A method for estimating internal layered deformation of slopes under physical constraints

Abstract

The present application relates to the technical field of internal slope deformation estimation and provides a method for layered deformation estimation within a slope under physical constraints. The method comprises: inferring geological layering information of each internal measurement point based on the deformation information of each internal measurement point, and inferring geological layering information of each surface measurement point based on the deformation information of each surface measurement point; dividing the target slope into multiple grid areas, and determining the layer corresponding to each grid area based on all geological layering information; calculating, for each layer, the deformation prediction values ​​of all grid areas in the layer based on the coordinates of the grid points in each grid area in the layer; constructing a global optimization objective function based on the deformation prediction values ​​of all grid areas of the target slope; and solving for the final deformation prediction value of each grid area of ​​the target slope based on the global optimization objective function. The method of the present application can improve the accuracy of deformation estimation within the slope.

Description

Technical Field

[0001] The present application relates to the technical field of slope internal deformation estimation, and in particular to a layered deformation estimation method for slope internal under physical constraints. Background Art

[0002] Monitoring and estimating slope deformation is crucial for early warning and prevention of geological hazards such as landslides. Slope deformation directly reflects slope stability and serves as a crucial early warning indicator before a landslide occurs. Therefore, accurately monitoring and estimating slope deformation, especially three-dimensional underground and surface deformation, is crucial for identifying potential risks in advance. Significant progress has been made in monitoring three-dimensional slope surface deformation. Traditional geodetic techniques, such as the Global Navigation Satellite System (GNSS), levels, and total stations, are widely used to monitor slope surface deformation. However, these techniques are limited by equipment cost and deployment density, resulting in low spatial resolution. In contrast, Interferometric Synthetic Aperture Radar (InSAR), a remote sensing monitoring method, offers the advantages of low cost, large coverage, and high spatial resolution (meter-level), providing dense historical deformation data.

[0003] However, compared to surface deformation, internal deformation is more important for early identification and early warning of slope risks. Surface deformation is typically the result of internal deformation being transferred to the slope surface, while subsurface deformation anomalies often precede surface deformation. Three-dimensional deformation at varying depths within a slope is primarily measured using sensors deployed in field boreholes (such as deep inclinometers). This method offers high accuracy and near-real-time performance, but it has limitations, making it difficult to obtain high-spatial-resolution data on subsurface 3D slope deformation. These limitations include the high cost of field drilling and the expensive purchase and maintenance of sensors. A dense deployment of borehole sensors significantly increases observation costs. Furthermore, the density of slope boreholes is negatively correlated with slope strength: higher borehole density indicates weaker slope shear strength. Consequently, current internal slope displacement observations typically consist of only two to three observation lines and a small number of measurement points, significantly limiting the spatial resolution of internal slope deformation estimates and making it difficult to objectively characterize the complex local deformation characteristics within the slope.

[0004] Currently, subsurface deformation modeling primarily relies on traditional geostatistical interpolation methods (such as kriging and Gaussian regression), which spatially interpolate sparse observations to estimate deformation values ​​at unknown locations. However, when observations are sparse and the deformation process is complex, these traditional methods lack accuracy and are difficult to apply in practice. In recent years, data-driven interpolation methods have become a research hotspot. For example, multi-point statistical methods employ spatial pattern matching strategies to simulate the location attributes of unobserved points in a nonparametric manner, significantly improving the ability to represent complex spatial structures. Furthermore, deep learning-based models, such as convolutional neural networks and generative adversarial networks, are widely used for spatiotemporal data interpolation due to their powerful feature extraction capabilities and nonlinear modeling advantages. While these methods enhance deformation representation, they still rely on a large number of observations and struggle with sparse sample sizes, such as in slope subsurfaces. Furthermore, numerical simulation methods, such as the finite element method, have also been used to estimate three-dimensional subsurface deformation in slopes. However, these methods rely on expensive physical and mechanical parameter testing, making it difficult to develop a universal model that accurately describes the deformation process. In summary, it is currently difficult to achieve high spatial resolution estimation of underground deformation using methods such as statistical interpolation and data-driven interpolation, resulting in low accuracy of deformation estimation inside the slope. Summary of the Invention

[0005] The present application provides a layered deformation estimation method for the interior of a slope under physical constraints, which can solve the problem of low accuracy in deformation estimation within the slope.

[0006] The present application provides a method for estimating the internal layered deformation of a slope under physical constraints. The method includes:

[0007] Obtain deformation information of multiple internal measurement points of the target slope, and obtain deformation information of multiple surface measurement points from InSAR data of the target slope surface, infer geological stratification information of each internal measurement point based on the deformation information of each internal measurement point, and infer geological stratification information of each surface measurement point based on the deformation information of each surface measurement point;

[0008] Divide the target slope into multiple grid areas, and determine the corresponding layer of each grid area based on all geological layer information;

[0009] For each layer, the deformation prediction values ​​of all grid areas in the layer are calculated based on the coordinates of the grid points in each grid area in the layer;

[0010] A global optimization objective function is constructed based on the deformation prediction values ​​of all grid areas of the target slope; the global optimization objective function is used to describe the accuracy of the deformation prediction values ​​of all grid areas;

[0011] Based on the global optimization objective function, the final deformation prediction value of each grid area of ​​the target slope is solved.

[0012] Optionally, determine the layer corresponding to each grid area based on all geological layer information, including:

[0013] Construct a basis function linear combination expression based on all geological layer information;

[0014] Determine the value of the sparse coefficient matrix in the linear combination expression of the basis functions;

[0015] Substitute the values ​​of the sparse coefficient matrix into the basis function linear combination expression to obtain the layer attribute information of each grid area; the layer attribute information is used to describe the layer corresponding to the grid area.

[0016] Optionally, the linear combination of basis functions is expressed as:

[0017] ;

[0018] ;

[0019] in, Represents the layer attribute information matrix of all grid areas, represents the set of basis functions, represents a sparse coefficient matrix, represents the total number of basis functions, Indicates the The weight coefficients corresponding to the basis functions are: Indicates the The values ​​of the basis functions on all grid areas are: represents the polynomial basis function that incorporates all geological layering information, represents the Gaussian radial basis function into which all geological layer information is substituted, ;

[0020] Determine the sparse coefficient matrix in the linear combination expression of the basis functions, including:

[0021] By formula:

[0022] ;

[0023] Determine the value of the sparse coefficient matrix;

[0024] in, represents the regularization parameter, The observation vector representing all geological layer information, represents the 2-norm operation, Represents the 1-norm operation.

[0025] Optionally, deformation prediction values ​​for all grid areas in the layer are calculated based on the coordinates of the grid points in each grid area in the layer, including:

[0026] Construct a stress-strain model based on the coordinates of all grid points in the layer;

[0027] Solve for the unknown parameter vector in the stress-strain model;

[0028] Substitute the unknown parameter vector into the stress-strain model to obtain the deformation prediction value of each grid area in the layer.

[0029] Optionally, the stress-strain model is:

[0030] ;

[0031] in, Indicates the The deformation vectors of all grid regions in a layer, , represents the number of layers in the target area, represents the stress-strain model coefficient matrix, Indicates the Unknown parameter vectors for each layer:

[0032] ;

[0033] ;

[0034] in, Indicates the The deformation prediction value of the 0th grid area in the layer on the first coordinate axis, Indicates the The deformation prediction value of the 0th grid area in the layer on the second coordinate axis, Indicates the The deformation prediction value of the first grid area in each layer on the first coordinate axis, Indicates the The deformation prediction value of the first grid area in each layer on the second coordinate axis, Indicates the The deformation prediction value of the second grid area in the layer on the first coordinate axis, Indicates the The deformation prediction value of the second grid area in the layer on the second coordinate axis, Indicates the In the layer The predicted deformation value of the grid area on the first coordinate axis, Indicates the In the layer The predicted deformation value of the grid area on the second coordinate axis, Indicates the The coordinates of the 0th grid point in the layer on the first coordinate axis, Indicates the The coordinates of the 0th grid point in the layer on the second coordinate axis, Indicates the The coordinates of the first grid point in the layer on the first coordinate axis, Indicates the The coordinates of the first grid point in each layer on the second coordinate axis, Indicates the The coordinates of the second grid point in the layer on the first coordinate axis, Indicates the The coordinates of the second grid point in the layer on the second coordinate axis, Indicates the In the layer The coordinates of the grid points on the first coordinate axis, Indicates the In the layer The coordinates of the grid points on the second coordinate axis, Indicates the The shear strain component of the target slope in each layer, Indicates the The normal strain component of the target slope in the first coordinate axis direction in each layer is: Indicates the The normal strain component of the target slope in the second coordinate axis direction in each layer is: Indicates the The rotational angular velocity of the target slope in each layer, Represents a transpose operation.

[0035] Optionally, solve for unknown parameter vectors in the stress-strain model, including:

[0036] Construct a minimization objective function;

[0037] Solve the minimization objective function to obtain the value of the unknown parameter vector.

[0038] Optionally, the global optimization objective function is:

[0039] ;

[0040] in, A matrix representing the deformation prediction values ​​for all grid areas, represents the kernel function matrix, represents the coefficient vector, represents the ridge regression regularization parameter, represents the 2-norm operation, Represents a transpose operation.

[0041] Optionally, based on the global optimization objective function, the final deformation prediction value of each grid area of ​​the target slope is solved, including:

[0042] Minimize the global optimization objective function to obtain the global optimization coefficient vector;

[0043] The final deformation prediction value of each grid area is calculated based on the globally optimized coefficient vector.

[0044] Optionally, calculate the final deformation prediction value for each grid area based on the globally optimized coefficient vector, including:

[0045] By formula:

[0046] ;

[0047] Calculate the matrix of final deformation prediction values ​​for all grid areas ;

[0048] in, Represents the coefficient vector for global optimization.

[0049] The above solution of the present application has the following beneficial effects:

[0050] In an embodiment of the present application, deformation information of internal measurement points within a target slope is obtained, and deformation information of multiple surface measurement points is obtained from InSAR data on the surface of the target slope. The geological stratification information of the internal measurement points is inferred based on the deformation information of each internal measurement point, and the geological stratification information of the surface measurement points is inferred based on the deformation information of each surface measurement point. The target slope is then divided into multiple grid areas. The corresponding layer of each grid area is determined based on all the geological stratification information. Then, for each layer, the deformation prediction values ​​of all grid areas in the layer are calculated based on the coordinates of the grid points in each grid area in the layer. Then, a global optimization objective function is constructed based on the deformation prediction values ​​of all grid areas of the target slope. Finally, based on the global optimization objective function, the final deformation prediction value of each grid area of ​​the target slope is solved. In this case, the target slope is stratified according to the deformation information of the measurement points, achieving reasonable stratification of the target slope. The deformation prediction values ​​are calculated based on the grid point information in the layer, effectively improving the accuracy of deformation prediction for the layered area. The construction and solution of the global optimization objective function can further improve the accuracy of deformation estimation within the slope.

[0051] Other beneficial effects of the present application will be described in detail in the subsequent specific implementation section. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments or descriptions of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0053] Figure 1 A flowchart of a method for estimating layered deformation within a slope under physical constraints provided in one embodiment of the present application;

[0054] Figure 2 A schematic diagram of the root mean square error provided in one embodiment of the present application. DETAILED DESCRIPTION

[0055] In the following description, specific details such as specific system structures and techniques are provided for purposes of illustration rather than limitation to facilitate a thorough understanding of the embodiments of the present application. However, it will be apparent to those skilled in the art that the present application may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid obscuring the description of the present application with unnecessary detail.

[0056] It should be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of described features, integers, steps, operations, elements and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or collections thereof.

[0057] It will also be understood that the term "and / or" used in this specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.

[0058] As used in this specification and the appended claims, the term "if" can be interpreted as "when" or "upon" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrase "if it is determined" or "if [described condition or event] is detected" can be interpreted as meaning "upon determination" or "in response to determining" or "upon detection of [described condition or event]" or "in response to detecting [described condition or event]," depending on the context.

[0059] In addition, in the description of the present application specification and the appended claims, the terms "first", "second", "third", etc. are only used to distinguish the descriptions and cannot be understood as indicating or implying relative importance.

[0060] References to "one embodiment" or "some embodiments" in this specification mean that a particular feature, structure, or characteristic described in conjunction with that embodiment is included in one or more embodiments of the present application. Thus, phrases such as "in one embodiment," "in some embodiments," "in other embodiments," and "in other embodiments" appearing in various places in this specification do not necessarily refer to the same embodiment, but rather mean "one or more but not all embodiments," unless otherwise specifically emphasized. The terms "including," "comprising," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0061] In response to the problem of low accuracy in existing deformation estimation inside slopes, an embodiment of the present application provides a layered deformation estimation method inside slopes under physical constraints. The layered deformation estimation method obtains deformation information of internal measurement points inside the target slope and deformation information of multiple surface measurement points from InSAR data on the surface of the target slope. The geological layering information of the internal measurement points is inferred based on the deformation information of each internal measurement point, and the geological layering information of the surface measurement points is inferred based on the deformation information of each surface measurement point. The target slope is then divided into multiple grid areas, and the layer corresponding to each grid area is determined based on all the geological layering information. For each layer, the deformation prediction values ​​of all grid areas in the layer are calculated based on the coordinates of the grid points in each grid area in the layer. A global optimization objective function is constructed based on the deformation prediction values ​​of all grid areas of the target slope. Finally, based on the global optimization objective function, the final deformation prediction value of each grid area of ​​the target slope is solved. Among them, the target slope is stratified according to the deformation information of the measurement points, which realizes the reasonable stratification of the target slope. The deformation prediction value is calculated according to the grid point information in the stratification, which effectively improves the accuracy of deformation prediction in the stratified area. The global optimization objective function is constructed and solved, which can further improve the accuracy of deformation estimation inside the slope.

[0062] Next, the layered deformation estimation method for the slope under physical constraints provided by this application is exemplified.

[0063] like Figure 1 As shown, the method for estimating the internal layered deformation of a slope under physical constraints provided by this application includes the following steps:

[0064] Step 11: Obtain deformation information of multiple internal measurement points of the target slope, and obtain deformation information of multiple surface measurement points from the InSAR data of the target slope surface, infer the geological stratification information of the internal measurement points based on the deformation information of each internal measurement point, and infer the geological stratification information of the surface measurement points based on the deformation information of each surface measurement point.

[0065] The target slope is the slope area where layered deformation estimation is required, including the slope surface and the internal area of ​​the slope. The deformation information of the surface measurement points refers to the displacement changes of the slope surface coordinate points obtained by InSAR data over a historical period of time. The internal measurement points refer to the displacement changes of the internal coordinate points of the slope over a historical period of time observed by measurement tools such as deep inclinometers. The geological layering information refers to the geological layer properties (such as soil layer, weathering layer, loose sedimentary layer, etc.) reflected by the distribution characteristics of displacement changes.

[0066] In some embodiments of the present application, deformation information inside the target slope can be obtained by using a deep inclinometer deployed in a sparse underground borehole, and the internal geological stratification information can be obtained by analyzing the information. InSAR deformation information of the slope surface can be obtained by performing small baseline set interferometry (SBAS-InSAR) processing on multi-temporal synthetic aperture radar (SAR) images, and preliminary geological stratification information of the surface measurement points can be obtained by analyzing the InSAR deformation information. The deformation information can be analyzed using geological layer inversion analysis methods, support vector machines, geological information integration models, etc. to obtain geological stratification information of the internal measurement points.

[0067] It should be noted that a plurality of surface measurement points on the target slope surface may be randomly determined, and the density of the measurement points is relatively low, such as only one measurement point per 10 cubic meters on average.

[0068] Step 12: Divide the target slope into multiple grid areas, and determine the layer corresponding to each grid area based on all geological layer information.

[0069] For example, the target slope (including the surface and internal areas) can be evenly divided to obtain multiple grid areas. The size of the grid area is set according to the actual situation. The size needs to satisfy that one grid area corresponds to only one type of geological layer, and avoids one grid area including two or more types of geological layers, and finally obtains a high-resolution grid area (it can be considered that the grid area obtained by dividing according to the grid area size that avoids one grid area including two or more types of geological layers is a high-resolution grid area).

[0070] In some embodiments of the present application, the step of determining the layer corresponding to each grid area based on all geological layer information includes:

[0071] In the first step, a linear combination expression of basis functions is constructed based on all geological layer information.

[0072] Specifically, the linear combination expression of basis functions is:

[0073] ;

[0074] ;

[0075] in, Represents the layer attribute information matrix of all grid areas, represents the set of basis functions, represents a sparse coefficient matrix, represents the total number of basis functions, Indicates the The weight coefficients corresponding to the basis functions are: Indicates the The values ​​of the basis functions on all grid areas are: represents the polynomial basis function that incorporates all geological layer information and is used to characterize the terrain deformation pattern with a global trend. represents the Gaussian radial basis function that incorporates all geological layer information and is used to characterize local nonlinear changes. .

[0076] The second step is to determine the value of the sparse coefficient matrix in the basis function linear combination expression.

[0077] Specifically, through the formula:

[0078] ;

[0079] Determine the value of the sparse coefficient matrix.

[0080] in, represents the regularization parameter, The observation vector representing all geological layer information, , Indicates the geological stratification information of the first observation point, Indicates the geological stratification information of the second observation point, Indicates the The geological layer information of each observation point, which can be an internal observation point or a surface observation point, is equal to the sum of the number of internal observation points and surface observation points, represents the 2-norm operation, Represents the 1-norm operation.

[0081] Exemplarily, the above formula is solved using the Lasso regression method to determine the value of the sparse coefficient matrix.

[0082] In the third step, the values ​​of the sparse coefficient matrix are substituted into the basis function linear combination expression to obtain the layer attribute information of each grid area.

[0083] The above layer attribute information is used to describe the layer corresponding to the grid area.

[0084] For example, the layer attribute information is a numerical value, and the size of the numerical value reflects the depth of the layer corresponding to the grid area. For example, the larger the numerical value, the deeper the layer corresponding to the grid area, and the smaller the numerical value, the shallower the layer corresponding to the grid area. Grid areas with the same layer attribute information are considered to belong to the same layer.

[0085] Step 13: For each layer, based on the coordinates of the grid points in each grid area in the layer, calculate the deformation prediction values ​​of all grid areas in the layer.

[0086] The coordinates of the grid points are coordinates in a two-dimensional coordinate system constructed with the layer as a plane. The grid points can be the center point of the grid area or a random point in the grid area.

[0087] In some embodiments of the present application, the step of calculating deformation prediction values ​​of all grid areas in the layer based on the coordinates of the grid points in each grid area in the layer includes:

[0088] In the first step, the stress-strain model is constructed based on the coordinates of all grid points in the layer.

[0089] Specifically, the stress-strain model is:

[0090] ;

[0091] in, Indicates the The deformation vectors of all grid regions in a layer, , represents the number of layers in the target area, represents the stress-strain model coefficient matrix, Indicates the Unknown parameter vectors for each layer:

[0092] ;

[0093] ;

[0094] in, Indicates the The deformation prediction value of the 0th grid area in the layer on the first coordinate axis, Indicates the The deformation prediction value of the 0th grid area in the layer on the second coordinate axis, Indicates the The deformation prediction value of the first grid area in each layer on the first coordinate axis, Indicates the The deformation prediction value of the first grid area in each layer on the second coordinate axis, Indicates the The deformation prediction value of the second grid area in the layer on the first coordinate axis, Indicates the The deformation prediction value of the second grid area in the layer on the second coordinate axis, Indicates the In the layer The predicted deformation value of the grid area on the first coordinate axis, Indicates the In the layer The predicted deformation value of the grid area on the second coordinate axis, Indicates the The coordinates of the 0th grid point in the layer on the first coordinate axis, Indicates the The coordinates of the 0th grid point in the layer on the second coordinate axis, Indicates the The coordinates of the first grid point in the layer on the first coordinate axis, Indicates the The coordinates of the first grid point in each layer on the second coordinate axis, Indicates the The coordinates of the second grid point in the layer on the first coordinate axis, Indicates the The coordinates of the second grid point in the layer on the second coordinate axis, Indicates the In the layer The coordinates of the grid points on the first coordinate axis, Indicates the In the layer The coordinates of the grid points on the second coordinate axis, Indicates the The shear strain component of the target slope in each layer, Indicates the The normal strain component of the target slope in the first coordinate axis direction in each layer is: Indicates the The normal strain component of the target slope in the second coordinate axis direction in each layer is: Indicates the The rotational angular velocity of the target slope in each layer, Represents a transpose operation.

[0095] It should be noted that the first coordinate axis is a coordinate axis in a two-dimensional coordinate system constructed with the layer as a plane, the second coordinate axis is another coordinate axis in the two-dimensional coordinate system, and the 0th grid point is the grid point with the smallest deformation among all the grid points in the layer.

[0096] The second step is to solve the value of the unknown parameter vector in the stress-strain model.

[0097] Specifically, we construct a minimization objective function, and then solve the minimization objective function to obtain the unknown parameter vector The value of .

[0098] The minimized objective function is:

[0099] ;

[0100] For example, the least squares principle can be used to solve the minimization objective function, and the value of the unknown parameter vector can be obtained as follows: .

[0101] In the third step, the value of the unknown parameter vector is substituted into the stress-strain model to obtain the deformation prediction value of each grid area in the layer.

[0102] It should be noted that the deformation predictions obtained in this step include the deformation predictions for the grid area along both coordinate axes. To facilitate the assessment of the overall deformation degree, the combined deformation value for each grid area can be calculated by taking the square root of the sum of the deformation components in both directions.

[0103] Step 14: construct a global optimization objective function based on the deformation prediction values ​​of all grid areas of the target slope.

[0104] The above global optimization objective function is used to describe the accuracy of deformation prediction values ​​in all grid areas.

[0105] Specifically, the global optimization objective function is:

[0106] ;

[0107] in, A matrix representing the deformation prediction values ​​for all grid areas, represents the kernel function matrix, represents the coefficient vector, represents the ridge regression regularization parameter, represents the 2-norm operation, Represents a transpose operation.

[0108] The above kernel function matrix is ​​defined as:

[0109] ;

[0110] in, and Represent the feature vectors (such as spatial coordinates or other representation information) of two different grid areas, which are used to calculate the similarity between the two areas. Represents the bandwidth parameter of the kernel function.

[0111] Step 15: Based on the global optimization objective function, the final deformation prediction value of each grid area of ​​the target slope is solved.

[0112] In some embodiments of the present application, the step of solving the final deformation prediction value of each grid area of ​​the target slope based on the global optimization objective function includes:

[0113] The first step is to minimize the global optimization objective function and obtain the global optimization coefficient vector.

[0114] Exemplarily, the least squares method may be used to minimize the global optimization objective function to obtain a global optimization coefficient vector.

[0115] In the second step, the final deformation prediction value of each grid area is calculated based on the globally optimized coefficient vector.

[0116] Specifically, through the formula:

[0117] ;

[0118] Calculate the matrix of final deformation prediction values ​​for all grid areas , which includes the final deformation prediction value of each grid area and has the dimension ,in is the total number of grid areas to be predicted. is the kernel function matrix, whose dimension is ,in is the number of observation points (including surface observation points and internal observation points).

[0119] in, Represents the coefficient vector of global optimization, whose dimension is , corresponding to the regression weight of each kernel function center (i.e., surface observation point and internal observation point).

[0120] It should be noted that after obtaining the final deformation prediction value of the grid area in each layer of the target slope, the deformation condition inside the target slope can be analyzed to facilitate monitoring the occurrence of disasters such as landslides on the target slope.

[0121] It is worth mentioning that the target slope is stratified according to the deformation information of the measurement points, which realizes the reasonable stratification of the target slope. The deformation prediction value is calculated according to the coordinates and deformation values ​​of the grid points in the stratification, which effectively improves the prediction accuracy of the terrain deformation in the stratified area. The kernel ridge regression optimization objective function is constructed and solved, which can further improve the accuracy of the deformation estimation inside the slope.

[0122] The method of the present application is illustrated below with reference to a specific example.

[0123] The slope numerical simulation was performed using the simulation software FLAC3D. The dimensions and gridding of the simulation area fully accounted for the actual geological conditions, ensuring accurate representation of the soil's physical properties, including density, shear modulus, and Mohr-Coulomb shear strength. The Mohr-Coulomb constitutive model was employed to rationally describe the relationship between the soil's shear strength and normal stress. The soil density was set to 2000 kg / m³, the bulk modulus to 3e9 Pa, and the shear modulus to 1e9 Pa. Key parameters such as the friction angle (20 degrees), cohesion (12,380 Pa), and tensile strength (1e6 Pa) were considered to describe the soil's deformation characteristics and failure behavior.

[0124] The simulation assumes 36 point-by-point GNSS / InSAR deformation observations of the dam's surface and three internally layered borehole inclinometer observations (27 internal deformation values). Based on these observations, all grid regions are first stratified. Then, based on the appropriate stratification, physical constraints are introduced, using the physical relationship between stress and strain to constrain the model's calculations, ensuring that the predicted displacement field conforms to the actual geological conditions. Finally, kernel ridge regression is used for optimization.

[0125] In order to verify the accuracy of the layered deformation estimation method under physical constraints provided in this application, the traditional Kriging interpolation and Convolutional Neural Network (CNN) methods were used for comparison. The root mean square error (RMSE) and the coefficient of determination ( , Coefficient of Determination) as the evaluation index, the comparison results are as follows Figure 2 As shown, Figure 2 The horizontal axis represents three methods (Kriging interpolation, CNN, and physical model (i.e., the method of this application)), the bar graph represents the root mean square error (RMSE), and the square points represent the R² value. Traditional Kriging interpolation and data-driven CNN methods have large prediction deviations and low correlation when estimating underground deformation of slopes, especially in areas where data is scarce. In contrast, the method proposed in this application can more accurately fit the simulation values ​​when estimating high-spatial-resolution deformation inside the slope, with an RMSE of 0.005m and an R² of 0.98. By introducing physical and mechanical constraints, the stress-strain relationship under complex geological conditions can be effectively captured, showing higher prediction accuracy. Therefore, the method of this application has shown strong advantages in practical applications, providing more accurate results for slope deformation prediction.

[0126] It can be seen from this that the method of the present application can better combine the rich InSAR data on the slope surface with the sparse measurement data inside. Through layering, physical and mechanical constraints and kernel ridge regression optimization, it achieves high-precision and high-resolution estimation of slope underground deformation under complex geological conditions, overcoming the defects of poor resolution and low accuracy of traditional methods when estimating internal deformation under sparse data.

[0127] The above is a preferred embodiment of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles described in the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

Claims

1. A method for estimating layered deformation within a slope under physical constraints, characterized by: include: Obtain deformation information of multiple internal measurement points of the target slope, and obtain deformation information of multiple surface measurement points from InSAR data of the target slope surface, infer geological stratification information of each internal measurement point based on the deformation information of each internal measurement point, and infer geological stratification information of each surface measurement point based on the deformation information of each surface measurement point; Dividing the target slope into a plurality of grid areas, and determining the layer corresponding to each grid area according to all geological layer information; For each layer, respectively, calculating deformation prediction values ​​of all grid areas in the layer based on the coordinates of the grid points in each grid area in the layer; Constructing a global optimization objective function based on deformation prediction values ​​of all grid areas of the target slope; The global optimization objective function is used to describe the accuracy of deformation prediction values ​​of all grid areas; Based on the global optimization objective function, a final deformation prediction value of each grid area of ​​the target slope is solved.

2. The hierarchical deformation estimation method according to claim 1, characterized in that: Determining the layer corresponding to each grid area according to all geological layer information includes: Construct a basis function linear combination expression based on all geological layer information; Determine the value of the sparse coefficient matrix in the basis function linear combination expression; Substituting the value of the sparse coefficient matrix into the basis function linear combination expression, the layer attribute information of each grid area is obtained; the layer attribute information is used to express the layer corresponding to the grid area.

3. The hierarchical deformation estimation method according to claim 2, characterized in that: The linear combination expression of the basis function is: ； ； in, Represents the layer attribute information matrix of all grid areas, represents the set of basis functions, represents a sparse coefficient matrix, represents the total number of basis functions, Indicates the The weight coefficients corresponding to the basis functions are: Indicates the The values ​​of the basis functions on all grid areas are: represents the polynomial basis function that incorporates all geological layering information, represents the Gaussian radial basis function into which all geological layer information is substituted, ; Determining the sparse coefficient matrix in the basis function linear combination expression includes: By formula: ； Determine the value of the sparse coefficient matrix; in, represents the regularization parameter, The observation vector representing all geological layer information, represents the 2-norm operation, Represents the 1-norm operation.

4. The hierarchical deformation estimation method according to claim 1, characterized in that: The calculating deformation prediction values ​​of all grid areas in the layer based on the coordinates of the grid points in each grid area in the layer includes: constructing a stress-strain model based on the coordinates of all grid points in the layer; solving for values ​​of unknown parameter vectors in the stress-strain model; The value of the unknown parameter vector is substituted into the stress-strain model to obtain a deformation prediction value of each grid area in the layer.

5. The hierarchical deformation estimation method according to claim 4, characterized in that: The stress-strain model is: ； in, Indicates the The deformation vectors of all grid regions in a layer, , represents the number of layers in the target area, represents the stress-strain model coefficient matrix, Indicates the Unknown parameter vectors for each layer: ； ； in, Indicates the The deformation prediction value of the 0th grid area in the layer on the first coordinate axis, Indicates the The deformation prediction value of the 0th grid area in the layer on the second coordinate axis, Indicates the The deformation prediction value of the first grid area in each layer on the first coordinate axis, Indicates the The deformation prediction value of the first grid area in each layer on the second coordinate axis, Indicates the The deformation prediction value of the second grid area in the layer on the first coordinate axis, Indicates the The deformation prediction value of the second grid area in the layer on the second coordinate axis, Indicates the In the layer The predicted deformation value of the grid area on the first coordinate axis, Indicates the In the layer The predicted deformation value of the grid area on the second coordinate axis, Indicates the The coordinates of the 0th grid point in the layer on the first coordinate axis, Indicates the The coordinates of the 0th grid point in the layer on the second coordinate axis, Indicates the The coordinates of the first grid point in the layer on the first coordinate axis, Indicates the The coordinates of the first grid point in each layer on the second coordinate axis, Indicates the The coordinates of the second grid point in the layer on the first coordinate axis, Indicates the The coordinates of the second grid point in the layer on the second coordinate axis, Indicates the In the layer The coordinates of the grid points on the first coordinate axis, Indicates the In the layer The coordinates of the grid points on the second coordinate axis, Indicates the The shear strain component of the target slope in each layer, Indicates the The normal strain component of the target slope in the first coordinate axis direction in each layer is: Indicates the The normal strain component of the target slope in the second coordinate axis direction in each layer is: Indicates the The rotational angular velocity of the target slope in each layer, Represents a transpose operation.

6. The hierarchical deformation estimation method according to claim 5, characterized in that: The step of solving the value of the unknown parameter vector in the stress-strain model includes: Construct a minimization objective function; The minimization objective function is solved to obtain the value of the unknown parameter vector.

7. The hierarchical deformation estimation method according to claim 1, characterized in that: The global optimization objective function is: ； in, A matrix representing the deformation prediction values ​​for all grid areas, represents the kernel function matrix, represents the coefficient vector, represents the ridge regression regularization parameter, represents the 2-norm operation, Represents a transpose operation.

8. The hierarchical deformation estimation method according to claim 7, characterized in that: Solving the final deformation prediction value of each grid area of ​​the target slope based on the global optimization objective function includes: Minimizing the global optimization objective function to obtain a global optimization coefficient vector; The final deformation prediction value of each grid area is calculated based on the globally optimized coefficient vector.

9. The hierarchical deformation estimation method according to claim 8, characterized in that: Calculating the final deformation prediction value of each grid area according to the globally optimized coefficient vector includes: By formula: ； Calculate the matrix of final deformation prediction values ​​for all grid areas ; in, Represents the coefficient vector for global optimization.

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