Foundation pit deformation control method based on tabPFN model and support axial force servo system

Abstract

The present application relates to a kind of based on TabPFN model and support axial force servo system's foundation pit deformation control method, S1.Servo support data simulation module, servo support force of support axial force servo system is used, and wall deformation response data is constructed servo support-wall deformation data set;S2.deformation prediction agent model module, constructs and optimizes TabPFN model, and deformation prediction agent model is quickly predicted according to the input servo support force the wall deformation caused by foundation pit excavation, obtains wall deformation prediction result;S3.cross-stage multi-objective optimization module, constructs the multi-objective optimization framework of fusion difference evolution algorithm, and sets multiple goals, input the wall deformation prediction result obtained in S2 in multi-objective optimization framework, cooperatively optimizes wall maximum deformation control and servo force unloading risk, obtains global optimal combination.The method is the multi-stage, multi-objective servo support optimization control method for foundation pit engineering.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering, and in particular to a method for controlling the deformation of foundation pits based on the TabPFN model and a support axial force servo system. Background Technology

[0002] Controlling foundation pit deformation in soft soil areas is challenging, and traditional support methods are no longer sufficient to meet increasingly stringent safety standards and refined management requirements. Therefore, deformation control and risk prevention have become research hotspots and key technological directions in the field of geotechnical engineering.

[0003] Existing foundation pit support systems mostly employ internal bracing systems. Ordinary internal bracing is a typical passive method for controlling foundation pit deformation, meaning that support force is gradually generated only after the retaining structure deforms, and dynamic adjustments cannot be made based on actual deformation during construction. To improve control effectiveness, hydraulic servo support systems have been introduced in recent engineering practices. This system integrates sensors and a hydraulic system into traditional support systems, enabling real-time monitoring and active adjustment of the support axial force, significantly improving the control of foundation pit deformation.

[0004] However, existing methods have the following shortcomings: First, the control strategy of the servo support system still relies on experience setting or manual adjustment, lacking a systematic, phased, and multi-objective optimization scheme, which can easily lead to hidden dangers such as uneven force distribution and local structural bending. Second, although the finite element method can simulate the interaction between the support structure and the soil well, the computational cost is high in the repeated iteration of support optimization, making it difficult to meet the real-time control requirements. Third, although existing surrogate models can speed up prediction, they are difficult to characterize the synergistic effect of multiple supports and their spatial arrangement characteristics, and their adaptability to changes in working conditions is poor, making it difficult to guarantee control accuracy and stability. Fourth, foundation pit excavation is usually divided into multiple stages, and there is strong coupling between each stage. Therefore, the optimal servo force combination obtained in a single stage is only the stage optimal and may not achieve the overall optimal control of all stages on a global scale. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the technical problem to be solved by the present invention is to provide a method for controlling the deformation of foundation pits based on the TabPFN model and a support axial force servo system. This method is a multi-stage, multi-objective servo support optimization control method for foundation pit engineering.

[0006] This invention is achieved by the following technical solution: a method for controlling the deformation of a foundation pit based on a TabPFN model and a support axial force servo system, comprising the following steps:

[0007] S1. Servo support data simulation module,

[0008] Based on finite element simulation, a servo support-wall deformation dataset is constructed using the servo support force and wall deformation response data of the servo support servo system.

[0009] S2. Deformation Prediction Agent Model Module

[0010] The TabPFN model is constructed and optimized to obtain the optimized deformation prediction proxy model. The deformation prediction proxy model quickly predicts the wall deformation caused by the foundation pit excavation based on the input servo support force, and obtains the wall deformation prediction result.

[0011] S3. Cross-stage multi-objective optimization module

[0012] A multi-objective optimization framework integrating differential evolution algorithm is constructed, and multiple objectives are set. The wall deformation prediction results obtained in S2 are input into the multi-objective optimization framework to collaboratively optimize the control of maximum wall deformation and the risk of servo force unloading, so as to obtain the global optimal combination.

[0013] Furthermore, the steps in S1 for constructing the dataset of support-wall deformation are as follows:

[0014] S11. Based on finite element simulation, a stage loading strategy is adopted to activate the servo support of multiple preset stages in sequence. In each stage, the newly added adjustable servo force and the support force set in the previous stage together form the cumulative input of the current stage.

[0015] S12. Multiple sets of input combinations are generated within the pre-set design axial force range of each support through Latin hypercube sampling, which serve as the loading boundary conditions for the finite element model;

[0016] S13. Simulate and output the maximum and minimum deformation values ​​of the retaining wall at each stage, and construct a servo support-wall deformation dataset that represents the relationship between input servo force and output wall deformation.

[0017] Further steps to optimize the deformation prediction surrogate model include:

[0018] S21. Synthetic Data Pre-training Module

[0019] By obtaining a synthetic dataset from millions of synthetic tasks generated by structural causal models, a pre-trained TabPFN model is obtained, and the trained TabPFN model is obtained, enabling the Transformer feature extractor of the TabPFN model to learn structural patterns.

[0020] S22. Bidirectional Hybrid Sparse Attention Feature Extraction Module

[0021] After training in S21, a bidirectional attention mechanism is introduced into the Transformer feature extractor of the TabPFN model. Based on the bidirectional attention mechanism, a support sample pruning mechanism and a local-global hybrid sparse attention mechanism are introduced to obtain the optimized TabPFN model.

[0022] S23. Small Sample Inference Module

[0023] The servo-support-wall deformation dataset in S1 is input into the optimized Transformer feature extractor in S22 for encoding. After encoding, small-sample inference is performed to obtain the predicted wall deformation results.

[0024] Furthermore, the steps for generating the synthetic dataset in the synthesis task of S21 are as follows:

[0025] 1) Randomly generate a directed acyclic graph (DAG), where each node represents a variable X. i The nonlinear structure function f with Gaussian noise i The function f is determined. i Describe how each variable depends on its parent node PA i Superimposed Gaussian noise Used to simulate disturbances and uncertainties in real-world working conditions;

[0026] 2) Variable X i Sampling is performed according to the topological order of the DAG to simulate the causal structure of soil parameters, support forces and structural deformation;

[0027] 3) Randomly select a portion of the intermediate variables as the input feature vector x (j) Randomly select one of the other target variables as the output y. (j) ;

[0028] 4) By repeating the above process under different graph structures, causal layouts and function types, a synthetic dataset DSCM with diverse structures can be generated for pre-training the TabPFN model to obtain the trained TabPFN model.

[0029] Furthermore, the bidirectional attention mechanism in S22 includes performing intra-sample attention and inter-sample attention. TabPFN alternately performs intra-sample (row-wise) and inter-sample (column-wise) attention in each encoder layer. Intra-sample attention is used to extract the linkage pattern between each support force in a single sample, while inter-sample attention learns the global importance of features at different locations from multiple samples.

[0030] Furthermore, the steps for using the sample pruning mechanism in S22 are as follows:

[0031] 1) Pre-coding and buffering: During the TabPFN model loading phase, all supporting samples are pre-coded independently, and the servo force-deformation feature encoding vector is cached in memory;

[0032] 2) Top-K filtering: During the inference phase, the top-K most relevant supporting samples are quickly filtered out based on the Euclidean distance between the query sample and the cached supporting samples.

[0033] 3) Re-encoding and inference: Only the Top-K sample and the query sample are input into the Transformer for encoding and inference, avoiding repeated operations on the full support set.

[0034] Furthermore, the local-global hybrid sparse attention mechanism in S22 replaces the original fully connected dot product attention, and the specific steps are as follows:

[0035] 1) Set a local window of fixed width for each servo force input position and perform attention calculations only between its adjacent support points to capture local spatial coupling relationships;

[0036] 2) Introduce a Top-K dynamic global attention mechanism. Based on the initial similarity score, select the K most influential remote positions from all supporting positions that have the greatest impact on the current query position, and add attention interaction between these positions to take into account the long-distance linkage effect.

[0037] 3) Sparse attention masks are used to mask irrelevant locations, effectively compressing the proportion of non-zero elements in the attention weight matrix, thus reducing the computational complexity of attention from the original... O ( n 2 Reduced to approximately O ( n ).

[0038] Furthermore, the specific steps for obtaining the predicted wall deformation results in S23 are as follows:

[0039] 1) Divide the centralized data of the servo support-wall deformation dataset into a query sample set and multiple support sample sets. Input the query sample set and multiple support sample sets into the optimized Transformer feature extractor in S22 for encoding. After encoding, the model calculates the similarity between itself and each support sample through attention weights, thereby identifying the support sample that is closest in terms of stress-deformation behavior.

[0040] 2) The TabPFN model assigns an attention weight to each support sample based on the similarity between the query sample and each support sample. α i The model supports value vectors containing labels in the support sample set. Vi We perform weighted fusion to aggregate a new vector representation. Z q ;

[0041] 3) Integrated Expression Z q The vector is fed into a multilayer perceptron (MLP) for decoding, and the MLP maps the vector to a vector within a predefined wall deformation range. y 1, y 2, … , y M The probability distribution on};

[0042] 4) The probability prediction output in 3) is converted into a continuous expected value of deformation by using a segmented distribution weighted average method to obtain the predicted wall deformation result.

[0043] Furthermore, the optimization objectives of the multi-objective optimization framework include controlling the maximum deformation, suppressing reverse bending, and minimizing the servo force unloading amount. Controlling the maximum deformation and suppressing reverse bending are the primary objectives, and the minimum servo force unloading amount is introduced as a secondary objective while satisfying the primary objective of deformation control.

[0044] Furthermore, the specific steps to obtain the globally optimal combination are as follows:

[0045] S31. The maximum wall deformation is limited to within 3% of the excavation depth H, and an 80% warning threshold is set at the same time.

[0046] S32. The main objective loss function is defined as follows:

[0047] ;

[0048] S33. After the main objectives of S31 and S32 are satisfied, an unloading penalty term is further introduced into the framework to suppress the unloading amount of servo force between adjacent excavation stages.

[0049] The wall deformation prediction results in S34.S2 are input into the multi-objective optimization framework. The solution set that satisfies the two main objectives and one secondary objective set in S31-S33 is selected. Then, the differential evolution algorithm is used to perform a group search in the multi-stage servo force combination space. The priority guided beam search method based on Pareto sort is used to select the optimal servo force solution set and obtain the global optimal combination.

[0050] Beneficial effects of this invention:

[0051] (1) Construct and optimize the efficient proxy model of TabPFN (Tabular Prior-Data Fitting Network) to realize the rapid prediction of the deformation of the retaining wall under servo force input, and significantly reduce the computational cost caused by repeated calls of finite element method;

[0052] (2) The TabPFN model introduces a bidirectional attention mechanism to accurately characterize the spatial coordination relationship and coupling effect between multiple supports, thereby enhancing the model's ability to express the wall deformation response under complex support conditions.

[0053] (3) Design a multi-objective optimization framework that integrates differential evolution algorithm to coordinate the control of maximum deformation of the wall and the risk of unloading servo force, thereby improving the stability and control robustness of the support system;

[0054] (4) A multi-path parallel evolution strategy is proposed to realize the global search of servo force combination in the multi-stage control process and ensure that the control path has overall optimality.

[0055] (5) The TabPFN model introduces a support sample pruning mechanism and a local-global hybrid sparse attention mechanism. The support sample pruning mechanism is used to filter input samples, avoiding repeated calculations on the full support set and significantly reducing the computational complexity of attention and inference time. The sparse attention mechanism optimizes the internal attention structure of the Transformer, significantly improving inference speed and reducing memory bandwidth pressure, while maintaining the ability to model the servo force-wall deformation response law. The two mechanisms work together to improve the inference efficiency of the TabPFN model. Attached Figure Description

[0056] Figure 1 A schematic diagram of servo-controlled wall deformation prediction during multi-stage excavation;

[0057] Figure 2 The wall deformation curves before and after each excavation stage were optimized;

[0058] Figure 3 Optimize paths for all servo support;

[0059] Figure 4 This represents the total unloaded amount across all paths.

[0060] Figure 5 This is a flowchart of a foundation pit deformation control method based on the TabPFN model and a support axial force servo system. Detailed Implementation

[0061] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0062] Reference Figures 1-5 As shown, this invention provides a method for controlling foundation pit deformation based on a TabPFN model and a support axial force servo system, the steps of which are as follows:

[0063] S1. Servo support data simulation module;

[0064] Based on finite element simulation, a servo support-wall deformation dataset is constructed using the servo support force and wall deformation response data of the servo support axial force servo system. The specific steps are as follows:

[0065] S11. Based on finite element simulation, a staged loading strategy is adopted to sequentially activate the servo support of multiple preset stages. In each stage, the newly added adjustable servo force and the support force set in the previous stage together constitute the cumulative input of the current stage;

[0066] S12. Multiple sets of input combinations are generated within the initial design axial force range of each support through Latin hypercube sampling, which serve as the loading boundary conditions for the finite element model;

[0067] S13. Simulate and output the maximum and minimum deformation values ​​of the retaining wall at each stage, and construct a servo support-wall deformation dataset that represents the relationship between input servo force and output wall deformation.

[0068] S2. Deformation Prediction Agent Model Module;

[0069] A TabPFN model is constructed and optimized to obtain an optimized deformation prediction proxy model. This model rapidly predicts the wall deformation caused by foundation pit excavation based on the input servo support force, thus obtaining the wall deformation prediction result. The optimized deformation prediction proxy model includes a synthetic data pre-training module, a bidirectional attention feature extraction module, and a few-shot inference module, as detailed below:

[0070] S21. Synthetic Data Pre-training Module.

[0071] By obtaining synthetic datasets from millions of synthetic tasks generated by structural causal models, a pre-trained TabPFN model is obtained, leading to the trained TabPFN model. The TabPFN model's Transformer feature extractor learns structural patterns and achieves good generalization ability under small sample conditions. The synthetic tasks involve causal relationships, such as input-output mappings, feedback structures, and parameter dependencies. These causal mechanisms are highly similar to the coupling relationships in geotechnical engineering systems, such as the strong correlation between soil parameters, support forces, and structural deformation. The specific steps for generating the synthetic dataset are as follows:

[0072] 1) Randomly generate a directed acyclic graph (DAG). A DAG is a directed graph without loops, where each node represents a variable. X i The nonlinear structure function with Gaussian noise f i Decide.

[0073] (1)

[0074] Among them, the function f i Describe how each variable depends on its parent node PA i Superimposed Gaussian noise Used to simulate disturbances and uncertainties in real-world working conditions, among which i It is the variable number index, indicating which variable it is, and N represents the normal distribution (Gaussian distribution). It is variance.

[0075] 2) Variables X i Sampling is performed according to the topological order of the DAG to simulate the causal structure of soil parameters, support forces, and structural deformation.

[0076] (2)

[0077] 3) Randomly select a portion of intermediate variables (such as the stress state of the wall) as the input feature vector. x (j) Randomly select one from other target variables (such as wall deformation or ground settlement) as the output. y (j) .

[0078] (3)

[0079] 4) By repeating the above process under different graph structures, causal layouts, and function types, synthetic datasets with diverse structures can be generated. D SCM , used for pre-training the TabPFN model.

[0080] (4).

[0081] S22. Bidirectional Hybrid Sparse Attention Feature Extraction Module.

[0082] A bidirectional attention mechanism is introduced into the Transformer feature extractor of the TabPFN model trained in S21 to model the coupling control and spatial cooperation relationship between servo supports. Based on this bidirectional attention mechanism, a support sample pruning mechanism and a local-global hybrid sparse attention mechanism are introduced to obtain the optimized TabPFN model. Details are as follows:

[0083] (1) Introduce a two-way attention mechanism.

[0084] The bidirectional attention mechanism includes performing intra-sample attention (row-wise attention) and inter-sample attention (column-wise attention). TabPFN alternately performs intra-sample (row-wise) and inter-sample (column-wise) attention in each encoder layer. Intra-sample attention (row-wise attention) is used to extract the linkage patterns between the support forces in a single sample, while inter-sample attention learns the global importance of features at different locations from multiple samples.

[0085] The bidirectional attention mechanism is particularly suitable for deep foundation pit support systems, where wall deformation depends not only on the total support force but also strongly on the force distribution at each support location. For example, in Sample 1, when S1 = 40 kN and S3 = 10 kN, the maximum wall deformation is 6 mm; while in Sample 2, when S1 = 10 kN and S3 = 40 kN, the deformation is only 2 mm. Although the total force is the same, the deformation response differs significantly due to the different force locations. The standard Transformer, lacking column attention, struggles to identify the influence of force location on deformation and may incorrectly treat the two samples as equivalent. TabPFN, however, aggregates cross-sample information through column attention, effectively learning location-sensitive patterns such as "a larger force at location S1 usually leads to a larger deformation," thereby improving the accuracy of predicting wall deformation under different servo force distributions.

[0086] (2) Introduce a support sample pruning mechanism.

[0087] Introducing a supportive sample pruning mechanism reduces the number of samples required for encoding in each round of inference from thousands to tens, shortening computation time and significantly reducing attention computational complexity and inference latency. The steps of the supportive sample pruning mechanism are as follows:

[0088] 1) Pre-coding and caching. During the TabPFN model loading phase, all supporting samples are pre-coded independently, and the servo force-deformation feature encoding vectors are cached in memory;

[0089] 2) Top-K Filtering. During the inference phase, the Top-K most relevant supporting samples are quickly selected based on the Euclidean distance between the query samples and the cached supporting samples;

[0090] 3) Re-encoding and inference. Only the Top-K samples and the query samples are input into the Transformer for encoding and inference, avoiding repeated operations on the entire support set.

[0091] (3) Introduce a local-global hybrid sparse attention mechanism.

[0092] To further reduce the computational complexity and memory access pressure of the attention matrix in the Transformer encoder, a local-global hybrid sparse attention mechanism is introduced to replace the original fully connected dot product attention. The specific steps are as follows:

[0093] 1) Set a local window of fixed width for each servo force input position and perform attention calculations only between its adjacent support points to capture local spatial coupling relationships;

[0094] 2) Introduce a Top-K dynamic global attention mechanism. Based on the initial similarity score, select the K most influential remote positions from all supporting positions that have the greatest impact on the current query position, and add attention interaction between these positions to take into account the long-distance linkage effect.

[0095] 3) Sparse attention masks are used to mask irrelevant locations, effectively compressing the proportion of non-zero elements in the attention weight matrix, thus reducing the computational complexity of attention from the original... O ( n 2 Reduced to approximately O ( n It significantly improves inference speed and reduces memory bandwidth pressure, while maintaining the ability to model the servo force-wall deformation response.

[0096] S23. Small Sample Inference Module.

[0097] The servo-support-wall deformation dataset in S1 is input into the optimized Transformer feature extractor in S22 for encoding. After encoding, few-sample inference is performed to obtain the predicted wall deformation results. The specific steps are as follows:

[0098] 1) The centralized data of the servo-supported wall deformation dataset is divided into a query sample set and multiple support sample sets. The query sample set and multiple support sample sets are input into the optimized Transformer feature extractor in S22 for encoding. After encoding, the model calculates the similarity between itself and each support sample through attention weights, thereby identifying the support sample that is closest in terms of stress-deformation behavior. The weight calculation formula is as follows:

[0099] (5)

[0100] in, This represents the encoded vector of the query sample. K i Indicates the first i The key vectors of the supporting samples, d Exp represents the vector dimension (used for scaling), and Exp stands for exponential function.

[0101] 2) The TabPFN model assigns an attention weight to each support sample based on the similarity between the query sample and each support sample. α i A higher weight indicates that it is more important for predicting the query sample; the model supports the value vectors containing labels in the support sample set. V i (Including the encoded information of its servo support force and wall deformation labels) are weighted and fused to form a new vector representation. Z q ,

[0102] (6)

[0103] 3) Integrated Expression Z q The vector is fed into a multilayer perceptron (MLP) for decoding, and the MLP maps the vector to a vector within a predefined wall deformation range. y 1 , y 2, …, y M The probability distribution over} is as follows:

[0104] (7)

[0105] in, y j Indicates the first j The center value of each wall deformation interval, S represents the support set. p ( y j | x q S) represents the query sample x q The probability that the predicted deformation falls within this interval.

[0106] 4) The probability prediction output from 3) is converted into continuous expected deformation values ​​using a piecewise weighted average method, thus obtaining the predicted wall deformation results. Specifically, the model divides the deformation values ​​into several fixed-interval intervals, each interval [ a i , b i ] Corresponds to a probability pi Final predicted value It is obtained by weighted summation of the products of the center point of each interval and its corresponding probability:

[0107] (8).

[0108] In the few-shot inference module, the servo force-deformation features of all support samples are pre-encoded into vector representations and cached in memory before inference. During each inference, the top-K support samples that are closest to the query sample are first selected by fast L2 distance calculation or dot product similarity. Then, Transformer encoding and attention inference are performed only on these support samples and the query sample, which significantly reduces the amount of computation and the frequency of memory access.

[0109] S3. Cross-stage multi-objective optimization module.

[0110] A multi-objective optimization framework integrating differential evolution algorithms is constructed, setting multiple optimization objectives to minimize the risk of support unloading while ensuring that the wall deformation meets the specification limits. The predicted wall deformation obtained in S2 is then input into the multi-objective optimization framework to collaboratively optimize the control of maximum wall deformation and the risk of servo force unloading, obtaining the globally optimal combination.

[0111] The optimization objectives include controlling maximum deformation, suppressing reverse bending, and minimizing servo force unloading. Controlling maximum deformation and suppressing reverse bending are the primary objectives; controlling maximum deformation ensures structural safety, while suppressing reverse bending prevents support system failure. Under the premise of satisfying the primary objective of deformation control, minimizing servo force unloading is introduced as a secondary objective to reduce the impact of unnecessary unloading on support stability and the reliability of the control strategy. The specific steps are as follows:

[0112] S31. Maximum wall deformation is limited to the excavation depth. H Within 3%, while setting an 80% warning threshold, when the maximum deformation... u max If the value is below the warning line, no penalty will be imposed; when the maximum deformation occurs... u max If the warning line is reached, a slight penalty proportional to the square of the deviation is applied to guide the deformation to remain within a safe range, until the maximum deformation... u max If the value exceeds the specification limit, a tenfold penalty will be imposed to strictly constrain the upper limit of deformation; when the maximum negative displacement... u min No penalty is applied if the value is greater than zero, and the maximum negative displacement is within zero. u min If it is less than zero, then its squared value is applied as a penalty;

[0113] S32. Main Objective Loss Function Ldef The definition is as follows:

[0114] (9)

[0115] S33. After setting the main objectives in S31 and S32, an unloading penalty item is further introduced into the framework. As a secondary objective, the servo force unloading between adjacent excavation stages is suppressed to avoid the risk of instability due to excessive unloading. For solutions that violate specification constraints (i.e.... L def If the limit has been exceeded, even if the uninstallation penalty is low, it will be directly excluded from the list of options. The uninstallation penalty is defined as follows:

[0116] (10)

[0117] in, S i,t Indicates the first t Phase 1 i Servo force applied at each support position;

[0118] S34. Input the wall deformation prediction results in S2 into the multi-objective optimization framework, filter out the solution set that satisfies the two main objectives and one secondary objective set in S31-S33 (satisfy the two main objectives first, then satisfy the secondary objective), and then use the differential evolution algorithm to perform a group search in the multi-stage servo force combination space. Use the priority guided beam search method based on Pareto sort to filter the optimal servo force solution set and obtain the global optimal combination.

[0119] Specifically, in each generation, a Pareto sorting front solution that balances deformation loss and servo unloading risk is identified through non-dominated sorting, due to the primary objective... L def Individuals with lower deformation loss are given higher priority in engineering and are selected first, followed by control scores. Secondary screening is performed, selecting the solution set with the lowest control risk from the Pareto solution set through bundle search. N beam Each candidate solution constitutes a path solution set for the current stage. These multiple candidate solutions will evolve in parallel in the next stage to preserve solution diversity. After each stage, the candidate solution with the lowest control cost will serve as an "attraction center" to guide the search direction of the population in the next stage. Ultimately, a globally optimal servo control solution sequence is obtained through multi-stage cooperative evolution.

[0120] Example: The effectiveness of the proposed optimization framework is verified through numerical simulation of servo-controlled support in a foundation pit project. Project details are as follows: The support structure is a diaphragm wall with a thickness of 0.8m and a depth of 37.6m. The original support system included one concrete support (C1), two conventional steel supports (S1 and S3), and two servo-controlled steel supports (S2 and S4). S1 has a diameter of 609mm, while S2 to S4 are uniformly designed to be 800mm, with a wall thickness of 16mm for all. The elastic moduli of concrete and steel are 30 × 10⁻⁶ and 30 × 10⁻⁶, respectively. 6 kN / m² and 205×10 6 The horizontal spacing between supports is 3m. The design prestressing force for S1 is 870kN, and for S3 it is 1080kN. Considering stress loss after installation, the actual initial axial force for both is set to 50% of the design value. The target axial force for S2 is 1740kN (corresponding to a distributed load of 580kN / m), and for S4 it is 1710kN (corresponding to a distributed load of 570kN / m). Concrete supports and conventional steel supports are modeled using "node-node anchor elements," while servo supports are modeled using concentrated loads. Wall deformation is monitored using inclinometers installed at 0.5m intervals below the ground surface, with data recorded at nodes corresponding to construction stages 3, 5, 7, 9, 11, and 12. The construction sequence was as follows: first, the diaphragm wall was constructed and the water level was pumped down to the foundation. Then, excavation was carried out in stages to -1.0m to install C1, followed by excavation to -4.4m, -7.4m, -10.4m, -13.0m, and -16.4m, with S1, S2, S3, and S4 installed sequentially at each stage. Servo adjustment of S2 was used to control the axial force during the installation of S3 and S4. Numerical simulation was performed using PLAXIS 2D software, and a hardened soil constitutive model was selected. Input parameters were calibrated through back analysis to match measured data. All soil layers were assumed to be in an undrained state.

[0121] The proposed multi-objective optimization framework is configured as follows: First, the servo axial force in the finite element model is set to range from 0 to 2000 kN / m. Within this range, 1000 labeled samples are generated using Latin hypercube sampling as the support set for the pre-trained TabPFN surrogate model. The servo force at each stage serves as the model input, and the output includes the maximum wall deformation (for code verification) and the minimum wall deformation (for inverse bending judgment). In the optimization method, each stage runs 5 rounds of evolutionary iterations, with a population size of 1000 per round, balancing global search capability with computational cost control. To prevent getting trapped in local optima, a 3% global perturbation probability is introduced. In the bundle search, the top 20 candidate paths with the best control effect (bundle width set to 20) are retained at each stage.

[0122] like Figure 1As shown, the TabPFN surrogate model was used for servo-controlled wall deformation prediction during a multi-stage excavation process. At each stage, the model was set to an adjustable servo force S(…) for the current stage. t As input, and retaining the servo force S(1:) determined in the previous stage. t -1), thus forming a progressively expanding input sequence. The model output is the maximum and minimum wall deformation values ​​for the current stage. This stage-by-stage modeling approach can reflect the progressive activation process of the four sets of servo supports in multiple preset stages (i.e., stages 5 to 12), and incorporates all historical servo force information in each stage. This input structure highly matches the time accumulation characteristics and causal order dependencies in the TabPFN pre-training task, enabling the model to perform inference without fine-tuning, and achieving fast and stable servo control prediction during multi-stage excavation.

[0123] like Figure 2 As shown, the wall deformation curves before and after optimization at each excavation stage are compared. The optimized results were calculated by reloading the selected servo force input into the finite element model. S1–S4 represent four servo-controlled supports. As excavation progresses, the location of the maximum deformation gradually moves downward. Overall, the optimization significantly reduces the maximum wall deformation while maintaining a smooth inclinometer curve without abrupt changes or reverse bending. In stage 5, due to the shallow excavation depth, only a small support force of 65.7 kN / m is needed to control the entire deformation curve within the specification limits for S1. As the excavation deepens, the lateral displacement gradually increases, and the difference between the curves before and after optimization also widens significantly. In stages 7, 9, 11, and 12, the maximum deformation decreases from 23.6 mm to 15.8 mm, 38.5 mm to 25.4 mm, 49.3 mm to 34.2 mm, and 66.3 mm to 45.4 mm, respectively, with an average reduction of approximately 30%–35%. Throughout the process, the proposed optimization framework searches for the optimal combination of each stage in the servo force space from S1 to S4, achieving multi-stage linkage control. Ultimately, the inclinometer curves of each stage all meet the specifications and show no reverse bending, verifying the effectiveness of the framework in controlling wall deformation across the entire depth range.

[0124] like Figure 3 The diagram illustrates the search paths obtained from the search. The search begins at S1 = 72 kN / m in stage 5 and increases to 848 kN / m in stage 6. The paths then begin to branch: S2 is 85 or 89 kN / m in stage 7, 758 or 785 kN / m in stage 8, and a combination of S2 = 682 or 706 kN / m and S3 = 278 or 327 kN / m appears in stage 9. This "expansion-filtering" operation continues until stage 12, resulting in 20 non-dominated global control paths.

[0125] like Figure 4As shown, the total unloading amount for each path is displayed. Among them, path number 8 performs best: its total unloading amount is 741 kN / m, significantly lower than the optimal local path's 792 kN / m, while still meeting all deformation control requirements. The results indicate that the proposed GP-APDE method can further reduce the risk of servo unloading through global path search, achieving more stable and efficient support control.

[0126] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for controlling the deformation of a foundation pit based on a TabPFN model and a support axial force servo system, characterized by the following steps: as follows: S1. Servo support data simulation module, Based on finite element simulation, a servo support-wall deformation dataset is constructed using the servo support force and wall deformation response data of the servo support servo system. S2. Deformation Prediction Agent Model Module A TabPFN model is constructed and optimized to obtain an optimized deformation prediction proxy model. This deformation prediction proxy model quickly predicts the wall deformation caused by the foundation pit excavation based on the input servo support force, thus obtaining the wall deformation prediction result. The steps for optimizing the deformation prediction surrogate model include: S21. Synthetic Data Pre-training Module By obtaining a synthetic dataset from millions of synthetic tasks generated by structural causal models, a pre-trained TabPFN model is obtained, and the trained TabPFN model is obtained, enabling the Transformer feature extractor of the TabPFN model to learn structural patterns. S22. Bidirectional Hybrid Sparse Attention Feature Extraction Module After training in S21, a bidirectional attention mechanism is introduced into the Transformer feature extractor of the TabPFN model. Based on the bidirectional attention mechanism, a support sample pruning mechanism and a local-global hybrid sparse attention mechanism are introduced to obtain the optimized TabPFN model. S23. Small Sample Inference Module The servo-support-wall deformation dataset in S1 is input into the optimized Transformer feature extractor in S22 for encoding. After encoding, few-sample inference is performed to obtain the predicted wall deformation results. S3. Cross-stage multi-objective optimization module A multi-objective optimization framework integrating differential evolution algorithm is constructed, and multiple objectives are set. The wall deformation prediction results obtained in S2 are input into the multi-objective optimization framework to collaboratively optimize the control of maximum wall deformation and the risk of servo force unloading, so as to obtain the global optimal combination.

2. The foundation pit deformation control method based on the TabPFN model and the support axial force servo system according to claim 1, characterized in that: The steps for constructing the dataset of support-wall deformation in S1 are as follows: S11. Based on finite element simulation, a stage loading strategy is adopted to activate the servo support of multiple preset stages in sequence. In each stage, the newly added adjustable servo force and the support force set in the previous stage together form the cumulative input of the current stage. S12. Multiple sets of input combinations are generated within the pre-set design axial force range of each support through Latin hypercube sampling, which serve as the loading boundary conditions for the finite element model; S13. Simulate and output the maximum and minimum deformation values ​​of the retaining wall at each stage, and construct a servo support-wall deformation dataset that represents the relationship between input servo force and output wall deformation.

3. The foundation pit deformation control method based on the TabPFN model and the support axial force servo system according to claim 1, characterized in that: The steps for generating the synthetic dataset in the S21 synthesis task are as follows: 1) Randomly generate a directed acyclic graph (DAG), where each node represents a variable. X i The nonlinear structure function with Gaussian noise f i Decision, function f i Describe how each variable depends on its parent node PA i Superimposed Gaussian noise Used to simulate disturbances and uncertainties in real-world working conditions; 2) Variables X i Sampling is performed according to the topological order of the DAG to simulate the causal structure of soil parameters, support forces and structural deformation; 3) Randomly select a portion of the intermediate variables as the input feature vector. x (j) Randomly select one from other target variables as the output. y (j) ; 4) By repeating the above process under different graph structures, causal layouts, and function types, synthetic datasets with diverse structures can be generated. D SCM This is used to pre-train the TabPFN model and obtain the trained TabPFN model.

4. The foundation pit deformation control method based on the TabPFN model and the support axial force servo system according to claim 1, characterized in that: The bidirectional attention mechanism in S22 includes performing intra-sample attention and inter-sample attention. TabPFN alternately performs intra-sample attention and inter-sample attention in each encoder layer. Intra-sample attention is used to extract the linkage pattern between the support forces in a single sample, while inter-sample attention learns the global importance of features at different locations from multiple samples.

5. The foundation pit deformation control method based on the TabPFN model and the support axial force servo system according to claim 1, characterized in that: The steps for using the sample pruning mechanism in S22 are as follows: 1) Pre-coding and buffering: During the TabPFN model loading phase, all supporting samples are pre-coded independently, and the servo force-deformation feature encoding vector is cached in memory; 2) Top-K filtering: During the inference phase, the top-K most relevant supporting samples are quickly filtered out based on the Euclidean distance between the query sample and the cached supporting samples. 3) Re-encoding and inference: Only the Top-K sample and the query sample are input into the Transformer for encoding and inference, avoiding repeated operations on the full support set.

6. The foundation pit deformation control method based on the TabPFN model and the support axial force servo system according to claim 1, characterized in that: The local-global hybrid sparse attention mechanism in S22 replaces the original fully connected dot product attention mechanism. The specific steps are as follows: 1) Set a local window of fixed width for each servo force input position and perform attention calculations only between its adjacent support points to capture local spatial coupling relationships; 2) Introduce a Top-K dynamic global attention mechanism. Based on the initial similarity score, select the K most influential remote positions from all supporting positions that have the greatest impact on the current query position, and add attention interaction between these positions to take into account the long-distance linkage effect. 3) Sparse attention masks are used to mask irrelevant locations, effectively compressing the proportion of non-zero elements in the attention weight matrix, thus reducing the computational complexity of attention from the original... O ( n 2 Reduced to approximately O ( n ).

7. The foundation pit deformation control method based on the TabPFN model and the support axial force servo system according to claim 1, 2, 3, 4, 5, or 6, is characterized in that: The specific steps to obtain the predicted wall deformation results in S23 are as follows: 1) Divide the centralized data of the servo support-wall deformation dataset into a query sample set and multiple support sample sets. Input the query sample set and multiple support sample sets into the optimized Transformer feature extractor in S22 for encoding. After encoding, the model calculates the similarity between itself and each support sample through attention weights and identifies the support sample that is closest in terms of stress-deformation behavior. 2) The TabPFN model assigns an attention weight to each support sample based on the similarity between the query sample and each support sample. α i The model supports value vectors containing labels in the support sample set. V i We perform weighted fusion to aggregate a new vector representation. Z q ; 3) Integrated Expression Z q The vector is fed into a multilayer perceptron (MLP) for decoding. The MLP maps the vector to a vector within a predefined range of wall deformation. y 1, y 2, ..., y M The probability distribution on}; 4) The probability prediction output in 3) is converted into a continuous expected value of deformation by using a segmented distribution weighted average method to obtain the predicted wall deformation result.

8. The foundation pit deformation control method based on the TabPFN model and the support axial force servo system according to claim 7, characterized in that: The optimization objectives of the multi-objective optimization framework include controlling the maximum deformation, suppressing reverse bending, and minimizing the servo force unloading amount. Controlling the maximum deformation and suppressing reverse bending are the primary objectives. Under the premise of satisfying the primary objective of deformation control, the minimum servo force unloading amount is introduced as a secondary objective.

9. The foundation pit deformation control method based on the TabPFN model and the support axial force servo system according to claim 1 or 8, characterized in that: The specific steps to obtain the globally optimal combination are as follows: S31. Maximum wall deformation is limited to the excavation depth. H Within 3%, while setting an 80% warning threshold; S32. Main Objective Loss Function L def The definition is as follows: ， Among them, u max It is the maximum deformation, u min It is the maximum negative displacement; S33. After the main objectives of S31 and S32 are satisfied, an unloading penalty term is further introduced into the framework. L ctrl Suppress the servo force unloading amount between adjacent excavation stages; The wall deformation prediction results in S34.S2 are input into the multi-objective optimization framework. The solution set that satisfies the two main objectives and one secondary objective set in S31-S33 is selected. Then, the differential evolution algorithm is used to perform a group search in the multi-stage servo force combination space. The priority guided beam search method based on Pareto sort is used to select the optimal servo force solution set and obtain the global optimal combination.

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