A mine shaft wellbore multi-fidelity full-field strain prediction and lightweight visualization method and system

Abstract

The application discloses a shaft wellbore multi-fidelity full-field strain prediction and lightweight visualization method and system, which uses equivalent temperature field coefficients, equivalent mechanical load coefficients and local equivalent water pressure as inputs, generates low, medium and high fidelity axial and ring total strain samples by using coarse, medium and fine grid finite element models; uses high fidelity nodes as a unified reference, and projects the samples to a shared eigen-orthogonal decomposition basis through a nearest neighbor inverse distance weighting implementation; K Low, medium and high three-level autoregressive collaborative radial basis function models are established for the same order modal coefficients, high fidelity modal coefficients are predicted and full-field strain is reconstructed through scale correction and adjacent fidelity residual compensation by using the models, and the predicted field is mapped to lightweight three-dimensional rendering vertices. The application can reduce high fidelity finite element calculation and online rendering burden, quickly obtain continuous full-field strain of a wellbore, assist in identifying strain concentration areas, and provide a basis for wellbore structure state evaluation, safety monitoring and maintenance.

Description

Technical Field

[0001] This invention belongs to the technical fields of mine structure safety monitoring, finite element proxy modeling, full-field physical quantity prediction and digital twin visualization, specifically involving a method and system for multi-fidelity full-field strain prediction and lightweight visualization of vertical shafts. Background Technology

[0002] Vertical shafts are crucial passageways for hoisting, ventilation, drainage, and personnel transportation in underground mines, enduring long-term effects from temperature, geostress, groundwater, and mining disturbances. The structural response of the shaft wall exhibits significant non-uniformity along its depth and circumference, with potential strain concentrations in localized areas. Existing strain gauges, fiber optic sensors, and displacement monitoring devices typically only provide discrete information at limited locations, making it difficult to directly establish a continuous, full-field strain distribution within the shaft.

[0003] While refined finite element models can capture the full-field structural response under complex loads, the high cost of solving single-case problems with fine mesh models makes them difficult to directly utilize online in digital twin platforms that require frequent updates. Using a single high-fidelity surrogate model limits the number of high-fidelity samples, potentially creating a trade-off between training costs and prediction accuracy. Furthermore, a single case contains tens of thousands of nodes with axial and circumferential strain outputs; establishing a surrogate model node-by-node would significantly increase the modeling scale and parameter management burden.

[0004] Using coarse, medium, and fine mesh finite element models, multi-fidelity data with different computational costs and accuracy levels can be obtained. However, the number of nodes and spatial locations of different fidelity meshes are not consistent, and a unified proxy relationship cannot be directly established for the corresponding nodes. If each fidelity is reduced in dimensionality separately, the modal coefficients of the same order may lack a consistent physical meaning, affecting the modeling of cross-fidelity differences.

[0005] Furthermore, high-resolution finite element prediction meshes and lightweight 3D rendering meshes typically differ in node count and spatial location. Directly reducing the size of the finite element prediction mesh results in a loss of spatial resolution of the full-field response, while directly using a high-resolution mesh for 3D rendering increases the burden of data loading, interaction, and refresh. Therefore, a method is needed that can unify the space of strain fields with different fidelity, compress high-dimensional full-field responses, fuse low, medium, and high-fidelity information, and independently map the high-fidelity prediction field to a lightweight rendering mesh. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for multi-fidelity full-field strain prediction and lightweight visualization of vertical shafts, in order to solve the problems of high cost of generating high-fidelity finite element samples, inconsistent node spaces of strain fields with different fidelities, difficulty in directly modeling high-dimensional full-field responses, and difficulty in balancing high-resolution prediction meshes and lightweight rendering meshes.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: Step 1: Construct multi-fidelity parametric finite element samples. Establish an equivalent parametric finite element model of the wellbore to obtain operating parameters characterizing the effects of wellbore temperature, mechanical load, and local water pressure. Under nested operating condition design, use coarse-grid, medium-grid, and fine-grid finite element models to obtain low-fidelity, medium-fidelity, and high-fidelity axial total strain fields and circumferential total strain fields, respectively.

[0008] Step two: Unify the strain field space with different fidelity levels. Using high-fidelity mesh nodes as a unified reference, through... K Nearest neighbor inverse distance weighting aligns the low-fidelity and medium-fidelity strain fields to the high-fidelity reference node, forming a multi-fidelity training matrix with consistent node dimensions and spatial location.

[0009] Step 3: Establish a low-dimensional representation of the shared POD. Construct axial total strain shared POD substrates and circumferential total strain shared POD substrates in a unified high-fidelity node space, respectively. Project low-fidelity, medium-fidelity, and high-fidelity snapshots onto the corresponding shared substrates to ensure that modal coefficients of the same order at each fidelity have a consistent spatial physical meaning.

[0010] Step four: Establish a three-level autoregressive Co-RBF model. Train the basic radial basis function model using low-fidelity modal coefficients, train the medium-low fidelity residual model using the residuals between medium-fidelity modal coefficients and scale-corrected low-fidelity predicted modal coefficients, and train the high-medium fidelity residual model using the residuals between high-fidelity modal coefficients and scale-corrected medium-fidelity predicted modal coefficients. Predict high-fidelity modal coefficients through stepwise scaling correction and residual compensation.

[0011] Step 5: Reconstruct high-fidelity full-field strain. After normalizing the input parameters of the target working condition, input them into the third-level autoregressive Co-RBF model to obtain the axial and circumferential high-fidelity modal coefficients. Then, reconstruct the full-field strain on the high-fidelity reference node using the corresponding shared POD spatial modes and mean strain field.

[0012] Step six: Perform lightweight visualization mapping. Offline pre-compute high-fidelity reference nodes to 3D lightweight rendering vertices. K Nearest neighbor index and inverse distance weighting are used to weight and map the reconstructed high-fidelity strain field to lightweight vertices in the online phase, thereby completing the 3D cloud map update, strain component switching, key area observation and threshold prompting.

[0013] The present invention also provides a system for implementing the above method, including a multi-fidelity finite element sample generation module, a strain field space unification module, a shared intrinsic orthogonal decomposition basis construction module, a three-level autoregressive collaborative radial basis function prediction module, a high-fidelity full-field strain reconstruction module, and a three-dimensional lightweight mapping and visualization module.

[0014] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention utilizes coarse, medium, and fine mesh finite element responses in a nested working condition design, enabling a large number of low-cost samples to be used to learn the overall variation law. Medium-fidelity samples serve as a transition layer between low and high fidelity, reducing the dependence on a large number of high-fidelity samples.

[0015] 2. This invention unifies strain fields of different fidelity to a high-fidelity reference node and uses a shared POD substrate for low-dimensional characterization, avoiding inconsistencies between different grid nodes and the problem of inconsistent modal coordinates caused by dimensionality reduction of each fidelity.

[0016] 3. This invention uses a three-level autoregressive Co-RBF model (low-medium-high) to progressively correct the scale relationship and residuals between adjacent fidelities, thereby improving the overall prediction capability under limited high-fidelity sample conditions.

[0017] 4. This invention separates high-fidelity full-field prediction from lightweight 3D mapping, without directly simplifying the high-fidelity prediction grid, thus decoupling numerical accuracy evaluation from the rendering grid size.

[0018] 5. In the online phase, this invention does not require calling the finite element solver or re-searching the node neighborhood. It only performs input normalization, prediction of a small number of modal coefficients, reconstruction of the full field matrix, and weighted summation of vertices, which can reduce the online computing and rendering burden of the digital twin platform. Attached Figure Description

[0019] Figure 1 Overall flowchart for multi-fidelity full-field strain prediction and lightweight visualization of vertical shafts.

[0020] Figure 2 A schematic diagram of low-dimensional POD characterization for unified and shared strain field space with different fidelity.

[0021] Figure 3 This is a schematic diagram of the structure of a three-level autoregressive Co-RBF model, from low to medium to high.

[0022] Figure 4 Framework diagram for realizing digital twin of vertical shaft.

[0023] Figure 5 This is a flowchart of the digital twin data transmission process for a vertical shaft.

[0024] Figure 6 This is a schematic diagram of the wellbore strain response and three-dimensional mapping under different typical loads.

[0025] Figure 7 This is a schematic diagram of the high-fidelity reference field and the prediction absolute error field.

[0026] Figure 8A schematic diagram of the functional interface of the digital twin platform for vertical shafts.

[0027] Table 1 shows the multi-fidelity finite element sample and node size.

[0028] Table 2 shows the input and algorithm parameters for the example.

[0029] Table 3 shows the high-fidelity leave-one-out verification results for different fidelity level combinations.

[0030] Table 4 shows the calculation efficiency of Co-RBF full-field strain prediction.

[0031] The present invention will be further described below through specific embodiments and in conjunction with the accompanying drawings. Detailed Implementation

[0032] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. The following embodiments are used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention.

[0033] like Figure 1 As shown, this embodiment includes an offline training phase and an online prediction and mapping phase. The offline training phase completes the generation of multi-fidelity finite element samples, unification of strain field spaces at different fidelities, construction of a shared POD base, three-level autoregressive Co-RBF training, and neighborhood indexing and weight pre-calculation from high-fidelity nodes to lightweight rendering vertices. The online phase inputs the target working condition parameters and sequentially completes modal coefficient prediction, high-fidelity full-field reconstruction, and lightweight vertex mapping. In this embodiment, the working condition input includes equivalent temperature field coefficients, equivalent mechanical load coefficients, and local equivalent water pressure, where the equivalent mechanical load coefficients are specifically used to characterize the scaling of the reference surrounding rock pressure field.

[0034] The surrounding rock and wellbore are modeled using concentric cylindrical equivalents. The wellbore material is concrete, and the surrounding rock material is a typical rock stratum material. Coarse, medium, and fine meshes use the same geometric, material, and load parameters, differing only in mesh density for fidelity. The finite element model uses cylindrical coordinates to extract strain components, where the axial total strain is the total strain component along the central axis of the wellbore, and the circumferential total strain is the total strain component along the tangential direction of the wellbore's circumference. The total strain is the total strain component output by the finite element solver in the corresponding direction and is not equivalent to the equivalent strain.

[0035] The finite element model uses normalized axial coordinates for calculation. ∈[0,16] mm, and with an engineering monitoring depth of 50~123 m. H Establish mapping relationship: (1) In the formula, H The depth of the well shaft is expressed in meters (m). The coordinates for axial calculation of the finite element model are in mm. =0mm corresponds to a depth of 123m. =16 mm corresponds to a depth of 50 m. This equivalent model is used to generate training samples for the surrogate model.

[0036] The input vector of the proxy model is represented as: (2) In the formula, This is the equivalent temperature field coefficient. This is the equivalent mechanical load factor. The local equivalent water pressure is expressed in MPa. The temperature field, surrounding rock pressure, and local equivalent water pressure are respectively represented as: (3) (4) (5) In the formula, For the material reference temperature, 22°C is used in this embodiment; The temperature field distributed along the wellbore axis under the reference operating conditions; This represents the surrounding rock pressure distributed along the wellbore depth under the baseline operating conditions. This refers to a pre-defined local equivalent water pressure region. This region can be defined by both the axial coordinate range and the circumferential angle range, or it can be defined using a set of named surfaces in the finite element model.

[0037] The input parameters are normalized before entering the proxy model. For the first... j The input components are normalized to the following: (6) In the formula, and The training samples are respectively the first j The system outputs the minimum and maximum values ​​of each input component. When the target condition exceeds the training parameter range, the system outputs an out-of-bounds warning and does not perform direct extrapolation, or it performs prediction after regenerating supplementary samples and updating the model.

[0038] To balance physical boundary states and parameter space coverage, the baseline, zero-load, single-factor, and boundary verification cases were constructed using a pre-defined method, while the remaining cases were generated using Latin hypercube sampling. A total of 120 low-fidelity samples were generated, 30 medium-fidelity samples were nested from the low-fidelity cases, and 10 high-fidelity samples were nested from the medium-fidelity cases, ensuring that the high-fidelity case set is contained within the medium-fidelity case set, and vice versa. The responses at shared parameter points at different fidelities were used for progressive scaling and residual modeling.

[0039] Table 1. Multifidelity Finite Element Samples and Node Sizes Table 2 Inputs and Algorithm Parameters for the Example In this embodiment, the equivalent mechanical load coefficient is used to scale the reference surrounding rock pressure field. For example... Figure 2 As shown, since the number and spatial location of nodes differ in finite element models of different fidelity, the 81492 nodes of the high-fidelity mesh are used as a unified reference to perform strain field analysis on low-fidelity and medium-fidelity models. K Nearest neighbor inverse distance weighted spatial mapping. For the th i target nodes Select the closest one from the source grid. K Nodes The node distance, normalized weights, and mapping results are as follows: (7) (8) (9) In the formula, For the target node With the j Source Node The Euclidean distance between them; ε To prevent extremely small positive numbers with a distance of zero; p The distance decay exponent; For normalized weights; This represents the strain value at the source node; This represents the mapped strain value at the target node. When the target node coincides with any source node, the strain value of that source node is directly used. In this embodiment, we take... K =8、 p =2. This method is used for low- and medium-fidelity field alignment during the offline training phase and for resampling high-fidelity prediction fields to lightweight vertices during the visualization phase.

[0040] Construct unified nodal space snapshot matrices for axial total strain and circumferential total strain respectively. Y The snapshot matrix is ​​then centered. To ensure consistent physical meaning for modal coefficients at different fidelity levels, low, medium, and high fidelity snapshots of axial total strain share the same axial shared POD substrate, and low, medium, and high fidelity snapshots of circumferential total strain share the same circumferential shared POD substrate. The singular value decomposition of the centered snapshot matrix is ​​as follows: (10) In the formula, For a centralized snapshot matrix, For length is A column vector of all 1s. The number of strain snapshots that participate in building a shared intrinsic orthogonal decomposition basis. The average strain field of the training samples. U and V These are singular vector matrices, Σ It is a singular value diagonal matrix. m This represents the total number of singular values ​​corresponding to the centered strain snapshot matrix. (Previous) r The cumulative energy contribution rate of the first mode is: (11) The number of retained modes is determined based on the cumulative energy contribution rate and the relative reconstruction error of the high-fidelity snapshot. r The singular vectors of the node space constitute a shared POD basis. Φ , No. n The modal coefficients and reconstructed fields for each working condition are as follows: (12) (13) In this embodiment, the total axial strain and the total circumferential strain retain three dominant modes, with cumulative energy contribution rates of 99.9084% and 99.9174%, respectively. The relative reconstruction errors of the high-fidelity snapshot are 0.2815% and 0.4820%, respectively, which compresses the surrogate prediction output of each strain component from 81492 dimensions to 3 dimensions.

[0041] like Figure 3 As shown, a three-level autoregressive Co-RBF model (low-medium-high) is established for each POD modal coefficient. For the ... r The first-order modal coefficients, low-fidelity prediction, medium-low-fidelity residuals, medium-fidelity prediction, high-medium-fidelity residuals, and high-fidelity prediction are respectively expressed as: (14) (15) (16) (17) (18) in, For the working condition input vector, L , M and H These represent low-fidelity, medium-fidelity, and high-fidelity levels, respectively. It is a low-fidelity RBF model; and These are the medium-low fidelity residual RBF model and the high-medium fidelity residual RBF model, respectively. and These are the scaling correction coefficients between adjacent fidelity values. The medium-low fidelity residual is obtained by subtracting the scale-corrected low-fidelity predicted mode coefficient from the medium-fidelity true mode coefficient, and the high-medium fidelity residual is obtained by subtracting the scale-corrected medium-fidelity predicted mode coefficient from the high-fidelity true mode coefficient.

[0042] At shared operating points, the scaling correction coefficients can be estimated using a least-squares closed-form estimation with a small ridge regularization term: (19) (20) In the formula, This represents the low-fidelity prediction mode coefficient vector at the medium-fidelity shared operating point. This represents the vector of medium-fidelity predicted modal coefficients at the high-fidelity shared operating point. and These are the medium-fidelity and high-fidelity true modal coefficient vectors at the corresponding shared operating point, respectively. For the ridge, the correct direction is the item.

[0043] The low-fidelity layer and the two residual layers are modeled using Gaussian radial basis functions, the general form of which is: (twenty one) (twenty two) In the formula, For the first j One training input point, N This represents the number of training samples for the corresponding RBF model. For radial basis function weights, θ The kernel function length scale, For the current input point and the first j The Euclidean distance between the training input points. The radial basis function weights are solved by regularizing the linear equation, and the kernel length scale and regularization parameters are determined by leave-one-out cross-validation. Three modal coefficient models are trained for axial and circumferential strain respectively, resulting in a total of six high-fidelity modal coefficient prediction models.

[0044] After obtaining the high-fidelity modal coefficients, the high-fidelity full-field strain is reconstructed using the corresponding shared POD spatial modes: (twenty three) In the formula, This is a high-fidelity full-field strain prediction vector. This represents the average strain field corresponding to the strain components. For the first r Predicted values ​​of high-fidelity modal coefficients. For the first r POD spatial modes of order,R To preserve the modal number, the total axial strain and total circumferential strain were reconstructed using their respective mean fields and a shared POD substrate, ultimately yielding strain results for 81,492 high-fidelity reference nodes.

[0045] From high-fidelity reference nodes to 6480 lightweight 3D rendering vertices K The nearest neighbor index and normalized weights are pre-calculated and stored offline. During online invocation, no neighborhood search or finite element solution is performed; only input normalization, prediction of six modal coefficients, reconstruction of the full-field matrix of 81492 nodes for two classes, and vertex weighted summation are conducted. The 3D visualization engine performs color interpolation and contour updates based on the vertex index. The upper and lower limits of the color mapping can use the minimum and maximum values ​​under the current working condition, or a fixed engineering threshold, to ensure color comparability between different working conditions.

[0046] like Figure 4 and Figure 5 As shown, the digital twin platform can be organized according to physical entities, twin models, twin data, data interaction, and visualization services. In one embodiment, the laboratory data link adopts the form of "sensor—programmable logic controller—industrial gateway—industrial communication server—database—3D visualization engine" to verify data writing, reading, model calling, and interface refreshing. Sensor data is mainly used for data link and interaction function verification and is not used as direct prediction input for the three-level Co-RBF model.

[0047] In the finite element model, the temperature field, surrounding rock pressure, and local equivalent water pressure are parameterized; for example... Figures 6-8 As shown, the system can display three-dimensional strain cloud maps of the wellbore under different load conditions, high-fidelity reference field and prediction error field, as well as the digital twin platform function interface.

[0048] To verify the high-fidelity correction capability of the three-level Co-RBF model, leave-one-out high-fidelity layer verification was conducted under the condition of shared design points. One high-fidelity load case was reserved as the verification object each time; the high-fidelity strain field of this load case was not used in the current POD base construction and model training, while the remaining high-fidelity samples were used to rebuild the prediction model. The low-fidelity and medium-fidelity information corresponding to the verification parameter points was retained according to the model level. The verification results are shown in Table 3.

[0049] Table 3. High-fidelity leave-one-out verification results for different fidelity level combinations As shown in Table 3, the axial and circumferential total strain RMSE of the third-level Co-RBF model are 1.2915 με and 1.6786 με, respectively, which are 9.35% and 2.80% lower than those of the MF-HF dual-fidelity model. This validation is used to illustrate the stepwise correction capability of different fidelity levels to the high-fidelity response under shared design point conditions, and does not represent the independent extrapolation accuracy under conditions where no parameter points are seen.

[0050] Table 4. Calculation efficiency of Co-RBF full-field strain prediction The proxy model timings in Table 4 were performed after the model file was loaded. The process involved 30 warm-ups, followed by 1000 repeated runs, with the average and 95th percentile times calculated. The 41.74 ms figure only includes axial and circumferential modal coefficient prediction and full-field reconstruction of 81492 nodes, excluding the initial loading of the model file and 3D lightweight vertex mapping. The finite element time and proxy model time are from the corresponding experimental environments, and the speedup ratio is used to illustrate the difference in computational time magnitude.

[0051] This invention is not limited to the embodiments described above. For different wellbore sizes, surrounding rock types, parameter domains, mesh sizes, strain components, or 3D rendering platforms, multi-fidelity samples, shared POD bases, three-level Co-RBF models, and node mapping relationships can be regenerated. All equivalent substitutions or conventional transformations made based on the technical concept of this invention should fall within the protection scope of this invention.

Claims

1. A method for multi-fidelity full-field strain prediction and lightweight visualization of vertical shafts, characterized in that, Includes the following steps: S1: Construct an equivalent parameterized finite element model of the vertical shaft, using the equivalent temperature field coefficient, equivalent mechanical load coefficient, and local equivalent water pressure as the working condition input parameters; Under the nested working condition design, low-fidelity, medium-fidelity, and high-fidelity axial total strain field samples and circumferential total strain field samples are generated using coarse-grid, medium-grid, and fine-grid finite element models, respectively. The high-fidelity working condition set is included in the medium-fidelity working condition set, and the medium-fidelity working condition set is included in the low-fidelity working condition set, so that adjacent fidelities have shared working condition points. S2: Using high-fidelity finite element mesh nodes as unified reference nodes, separate methods are adopted for the axial total strain field and the circumferential total strain field. K The nearest-neighbor inverse distance weighting method maps low-fidelity and medium-fidelity strain fields to a high-fidelity reference node space, so that strain fields of different fidelities have consistent node dimensions and spatial locations. S3: Construct a shared intrinsic orthogonal decomposition basis for the axial total strain and the circumferential total strain respectively. Center the low-fidelity, medium-fidelity and high-fidelity strain snapshots unified to the high-fidelity reference node space using the same average strain field and project them onto the same shared intrinsic orthogonal decomposition basis so that the low-fidelity, medium-fidelity and high-fidelity modal coefficients of the same order are located in a consistent low-dimensional coordinate space. S4: Establish a three-level autoregressive collaborative radial basis function model for each order of modal coefficients, namely low-fidelity mode coefficients, medium-fidelity mode coefficients, and high-fidelity mode coefficients. Establish a scale correction relationship and a medium-low fidelity residual radial basis function model at the low-fidelity and medium-fidelity shared operating points. Establish a scale correction relationship and a high-medium fidelity residual radial basis function model at the medium-fidelity and high-fidelity shared operating points. Obtain a high-fidelity mode coefficient prediction model through stepwise scale correction and adjacent fidelity residual compensation. S5: After normalizing the target working condition input parameters, input them into the low-medium-high three-level autoregressive collaborative radial basis function model to predict the high-fidelity modal coefficients of the axial total strain and circumferential total strain, and perform high-fidelity full-field strain reconstruction. Based on the corresponding shared intrinsic orthogonal decomposition basis and average strain field, reconstruct the axial total strain field and circumferential total strain field on the high-fidelity reference node. S6: Perform 3D lightweight mapping: In the offline stage, the neighborhood index and normalized weight between the high-fidelity reference node and the 3D lightweight rendering vertex are pre-established and stored. In the online stage, the node resolution of the high-fidelity full-field strain obtained in step S5 is kept unchanged. The high-fidelity full-field strain is mapped to the 3D lightweight rendering vertex according to the neighborhood index and normalized weight, and the 3D strain cloud map of the shaft is updated according to the vertex strain value.

2. The method for multi-fidelity full-field strain prediction and lightweight visualization of vertical shafts according to claim 1, characterized in that, The operating condition input parameters in step S1 include the equivalent temperature field coefficient. Equivalent mechanical load factor and local equivalent water pressure ; The equivalent temperature field coefficient The equivalent mechanical load factor is used to scale the temperature difference between the reference temperature field and the material reference temperature. The local equivalent water pressure is used to scale the reference surrounding rock pressure field distributed along the wellbore depth. Used to characterize the pressure load within a predefined local water pressure area; the target operating condition input parameters are limited to the parameter domain formed by the training samples.

3. The method for multi-fidelity full-field strain prediction and lightweight visualization of vertical shafts according to claim 1, characterized in that, The nested operating condition design in step S1 includes: selecting medium-fidelity operating conditions from the low-fidelity operating condition set, and further selecting high-fidelity operating conditions from the medium-fidelity operating condition set, so that the high-fidelity operating condition set is included in the medium-fidelity operating condition set and the medium-fidelity operating condition set is included in the low-fidelity operating condition set; the low-fidelity and medium-fidelity shared operating condition points are used to establish medium-low fidelity scale correction relationships and residual relationships, and the medium-fidelity and high-fidelity shared operating condition points are used to establish high-medium fidelity scale correction relationships and residual relationships.

4. The method for multi-fidelity full-field strain prediction and lightweight visualization of vertical shafts according to claim 1, characterized in that, In step S2 K The nearest neighbor inverse distance weighting method specifically includes: for the first nearest neighbor in the high-fidelity reference node space... i target nodes Select the node closest to the target node from the low-fidelity or medium-fidelity source mesh to be mapped. K Source Node The target node and the first j The Euclidean distance, normalized weights, and mapping results among the source nodes are as follows: (1) (2) (3) in, For the target node With source node The Euclidean distance between them To normalize the weights, This represents the strain value at the source node. This represents the mapped strain value at the target node. To prevent extremely small positive numbers with a distance of zero, The distance decay index is used; when the target node coincides with any source node, the strain value of that source node is directly adopted.

5. The method for multi-fidelity full-field strain prediction and lightweight visualization of vertical shafts according to claim 1, characterized in that, The shared intrinsic orthogonal decomposition basis in step S3 is constructed as follows: the axial total strain snapshots and the circumferential total strain snapshots unified to the high-fidelity reference node space are respectively used to form corresponding strain snapshot matrices. The strain snapshot matrix Each column corresponds to a strain snapshot under a working condition; the same average strain field is used to center the low-fidelity, medium-fidelity, and high-fidelity snapshots of the same strain component, and singular value decomposition is performed on the centered strain snapshot matrix: (4) The number of retained modes is determined based on the cumulative energy contribution rate of the singular values, and the retained left singular vectors form a shared eigenorthogonal decomposition basis; n The modal coefficients of each strain snapshot and the reconstructed field obtained from the predicted modal coefficients are as follows: (5) (6) in, For the centered strain snapshot matrix, This is a strain snapshot matrix, where each column corresponds to a full-field strain snapshot for a given working condition. The average strain field of the training samples. For length is The whole Column vector, The number of strain snapshots used to construct a shared intrinsic orthogonal decomposition basis; and It is a singular vector matrix. It is a singular value diagonal matrix; It is a shared eigenorthogonal decomposition basis consisting of the preserved left singular vectors; For the first n Strain snapshot vector for each working condition; For the first n The modal coefficient vector obtained by projecting each strain snapshot onto a shared eigenorthogonal decomposition basis; The modal coefficient vector obtained from the surrogate model prediction; The total strain vector is reconstructed from the predicted modal coefficients; the total axial strain and the total circumferential strain are obtained by using their respective mean strain fields and a shared intrinsic orthogonal decomposition basis.

6. The method according to claim 1, characterized in that, For each modal coefficient in step S4, arbitrarily select one and denote its order as . r The low-medium-high three-level autoregressive cooperative radial basis function model satisfies: (7) (8) (9) (10) (11) in, For the working condition input vector, L , M and H These represent low-fidelity, medium-fidelity, and high-fidelity levels, respectively. For low-to-medium fidelity shared operating point, the medium fidelity first r The true modal coefficients of the first order, For high-fidelity shared operating point, the first high-fidelity first r True modal coefficients of order 1; , , They are low fidelity, medium fidelity, and high fidelity, respectively. r Predicted values ​​of first-order modal coefficients; and These are medium-low fidelity residuals and high-medium fidelity residuals, respectively. and This refers to the scale correction factor between adjacent fidelities. It is a low-fidelity radial basis function model. and These are the medium-low fidelity residual radial basis function model and the high-medium fidelity residual radial basis function model, respectively.

7. The method for multi-fidelity full-field strain prediction and lightweight visualization of vertical shafts according to claim 6, characterized in that, The low-fidelity radial basis function model, the medium-low fidelity residual radial basis function model, and the high-medium fidelity residual radial basis function model in step S4 are all constructed using Gaussian radial basis functions, and their general form is as follows: (12) (13) in, For the first j One training condition input point, N This represents the number of training samples for the corresponding radial basis function model. For radial basis function weights, d Let Euclidean distance be the distance between the input points. θ The length scale of the Gaussian kernel function is used; the radial basis function weights are solved by regularizing the linear equation; the kernel function length scale and regularization parameters are determined through cross-validation; and the scale correction coefficients are used. and Determined by least squares estimation with regularization terms at adjacent fidelity-shared operating points.

8. The method for multi-fidelity full-field strain prediction and lightweight visualization of vertical shafts according to claim 1, characterized in that, The high-fidelity full-field strain reconstruction in step S5 includes linearly combining the predicted high-fidelity modal coefficients of each order with the corresponding shared intrinsic orthogonal decomposition spatial modes, and superimposing the average strain field of the corresponding strain components; the 3D lightweight mapping in step S6 includes pre-calculating and storing the neighborhood index and normalized weight between the high-fidelity reference node and the 3D lightweight rendering vertex in the offline stage, and maintaining the high-fidelity full-field strain reconstruction resolution unchanged in the online stage, mapping the high-fidelity full-field strain to the 3D lightweight rendering vertex according to the neighborhood index and normalized weight; the high-fidelity full-field strain prediction vector is represented as: (14) in, H ( x () represents the high-fidelity full-field strain prediction vector under the target working condition. This represents the average strain field corresponding to the strain components. â H,r ( x ) is the first r Predicted values ​​of high-fidelity modal coefficients. For the first r Modes in the shared intrinsic orthogonal decomposition space. R To preserve the number of modes.

9. A multi-fidelity full-field strain prediction and lightweight visualization system for vertical shafts, used to implement the method described in any one of claims 1-8, characterized in that, include: The multi-fidelity finite element sample generation module is used to construct an equivalent parametric finite element model of the vertical shaft. It uses the equivalent temperature field coefficient, equivalent mechanical load coefficient, and local equivalent water pressure as working condition input parameters. Under the nested working condition design, it generates low-fidelity, medium-fidelity, and high-fidelity axial total strain field samples and circumferential total strain field samples using coarse-grid, medium-grid, and fine-grid finite element models, respectively. The strain field space unification module is used to employ high-fidelity finite element mesh nodes as unified reference nodes, and to separately apply different methods to the axial total strain field and the circumferential total strain field. K The nearest-neighbor inverse distance weighting method maps low-fidelity and medium-fidelity strain fields to a high-fidelity reference node space; The shared intrinsic orthogonal decomposition basis construction module is used to construct shared intrinsic orthogonal decomposition basis for axial total strain and circumferential total strain respectively. The low-fidelity, medium-fidelity and high-fidelity strain snapshots unified to the high-fidelity reference node space are centered using the same average strain field and projected onto the same shared intrinsic orthogonal decomposition basis to obtain the modal coefficients of each fidelity. The three-level autoregressive collaborative radial basis function prediction module is used to establish low-medium-high three-level autoregressive collaborative radial basis function models for modal coefficients of each order. High-fidelity modal coefficient prediction results are obtained through stepwise scaling correction and adjacent fidelity residual compensation. The high-fidelity full-field strain reconstruction module is used to normalize the input parameters of the target working condition and input them into the low-medium-high three-level autoregressive cooperative radial basis function model to obtain the high-fidelity modal coefficients of the axial total strain and circumferential total strain. Based on the corresponding shared intrinsic orthogonal decomposition basis and mean strain field, the axial total strain field and circumferential total strain field on the high-fidelity reference node are reconstructed. The 3D lightweight mapping and visualization module is used to pre-establish and store the neighborhood index and normalized weight between high-fidelity reference nodes and 3D lightweight rendering vertices in the offline stage. In the online stage, the node resolution of the reconstructed high-fidelity full-field strain remains unchanged. Based on the neighborhood index and normalized weight, the reconstructed high-fidelity full-field strain is mapped to the 3D lightweight rendering vertices, and the 3D strain cloud map of the shaft is updated according to the vertex strain value.

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