can be calculated using finite element method (FEM) numerical simulation and qualitatively compared with InSAR observations.

[0023] While the aforementioned time-series InSAR technology facilitates the transition from deformation observation to structural health diagnosis, the water level-deformation analysis process remains at the level of statistical description or response parameter extraction. Methods such as global cross-correlation analysis, cross-wavelet transform, or linear regression are used to output water level-deformation correlation coefficients or regression slopes. However, these analytical methods lack a physical mapping mechanism from deformation response to structural mechanical parameters, failing to decompose the observed deformation into components with clear physical meaning. In other words, they cannot diagnose which deformations originate from the elastic loading effect of reservoir water on the crust, which from the structural deflection of the dam body under water pressure, and which from seepage deformation caused by changes in pore water pressure in the reservoir bank soil and rock.

[0024] Furthermore, the output of the above analysis method is essentially the response parameters at the deformation level, rather than the mechanical parameters of the structure itself. The changes in the response parameters may be the result of the coupling of multiple factors such as water level fluctuations and structural stiffness degradation, making it difficult to directly use for quantitative diagnosis of structural health status and reducing the accuracy of the diagnostic results.

[0025] In some embodiments, dam diagnosis can also be performed by inverting dam parameters. This involves setting up a small number of discrete points on the dam, such as Global Navigation Satellite System (GNSS) measurement points or corner reflectors, extracting the InSAR deformation time series of these discrete points, and then inverting the global material parameters of the entire dam by matching the forward model calculation of the finite element model with the observations of these discrete points.

[0026] However, the above-mentioned dam parameter inversion process relies on discrete point constraints, making it difficult to obtain a spatially distributed parameter field. Furthermore, the spatial density of discrete points is limited, failing to reflect the stiffness of different parts of the dam, such as the abutment, heel, toe, and dam sections at different elevations. Spatial variations in material properties caused by differences in concrete pouring quality, aging, or local damage reduce the accuracy of the diagnostic results.

[0027] To address the low accuracy of diagnostic results from time-series InSAR methods, this application provides a method for diagnosing the equivalent stiffness of dams based on InSAR residual inversion in some embodiments. This method utilizes synthetic aperture radar interferometry, structural health monitoring of hydraulic structures, and geotechnical parameter inversion. It integrates a multi-layered coupled physical model of crustal elastic load forward modeling, closed-form solution of dam static response, and forward modeling of unsaturated seepage on the reservoir bank. Using time-series InSAR line-of-sight deformation observations as constraints, it minimizes the residual between forward predictions and InSAR observations, inverting the spatial distribution of the dam's equivalent elastic modulus and the spatial distribution of the reservoir bank's equivalent unsaturated permeability coefficient. Furthermore, it constructs an early warning index based on the time-series drift rate of the water level-deformation transfer gain, thus upgrading from deformation monitoring to structural stiffness diagnosis.

[0028] The method constructs a closed-loop processing framework of multi-layer physical forward modeling, LOS projection, and residual inversion. It first encapsulates various physical processes, such as the elastic load effect of reservoir water on the crust, the static flexural response of the dam body under water pressure, and the unsaturated seepage deformation of the reservoir bank soil and rock caused by water level rise and fall, into multiple forward modeling layers using mechanical models. After superposition, these layers are projected onto the InSAR line of sight to form a differentiable forward modeling operator, thereby decomposing the LOS deformation observed by InSAR into multiple components with clear physical meaning.

[0029] Then, using pixel-level LOS deformation observations acquired by single-track time-series InSAR as constraints, the spatial distributions of the dam's equivalent elastic modulus (Eeq) and the reservoir bank's equivalent unsaturated hydraulic conductivity (kunsat) are inverted pixel by pixel by minimizing the residual between the forward modeling prediction and the InSAR observations. This transforms InSAR monitoring from a deformation response description into a structural stiffness diagnosis. Based on this, the temporal drift rate of the water level deformation transfer gain (G) is extracted from the inversion process. As an early warning indicator that is earlier than the displacement threshold, it enables an upgrade from deformation monitoring to structural health diagnosis.

[0030] The method can be applied to a dam equivalent stiffness diagnostic system based on InSAR residual inversion, or to an electronic device that establishes a communication connection with the diagnostic system and has data processing capabilities. The electronic device includes, but is not limited to, computers, servers, mobile terminals, smart wearable devices, and industrial control computers. For ease of description, the diagnostic system is used as the execution subject of the method in this embodiment. It should be understood that the method can also be applied to other types of execution subjects, which are not shown one by one in this embodiment. Figure 1 As shown, the method includes: S101. Obtain multi-source data.

[0031] When performing dam body diagnosis based on InSAR, the diagnostic system can first acquire multi-source data to prepare input data for subsequent three-layer physical forward modeling and residual inversion. For example... Figure 2 As shown, when acquiring multi-source data, pixel-level LOS deformation time series can be obtained from the single-track time series InSAR processing results, and the reservoir water level process line and dam geometric parameters required to drive the forward model can be obtained simultaneously. Therefore, the multi-source data includes the InSAR observation line-of-sight deformation time series, water level process line, dam geometric parameters, and digital elevation model (DEM) of the target dam area.

[0032] InSAR line-of-sight deformation time series refers to the time series of surface deformation measured by acquiring SAR images of the target dam area and analyzing the displacement detection algorithm of synthetic aperture radar interferometry. Surface deformation refers to the displacement along the line-of-sight direction of the radar satellite. Therefore, when acquiring multi-source data, a single-track time series InSAR deformation time series dataset covering the target dam area can be obtained. This dataset can be generated using the Small BaselineSubset InSAR processing workflow. It is in raster format, with each pixel containing the cumulative LOS displacement value at N time points, denoted as . ,in, p For pixel index, t i For the i-th SAR imaging time, i =1, 2, ..., N This dataset can serve as the core observation input to constrain subsequent parameter inversion.

[0033] like Figure 3 As shown, in order to obtain the time series of directional deformation along the InSAR observation line, in some embodiments, when acquiring multi-source data, InSAR observation data collected for the target dam area can be acquired first. The InSAR observation data includes a single-track time-series SAR image sequence covering the target dam area; the time span of the InSAR observation data covers at least one complete water level regulation cycle of the reservoir corresponding to the target dam area.

[0034] Then, the master image and slave image are selected from the InSAR observation data, and the slave image is aligned to the slant range and azimuth coordinate system of the master image through registration and resampling. Interferometric pairs are then determined based on the registered and resampled master and slave images. Based on the unwrapped phase of the interferometric pairs, the minimum norm solution is obtained using singular value decomposition. The cumulative line-of-sight deformation value at each SAR imaging time is obtained through integration, and the InSAR observation line-of-sight deformation time series is generated based on the cumulative line-of-sight deformation value.

[0035] For example, when acquiring multi-source data, InSAR observation data can be acquired first, which is a single-track time-series SAR image sequence covering the target dam area. The time span covers at least one complete water level regulation cycle of the reservoir, including multiple "water storage-water release" cycles, totaling N SAR images. SAR images can also be downloaded from public data distribution platforms, along with corresponding precise orbit determination ephemeris files, to replace the original orbit information in the SAR data.

[0036] After acquiring InSAR observation data, a single SAR image covering the target dam area is selected as the super master image, such as a SAR image located in the middle of the time series and with good baseline connectivity to other SAR images. Other SAR images besides the master image are referred to as slave images. For slave images, precise registration and resampling can be used to align all slave images to the slant-range-azimuth coordinate system of the master image, achieving a registration accuracy better than 1 / 10 pixel.

[0037] Then, based on precise orbital data, the spatial vertical baseline and temporal baseline between all image pairs are calculated, and valid interferometric pairs are selected according to preset spatiotemporal baseline thresholds. Differential interferometry is then performed on each interferometric pair to generate interferograms, which are then subjected to multi-view processing. External DEM simulation is used to remove terrain phase. Furthermore, adaptive filtering methods are employed to suppress phase noise, a phase unwrapping algorithm is used to recover true continuous phase values, a polynomial model is used to remove orbital errors, and atmospheric correction data is used to correct tropospheric atmospheric delay.

[0038] Based on the unwrapped phase of all interferometric pairs, the singular value decomposition method is used to solve for the minimum norm solution, and the cumulative LOS deformation value at each SAR imaging time is obtained by integration. The final output time-series InSAR deformation dataset is in raster format, with each pixel containing the cumulative LOS displacement value at N time points.

[0039] A water level hydrograph, also known as a reservoir water level hydrograph, is a continuous recorded curve showing the change in reservoir water level over time within a target dam area. If the water level hydrograph can be represented using a functional coordinate system, the horizontal axis represents time, such as days, weeks, or months, and must be aligned with the imaging time of the SAR image. The vertical axis represents the reservoir water level elevation, in meters. Therefore, the water level hydrograph represents continuous time-series data recorded daily.

[0040] The water level process curve can be calculated from the reservoir water level data. Therefore, when acquiring multi-source data, a daily water level process curve h(t) consistent with the time range covered by the InSAR data can be obtained. The reservoir water level data is obtained daily records from the reservoir management department, in meters. Since the acquisition time interval of InSAR images is often uneven due to image quality, and the water level data is a continuous daily record, it is necessary to align the water level data to each InSAR imaging time. Therefore, an interpolation method can be used to map the daily water level sequence to each InSAR imaging time, resulting in a water level sequence that is completely aligned with the deformation time series in the time dimension. .

[0041] The geometric parameters of the dam body can include the dam height. dam crest length Parameters such as dam type category are used to characterize the physical and geometric properties of the dam body. Furthermore, the dam body geometric parameters can be extracted from remote sensing imagery or digital elevation models. The dam type category can include gravity dams, arch dams, or earth-rock dams, etc., used to select the corresponding forward modeling model for the dam body's static response.

[0042] To obtain the water level hydrograph and dam geometry parameters, in some embodiments, when acquiring multi-source data, the diagnostic system can first acquire reservoir water level data, optical remote sensing images, and a digital elevation model of the target dam area. The reservoir water level data is a scheduling record consistent with the time range covered by the SAR observation data. The reservoir water level data is then aligned to the imaging time of the SAR observation data, and a water level hydrograph is generated based on the aligned reservoir water level data.

[0043] For example, water level gauges deployed at hydrological stations or reservoirs can be used to automatically and continuously record water level changes, obtaining raw reservoir water level data. Then, the reservoir water level data undergoes format conversion, omission and filling, and obvious errors are removed. Missing data in the reservoir water level data is supplemented using data interpolation algorithms such as mathematical interpolation, process line interpolation, and correlation interpolation. Next, the water level data is combined with the water level-reservoir capacity relationship curve, and the corresponding reservoir capacity change is calculated using interpolation and other methods. Finally, the processed time series data is visualized, and a process line graph is generated to obtain the water level process line.

[0044] After generating the water level process line, the diagnostic system can also visually interpret optical remote sensing images, measure the dam crest length and dam outline of the target dam area, and extract dam height information from the digital elevation model to obtain the dam geometric parameters.

[0045] For example, the diagnostic system can acquire high-resolution optical remote sensing images covering the dam area using Google Earth imagery or domestic high-resolution satellite imagery databases, and perform visual interpretation to measure the dam crest length and dam outline. Then, it combines these with a digital elevation model to extract dam height information, thus obtaining the dam's geometric parameters. The dam type can be determined through image features.

[0046] In addition to the data mentioned above, the diagnostic system can also acquire digital elevation models (DEMs) covering the reservoir bank area when obtaining multi-source data. DEM data is used for reservoir bank slope calculations and load distribution calculations in crustal load forward modeling, and can utilize publicly available global or regional datasets.

[0047] For example, digital elevation models can utilize publicly available global or regional datasets, such as SRTM, ASTER GDEM, or Copernicus GLO-30. In some instances of this application, Copernicus GLO-30 is used as an example of a digital elevation model with a spatial resolution of 30 meters.

[0048] In some embodiments, the multi-source data further includes temperature data, which may include the daily temperature process curve T(t) of the target dam area. The daily temperature process curve is a curve showing the continuous change of temperature over time within a day. Temperature data can be used in subsequent residual analysis to remove temperature deformation components and improve inversion accuracy. Temperature data can be obtained from the nearest meteorological station or a reanalysis dataset.

[0049] For example, daily average temperature data, in degrees Celsius, can be obtained from the nearest meteorological station to the target dam area. If there is no meteorological station near the target dam area, daily average temperature data for the corresponding grid points can be extracted from the ERA5 reanalysis dataset. When temperature data is available, it is incorporated into the forward model to improve inversion accuracy; when temperature data is unavailable, the forward model performs inversion based solely on water level-driven inversion.

[0050] S102. Construct a physical forward model and generate forward prediction results based on multi-source data using the physical forward model.

[0051] After acquiring multi-source data, the diagnostic system can also construct a physical forward model. This physical forward model is used to perform forward modeling predictions on multiple physical processes, taking water level hydrographs, dam geometric parameters, and a digital elevation model as inputs.

[0052] A physical forward model can cascade forward models of multiple physical processes into a differentiable forward operator, taking the water level hydrograph and dam geometry parameters as inputs and outputting the theoretical LOS displacement for each pixel. Depending on the number of cascaded physical process forward models, a physical forward model can include multiple forward layers.

[0053] like Figure 4 As shown, in some embodiments, the physical forward model includes a crustal elastic load forward model layer, a dam static response forward model layer, and a reservoir bank unsaturated seepage forward model layer, which correspond to the elastic load effect of reservoir water on the crust, the static flexural response of the dam under water pressure, and the unsaturated seepage deformation of the reservoir bank soil and rock caused by water level rise and fall, respectively.

[0054] The overall coupling formula for the three-layer forward modeling of the physical forward model can then be expressed as:

[0055] in, The LOS deformation (displacement) is predicted by the forward model at pixel position p and time t. This represents the three-dimensional displacement vector output from the forward modeling layer of crustal elastic load; This is the three-dimensional displacement vector output from the forward modeling layer of the dam's static response; The three-dimensional displacement vector output by the forward modeling layer of unsaturated seepage on the reservoir bank; This is a projection operator that projects a three-dimensional displacement vector onto the satellite line of sight.

[0056] The constructed physical forward model can then be used to perform forward predictions based on multi-source data to generate forward prediction results, which include the theoretical line-of-sight displacement for each pixel. Therefore, when generating the theoretical line-of-sight displacement for each pixel based on multi-source data using the physical forward model, a three-dimensional displacement field can be obtained first. The three-dimensional displacement field includes the first displacement field output from the crustal elastic load forward model layer, the second displacement field output from the dam static response forward model layer, and the third displacement field output from the reservoir bank unsaturated seepage forward model layer.

[0057] For crustal elastic loads, in some embodiments, the crustal elastic load forward modeling layer is used to calculate the crustal surface elastic displacement field caused by changes in reservoir water load based on elastic load theory. When obtaining the three-dimensional displacement field, the reservoir water surface can first be discretized into multiple grid cells based on the dam's geometric parameters. Then, for each grid cell, the crustal surface displacement response caused by a unit point load is calculated according to the Green's function. Finally, by superimposing the crustal surface displacement responses of all grid cells, a first displacement field is obtained, which characterizes the crustal elastic displacement field of the entire reservoir area.

[0058] The crustal elastic load forward modeling layer can calculate the elastic displacement field of the crustal surface caused by changes in reservoir water load, based on elastic load theory. When the reservoir water level changes, the weight of the water in the reservoir area changes accordingly. This additional load acts on the crustal surface, causing elastic settlement or rebound of the crust. The spatial distribution of this effect depends on the geometry of the reservoir water surface and the amount of water level change. The crustal elastic load forward modeling layer uses the layered elastic load Green's function method, discretizing the reservoir water surface into grid cells. For each grid cell, the crustal surface displacement response caused by a unit point load is calculated, and then the contributions of all grid cells are superimposed to obtain the crustal elastic displacement field of the entire reservoir area. The three-dimensional displacement field output by this layer contains horizontal and vertical components, and its amplitude is linearly related to the water level change Δh(t). The scaling factor is determined by the crustal elastic structure and reservoir geometry.

[0059] For example, when calculating the elastic displacement field of the crustal surface caused by changes in reservoir water load based on the Farrell layered elastic load Green's function theory, the change in the weight of the water body in the reservoir area when the reservoir water level changes from the initial water level h0 to the current water level h(t) is as follows:

[0060] in, Let be the change in water weight in the reservoir at time t; The density of water; It is the acceleration due to gravity; The water surface area of ​​the reservoir area; This represents the change in water level. Changes in the weight of water in the reservoir can act as an additional load on the Earth's crust, causing an elastic response in the crust.

[0061] Therefore, the reservoir water surface can be discretized into M grid cells, with the center coordinates of each grid cell being... The area is For each grid cell, the crustal surface displacement response caused by a unit point load is calculated, i.e., the Green's function. Where r is the location of the observation point, The subscripts i and j in the Green's function represent the location of the load point, indicating the direction of the displacement component. Calculating the Green's function requires parameters of the Earth's elastically layered structure, including the thickness of each layer, Young's modulus, and Poisson's ratio. In the absence of regional crustal structure data, global average crustal model parameters can be used.

[0062] The crustal elastic displacement at observation point r caused by the combined loads of all grid elements is:

[0063] in, Let M be the crustal elastic load displacement vector at observation point location r and time t; M is the number of grid cells. The matrix represents the Green's function. The position vector of the observation point; The position vector of the m-th grid cell; The density of water; It is the acceleration due to gravity; Let m be the area of ​​the m-th grid cell; This represents the change in water level. It can be seen that... Over time, It also changes over time, and with The relationship is linear.

[0064] The crustal elastic load forward modeling layer can output each pixel p at every time point. The three-dimensional displacement vector, i.e.:

[0065] in, Let p be the pixel location and the i-th SAR imaging time. The crustal elastic load displacement vector; This represents the displacement component in the x-direction; This represents the displacement component in the y-direction; Let z be the displacement component in the z-direction.

[0066] It should be noted that the main uncertainty in the forward modeling of crustal elastic loading stems from prior knowledge of the crustal elastic stratification structure. In the absence of regional crustal structure data, globally averaged model parameters can be used. These parameters do not participate in subsequent inversions but serve as fixed inputs.

[0067] For the static response of the dam body, in some embodiments, the forward modeling layer of the static response of the dam body is used to calculate the static flexural displacement of the dam body under water pressure based on structural mechanics. When obtaining the three-dimensional displacement field, the spatial position of the dam surface can be extracted from the digital elevation model and the dam body geometric parameters, and the height coordinates corresponding to each pixel on the dam surface can be determined based on the spatial position. Then, the dam type category is extracted from the dam body geometric parameters, and a closed analytical model is called according to the dam type category. Specifically, when the dam type category is a gravity dam, the closed analytical model adopts a cantilever beam model; when the dam type category is an arch dam, the closed analytical model adopts a thin shell analytical model or a simplified model of the arch-beam load distribution method. Then, based on the closed-form analytical model, the displacement component along the river is calculated using the height coordinates, current water level, and the equivalent elastic modulus of the dam body. According to the Poisson effect, the lateral and vertical displacement components are estimated from the displacement component along the river. The displacement components along the river, lateral, and vertical are then combined into a three-dimensional displacement vector to obtain the second displacement field. The forward modeling layer of the dam body's static response can be based on structural mechanics theory to calculate the static deflection displacement of the dam body under water pressure. Depending on the dam type, a corresponding closed-form analytical model can be used. For gravity dams, a closed-form solution of static deflection under triangular distributed water pressure using a cantilever beam model is adopted; for arch dams, a thin-shell analytical model or a simplified form of the arch-beam load distribution method is used. The choice of a closed-form solution ensures the differentiability of the forward modeling operator, allowing subsequent inversion to be performed efficiently using the gradient descent method. The three-dimensional displacement field output by the forward modeling layer of the dam body's static response includes the displacement components along the river, vertical, and lateral on the dam surface. The core control parameter of the forward modeling layer of the dam body's static response is the equivalent elastic modulus of the dam body. This parameter varies spatially with the pixel position.

[0068] For example, taking a concrete gravity dam as an example, the forward modeling layer of the dam's static response can be achieved using the Euler-Bernoulli cantilever beam model with a closed-form solution for static deflection under triangularly distributed water pressure. This is achieved by simplifying the gravity dam as a cantilever beam with a fixed bottom and a free top, bearing water pressure distributed in a triangular pattern along the dam's height. The water pressure distribution is as follows:

[0069] in, The vertical water pressure distribution is represented by z; z is the height coordinate, indicating the vertical distance of the pixel from the bottom of the dam. The density of water; It is the acceleration due to gravity; Let be the dam height. Then, for any point on the dam surface, its deflection along the river is derived from the bending differential equation of the beam.

[0070] For the deflection of a cantilever beam under a triangular distributed load, the closed-form expression for the displacement of any point on the dam surface in the longitudinal direction along the river is: ; in, Let z be the flexural displacement of the dam body along the river at a height z on the dam surface and at time t; z is the vertical distance from the dam bottom. The density of water; It is the acceleration due to gravity; The dam is high; Let be the equivalent elastic modulus of the dam body at pixel p; I be the moment of inertia of the dam body section, determined by the dam body geometry; and h(t) be the current water level. This formula applies to the region z ≤ h(t), i.e., the dam body below the water level; for the region z > h(t), i.e., the dam body above the water level, the water pressure is zero, and the displacement is determined by the bending moment and shear force transmitted from the lower part.

[0071] In practical applications, for each pixel on the dam surface, its corresponding z-coordinate needs to be determined based on its spatial location. The height coordinate z, as a geometric input, can be used to determine the pixel's spatial position on the dam surface from the DEM and the dam contour, yielding the vertical height of that point from the dam base. This height is then used in the closed-form solution of the cantilever beam to determine whether the point is below the water level and to be substituted into the deflection formula. For gravity dams, the downstream displacement of points on the dam surface is mainly affected by... Control, then the downstream displacement component u x The main output of the closed-loop analytical model can be obtained from the cantilever beam deflection formula under triangular water pressure, calculated based on the height coordinate z, the current water level h(t), and the equivalent elastic modulus Eeq of the dam body. The vertical and lateral displacements are relatively small compared to the downstream displacement and can be estimated using the Poisson effect, i.e., the lateral displacement component u. y Vertical displacement component u z It is after obtaining the downstream displacement component u x Then, the derived displacement components are estimated based on the Poisson effect.

[0072] Therefore, the forward modeling layer of the dam's static response can output the state of each pixel p at every time point t. i The three-dimensional displacement vector, i.e.:

[0073] in, Let p be the pixel location and the i-th SAR imaging time. The static response displacement vector of the dam body; Let x be the static response displacement component of the dam body in the x-direction; The displacement component of the dam body in the y direction represents the static response of the dam body. Let z be the static displacement component of the dam body in the z-direction.

[0074] It should be noted that the core control parameter of the forward modeling layer of the dam's static response is the equivalent elastic modulus of the dam body. This parameter varies spatially with the pixel position. It is not the actual elastic modulus of concrete, but an equivalent parameter that takes into account factors such as dam geometry, boundary conditions, and material nonlinearity. Its spatial distribution reflects the relative stiffness of different parts of the dam.

[0075] For unsaturated seepage along the reservoir bank, in some embodiments, the unsaturated seepage forward modeling layer is used to calculate the shallow deformation of the reservoir bank caused by the rise and fall of the reservoir water level, based on the unsaturated seepage theory. When obtaining the three-dimensional displacement field, the reservoir bank parameters can be calculated first based on the dam's geometric parameters and the digital elevation model. These parameters include the distance and elevation of each pixel in the reservoir bank region to the reservoir bank.

[0076] A nonsaturated seepage model is then established based on reservoir bank parameters and water level hydrographs. This model describes the relationship between groundwater level and reservoir water level. Following this model, the change in saturated zone thickness caused by water level changes is calculated using soil-water characteristic curves and permeability coefficient functions. Finally, shallow displacement is calculated based on the effective stress principle and the change in saturated zone thickness, yielding the third displacement field.

[0077] The unsaturated seepage forward model layer for reservoir banks can be used to calculate shallow deformation of the reservoir bank caused by changes in reservoir water level, based on the theory of unsaturated seepage. When the reservoir water level rises, the groundwater level on the reservoir bank rises accordingly, the thickness of the saturated zone increases, pore water pressure increases, and effective stress decreases, causing expansion and deformation of the soil and rock mass; when the reservoir water level falls, the process is reversed. The unsaturated seepage forward model layer for reservoir banks can use an unsaturated seepage model to describe this process, calculate the change in saturated zone thickness caused by water level changes through soil-water characteristic curves and permeability coefficient functions, and then calculate shallow displacement based on the principle of effective stress. The three-dimensional displacement field output by the unsaturated seepage forward model layer for reservoir banks is mainly distributed in the reservoir bank area, and the core control parameter is the equivalent unsaturated permeability coefficient of the reservoir bank. The equivalent unsaturated permeability coefficient of the reservoir bank varies spatially with pixel position.

[0078] For example, for each pixel in the reservoir bank area, the relationship between the groundwater level and the reservoir water level at that location is first determined based on its distance from the reservoir bank and its elevation. A simplified one-dimensional vertical seepage model is then used, assuming that changes in the groundwater level on the reservoir bank lag behind changes in the reservoir water level, with the lag time determined by the permeability characteristics of the reservoir bank medium and the seepage path length.

[0079] The relationship between the change in saturated zone thickness ΔS(p,t) and the change in water level Δh(t) can be described by a simplified solution of the unsaturated seepage equation:

[0080] in, Let p be the change in saturation band thickness at pixel position p and time t. For past moments, it serves as the integration variable; The rate of change of water level; This is the seepage response function, whose form is equivalent to the unsaturated permeability coefficient of the reservoir bank. Related. Then The larger the value, the faster the seepage response and the shorter the hysteresis time.

[0081] Based on the effective stress principle, the vertical displacement caused by the change in saturation zone thickness is:

[0082] in, The vertical displacement caused by the change in saturation band thickness at pixel position p and time t; Let p be the change in saturation band thickness at pixel position p and time t. The compressibility coefficient of the reservoir bank soil and rock mass can be set as an empirical value based on regional geological data. The horizontal displacement component can be estimated based on the Poisson effect and the reservoir bank slope.

[0083] The forward modeling layer for unsaturated seepage on the reservoir bank can output the three-dimensional displacement vector of each pixel p at each time point ti, that is:

[0084] in, Let p be the pixel location and the i-th SAR imaging time. The unsaturated seepage displacement vector of the reservoir bank; The unsaturated seepage displacement component of the reservoir bank in the x-direction; The unsaturated seepage migration component of the reservoir bank in the y-direction; This represents the unsaturated seepage displacement component of the reservoir bank in the z-direction. For pixels in the dam body region far from the reservoir bank, the output of this layer is zero.

[0085] It should be noted that the core control parameter of the unsaturated seepage forward modeling layer on the reservoir bank is the equivalent unsaturated permeability coefficient of the reservoir bank. This parameter varies spatially with the pixel position. It reflects the drainage / absorption capacity of the reservoir bank soil and rock mass under water level changes, and its spatial distribution can be used to identify areas of abnormal seepage on the reservoir bank.

[0086] After obtaining the first displacement field, the second displacement field, and the third displacement field, the total three-dimensional displacement vector can be obtained by superimposing the first displacement field, the second displacement field, and the third displacement field. The total three-dimensional displacement vector is then projected onto the line of sight of the InSAR satellite to obtain the theoretical line of sight displacement.

[0087] After superimposing the three-dimensional displacement fields output from the three forward modeling layers, the total three-dimensional displacement vector of each pixel at each time point is obtained. Through multi-layer coupled forward modeling, the LOS deformation observed by InSAR can be decomposed into multiple components with clear physical meanings. For example, the crustal elastic load component reflects the overall elastic response of the crust caused by reservoir water load, and its spatial distribution is closely related to the water surface morphology of the reservoir area; the dam static deflection component reflects the elastic deformation of the dam structure under water pressure, and its amplitude is controlled by the equivalent elastic modulus of the dam body; the reservoir bank seepage deformation component reflects the shallow deformation of the reservoir bank soil and rock caused by water level rise and fall, and its temporal morphology is controlled by the equivalent permeability coefficient of the reservoir bank.

[0088] For example, when performing three-layer displacement stacking and LOS projection, the three-dimensional displacement vectors output by the three-layer forward model can be stacked first to obtain the total three-dimensional displacement vector of each pixel at each time point:

[0089] in, Let p be the pixel location and the i-th SAR imaging time. The total three-dimensional displacement vector; Let p be the pixel location and the i-th SAR imaging time. The crustal elastic load displacement vector; Let p be the pixel location and the i-th SAR imaging time. The static response displacement vector of the dam body; Let p be the pixel location and the i-th SAR imaging time. The unsaturated seepage displacement vector of the reservoir bank.

[0090] The total three-dimensional displacement vector is then projected onto the line-of-sight of the InSAR satellite to obtain the theoretical LOS displacement time series. Projection operator Determined by the satellite's incident angle θ and azimuth angle α, its form is:

[0091] in, Here, θ is the projection operator; θ is the incident angle; α is the azimuth angle. , , These are the components of the three-dimensional displacement vector in the east-west, vertical, and north-south directions, respectively.

[0092] In some embodiments, when temperature data is included in the multi-source data, temperature-driven terms can be added during forward modeling. Therefore, when temperature data is available, temperature-driven terms can be added to the forward model. Temperature changes primarily cause expansion and contraction deformation of the dam body and reservoir banks through thermoelastic effects. For the dam body area, rising temperatures cause concrete expansion, resulting in displacement in the LOS direction; for the reservoir bank area, temperature changes affect the temperature field of the shallow soil and rock mass, causing thermoelastic deformation.

[0093] Assuming that the effect of temperature on deformation is linear, and that there is a certain lag time. This represents the time delay of heat conduction from the surface to the interior. Therefore, by modeling the temperature driving term, we can obtain its form as:

[0094] in, The temperature driving term is the pixel position p and time t. For temperature transfer gain, This represents the temperature lag time. and The optimal lag can be pre-determined using a two-dimensional grid search method. This involves traversing all candidate lag times within a pre-defined search range, performing linear regression on each candidate lag time, and selecting the lag time that minimizes the sum of squared residuals as the optimal lag. This step can be completed independently before forward and inversion models and is not involved in subsequent stiffness parameter inversion.

[0095] When temperature data is unavailable, the forward model does not include a temperature-driven term and inversion is performed solely based on water level. In this case, the deformation caused by temperature changes will be absorbed into the residuals, which may slightly reduce the inversion accuracy but will not affect the normal operation of the method.

[0096] It is evident that by establishing a physical mapping mechanism from deformation response to structural mechanical parameters, the multi-layer physical forward modeling prediction process can be coupled, decomposing the LOS deformation observed by InSAR into three components with clear physical meaning: crustal elastic load, dam static deflection, and reservoir bank seepage deformation. Based on this, the spatial distribution of the dam's equivalent elastic modulus and the reservoir bank's equivalent permeability coefficient can be inverted, thus upgrading InSAR monitoring from deformation description to stiffness diagnosis.

[0097] S103. Solve the parameter field by performing residual inversion based on the theoretical line-of-sight displacement to obtain spatial distribution information.

[0098] After constructing the physical forward model and generating forward prediction results, the parameter field can be solved by residual inversion based on the theoretical line-of-sight displacement in the forward prediction results to obtain spatial distribution information. Specifically, the residual inversion uses the InSAR observation line-of-sight deformation time series as the objective value and the physical forward model as the forward operator. By minimizing the residual between the theoretical line-of-sight displacement and the InSAR observation line-of-sight deformation, the spatial distribution of the dam's equivalent elastic modulus and the reservoir bank's equivalent permeability coefficient is inverted pixel-by-pixel.

[0099] like Figure 5 As shown, in some embodiments, when performing residual inversion to solve the parameter field based on the theoretical line-of-sight displacement to obtain spatial distribution information, an objective function can be defined first. The objective function is the sum of squared residuals between the InSAR observation line-of-sight deformation and the theoretical line-of-sight displacement over the entire monitoring period, plus a spatial smoothing regularization term.

[0100] The gradients of the objective function with respect to the equivalent elastic modulus of the dam body and the equivalent permeability coefficient of the reservoir bank are then calculated analytically using the chain rule. Based on these gradients, iterative optimization and inversion are performed to output spatial distribution information. This spatial distribution information includes spatial distribution maps of the equivalent elastic modulus of the dam body and the equivalent permeability coefficient of the reservoir bank.

[0101] For example, in the process of solving the parameter field based on residual inversion, the LOS deformation time series observed by InSAR is used as the objective value, and the three-layer forward model is used as the forward operator. By minimizing the residual between the forward prediction and the InSAR observation, the spatial distribution of the equivalent elastic modulus of the dam body and the equivalent permeability coefficient of the reservoir bank is inverted pixel by pixel.

[0102] First, define the objective function. For each pixel p, the objective function is defined as the sum of squared residuals between the InSAR observed LOS displacement and the forward model predicted LOS displacement over the entire monitoring period, plus a spatial smoothing regularization term, i.e.: ; in, The objective function value is at pixel location p; N is the total number of scenes in the time-series InSAR imagery. For the i-th SAR imaging time t i The actual observed line-of-sight deformation value at pixel p; The equivalent elastic modulus of the dam body; The equivalent permeability coefficient of the reservoir bank; For and The output of the forward model with parameters; This is the regularization intensity coefficient; This is the space smoothing regularization term.

[0103] Spatial smoothing regularization term Using the second-order Laplace operator form:

[0104] in, For spatial smoothing regularization; It is the Laplacian operator, which can be approximated on a discrete grid by the difference between adjacent pixels; The equivalent elastic modulus of the dam body; λ represents the equivalent permeability coefficient of the reservoir bank. The regularization intensity coefficient λ controls the degree of spatial smoothness; the larger λ is, the smoother the inversion result. The value of λ can be determined by the L-curve method or cross-validation.

[0105] Then, gradient calculation is performed. Since the forward model uses a closed analytical form, the gradient of the objective function with respect to the parameters to be inverted can be calculated analytically using the chain rule. Therefore, the gradient of the objective function with respect to... The gradient is: ; in, It can be directly derived from the closed-form solution of the forward modeling layer of the dam's static response. Because... The included dam body deflection component and Inversely proportional, therefore ,in, This represents the projection value of the dam body deflection component in the LOS direction.

[0106] The objective function is about The gradient is: ; in, It can be obtained by differentiating the analytical form of the unsaturated seepage forward model layer on the reservoir bank. The main factor affecting the seepage response is the hysteresis time; gradient calculation involves the seepage response function. The derivative of .

[0107] Then, optimization is performed, i.e., iterative optimization using gradient descent or the Levenberg-Marquardt algorithm. Taking the Levenberg-Marquardt algorithm as an example, the parameter update amount for each iteration is:

[0108] in, Let J be the parameter vector to be inverted, and J be the Jacobian matrix with elements of J. ; r is the fitted residual vector, and the elements of the fitted residual vector are μ is the damping factor; I is the identity matrix.

[0109] The iteration terminates under one of the following three conditions: the parameter update amount is less than a preset threshold, the objective function decrease is less than a preset threshold, or the maximum number of iterations is reached.

[0110] In some embodiments, the inversion process employs a pixel-by-pixel or block-by-block strategy to improve computational efficiency. Therefore, for pixels in the dam region, the main inversion parameter is the equivalent elastic modulus of the dam body. Equivalent permeability coefficient of the reservoir bank The impact on this area is relatively small and can be fixed as the regional background value. The extent of the dam area can be determined by a dam outline mask.

[0111] For pixels in the reservoir bank area, the main inversion parameter is the equivalent permeability coefficient of the reservoir bank. Equivalent elastic modulus of the dam body The impact on this area is relatively small and can be fixed as the regional background value. The extent of the reservoir bank area can be determined by a regional mask within a certain buffer distance from the reservoir bank. For pixels in the boundary area between the dam body and the reservoir bank, both parameters are inverted simultaneously. The extent of the boundary area can be determined by extending the dam body outline outward by a certain distance.

[0112] During the inversion process, the transfer gain and drift rate can also be calculated, that is, the time-series variation of the water level-deformation transfer gain G(t) can be extracted simultaneously. The transfer gain is defined as the response sensitivity of the LOS displacement predicted by the forward model to a unit water level change.

[0113] Since the forward model is in closed analytical form, the transfer gain can be directly calculated through analytical differentiation. For each time point... The transfer gain is:

[0114] in, For time points Water level-deformation transfer gain; The LOS deformation predicted by the forward model, i.e., at pixel p and time point The theoretical LOS displacement is output. For time points The water level elevation. This derivative can be used to summarize the sensitivity of three components—the crustal load layer, the dam body static response layer, and the reservoir bank seepage layer—to water level changes.

[0115] Transfer gain drift rate Numerical difference calculations are performed using the transfer gain timing. For discrete time points, a central difference scheme is used:

[0116] in, For time points The transfer gain drift rate; For the next moment The transfer gain; For the previous moment The transfer gain. For the first and last time points, either forward difference or backward difference schemes are used.

[0117] It is evident that pixel-level inversion of the spatially distributed parameter field can be achieved through residual inversion. The inversion process uses InSAR surface observations as constraints, rather than relying on a small number of discrete points, to invert the equivalent elastic modulus of the dam body and the equivalent permeability coefficient of the reservoir bank pixel by pixel, outputting the spatially distributed parameter field and revealing the spatial variation in stiffness of different parts of the dam body caused by material differences, aging degrees, or local damage. Furthermore, combined with the forward modeling prediction process, an engineering-deployable forward-inversion closed-loop framework can be constructed. This encapsulates the three-layer physical forward model into a differentiable forward operator, using InSAR observations as constraints. Through iterative optimization of the inverted physical parameter field, an automated closed-loop technical solution is formed, reducing reliance on classified drawings and multi-sensor data.

[0118] S104. Generate diagnostic results based on spatial distribution information.

[0119] After completing forward modeling and residual inversion, the diagnostic system can also generate diagnostic results based on spatial distribution information. That is, by summarizing all calculation results, it generates multi-level pixel-level output products and constructs early warning logic based on the transfer gain drift rate.

[0120] For example, during the process of generating diagnostic results, the diagnostic system can combine the above calculation results to generate pixel-level raster products as diagnostic results. All pixel-level raster products have the same spatial extent and resolution as the input InSAR raster.

[0121] The diagnostic results may include the equivalent elastic modulus diagram of the dam body. Equivalent permeability coefficient diagram of reservoir bank The raster values ​​of the dam body equivalent elastic modulus map represent the equivalent elastic modulus of the dam body for each pixel, in gigapascals (GPa), reflecting the stiffness of different parts of the dam body. The raster values ​​of the reservoir bank equivalent permeability coefficient map represent the equivalent unsaturated permeability coefficient of the reservoir bank for each pixel, in meters per day, reflecting the permeability characteristics of different areas of the reservoir bank.

[0122] The diagnostic results may also include displacement component maps. Specifically, the grid values ​​of the crustal load displacement component map represent the LOS displacement contributed by the crustal elastic load layer in the forward model, in millimeters, and are used to show the overall elastic response of the crust caused by reservoir water load. The grid values ​​of the dam body deflection displacement component map represent the LOS displacement contributed by the dam body static response layer in the forward model, in millimeters, and are used to show the structural deflection of the dam body under water pressure. The grid values ​​of the reservoir bank seepage displacement component map represent the LOS displacement contributed by the reservoir bank unsaturated seepage layer in the forward model, in millimeters, and are used to show the seepage deformation of the reservoir bank caused by water level rise and fall.

[0123] In addition, diagnostic results may include a model fitting residual plot r(p,t), where the grid values ​​represent the residuals between InSAR observations and forward predictions in millimeters, used to identify deformation patterns not captured by the model; a water level-deformation transfer gain time series plot G(t), where the grid values ​​represent the transfer gain at each time point in millimeters / meters, reflecting the temporal variation of the system's response sensitivity; and a transfer gain drift rate plot. The grid value represents the time rate of change of the transfer gain, in millimeters per meter per year.

[0124] By applying the technical solutions of the above embodiments, the dam equivalent stiffness diagnosis method based on InSAR residual inversion described in the above embodiments can construct a forward modeling operator that integrates multiple physical mechanisms, realizing the transformation from deformation response description to structural stiffness diagnosis. By constructing a multi-layer coupled physical forward model that includes crustal elastic load, dam static deflection, and unsaturated seepage on the reservoir bank, the LOS deformation observed by InSAR is decomposed into multiple components with clear physical meaning. Furthermore, through the dam static response forward modeling layer, a quantitative physical relationship between the dam's equivalent elastic modulus and LOS deformation is established. Based on this, the spatial distribution of the dam's equivalent elastic modulus map is directly solved through residual inversion, enabling the method to directly answer core diagnostic questions such as whether structural stiffness has degraded and in which locations the degradation occurs.

[0125] The method can also be based on a pixel-level parameter inversion framework constrained by surface observations. Using surface observation data from a single-track time-series InSAR as the sole constraint source, the three-layer forward model is encapsulated into a differentiable forward operator. By minimizing the residual between the forward prediction and the InSAR observation, the spatial distribution of the dam's equivalent elastic modulus and the reservoir bank's equivalent permeability coefficient is inverted pixel-by-pixel. This method does not rely on any contact sensor data; it only requires publicly available water level data and remote sensing imagery, significantly reducing reliance on multi-source data and high-cost sensors. Simultaneously, the output spatial distribution parameter field can finely characterize the stiffness differences of key components such as the dam shoulder, heel, and toe, providing unprecedented spatial resolution for identifying local weak areas.

[0126] In some embodiments, as a refinement and extension of the specific implementation of the above embodiments, and to fully illustrate the specific implementation process of this embodiment, some embodiments of this application also provide a method for dam equivalent stiffness diagnosis based on InSAR residual inversion. The difference between this method and the above embodiments is that it can perform graded early warning based on the transfer gain drift rate. By extracting the temporal drift rate of the water level-deformation transfer gain from the inversion process, it serves as an early indicator of structural stiffness degradation, providing a physical mechanism-driven decision-making basis for dam structural health management. Figure 6 As shown, the method includes: S201. Obtain InSAR raster information corresponding to the deformation time sequence along the InSAR observation line; S202. Define the output format based on InSAR raster information; S203. Convert the spatial distribution information into output products according to the output format; S204. Construct a hierarchical early warning mechanism based on the transfer gain drift rate, and generate diagnostic results according to the hierarchical early warning mechanism.

[0127] When generating diagnostic results based on spatial distribution information, the diagnostic system can first acquire InSAR raster information corresponding to the deformation time series along the InSAR observation line, and define an output format based on the InSAR raster information. The output format includes the same spatial range and resolution as the InSAR raster information.

[0128] Then, the spatial distribution information is converted into an output product according to the output format, wherein the output product includes spatial distribution information and transfer gain drift rate. A hierarchical early warning mechanism is then constructed based on the transfer gain drift rate, and diagnostic results are generated according to the hierarchical early warning mechanism.

[0129] For example, such as Figure 7 As shown, to generate diagnostic results that include early warning outcomes, the diagnostic system can construct a hierarchical early warning mechanism based on the transfer gain drift rate. The input to the early warning mechanism is the transfer gain drift rate. The time series curve and model fitting residual plot r(p,t) are obtained. A tiered early warning mechanism can include multiple warning levels, such as attention level, alert level, and action level.

[0130] Among them, the attention level is a yellow warning, which refers to the transfer gain drift rate of a certain pixel or region. A yellow alert is triggered when a value remains positive for multiple consecutive monitoring periods and its absolute value exceeds a preset threshold. A yellow alert indicates potential stiffness degradation at that location, suggesting increased monitoring frequency and close monitoring of its development. The threshold can be set by referring to the statistical distribution of the transfer gain drift rate in the initial monitoring phase, such as the statistical distribution of the transfer gain drift rate in the first three water level cycles, and taking the upper quartile of the distribution, or by setting it based on engineering experience.

[0131] The warning level is orange, which indicates the transfer gain drift rate in a certain pixel or area. An orange alert is triggered when the drift rate exhibits an accelerating upward trend, such as when the time derivative of the drift rate is positive and its absolute value exceeds a preset warning threshold. An orange alert indicates that the stiffness degradation process at that location is accelerating, and it is recommended to arrange specialized tests such as ground-penetrating radar detection and acoustic wave detection to confirm the structural condition. The warning threshold can be set by referring to historical statistical data from similar projects or determined based on the structural safety level.

[0132] The action level is a red alert, which is triggered when a pixel or region simultaneously meets the following two conditions: Condition 1, transfer gain drift rate. The first condition is that the residual value remains positive and exceeds the warning threshold; the second condition is that the model fitting residual r(p,t) at this location has increased significantly in recent times, such as exceeding twice the standard deviation of the previous residual mean. The simultaneous fulfillment of both conditions indicates that not only has stiffness degradation occurred at this location, but new deformation modes that were not captured by the model may have also emerged, such as crack propagation or localized failure. The structural safety may be substantially threatened, and it is recommended to immediately organize a detailed on-site investigation and take appropriate measures.

[0133] The hierarchical early warning mechanism based on the transfer gain drift rate can trigger a yellow warning when the transfer gain drift rate remains positive and exceeds a preset threshold, indicating potential stiffness degradation in the dam structure. An orange warning is triggered when the transfer gain drift rate accelerates over multiple consecutive time periods, indicating an accelerated stiffness degradation process. A red warning is triggered when the transfer gain drift rate continues to rise while the model fitting residuals significantly increase in a certain region, suggesting the potential emergence of new deformation patterns not captured by the model in that region.

[0134] In some embodiments, the attention threshold, warning threshold, residual increase factor, and other thresholds used in the above-mentioned graded early warning mechanism can be calibrated and adjusted according to factors such as dam type differences, dam age, historical monitoring data, and risk tolerance.

[0135] Regarding dam type differences: gravity dams, arch dams, and earth-rock dams exhibit different stiffness degradation patterns, and therefore, threshold values ​​should differ. The transfer gain drift rate of gravity dams is typically relatively gradual, while arch dams may be more sensitive. Regarding dam age, the normal degradation rate of older dams differs from that of newer dams, and the threshold value should consider the impact of dam age. For new dams, the threshold value can be appropriately tightened; for older dams, the normal material aging rate needs to be considered. For historical monitoring data, if there is accumulated data over many years, the threshold value can be determined based on historical statistics. For example, the threshold multiple can be set based on the mean and standard deviation of the transfer gain drift rate during the historical monitoring period. Regarding risk tolerance, projects with higher safety requirements should adopt stricter threshold values, such as those in densely populated downstream areas or upstream of important infrastructure.

[0136] By applying the technical solutions of the above embodiments, the dam equivalent stiffness diagnosis method based on InSAR residual inversion described in the above embodiments can provide a more accurate structural degradation early warning capability than the displacement threshold, based on the physical mechanism early warning index of transfer gain drift rate. By using the transfer gain drift rate as the core early warning index, when the stiffness of the dam structure deteriorates, the deformation response caused by the same water level change will increase, leading to an increase in transfer gain. Its drift rate will change significantly before the displacement increment. This index directly captures abnormal signals from changes in the structural mechanical properties (stiffness), theoretically reflecting the deterioration of the structural state earlier than the displacement threshold. It provides a more forward-looking physical mechanism-driven index for dam safety early warning, realizing the shift from post-event alarm to early warning.

[0137] In some embodiments, as a specific implementation of the dam equivalent stiffness diagnosis method based on InSAR residual inversion described in the above embodiments, some embodiments of this application also provide a dam equivalent stiffness diagnosis system based on InSAR residual inversion, such as... Figure 8 As shown, the system includes: The data acquisition module is used to acquire multi-source data, including the InSAR observation line deformation time series, water level process line, dam body geometric parameters, and digital elevation model of the target dam area; The physical forward modeling module is used to construct a physical forward modeling model and generate forward prediction results based on the multi-source data using the physical forward modeling model; the physical forward modeling model is used to perform forward prediction on multiple physical processes using the water level process line, the dam body geometric parameters, and the digital elevation model as inputs; the forward prediction results include the theoretical line-of-sight displacement of each pixel; The residual inversion module is used to solve the parameter field based on the theoretical line-of-sight displacement to obtain spatial distribution information. The residual inversion is used to take the InSAR observation line-of-sight deformation time series as the target value and the physical forward model as the forward operator, and to invert the spatial distribution of the dam body equivalent elastic modulus and the reservoir bank equivalent permeability coefficient pixel by pixel by minimizing the residual between the theoretical line-of-sight displacement and the InSAR observation line-of-sight deformation. The result output module is used to generate diagnostic results based on the spatial distribution information.

[0138] By applying the technical solutions of the above embodiments, the dam equivalent stiffness diagnosis system based on InSAR residual inversion described in the above embodiments can, after the data acquisition module acquires multi-source data, the physical forward modeling module constructs a physical forward model and generates forward prediction results based on the multi-source data using the physical forward modeling module. Then, the residual inversion module solves for the parameter field of the residual inversion based on the theoretical line-of-sight displacement in the forward prediction results to obtain spatial distribution information. The result output module then generates diagnosis results based on the spatial distribution information. The system can construct a closed-loop processing framework of physical forward modeling and residual inversion, encapsulating the classical mechanical model into multiple forward modeling layers, which are then superimposed and projected onto the InSAR line of sight to form a differentiable forward modeling operator. This decomposes the LOS deformation observed by InSAR into multiple components with clear physical meaning. In the residual inversion process, the deformation time series along the InSAR line of sight is used as the target value, and the physical forward model is used as the forward operator. By minimizing the residual between the theoretical line of sight displacement and the InSAR line of sight deformation, the spatial distribution of the dam's equivalent elastic modulus and the reservoir bank's equivalent permeability coefficient is inverted pixel by pixel. This transforms InSAR monitoring from deformation response description to structural stiffness diagnosis, improving the accuracy of the diagnostic results.

[0139] It should be noted that other corresponding descriptions of the functional units involved in the dam equivalent stiffness diagnosis system based on InSAR residual inversion provided in this application embodiment can be found in the corresponding descriptions in the dam equivalent stiffness diagnosis method based on InSAR residual inversion provided in the above embodiment, and will not be repeated here.

[0140] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0141] The embodiments described above are merely examples of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application.

Claims

1. A method for diagnosing the equivalent stiffness of a dam body based on InSAR residual inversion, characterized in that, The method includes: Acquire multi-source data, including InSAR observation line-of-sight deformation time series, water level process line, dam body geometric parameters, and digital elevation model of the target dam area; A physical forward model is constructed, and forward prediction results are generated based on the multi-source data using the physical forward model; the physical forward model is used to perform forward prediction on multiple physical processes with the water level process line, the dam body geometric parameters and the digital elevation model as input; the forward prediction results include the theoretical line-of-sight displacement of each pixel; Based on the theoretical line-of-sight displacement, the parameter field is solved by residual inversion to obtain spatial distribution information. The residual inversion is used to take the InSAR observation line-of-sight deformation time series as the target value and the physical forward model as the forward operator. By minimizing the residual between the theoretical line-of-sight displacement and the InSAR observation line-of-sight deformation, the spatial distribution of the dam body's equivalent elastic modulus and the reservoir bank's equivalent permeability coefficient is inverted pixel by pixel. Diagnostic results are generated based on the spatial distribution information.

2. The method according to claim 1, characterized in that, Acquire multi-source data, including: Acquire InSAR observation data for the target dam area, wherein the InSAR observation data includes a single-track time-series SAR image sequence covering the target dam area; the time span of the InSAR observation data covers at least one complete water level regulation cycle of the reservoir corresponding to the target dam area. Select the master image and slave image from the InSAR observation data; By registration and resampling, the image is aligned to the slant range azimuth coordinate system of the main image; The interference pair is determined based on the registered and resampled master image and slave image; Based on the unwrapped phase of the interferometric pair, the minimum norm solution is obtained by singular value decomposition, and the cumulative line-of-sight deformation value at each SAR imaging time is obtained by integration. The InSAR observation line-of-sight deformation time series is generated based on the accumulated line-of-sight deformation value.

3. The method according to claim 2, characterized in that, Acquire multi-source data, including: Acquire reservoir water level data, optical remote sensing images, and digital elevation models for the target dam area. The reservoir water level data is a scheduling record that is consistent with the time range covered by the SAR observation data. Align the reservoir water level data to the imaging time of the SAR observation data; The water level process line is generated based on the aligned reservoir water level data; The crest length and outline of the target dam area are measured by visually interpreting the optical remote sensing images. The dam height information is extracted from the digital elevation model to obtain the geometric parameters of the dam body.

4. The method according to claim 1, characterized in that, The physical forward model includes a crustal elastic load forward model layer, a dam body static response forward model layer, and a reservoir bank unsaturated seepage forward model layer. The theoretical line-of-sight displacement of each pixel is generated based on the multi-source data using the physical forward model, including: A three-dimensional displacement field is obtained, which includes a first displacement field output by the crustal elastic load forward modeling layer, a second displacement field output by the dam body static response forward modeling layer, and a third displacement field output by the reservoir bank unsaturated seepage forward modeling layer. By superimposing the first displacement field, the second displacement field, and the third displacement field, a total three-dimensional displacement vector is obtained; The total three-dimensional displacement vector is projected onto the line of sight of the InSAR satellite to obtain the theoretical line-of-sight displacement.

5. The method according to claim 4, characterized in that, The crustal elastic load forward modeling layer is used to calculate the crustal surface elastic displacement field caused by changes in reservoir water load based on elastic load theory. Obtaining the three-dimensional displacement field includes: Based on the dam's geometric parameters, the reservoir's water surface is discretized into multiple grid units; For each of the aforementioned grid cells, the crustal surface displacement response caused by a unit point load is calculated using the Green's function; The first displacement field is obtained by superimposing the crustal surface displacement responses of all the grid cells. The first displacement field is used to characterize the crustal elastic displacement field of the entire reservoir area.

6. The method according to claim 4, characterized in that, The static response forward modeling layer of the dam body is used to calculate the static flexural displacement of the dam body under water pressure based on structural mechanics. Obtaining the three-dimensional displacement field includes: Extract the spatial location of the dam surface from the digital elevation model and the dam geometric parameters; Determine the height coordinates of each pixel on the dam surface based on the spatial location; The dam type category is extracted from the dam body geometric parameters, and a closed analytical model is called according to the dam type category. When the dam type category is a gravity dam, the closed analytical model adopts a cantilever beam model; when the dam type category is an arch dam, the closed analytical model adopts a thin shell analytical model or a simplified model of the arch beam load distribution method. Based on the closed analytical model, the displacement component along the river is calculated by combining the height coordinates, the current water level, and the equivalent elastic modulus of the dam body. Based on the Poisson effect, the lateral and vertical displacement components are estimated from the downstream displacement components. The downstream displacement component, the lateral displacement component, and the vertical displacement component are combined into a three-dimensional displacement vector to obtain the second displacement field.

7. The method according to claim 4, characterized in that, The unsaturated seepage forward modeling layer of the reservoir bank is used to calculate the shallow deformation of the reservoir bank caused by the rise and fall of the reservoir water level based on the unsaturated seepage theory. Obtaining the three-dimensional displacement field includes: The reservoir bank parameters are calculated based on the dam body geometric parameters and the digital elevation model. The reservoir bank parameters include the distance and elevation of each pixel in the reservoir bank area to the reservoir bank. An unsaturated seepage model is established based on the reservoir bank parameters and the water level process line. The unsaturated seepage model is used to describe the relationship between the groundwater level and the reservoir water level. According to the unsaturated seepage model, the change in saturated zone thickness caused by water level change is calculated using soil-water characteristic curves and permeability coefficient functions. The shallow displacement is calculated based on the effective stress principle and the change in the thickness of the saturated zone, and the third displacement field is obtained.

8. The method according to claim 1, characterized in that, Based on the aforementioned theoretical line-of-sight displacement, residual inversion is performed to solve the parameter field, thereby obtaining spatial distribution information, including: Define an objective function, which is the sum of squared residuals between the InSAR observation line-of-sight deformation and the theoretical line-of-sight displacement over the entire monitoring period, plus a spatial smoothing regularization term; The gradient of the objective function with respect to the equivalent elastic modulus of the dam body and the equivalent permeability coefficient of the reservoir bank is calculated analytically using the chain rule. Iterative optimization and inversion are performed based on the gradient to output the spatial distribution information; the spatial distribution information includes a spatial distribution map of the dam body's equivalent elastic modulus and a spatial distribution map of the reservoir bank's equivalent permeability coefficient.

9. The method according to claim 1, characterized in that, Based on the spatial distribution information, a diagnostic result is generated, including: Obtain the InSAR raster information corresponding to the deformation time sequence of the InSAR observation line; An output format is defined based on the InSAR raster information, and the output format includes the same spatial range and resolution as the InSAR raster information. The spatial distribution information is converted into an output product according to the output format, and the output product includes the spatial distribution information and the transfer gain drift rate. A hierarchical early warning mechanism is constructed based on the transfer gain drift rate, and the diagnostic results are generated according to the hierarchical early warning mechanism.

10. A dam equivalent stiffness diagnostic system based on InSAR residual inversion, characterized in that, The system includes: The data acquisition module is used to acquire multi-source data, including the InSAR observation line deformation time series, water level process line, dam body geometric parameters, and digital elevation model of the target dam area; The physical forward modeling module is used to construct a physical forward modeling model and generate forward prediction results based on the multi-source data using the physical forward modeling model; the physical forward modeling model is used to perform forward prediction on multiple physical processes using the water level process line, the dam body geometric parameters, and the digital elevation model as inputs; the forward prediction results include the theoretical line-of-sight displacement of each pixel; The residual inversion module is used to solve the parameter field based on the theoretical line-of-sight displacement to obtain spatial distribution information. The residual inversion is used to take the InSAR observation line-of-sight deformation time series as the target value and the physical forward model as the forward operator, and to invert the spatial distribution of the dam body equivalent elastic modulus and the reservoir bank equivalent permeability coefficient pixel by pixel by minimizing the residual between the theoretical line-of-sight displacement and the InSAR observation line-of-sight deformation. The result output module is used to generate diagnostic results based on the spatial distribution information.

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