Three-dimensional tunnel model strength interpolation method

Abstract

This invention provides a three-dimensional tunnel model strength interpolation method, comprising: providing several initial calculation points within a predetermined spatial range of a tunnel rock mass, wherein each initial calculation point has known values ​​of real rock mass mechanical parameters; establishing a coordinate system to obtain the coordinates of each initial calculation point; training a neural network model based on an attention mechanism, according to the coordinates of the initial calculation points and the real rock mass mechanical parameters, so that the neural network model can output the interpolated rock mass mechanical parameters of the points within the predetermined spatial range, based on the coordinates of the points provided by the coordinate system; providing the coordinates of several unknown calculation points based on the coordinate system, calling the neural network model, and outputting the interpolated rock mass mechanical parameters of the unknown calculation points. This invention can more accurately simulate the stress distribution of the surrounding rock mass of a project, assess the stability of the surrounding rock, and provide more effective support for tunnel engineering construction.

Description

Technical Field

[0001] This invention relates to the field of rock mass engineering modeling technology, specifically to a method for interpolating the strength of a three-dimensional tunnel model. Background Technology

[0002] In tunnel engineering, due to the complexity of the geological environment, especially the differences in strata lithology, the mechanical parameters of the surrounding rock of the tunnel exhibit significant dispersion. Even under the same lithological classification, the mechanical parameters of the surrounding rock (such as compressive strength and elastic modulus) still show high dispersion due to differences in mineral composition, degree of cementation, and subsequent weathering. This characteristic means that if the spatial variability of rock mass parameters is ignored in the tunnel stability assessment, the safety risk of locally weakened areas will be significantly underestimated.

[0003] In densely built-up urban areas, subway tunnel construction faces multiple constraints: the intricate underground pipe network, the limitations of existing building foundations, and surface traffic control, resulting in insufficient density of exploration boreholes and significant non-uniformity in spatial distribution, such as the "data voids" formed by avoiding important facilities. Therefore, the data obtained by conventional exploration methods is relatively limited, making it difficult to construct a three-dimensional geological model that matches reality.

[0004] The geological characteristics of different strata in the engineering site vary considerably. During the construction of the subway tunnel, new geological information is revealed during the construction period. For example, during tunnel excavation, more detailed geological information around the tunnel is revealed, and more rock mechanics parameters can be obtained. Traditional methods require complex interpolation and fitting to update the data, which is cumbersome and time-consuming, and it is difficult to quickly adapt to new geological data.

[0005] Traditional methods, when dealing with the spatial correlation of rock mass mechanical parameters, can only analyze correlations at a single scale and struggle to simultaneously resolve multi-level geological features, such as regional trends, local clusters, and outliers. Therefore, they fail to capture the complex dependencies between different locations. This not only limits the model's predictive capabilities, preventing it from providing accurate data for construction risk assessment and support design, but also leads to low computational efficiency or insufficient accuracy.

[0006] With the rapid development of urban rail transit infrastructure construction in China, subway tunnel engineering projects inevitably face various complex engineering geological environments. As the main support for tunnel stability, the complexity and variability of rock mass mechanical properties will inevitably have a significant impact on the safety, stability, and applicability of tunnel engineering.

[0007] Due to differences in formation processes, geological history, internal mineral composition, and environmental factors, rock masses exhibit significant variations in their geological properties. Even rock masses of the same lithology can show considerable fluctuations in their rock mechanical parameters. Therefore, accurately describing the geological characteristics of the surrounding rock masses is particularly important during subway tunnel construction.

[0008] However, conducting a comprehensive and accurate geological survey along the project route during the early stages of the project will increase engineering costs. Conversely, conducting surveys only in localized areas will result in insufficient and inaccurate consideration of the rock mass's mechanical properties due to the limited survey area.

[0009] Traditional geological interpolation methods are prone to geometric distortion when dealing with complex geological structures, resulting in insufficient model smoothness and accuracy. When addressing the spatial correlation of rock mass mechanical parameters, they often struggle to capture the complex dependencies between different locations, leading to limited predictive power or insufficient generalization ability. To achieve better mechanical parameter interpolation, existing techniques often employ multiple numerical fitting and interpolation methods, resulting in overly cumbersome and time-consuming data preprocessing. The resulting models still require significant time for debugging to adapt to the corresponding geological conditions.

[0010] Existing technologies struggle to accurately analyze and describe the geological characteristics of rock masses along project routes while ensuring the project's economic viability. Therefore, there is an urgent need for a numerical modeling method capable of accurately describing the geological characteristics of the surrounding rock mass. This would allow for more precise simulation of stress distribution in the surrounding rock, assessment of rock stability, and ultimately, more effective support for tunnel construction. Summary of the Invention

[0011] The purpose of this invention is to provide a method for interpolating mechanical parameters of a three-dimensional tunnel model, thereby constructing a numerical model that matches the actual strength of the surrounding rock mass, more accurately simulating the stress distribution of the surrounding rock mass, evaluating the stability of the surrounding rock, and providing more effective support for tunnel construction.

[0012] To achieve the above objectives, this invention provides a three-dimensional tunnel model strength interpolation method, comprising the following steps: within a preset spatial range of a tunnel rock mass, providing several initial calculation points, each initial calculation point having known values ​​of real rock mass mechanical parameters; establishing a coordinate system to obtain the coordinates of each initial calculation point; based on an attention mechanism, training a neural network model according to the coordinates of the initial calculation points and the real rock mass mechanical parameters, so that the neural network model can output the interpolated rock mass mechanical parameters of the points within the preset spatial range, based on the coordinates of the points provided by the coordinate system; providing the coordinates of several unknown calculation points based on the coordinate system, calling the neural network model, and outputting the interpolated rock mass mechanical parameters of the unknown calculation points.

[0013] Optionally, the step of training a neural network model based on the attention mechanism, according to the coordinates of the initial calculation point and the actual rock mass mechanics parameters, so that the neural network model can output the interpolated rock mass mechanics parameters of the point within the preset space based on the coordinates of the point provided by the coordinate system, specifically includes: a trial calculation stage: randomly dividing the initial calculation point into a first calculation point and a second calculation point according to a fixed ratio, calculating the mechanical parameter aggregation feature matrix between the first calculation point and the second calculation point based on the attention mechanism, inputting the mechanical parameter aggregation feature matrix into a first feedforward neural network, and outputting a model mechanical parameter prediction matrix; a verification stage: judging whether the model rock mass mechanics parameter prediction matrix is ​​qualified based on the model rock mass mechanics parameter prediction matrix and the actual rock mass mechanics parameters of the first calculation point; if yes, the neural network model is qualified and can be called; if no, the neural network model is adjusted and the trial calculation stage is repeated until the neural network model is qualified.

[0014] Optionally, the step of calculating the aggregated feature matrix of mechanical parameters between the first calculation point and the second calculation point based on the attention mechanism specifically includes: providing a query vector parameter matrix and a key vector parameter matrix; obtaining a first coordinate feature transformation matrix for each first calculation point based on a second feedforward neural network according to the coordinates of each first calculation point; obtaining a second coordinate feature transformation matrix for each second calculation point based on a third feedforward neural network according to the coordinates of each second calculation point; obtaining a query vector for each first calculation point based on the first coordinate feature transformation matrix and the query vector parameter matrix; obtaining a key vector for each second calculation point based on the second coordinate feature transformation matrix and the key vector parameter matrix; obtaining an order value vector for each second calculation point based on the second coordinate feature transformation matrix and the actual rock mass mechanical parameters of the second calculation point; obtaining a first spatial similarity between any first calculation point and the second calculation point based on the query vector of the first calculation point and the key vector of the second calculation point; and obtaining the aggregated feature matrix of mechanical parameters between any first calculation point and the second calculation point based on the first spatial similarity and the order value vector of each second calculation point.

[0015] Optionally, obtaining the order vector of each second calculation point based on the second coordinate feature transformation matrix and the actual rock mass mechanical parameters of the second calculation point specifically includes: using the second coordinate feature transformation matrix and the actual rock mass mechanical parameters of the second calculation point as material for feature extraction by a fourth feedforward neural network; and using the second coordinate feature transformation matrix and the actual rock mass mechanical parameters of the second calculation point processed by the fourth feedforward neural network as material for feature extraction by a fifth feedforward neural network to obtain the order vector of each second calculation point.

[0016] Optionally, at least one of the following adjustment operations may be performed based on the gradient descent algorithm: adjusting the query vector parameter matrix; adjusting the key vector parameter matrix; randomly re-dividing the initial calculation points into the first calculation point and the second calculation point according to the preset ratio to adjust the first coordinate feature transformation matrix and the second coordinate feature transformation matrix; adjusting at least one of the first feedforward neural network, the second feedforward neural network, the third feedforward neural network, the fourth feedforward neural network, and the fifth feedforward neural network.

[0017] Optionally, providing coordinates of several unknown calculation points based on the coordinate system, calling the neural network model, and outputting the interpolated rock mass mechanics parameters of the unknown calculation points specifically includes: obtaining a query vector for each unknown calculation point based on the coordinate matrix of each unknown calculation point and the query vector parameter matrix of the qualified neural network model; obtaining a key vector for each initial calculation point based on the coordinate matrix of each initial calculation point and the key vector parameter matrix of the qualified neural network model; obtaining a second spatial similarity between each unknown calculation point and each initial calculation point based on the key vector of each initial calculation point and the query vector of each unknown calculation point; obtaining an interpolated mechanics parameter aggregation feature matrix between each unknown calculation point and each initial calculation point based on the second spatial similarity and the qualified order value vector of each initial calculation point; and inputting the interpolated mechanics parameter aggregation feature matrix into the first feedforward neural network to output an interpolated mechanics parameter prediction matrix.

[0018] Optionally, it also includes: performing inverse normalization processing on the interpolated rock mass mechanical parameter prediction matrix based on the interpolated rock mass mechanical parameter prediction matrix to obtain the interpolated rock mass mechanical parameters of the unknown calculation point.

[0019] Optionally, it further includes: performing normalization processing based on the actual rock mass mechanics parameters of each initial calculation point, specifically including: obtaining the average value of the actual rock mass mechanics parameters of all the initial calculation points; obtaining the standard deviation of the actual rock mass mechanics parameters of all the initial calculation points; obtaining the strength normalization term of any initial calculation point based on the value of the actual rock mass mechanics parameters, the average value, and the standard deviation; and calculating the loss function with the rock mass mechanics parameter prediction matrix based on the normalization term.

[0020] Optionally, determining whether the model rock mass mechanical parameter prediction matrix is ​​qualified based on the model rock mass mechanical parameter prediction matrix and the actual rock mass mechanical parameters specifically includes: comparing the model rock mass mechanical parameter prediction matrix with the actual mechanical parameter matrix of the first calculation point using a loss function to determine whether the model rock mass mechanical parameter prediction matrix is ​​qualified.

[0021] Optionally, the coordinate system is a polar coordinate system, and the coordinates are polar coordinates.

[0022] Optionally, there are multiple rock mass mechanical parameters, and the attention mechanism includes a multi-head attention mechanism.

[0023] The present invention provides the following beneficial effects:

[0024] This invention provides a method for strength interpolation in a three-dimensional tunnel model, comprising: providing several initial calculation points within a predetermined spatial range of a tunnel rock mass, each initial calculation point having known values ​​of real rock mass mechanical parameters; establishing a coordinate system to obtain the coordinates of each initial calculation point; training a neural network model based on an attention mechanism, according to the coordinates of the initial calculation points and the real rock mass mechanical parameters, so that the neural network model can output the interpolated rock mass mechanical parameters of the points within the predetermined spatial range, based on the coordinates of the points provided by the coordinate system; providing the coordinates of several unknown calculation points based on the coordinate system, calling the neural network model, and outputting the interpolated rock mass mechanical parameters of the unknown calculation points. This invention rationally optimizes the attention mechanism and applies it to the tunnel modeling interpolation scenario, establishing a neural network model that performs interpolation calculations from known initial calculation points to unknown calculation points. This enables more accurate simulation of the stress distribution of the surrounding rock mass, assessment of the stability of the surrounding rock, and provides more effective support for tunnel construction. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating a three-dimensional tunnel model strength interpolation method provided in an embodiment of the present invention.

[0026] Figure 2 A schematic diagram illustrating the conversion of Cartesian coordinates to polar coordinates according to an embodiment of the present invention;

[0027] Figure 3 This is a block diagram of an electronic device provided in an embodiment of the present invention.

[0028] The attached figures are labeled as follows:

[0029] 101-Processor; 102-Communication interface; 103-Memory; 104-Communication bus; 105-Display. Detailed Implementation

[0030] To make the objectives, advantages, and features of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the drawings are all in a very simplified form and are not drawn to scale, and are only used to facilitate and clarify the explanation of the embodiments of this invention. Furthermore, the structures shown in the drawings are often part of the actual structures. In particular, different figures may emphasize different aspects and may sometimes use different scales.

[0031] It should be understood that when an element or layer is referred to as "on" or "connected to" other elements or layers, it may be directly on or connected to other elements or layers, or there may be intervening elements or layers. Conversely, when an element is referred to as "directly on" or "directly connected to" other elements or layers, there are no intervening elements or layers. Although the terms first, second, third, etc., may be used to describe various elements, components, areas, layers, and / or portions, these elements, components, areas, layers, and / or portions should not be limited by these terms. These terms are only used to distinguish one element, component, area, layer, or portion from another element, component, area, layer, or portion. Therefore, without departing from the teachings of this invention, the first element, component, area, layer, or portion discussed below may be referred to as a second element, component, area, layer, or portion. Spatial relation terms such as "below," "under," "below," "above," "on top," "above," etc., may be used herein for convenience of description to describe the relationship between one element or feature shown in the figures and other elements or features. It should be understood that, in addition to the orientations shown in the figures, spatial relational terms are intended to also include different orientations of the devices in use and operation. For example, if the devices in the figures are flipped, then elements or features described as “below,” “under,” or “below” will be oriented “on” other elements or features. Devices may be oriented additionally (rotated 90 degrees or otherwise) and the spatial descriptive terms used herein will be interpreted accordingly. The terminology used herein is intended only to describe particular embodiments and is not intended to limit the invention. When used herein, the singular forms “a,” “an,” and “the” are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “comprising” is used to identify the presence of features, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups. When used herein, the terms “and / or” include any and all combinations of the associated listed items.

[0032] The purpose of this invention is to provide a method for interpolating mechanical parameters of a three-dimensional tunnel model, thereby constructing a numerical model that matches the actual strength of the surrounding rock mass, thus more accurately simulating the stress distribution of the surrounding rock mass, evaluating the stability of the surrounding rock, and providing more effective support for tunnel construction.

[0033] To achieve the above objectives, the present invention provides a method for interpolating the intensity of a three-dimensional tunnel model, comprising the following steps:

[0034] Within a predetermined spatial range of a tunnel project, several initial calculation points are provided, each of which has known values ​​of real rock mass mechanical parameters;

[0035] Establish a coordinate system to obtain the coordinates of each of the initial calculation points;

[0036] Based on the attention mechanism, a neural network model is trained according to the coordinates of the initial calculation point and the actual rock mass mechanics parameters, so that the neural network model can output the interpolated rock mass mechanics parameters of the point within the preset space range, based on the coordinates of the point provided by the coordinate system.

[0037] The system provides coordinates of several unknown calculation points based on the coordinate system, calls the neural network model, and outputs the interpolated rock mechanics parameters of the unknown calculation points.

[0038] By employing this configuration, the present invention rationally optimizes the application of the attention mechanism in the tunnel modeling process, specifically in the mechanical parameter interpolation scenario. It establishes a neural network model that performs mechanical parameter interpolation calculations from known initial calculation points to unknown calculation points, thereby constructing a numerical model that accurately reflects the true strength of the surrounding rock mass. This allows for a more precise simulation of the stress distribution in the surrounding rock mass, assessing the stability of the surrounding rock and providing more effective support for tunnel construction. It should be noted that the rock mass mechanical parameters refer to parameters within the field of rock mechanics, which include various types such as compressive strength, elastic modulus, tensile-compressive ratio, Poisson's ratio, cohesion, and internal friction angle. Each single-head attention mechanism targets only one type of rock mass mechanical parameter. When multiple rock mass mechanical parameters need to be studied simultaneously, a multi-head attention mechanism can be further introduced. In this case, each mechanical parameter is trained independently along different dimensions, and its spatial correlation is independently evaluated, thereby enhancing the model's adaptability and generalization ability to complex geological conditions.

[0039] Furthermore, the attention-based mechanism, based on the coordinates of the initial calculation point and the actual rock mass mechanics parameters, trains a neural network model so that the neural network model can output the interpolated rock mass mechanics parameters of the point within the preset spatial range, based on the coordinates of the point provided by the coordinate system. Specifically, this includes:

[0040] Trial calculation phase: Initial calculation points are randomly divided into first and second calculation points according to a fixed ratio (e.g., j:i). Based on the attention mechanism, the mechanical parameter aggregation feature matrix between the first and second calculation points is obtained.

[0041] The aggregated feature matrix of mechanical parameters is input into the first feedforward neural network, which outputs the model's mechanical parameter prediction matrix.

[0042] Verification phase: Based on the predicted rock mass mechanics parameters of the model and the actual rock mass mechanics parameters, determine whether the predicted rock mass mechanics parameters of the model are qualified;

[0043] If so, the neural network model is qualified and can be used.

[0044] If not, adjust the neural network model and repeat the trial calculation phase until the neural network model is qualified.

[0045] This setup is because the present invention requires debugging based on the output results to ultimately train a qualified neural network model. It should be noted that during the training phase, we treat the first calculation point as an "unknown point" and the second calculation point as a "known point" (although the relevant information of the first calculation point is actually known).

[0046] The technical solution of the present invention will be described in detail below with reference to relevant technical principles.

[0047] Specifically, the process of obtaining the aggregated feature matrix of mechanical parameters between all first calculation points and all second calculation points based on the attention mechanism includes:

[0048] Based on the coordinates of each of the first calculation points, the first coordinate feature transformation matrix of each of the first calculation points is obtained using the second feedforward neural network.

[0049] Based on the coordinates of each second calculation point, the second coordinate feature transformation matrix of each second calculation point is obtained using the third feedforward neural network;

[0050] Based on the first coordinate feature transformation matrix and the query vector parameter matrix, obtain the query vector for each of the first calculation points;

[0051] Based on the second coordinate feature transformation matrix and the key vector parameter matrix, obtain the key vector of each second calculation point;

[0052] Based on the second coordinate feature transformation matrix and the actual rock mass mechanics parameters of the second calculation point, obtain the order value vector of each second calculation point;

[0053] Based on the query vector of the first calculation point and the key vector of the second calculation point, obtain the first spatial similarity between any first calculation point and the second calculation point;

[0054] Based on the first spatial similarity and the order value vector of each second calculation point, obtain the aggregated feature matrix of model mechanical parameters between any first calculation point and second calculation point.

[0055] The technical principle behind this setup is to provide a query vector parameter matrix and a key vector parameter matrix based on a cross-attention mechanism, namely the initial query vector parameter matrix Q and key vector parameter matrix K. Then, the Q and K matrices are used to obtain the first spatial similarity between any first calculation point and a second calculation point.

[0056] After obtaining the first spatial similarity, the mechanical parameter aggregation feature matrix can be obtained using the order value vector matrix to realize the transformation operation of interpolation calculation. Further, the method for obtaining the order value vector matrix is ​​as follows: based on the second coordinate feature transformation matrix and the actual rock mass mechanical parameters of the second calculation point, the order value vector of each second calculation point is obtained. Specifically, this includes: using the second coordinate feature transformation matrix and the actual rock mass mechanical parameters of the second calculation point as material for feature extraction by a fourth feedforward neural network; and using the second coordinate feature transformation matrix and the actual rock mass mechanical parameters of the second calculation point processed by the fourth feedforward neural network as material for feature extraction by a fifth feedforward neural network to obtain the order value vector of each second calculation point. The difference between this invention and the prior art is that this invention uses points in space as the research object of the cross-attention mechanism and utilizes the cross-attention mechanism to perform mechanical parameter interpolation calculation of points in space to achieve the transformation.

[0057] In summary, it is easy to understand that in the implementation of this invention, iterative adjustments to the weight parameters and biases of the feedforward neural network, specifically the order vector parameter matrix V, are required to ultimately form the query vector parameter matrix Q, the key vector parameter matrix K, and the order vector parameter matrix V, which can be applied to interpolation calculations. This is also the specific process of training the neural network model. In an exemplary embodiment, adjusting the neural network model specifically includes:

[0058] Perform at least one of the following adjustment operations based on the gradient descent algorithm:

[0059] Adjust the query vector parameter matrix;

[0060] Adjust the key vector parameter matrix;

[0061] The initial calculation points are randomly re-divided into the first calculation point and the second calculation point according to the preset ratio, so as to adjust the first coordinate feature transformation matrix and the second coordinate feature transformation matrix;

[0062] Adjust at least one of the first feedforward neural network, the second feedforward neural network, the third feedforward neural network, the fourth feedforward neural network, and the fifth feedforward neural network.

[0063] Based on the model rock mass mechanics parameter prediction matrix and the actual rock mass mechanics parameters, determine whether the model rock mass mechanics parameter prediction matrix is ​​qualified.

[0064] In one exemplary embodiment, the qualification of the model rock mechanics parameter prediction matrix can be determined by calculating the loss function between the first matrix and the second matrix.

[0065] In summary, the main purpose of obtaining the aggregated feature matrix of model rock mechanics parameters between any first calculation point and second calculation point is to iteratively train the neural network model using known initial calculation points, thereby obtaining a query vector parameter matrix Q, a key vector parameter matrix K, and an order vector parameter matrix V that can be applied to interpolation calculations under qualified conditions, especially obtaining the weights and biases of the feedforward neural network corresponding to the V matrix. After obtaining qualified Q, K, and V matrices, the qualified neural network model can be used to call the qualified query vector parameter matrix Q, key vector parameter matrix K, and order vector parameter matrix V to perform rock mechanics parameter interpolation calculations from known initial calculation points to unknown calculation points. Based on this, the present invention further provides the following technical solution: providing the coordinates of several unknown calculation points based on the coordinate system, calling the neural network model, and outputting the interpolated rock mechanics parameters of the unknown calculation points, specifically including:

[0066] Based on the coordinate matrix of each unknown calculation point and the query vector parameter matrix of the qualified neural network model, obtain the query vector of each unknown calculation point;

[0067] Based on the coordinate matrix of each initial calculation point and the key vector parameter matrix of the qualified neural network model, obtain the key vector of each initial calculation point;

[0068] Based on the key vector of each initial calculation point and the query vector of each unknown calculation point, obtain the second spatial similarity between each unknown calculation point and each initial calculation point;

[0069] Based on the second spatial similarity and the qualified order value vector of each initial calculation point, obtain the interpolation mechanical parameter aggregation feature matrix between each unknown calculation point and each initial calculation point;

[0070] The interpolated mechanical parameter aggregated feature matrix is ​​input into the first feedforward neural network, and the interpolated rock mass mechanical parameter prediction matrix is ​​output.

[0071] Based on the interpolated rock mass mechanical parameter prediction matrix, the interpolated rock mass mechanical parameter prediction matrix can be inversely normalized to obtain the interpolated rock mass mechanical parameters for the unknown calculation points.

[0072] Regarding how to determine whether the predicted rock mass mechanical parameters matrix of the model is qualified, the present invention further provides the following technical solution:

[0073] The step of determining whether the model rock mass mechanics parameter prediction matrix is ​​qualified based on the model rock mass mechanics parameter prediction matrix and the actual rock mass mechanics parameters specifically includes:

[0074] Based on the actual rock mass mechanics parameters of each initial calculation point, the initial calculation points are first randomly divided into first calculation points and second calculation points according to a fixed ratio, and the first spatial similarity of the actual rock mass mechanics parameters of any first calculation point and second calculation point is obtained.

[0075] Regarding the method for obtaining the actual rock mass mechanical parameters, the present invention further provides the following technical solution:

[0076] The normalization process based on the actual rock mass mechanics parameters of each initial calculation point specifically includes:

[0077] Obtain the average value of the actual rock mass mechanical parameters for all the initial calculation points;

[0078] Obtain the standard deviation of the actual rock mass mechanical parameters for all the initial calculation points;

[0079] Based on the values ​​of the actual rock mass mechanical parameters, the average value, and the standard deviation of any initial calculation point, obtain the strength normalization term for that initial calculation point;

[0080] The loss function of the rock mechanics parameter prediction matrix can be calculated based on the normalization term.

[0081] Preferably, the coordinate system is a polar coordinate system, and the coordinates are polar coordinates. This configuration allows for the fusion of the spatial correlation of the surrounding rock mechanical parameters of tunnel engineering with radial distance and angular information using polar coordinates, thereby accurately capturing their spatial variation patterns, improving the stability of the input data, and helping to accelerate the model convergence process.

[0082] The technical solution of the present invention will be described in detail below with reference to specific embodiments. It should be noted that the present invention is not limited to the embodiments.

[0083] Example

[0084] In this embodiment, the actual geographical scope of the tunnel project is determined based on its scale. Point cloud data of the project site is acquired through oblique photography using a drone and imported into Lidar360 software to convert the point cloud data into DEM data. Based on the actual burial depth and geometric dimensions of the tunnel, and combined with the DEM data, a three-dimensional geological model containing the tunnel and consistent with the terrain of the project site is generated using modeling software.

[0085] Collect actual rock samples from the site area, or directly sample borehole cores for mechanical experiments to obtain rock mass mechanical parameters (compressive strength, elastic modulus, tensile-compressive ratio, Poisson's ratio, cohesion, and internal friction angle). Simultaneously, analyze the rock mass mechanical parameters (compressive strength...) Elastic modulus Tension-compression ratio Poisson's ratio Cohesion and internal friction angle As a parameter variable of the model, it is defined as a parameter vector: the first parameter within the field area. Mechanical parameters at the second calculation point It can be represented as:

[0086]

[0087] in, Indicates the number within the field area The compressive strength at the second calculation point Indicates the number within the field area The elastic modulus at the second calculation point Indicates the number within the field area The tension-compression ratio at the second calculation point Indicates the number within the field area Poisson's ratio at the second calculation point Indicates the number within the field area The cohesion at the second calculation point Indicates the number within the field area The internal friction angle at the second calculation point.

[0088] In this embodiment, the method for constructing and training the neural network model is as follows:

[0089] Using the center point of the engineering site as the origin, the Cartesian coordinates of each of the initial calculation points in the engineering site are converted into spherical coordinates to obtain the three-dimensional polar coordinates of each of the initial calculation points in the engineering site.

[0090] Specifically, in this embodiment, the coordinates of the center point of the field area are recorded. And the center point of the field is used as the origin of the polar coordinate system, and a polar coordinate system is constructed accordingly. For example... Figure 2 As shown, the coordinates of any point within the field area are Transform the Cartesian coordinate system into a spherical coordinate system:

[0091] spherical radius :

[0092]

[0093] Representing the coordinates of the origin in the Cartesian coordinate system, sort the sphere radii and find the largest sphere radius, denoted as . The coordinates of all points within the field area are scaled for easier subsequent calculations. The scaled radius of the sphere is denoted as... :

[0094]

[0095] The horizontal angle is:

[0096]

[0097] The position angle is:

[0098]

[0099] in, Represents the arctangent function. Represents the inverse cosine function. Therefore, each three-dimensional polar coordinate vector within the field area can be represented as: .

[0100] In this embodiment, there are N initial calculation points, each of which has known values ​​of real rock mass mechanical parameters.

[0101] In this embodiment, the initial calculation points all have known values ​​of real rock mass mechanics parameters. However, during the trial calculation stage of the neural network model, the coordinate feature transformation matrix E needs to be divided into first calculation points and second calculation points according to a fixed ratio. The first calculation point is used for feature extraction through a second feedforward neural network to obtain the coordinate feature transformation matrix E of the first calculation point. q The second calculation point undergoes feature extraction via a third feedforward neural network to obtain the coordinate feature transformation matrix E of the second calculation point. k ,

[0102]

[0103] in , W k and W q It is a weight matrix (3×) ), b k and b q It is the bias matrix (b) k Dimension i×1, b q Dimension j×1).

[0104] Meanwhile, the h-th true mechanical parameter at the second calculation point is denoted as... , Although the actual mechanical parameters of the first calculation point are known, in order for the model to better capture the spatial correlation of point intensity within the field area, the first calculation point needs to be treated as an "unknown point".

[0105] Furthermore, the parameter matrix is ​​defined to perform a linear transformation on the feature transformation matrix of each second calculation point coordinate, thereby obtaining the feature vector of each second calculation point within the engineering site area;

[0106] Specifically, define the query vector and key vector parameter matrices, denoted as follows: , Both matrices are of size , It refers to the feature dimension of the query vector or key vector (the feature dimension of the query vector, key vector, and value vector are consistent). ,in, Hyperparameters are specified by the user. It is defined as the number of mechanical parameters that need to be set at each point within the field area.

[0107] According to the parameter matrix , Perform a linear transformation on the position code of each second calculation point:

[0108]

[0109] in, Represents the first calculation point j's... Rank query vector, Represents the second calculation point i's... Order bond vector, This represents the coordinate characteristic transformation matrix of the first calculation point j. This represents the coordinate characteristic transformation matrix of the second calculation point i.

[0110] The construction of the order vector requires combining the coordinate feature transformation matrix of the second calculation point. and the h-th true mechanical parameter at the second calculation point , Same as above This is defined as the number of mechanical parameters that need to be set at each point within the field area. First, it is necessary to... After normalization, the data is then processed by a fourth feedforward neural network for linear transformation to extract features, resulting in z. k , (z k Dimension i×d y ), here d y These are hyperparameters that are manually set (generally integers between 6 and 54). and z k Perform splicing. Obtain V. inV in ∈ V in The dimension is i×( +d y V in As input to the fifth feedforward neural network, feature extraction is performed through the fifth feedforward neural network to obtain the order vector matrix V. h , (V) h Dimension j× ).

[0111] Further merging and combining yields three feature vectors. , and :

[0112]

[0113]

[0114]

[0115] in, The first calculation point within the field area The first-order query vector represents the projection of the point's positional features onto the second-order query vector. The query subspace of each attention head is used to generate a set of direction-sensitive vectors for relevance retrieval for each point, which are used to calculate similarity with the key vectors of other points, thereby expressing spatial relevance. The second calculation point within the field area The first-order bond vector represents the projection of the point's positional features onto the second-order bond vector. The key subspace of each attention head is used as the coordinate feature value of the "retrieved end" in similarity calculation. Used to quantize the first calculation point Second calculation point In the Spatial similarity under individual attention; The second calculation point within the field area The order value vector represents an information-carrying vector that can be weighted and aggregated. It is used to weight and converge the representation of the first computation point in cross-attention; it can also be used to quantify the relationship between each second computation point and the first computation point. The The combined effect of individual attention on representation.

[0116] Calculate the spatial similarity between the first calculation point and the second calculation point within the engineering site, construct the mechanical parameter aggregation feature matrix between the first calculation point and the second calculation point, and the mechanical parameter prediction matrix;

[0117] Specifically, for feature vectors and Perform a vector dot product operation, measuring the first computation point. Second calculation point No. The spatial similarity of the mechanical parameters is calculated using the following formula:

[0118]

[0119] in, Indicates the first calculation point Second calculation point The Spatial similarity of mechanical parameters.

[0120]

[0121] Then, the first spatial similarity matrix representing all first calculation points and all second calculation points within the field area is calculated. , Represents the set of real numbers; points with high similarity in mechanical parameters will be assigned higher "attention" weights; the first calculation point (query point). The The dth mechanical parameter k The similar feature values ​​are represented as :

[0122]

[0123] in, Indicates the second calculation point The The order value vector is then used to obtain the aggregated feature matrix of mechanical parameters of the first calculation point relative to the second calculation point within the engineering site area. :

[0124]

[0125] in, Indicates the first calculation point within the engineering site. The dth k The aggregated characteristic values ​​of the mechanical parameters.

[0126] In this embodiment, the mechanical parameter prediction matrix P is composed of the mechanical parameter aggregation feature matrix. The features are aggregated from the first feedforward neural network, forming a feature matrix of mechanical parameters. The multi-dimensional spatial mechanical parameter aggregation feature matrix of different dimensions is used as the input of the first feedforward neural network. After feature aggregation through multiple hidden layers, the output result is the mechanical parameter prediction matrix P.

[0127]

[0128] in, Indicates the first calculation point The Predicted values ​​for several mechanical parameters.

[0129] Through the loss function The predicted mechanical parameter matrix at the first calculation point is compared with the actual mechanical parameter matrix at the first calculation point. The hidden layer weights and parameter matrices are then adjusted using the gradient descent algorithm. , The feedforward neural network is iterated to ensure that the predicted mechanical parameters of the first calculation point are within the error range of their actual mechanical parameters.

[0130] In this embodiment, the rock mechanics parameters to be interpolated are used to assign a value to h. There are a total of 6 mechanics parameters, so h=6. To learn the spatial correlation of regional rock mechanics parameters and achieve better generalization ability in regional rock mechanics parameter prediction, a model training target value needs to be introduced. This embodiment divides the initial calculation points of all known real rock mechanics parameters into two parts: the first calculation point and the second calculation point. The real value of the rock mechanics parameters at the first calculation point is used as the model training target value.

[0131] Indicates the first calculation point The The standardized term of each real mechanical parameter is calculated using the following formula:

[0132]

[0133] in, Indicates the first calculation point The A true mechanical parameter, Represents the initial point of all fields. The mean of a real mechanical parameter, Represents the initial point of all fields. The standard deviation of a true mechanical parameter.

[0134] Finally, the true mechanical parameter matrix of the first calculation point in the initial calculation points within the field area is obtained. ,in, This represents the first calculation point among the initial calculation points within the field area. Given a matrix of real mechanical parameters:

[0135]

[0136] in, Represents the first calculation point in the initial calculation points. Normalized True values ​​of each mechanical parameter

[0137] Based on the predicted mechanical parameters of each first calculation point and the actual mechanical parameters of each first calculation point, a loss function is designed to perform initial training on the neural network model, resulting in a neural network model trained by multi-head cross-attention.

[0138] Specifically, the spatial correlation of the true mechanical parameters at the second computation point is supervised by defining the following loss function: for:

[0139]

[0140] in, This represents the total number of the first calculation points among the initial calculation points within the field area. This represents the first calculation point among the initial calculation points within the engineering field area where the model is learned. The Predicted values ​​of one mechanical parameter Represents the first calculation point in the initial calculation points. The The true values ​​of each mechanical parameter The smaller the value, the closer the spatial correlation of the mechanical parameters learned by the model is to the real situation.

[0141] Input all first and second calculation points in the engineering site into the neural network model trained by multi-head cross attention, and output the rock mechanics parameter prediction matrix that needs to be interpolated for all first calculation points in the engineering site.

[0142] After subsequent model training, the mechanical parameters of the first calculation point in the target tunnel area are inferred using the parameters obtained and fixed during the training phase. The coordinates of all the first calculation points are then processed by the second feedforward neural network to obtain the first coordinate feature transformation matrix E. u The second coordinate feature transformation matrix E is obtained by passing all second calculation points within the field area through the third feedforward neural network. Similar to the model training process, all first calculation points E are multiplied by W. q To obtain Q, multiply all second calculation points E by W. k After obtaining K, the coordinate matrix E of all second calculation points is combined with their actual mechanical parameters. This is then processed by the fifth feedforward neural network for feature extraction to obtain V. The output of the attention mechanism, after passing through the FFN feedforward neural network, is denormalized to obtain the predicted mechanical parameters for all first calculation points.

[0143]

[0144] in, Represents the first calculation point. A matrix of predicted values ​​for each mechanical parameter; Represents the first calculation point. The matrix of predicted values ​​of each mechanical parameter after denormalization; Represents the initial point of all fields. The mean of a real mechanical parameter, Represents the initial point of all fields. The standard deviation of a true mechanical parameter.

[0145] In summary, this invention utilizes a cross-attention mechanism, taking each coordinate point in the tunnel space as the research object, training a neural network model including a QKV three-matrix for transformation, and verifying and adjusting the neural network model using a loss function. Based on the actual mechanical parameters of the second calculation point, the mechanical parameter interpolation of the first calculation point is calculated as a parameter index for constructing the tunnel's three-dimensional geological model. This proposes a complete and specific training method for a neural network model applied to the calculation of mechanical parameter interpolation in tunnel engineering, enabling mechanical parameter interpolation prediction for rock masses at any new location in the site. As the tunnel project progresses, more detailed geological information around the tunnel is revealed, and more rock mass mechanical parameters can be obtained.

[0146] Please refer to Figure 3 , Figure 3 This is a block diagram of an electronic device according to an embodiment of the present invention. Figure 3 As shown, the present invention also provides an electronic device, the electronic device comprising:

[0147] Memory 103 stores computer programs;

[0148] The processor 101 is communicatively connected to the memory and executes the three-dimensional tunnel model intensity interpolation method described above when calling the computer program;

[0149] Display 105, which is communicatively connected to the processor and the memory, is used to display a GUI interactive interface related to the three-dimensional tunnel model intensity interpolation method.

[0150] Since the electronic device and the three-dimensional tunnel model strength interpolation method belong to the same inventive concept, the electronic device can reasonably optimize the application of the attention mechanism to the tunnel modeling interpolation scenario, and establish a neural network model that performs interpolation calculations from known initial calculation points to unknown calculation points. This can more accurately simulate the stress distribution of the surrounding rock mass, evaluate the stability of the surrounding rock, and provide more effective support for tunnel engineering construction.

[0151] Since the electronic device provided by this invention and the three-dimensional tunnel model strength interpolation method described above belong to the same inventive concept, the electronic device provided by this invention has all the advantages of the three-dimensional tunnel model strength interpolation method described above. Therefore, the beneficial effects of the electronic device provided by this invention will not be described in detail here.

[0152] like Figure 3 As shown, the electronic device also includes a communication interface 102 and a communication bus 104, wherein the processor 101, the communication interface 102, and the memory 103 communicate with each other via the communication bus 104. The communication bus 104 can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus 104 can be divided into an address bus, a data bus, a control bus, etc. For ease of illustration, only one thick line is used in the figure, but this does not indicate that there is only one bus or one type of bus. The communication interface 102 is used for communication between the aforementioned electronic device and other devices.

[0153] The processor 101 referred to in this invention can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor. The processor 101 is the control center of the electronic device, connecting various parts of the entire electronic device through various interfaces and lines.

[0154] The memory 103 can be used to store the computer program. The processor 101 implements various functions of the electronic device by running or executing the computer program stored in the memory 103 and calling the data stored in the memory 103.

[0155] The memory 103 may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0156] The present invention also provides a storage medium storing a computer program that, when executed by a processor, implements the three-dimensional tunnel model intensity interpolation method described in any of the preceding claims.

[0157] Since the storage medium and the three-dimensional tunnel model strength interpolation method belong to the same inventive concept, the storage medium can reasonably optimize the application of the attention mechanism to the tunnel modeling interpolation scenario, and establish a neural network model that performs interpolation calculations from known initial calculation points to unknown calculation points. This can more accurately simulate the stress distribution of the surrounding rock mass, evaluate the stability of the surrounding rock, and provide more effective support for tunnel engineering construction.

[0158] Since the storage medium provided by this invention and the three-dimensional tunnel model strength interpolation method described above belong to the same inventive concept, the storage medium provided by this invention has all the advantages of the three-dimensional tunnel model strength interpolation method described above. Therefore, the beneficial effects of the storage medium provided by this invention will not be described in detail here.

[0159] The storage medium of embodiments of the present invention can be any combination of one or more computer-readable media. The readable medium can be a computer-readable signal medium or a computer-readable storage medium. Computer-readable storage media can be, for example, but not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatuses, or devices, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: electrical connections having one or more wires, portable computer hard disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, apparatus, or device.

[0160] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of transmitting, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium may be transmitted using any suitable medium, including but not limited to wireless, wireline, optical fiber, RF, etc., or any suitable combination thereof.

[0161] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the three-dimensional tunnel model intensity interpolation method described in any of the preceding claims.

[0162] Since the computer program product and the three-dimensional tunnel model strength interpolation method belong to the same inventive concept, the computer program product can reasonably optimize the application of the attention mechanism to the tunnel modeling interpolation scenario, and establish a neural network model that performs interpolation calculations from known initial calculation points to unknown calculation points. This can more accurately simulate the stress distribution of the surrounding rock mass, evaluate the stability of the surrounding rock, and provide more effective support for tunnel engineering construction.

[0163] Since the computer program product provided by this invention and the three-dimensional tunnel model strength interpolation method described above belong to the same inventive concept, the computer program product provided by this invention has all the advantages of the three-dimensional tunnel model strength interpolation method described above. Therefore, the beneficial effects of the computer program product provided by this invention will not be described in detail here.

[0164] If this invention is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0165] It should also be noted that although the present invention has been disclosed above with reference to preferred embodiments, these embodiments are not intended to limit the present invention. For any person skilled in the art, many possible variations and modifications can be made to the technical solutions of the present invention based on the disclosed technical content, or equivalent embodiments can be modified accordingly, without departing from the scope of the present invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the present invention shall still fall within the scope of protection of the present invention.

[0166] It should also be understood that, unless otherwise specified or indicated, the terms “first,” “second,” “third,” etc., in the specification are used only to distinguish the various components, elements, and steps in the specification, and not to indicate the logical or sequential relationships between the various components, elements, and steps.

[0167] Furthermore, it should be recognized that the terminology described herein is used only to describe particular embodiments and not to limit the scope of the invention. It must be noted that the singular forms “a” and “an” used herein and in the appended claims include plural bases unless the context clearly indicates otherwise. For example, a reference to “a step” or “an apparatus” means a reference to one or more steps or apparatuses, and may include secondary steps and secondary apparatuses. All conjunctions used should be understood in the broadest sense. And the word “or” should be understood to have the definition of logical “or” rather than logical “exclusive OR”, unless the context clearly indicates otherwise. Furthermore, implementation of embodiments of the invention may include performing selected tasks manually, automatically, or in combination.

Claims

1. A method for interpolating the strength of a three-dimensional tunnel model, characterized in that, Includes the following steps: Within a predetermined spatial range of a tunnel rock mass, several initial calculation points are provided, each of which has known values ​​of real rock mass mechanical parameters; Establish a coordinate system to obtain the coordinates of each of the initial calculation points; Based on the attention mechanism, a neural network model is trained according to the coordinates of the initial calculation point and the actual rock mass mechanics parameters, so that the neural network model can output the interpolated rock mass mechanics parameters of the point within the preset space range, based on the coordinates of the point provided by the coordinate system. Provide the coordinates of several unknown calculation points based on the coordinate system, call the neural network model, and output the interpolated rock mass mechanical parameters of the unknown calculation points; The attention-based mechanism trains a neural network model based on the coordinates of the initial calculation point and the actual rock mass mechanics parameters. This enables the neural network model to output the interpolated rock mass mechanics parameters of the point within the preset spatial range, based on the coordinates provided by the coordinate system. Specifically, this includes: Trial calculation phase: Initial calculation points are randomly divided into first and second calculation points according to a fixed ratio. Based on the attention mechanism, the mechanical parameter aggregation feature matrix between the first and second calculation points is calculated. The mechanical parameter aggregation feature matrix is ​​input into the first feedforward neural network, and the model mechanical parameter prediction matrix is ​​output. Verification phase: Based on the predicted rock mass mechanics parameters of the model and the actual rock mass mechanics parameters of the first calculation point, determine whether the predicted rock mass mechanics parameters of the model are qualified; If so, the neural network model is qualified and can be used. If not, adjust the neural network model and repeat the trial calculation phase until the neural network model is qualified; The calculation of the mechanical parameter aggregation feature matrix between the first calculation point and the second calculation point based on the attention mechanism specifically includes: Provide query vector parameter matrix and key vector parameter matrix; Based on the coordinates of each of the first calculation points, the first coordinate feature transformation matrix of each of the first calculation points is obtained using the second feedforward neural network. Based on the coordinates of each second calculation point, the second coordinate feature transformation matrix of each second calculation point is obtained using the third feedforward neural network; Based on the first coordinate feature transformation matrix and the query vector parameter matrix, obtain the query vector for each of the first calculation points; Based on the second coordinate feature transformation matrix and the key vector parameter matrix, obtain the key vector of each second calculation point; Based on the second coordinate feature transformation matrix and the actual rock mass mechanics parameters of the second calculation point, obtain the order value vector of each second calculation point; Based on the query vector of the first calculation point and the key vector of the second calculation point, obtain the first spatial similarity between any first calculation point and the second calculation point; Based on the first spatial similarity and the order value vector of each second calculation point, obtain the mechanical parameter aggregation feature matrix between any first calculation point and second calculation point.

2. The three-dimensional tunnel model strength interpolation method as described in claim 1, characterized in that, The step of obtaining the order vector of each second calculation point based on the second coordinate feature transformation matrix and the actual rock mass mechanics parameters of the second calculation point specifically includes: The second coordinate feature transformation matrix and the actual rock mass mechanical parameters of the second calculation point are used as materials for feature extraction by the fourth feedforward neural network. The second coordinate feature transformation matrix and the actual rock mass mechanical parameters of the second calculation point after processing by the fourth feedforward neural network are used as materials for feature extraction by the fifth feedforward neural network to obtain the order value vector of each second calculation point.

3. The three-dimensional tunnel model strength interpolation method as described in claim 2, characterized in that, The adjustment of the neural network model specifically includes performing at least one of the following adjustment operations based on the gradient descent algorithm: Adjust the query vector parameter matrix; Adjust the key vector parameter matrix; The initial calculation points are randomly re-divided into the first calculation point and the second calculation point according to a preset ratio, so as to adjust the first coordinate feature transformation matrix and the second coordinate feature transformation matrix; Adjust at least one of the first feedforward neural network, the second feedforward neural network, the third feedforward neural network, the fourth feedforward neural network, and the fifth feedforward neural network.

4. The three-dimensional tunnel model strength interpolation method as described in claim 3, characterized in that, The process of providing coordinates of several unknown calculation points based on the coordinate system, calling the neural network model, and outputting the interpolated rock mass mechanics parameters of the unknown calculation points specifically includes: Based on the coordinate matrix of each unknown calculation point and the query vector parameter matrix of the qualified neural network model, obtain the query vector of each unknown calculation point; Based on the coordinate matrix of each initial calculation point and the key vector parameter matrix of the qualified neural network model, obtain the key vector of each initial calculation point; Based on the key vector of each initial calculation point and the query vector of each unknown calculation point, a second spatial similarity between each unknown calculation point and each initial calculation point is obtained; Based on the second spatial similarity and the qualified order value vector of each initial calculation point, obtain the interpolation mechanical parameter aggregation feature matrix between each unknown calculation point and each initial calculation point; The interpolated mechanical parameter aggregated feature matrix is ​​input into the first feedforward neural network, and the interpolated mechanical parameter prediction matrix is ​​output.

5. The three-dimensional tunnel model strength interpolation method as described in claim 4, characterized in that, Also includes: Based on the interpolated rock mass mechanical parameter prediction matrix, the interpolated rock mass mechanical parameter prediction matrix is ​​inversely normalized to obtain the interpolated rock mass mechanical parameters of the unknown calculation point.

6. The three-dimensional tunnel model strength interpolation method as described in claim 1, characterized in that, Also includes: Based on the actual rock mass mechanics parameters of each initial calculation point, a normalization process is performed, specifically including: Obtain the average value of the actual rock mass mechanical parameters for all the initial calculation points; Obtain the standard deviation of the actual rock mass mechanical parameters for all the initial calculation points; Based on the values ​​of the actual rock mass mechanical parameters, the average value, and the standard deviation of any initial calculation point, obtain the strength normalization term for that initial calculation point; Based on the normalization term, calculate the loss function relative to the predicted rock mass mechanics parameters matrix.

7. The three-dimensional tunnel model strength interpolation method as described in claim 1, characterized in that, The step of determining whether the model rock mass mechanical parameter prediction matrix is ​​qualified based on the model rock mass mechanical parameter prediction matrix and the actual rock mass mechanical parameters specifically includes: The model rock mass mechanical parameter prediction matrix is ​​compared with the actual mechanical parameter matrix of the first calculation point using a loss function to determine whether the model rock mass mechanical parameter prediction matrix is ​​qualified.

8. The three-dimensional tunnel model strength interpolation method as described in claim 1, characterized in that, The coordinate system is a polar coordinate system, and the coordinates are polar coordinates.

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