Foundation pit deformation control method based on TabPFN model and supporting axial force servo system

Abstract

The invention relates to a foundation pit deformation control method based on a TabPFN model and a supporting axial force servo system, and the method comprises the steps: S1, constructing a servo supporting-wall deformation data set through a servo supporting data simulation module according to the servo supporting force of the supporting axial force servo system and wall deformation response data; s2, a deformation prediction agent model module constructs and optimizes a TabPFN model, the deformation prediction agent model rapidly predicts wall deformation caused by foundation pit excavation according to the input servo supporting force, and a wall deformation prediction result is obtained; and S3, a cross-stage multi-objective optimization module constructs a multi-objective optimization framework fused with a differential evolution algorithm, sets a plurality of objectives, inputs the wall deformation prediction result obtained in the step S2 into the multi-objective optimization framework, and collaboratively optimizes wall maximum deformation control and servo force unloading risks to obtain a global optimal combination. The method is a multi-stage and multi-target servo support optimization control method oriented to foundation pit engineering.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of geotechnical engineering, in particular to a foundation pit deformation control method based on a TabPFN model and a support axial force servo system. BACKGROUND

[0002] The deformation control of foundation pits in soft soil areas is difficult, and traditional supporting methods have been difficult to meet the increasingly stringent safety standards and refined management requirements. Therefore, deformation control and risk prevention and control have become a research hotspot and key technology direction in the field of geotechnical engineering.

[0003] The existing foundation pit support adopts an internal support system. The ordinary internal support is a typical passive control method of foundation pit deformation, that is, the support force is gradually generated after the deformation of the enclosure structure, and cannot be dynamically adjusted according to the actual deformation during the construction process. In order to improve the control effect, a hydraulic servo support system has been introduced in engineering practice in recent years. The system integrates sensors and hydraulic systems on the basis of traditional supports, and can realize real-time monitoring and active adjustment of support axial force, which significantly improves the control effect of foundation pit deformation.

[0004] However, the existing method mainly has the following deficiencies: first, the servo support system still relies on experience setting or manual adjustment in the control strategy, lacks a systematic, phased and multi-target optimization scheme, and is prone to uneven force distribution, local bending of the structure and other hidden dangers; second, although the finite element method can better simulate the interaction between the support structure and the soil, the calculation cost is high in the repeated iteration of support optimization, which is difficult to meet the real-time control demand; third, although the existing proxy model can speed up the prediction, it is difficult to depict the collaborative action of multiple supports and its spatial arrangement characteristics, and the adaptability to working condition changes is poor, which is difficult to guarantee the control accuracy and stability; fourth, the foundation pit excavation is usually divided into multiple stages, and there is strong coupling between stages, so the optimal servo force combination obtained in a single stage is only a stage optimal, and the overall optimal control of all stages may not be achieved in the global scale. SUMMARY

[0005] In view of the deficiencies in the background art, the technical problem to be solved by the present application is to provide a foundation pit deformation control method based on a TabPFN model and a support axial force servo system. The method is a multi-stage and multi-target servo support optimization control method for foundation pit engineering.

[0006] The present application is accomplished by adopting the following technical solutions: a foundation pit deformation control method based on a TabPFN model and a support axial force servo system, the steps being as follows: S1. a servo support data simulation module, Based on finite element simulation, the servo support force of the support axial force servo system and the wall deformation response data are used to construct a servo support-wall deformation data set; S2. A deformation prediction proxy model module, The TabPFN model is constructed and optimized to obtain an optimized deformation prediction proxy model, which quickly predicts the wall deformation caused by foundation pit excavation according to the input servo support force, and obtains a wall deformation prediction result; S3. A cross-stage multi-objective optimization module, A multi-objective optimization framework integrating a differential evolution algorithm is constructed, multiple objectives are set, the wall deformation prediction result obtained in S2 is input into the multi-objective optimization framework, and the wall maximum deformation control and servo force unloading risk are optimized in coordination to obtain a globally optimal combination.

[0007] Further, the step of constructing the support-wall deformation dataset in S1 is as follows: S11. Based on finite element simulation, a stage loading strategy is used to activate multiple preset stages of servo support in sequence. In each stage, the newly added adjustable servo force and the support force set in the previous stage jointly constitute the cumulative input of the current stage. S12. A Latin hypercube sampling is used to generate multiple sets of input combinations within the pre-set design axial force range of each support, as the loading boundary conditions of the finite element model. S13. The maximum and minimum deformation values of the retaining wall in each stage are simulated to construct a servo support-wall deformation dataset of input servo force-output wall deformation relationship.

[0008] Further, the steps of optimizing the deformation prediction proxy model include: S21. A synthetic data pre-training module, A TabPFN model is pre-trained by generating synthetic datasets from millions of synthetic tasks generated by structural causal models, and a trained TabPFN model is obtained, so that the Transformer feature extractor of the TabPFN model learns the structural pattern; S22. A bidirectional mixed sparse attention feature extraction module, A bidirectional attention mechanism is introduced into the Transformer feature extractor of the TabPFN model trained in S21, and on the basis of the bidirectional attention mechanism, a support sample pruning mechanism and a local-global mixed sparse attention mechanism are introduced to obtain an optimized TabPFN model; S23. A small sample inference module, The servo support-wall deformation dataset in S1 is input into the optimized Transformer feature extractor in S22 for encoding, and after encoding, small sample inference is performed to obtain a predicted wall deformation result.

[0009] Further, the steps of generating synthetic datasets in the synthetic task generation process in S21 are as follows: 1) Randomly generate a directed acyclic graph (DAG), where each node represents a variable X i , with a nonlinear structure function f i determined, function f i describes how each variable depends on its parent nodes PA i , superimposed Gaussian noise to simulate disturbances and uncertainties in real working conditions; 2) The variables X i are sampled in topological order according to the DAG, simulating the causal structure of soil parameters, support forces and structural deformations; 3) Randomly select a part of the intermediate variables as the input feature vector x (j) , and randomly select one of the other target variables as the output y (j) ; 4) By repeating the above process under different graph structures, causal layouts and function types, a synthetic data set DSCM with diverse structures can be generated, which is used to pretrain the TabPFN model to obtain the trained TabPFN model.

[0010] Further, the bidirectional attention mechanism in S22 includes performing intra-sample attention and inter-sample attention, and TabPFN alternately performs intra-sample (row direction) and inter-sample (column direction) attention in each encoder. The intra-sample attention is used to extract the linkage mode between the support forces in a single sample, and the inter-sample attention learns the global importance of features at different positions from multiple samples.

[0011] Further, the support sample pruning mechanism in S22 uses the following steps: 1) Pre-encoding and buffering, during the TabPFN model loading stage, all support samples are independently encoded in advance, and the servo force-deformation feature encoding vector is cached in memory; 2) Top-K screening, during the inference stage, first screen out the Top-K most relevant support samples based on the Euclidean distance between the query sample and the cached support samples; 3) Recoding and inference, only the Top-K samples and the query sample are input into the Transformer for encoding and inference to avoid repeated operations on the full support set.

[0012] Further, the local-global hybrid sparse attention mechanism in S22 replaces the original full connection point multiplication attention, and the specific steps are as follows: 1) Set a fixed-width local window for each servo force input position, and only perform attention calculation between its adjacent support points to capture local spatial coupling relationships; 2) Introduce Top-K dynamic global attention mechanism, according to the preliminary similarity score, select the K most influential remote positions from all support positions for the current Query position, and add attention interaction between these positions, taking into account the long-distance linkage effect; 3) Use sparse attention mask to shield irrelevant positions, effectively compress the proportion of non-zero elements in the attention weight matrix, and reduce the attention calculation complexity from the original O ( n 2 ) to approximately O ( n ).

[0013] Further, the specific steps of obtaining the predicted wall deformation result in S23 are as follows: 1) Divide the servo support-wall deformation data set 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 each support sample through attention weight, and identifies the support sample closest in stress-deformation behavior; 2) TabPFN model assigns an attention weight α i to each support sample according to the similarity between the query sample and each support sample V i , the model weights and fuses the value vector Z q containing the label in the support sample set, and aggregates into a new vector representation Z q ; y 1, y 2, … , y M} on the predefined wall deformation interval{ 4) Output the probability prediction in 3), use the weighted average method of segmented distribution to convert the prediction interval probability into a continuous deformation expectation value, and obtain the predicted wall deformation result.

[0014] Further, the optimization objectives of the multi-objective optimization framework include controlling maximum deformation, suppressing reverse bending, and minimizing servo force unloading amount, the control of maximum deformation and the suppression of reverse bending are the main objectives, and under the premise of meeting the deformation control main objective, the minimum servo force unloading amount is introduced as a secondary objective.

[0015] ​Further, the specific steps of obtaining the global optimal combination are as follows: S31. The maximum wall deformation is limited within 3% of the excavation depth H, and an early warning threshold of 80% is set; S32. The main target loss function is defined as follows: ; S33. After the main target of S31 and S32 is met, an unloading penalty term is further introduced in the framework to suppress the servo force unloading amount between adjacent excavation stages; S34. The wall deformation prediction result in S2 is input into the multi-objective optimization framework, and the solution set that meets the two main targets and one secondary target set in S31-S33 is screened out. Then, a differential evolution algorithm is used to search the population in the multi-stage servo force combination space. A priority guided beam search method based on Pareto sorting is used to screen the optimal servo force solution set, and the global optimal combination is obtained.

[0016] The beneficial effects in the application are: (1) An efficient proxy model of TabPFN (Tabular Prior-Data Fitting Network) is constructed and optimized to realize fast prediction of the deformation of the enclosing wall under the input of the servo force, and the calculation cost caused by repeated calling of the finite element is significantly reduced; (2) The TabPFN model introduces a bidirectional attention mechanism to accurately depict the spatial coordination relationship and coupling effect between multiple supports, and enhance the expression ability of the model to the wall deformation response under complex support conditions; (3) A multi-objective optimization framework integrating the differential evolution algorithm is designed to cooperatively optimize the maximum deformation control of the wall and the servo force unloading risk, and improve the stability and control robustness of the support system; (4) A multi-path parallel evolution strategy is proposed to realize global search of the servo force combination in the multi-stage control process, and ensure the overall optimality of the control path.

[0017] (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 for input sample screening to avoid repeated operation on the full support set, significantly reducing the attention calculation complexity and reasoning time. The sparse attention mechanism optimizes the internal attention structure of the Transformer, significantly improves the reasoning speed and reduces the memory bandwidth pressure, while maintaining the modeling ability of the servo force-wall deformation response law. The two mechanisms together improve the reasoning efficiency of the TabPFN model. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 It is a schematic diagram for servo control wall deformation prediction in a multi-stage excavation process. Figure 2 Optimize the wall deformation curve before and after each excavation stage; Figure 3 Optimize the path for all servo supports; Figure 4 Optimize the total unloading amount for each path; Figure 5 Flowchart of the foundation pit deformation control method based on the TabPFN model and the support axial force servo system. DETAILED DESCRIPTION

[0019] To further illustrate the technical means and effects adopted by the present application to achieve the predetermined invention purposes, the specific embodiments, structures, features and effects according to the present application are described in detail below in combination with the drawings and preferred embodiments.

[0020] Referring to Figures 1-5 The present application provides a foundation pit deformation control method based on a TabPFN model and a support axial force servo system, and the steps are as follows: S1. Servo support data simulation module; Based on finite element simulation, the servo support force and wall deformation response data of the support axial force servo system are used to construct a servo support-wall deformation data set, and the specific steps are as follows: S11. Based on finite element simulation, the servo support of multiple preset stages is activated in turn using a stage loading strategy. 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; S12. Generate multiple sets of input combinations within the design axial force range initially set for each support by Latin hypercube sampling, as the loading boundary conditions of the finite element model; S13. Simulate the maximum and minimum deformation values of the retaining wall in each stage to construct a servo support-wall deformation data set of the input servo force-output wall deformation relationship.

[0021] S2. Deformation prediction proxy model module; A TabPFN model is constructed and optimized to obtain an optimized deformation prediction proxy model. The deformation prediction proxy model quickly predicts the wall deformation caused by foundation pit excavation according to the input servo support force to obtain a 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 small sample reasoning module, and the details are as follows: S21. Synthetic data pre-training module.

[0022] The TabPFN model is pre-trained on synthetic datasets generated by millions of synthetic tasks from structural causal models, and the trained TabPFN model is obtained, so that the Transformer feature extractor of the TabPFN model learns the structural patterns and achieves good generalization ability under small sample conditions. The synthetic tasks include causal relationships such as input-output mapping, feedback structure and parameter dependence. 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 deformations. The specific steps for generating synthetic datasets are as follows: 1) Randomly generate a directed acyclic graph (DAG), which is a directed graph without loops, where each node represents a variable X i , a nonlinear structural function with Gaussian noise f i determines.

[0023] (1) where the function f i describes how each variable depends on its parent nodes PA i , and the superimposed Gaussian noise is used to simulate disturbances and uncertainties in real working conditions, where i is the variable number index, indicating the number of variables, N represents the normal distribution (Gaussian distribution), is the variance.

[0024] 2) Variable X i is sampled in topological order according to the DAG, simulating the causal structure of soil parameters, support forces and structural deformations, (2) 3) Randomly select a part of the intermediate variables (such as wall stress state) as input feature vectors x (j) , and randomly select one of the other target variables (such as wall deformation or ground settlement) as output y (j) .

[0025] (3) 4) By repeating the above process under different graph structures, causal layouts and function types, a synthetic dataset with diverse structures can be generated D SCM , which is used to pre-train the TabPFN model.

[0026] (4).

[0027] S22. Bidirectional mixed sparse attention feature extraction module.

[0028] The bidirectional attention mechanism is introduced in the Transformer feature extractor of the TabPFN model trained in S21, which is used to model the coupling control and spatial coordination relationship between the servo supports. On the basis of the bidirectional attention mechanism, a support sample pruning mechanism and a local-global mixed sparse attention mechanism are introduced to obtain an optimized TabPFN model. Specifically as follows: (1) Introduce bidirectional attention mechanism.

[0029] The bidirectional attention mechanism includes 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 layer of the encoder. Intra-sample attention (row-wise attention) is used to extract the linkage mode between each support force in a single sample, and inter-sample attention learns the global importance of features at different positions from multiple samples.

[0030] The bidirectional attention mechanism is particularly suitable for deep foundation pit support systems, in which wall deformation depends not only on the total support force, but also strongly on the force distribution at each support position. For example, in sample 1, S1=40kN, S3=10kN, the maximum wall deformation is 6mm; while in sample 2, S1=10kN, S3=40kN, the deformation is only 2mm. Although the total force is the same, the deformation response is significantly different due to the different force positions. The standard Transformer, due to the lack of column-wise attention, cannot identify the influence of force position on deformation, and may mistakenly consider the above two samples as equivalent, while TabPFN can effectively learn position-sensitive rules such as "larger force at S1 position usually leads to larger deformation" through column-wise attention, thereby improving the prediction accuracy of wall deformation under different servo force distribution.

[0031] (2) Introduce support sample pruning mechanism.

[0032] The introduction of the support sample pruning mechanism reduces the number of samples involved in encoding for each inference from the original thousands to dozens, shortens the calculation time, and significantly reduces the attention calculation complexity and inference delay. The steps of the support sample pruning mechanism are as follows: 1) Pre-encoding and buffering. During the loading stage of the TabPFN model, all support samples are independently encoded in advance, and the servo force-deformation feature encoding vectors are cached in memory; 2) Top-K selection. In the inference stage, first, the Top-K most relevant support samples are quickly selected based on the Euclidean distance between the query sample and the cached support samples; 3) Re-encoding and reasoning. Only the Top-K samples and the query sample are jointly input into the Transformer for encoding and reasoning, avoiding repeated operations on the full support set.

[0033] (3) Introduce a local-global hybrid sparse attention mechanism.

[0034] 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: 1) Set a fixed-width local window for each servo force input position, and only perform attention calculation between its adjacent support points to capture the local spatial coupling relationship; 2) Introduce a Top-K dynamic global attention mechanism, which selects the K most influential remote positions from all support positions based on the preliminary similarity scores, and adds attention interaction between these positions, taking into account the long-range coupling effect; 3) Use sparse attention masks to mask irrelevant positions, effectively compressing the proportion of non-zero elements in the attention weight matrix, reducing the attention calculation complexity from the original O ( n 2 ) to approximately O ( n ). This significantly improves the inference speed and reduces the memory bandwidth pressure, while maintaining the ability to model the servo force-wall deformation response law.

[0035] S23. Small sample reasoning module.

[0036] The servo support-wall deformation dataset in S1 is input into the optimized Transformer feature extractor in S22 for encoding. After encoding, small sample reasoning is performed to obtain the predicted wall deformation result. The specific steps are as follows: 1) Divide the servo support-wall deformation dataset into a query sample set and multiple support sample sets, and 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 each support sample through attention weight calculation, thereby identifying the closest support sample in terms of stress-deformation behavior. The weight calculation formula is as follows: (5) where represents the encoding vector of the query sample, K i represents the key vector of the i th support sample, dis the vector dimension (used for scaling), Exp denotes the exponential function.

[0037] 2) TabPFN model assigns an attention weight to each support sample according to the similarity between the query sample and each support sample α i , the higher the weight, the more important it is to the prediction of the query sample, the model weights and fuses the value vectors of the support samples in the support set containing the label V i (including its servo support force and the encoded information of the wall deformation label), and aggregates them into a new vector representation Z q , (6) 3) The fused representation Z q is sent to the multi-layer perception (MLP) for decoding, and the MLP maps the vector to a probability distribution over the predefined wall deformation interval { y 1 , y 2, …, y M} as follows: (7) where, y j is the center value of the j th wall deformation interval, S represents the support set, p ( y j | x q , S) represents the probability that the predicted deformation of the query sample x q falls in the interval.

[0038] 4) The probability prediction output in 3) is converted into a continuous deformation expectation value by using the weighted average method of piecewise distribution, and the predicted wall deformation result is obtained. Specifically, the model divides the deformation value into several fixed interval intervals, each interval [ a i , b i ] corresponds to a probability p i . The final prediction value is obtained by weighted summation of the center point of each interval and its corresponding probability: (8).

[0039] 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.

[0040] S3. Cross-stage multi-objective optimization module.

[0041] 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.

[0042] 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: 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; S32. Main Objective Loss Function L def The definition is as follows: (9) 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 amount between adjacent excavation stages is suppressed to avoid the risk of instability when unloading too much. For solutions that violate the specification limit (i.e. L def have exceeded the limit), even if their unloading loss is low, they will be directly excluded from the options. Among them, the unloading loss is defined as follows: (10) wherein, S i,t denotes the servo force applied at the i-th support position in the j-th stage; t i S34. The wall deformation prediction results in S2 are input into the multi-objective optimization framework, and the solution set that meets the two primary objectives and one secondary objective set in S31-S33 is screened out (first meet the two primary objectives, and then meet the secondary objective), and then the differential evolution algorithm is used to search the population in the multi-stage servo force combination space, the priority guided beam search method based on Pareto sorting is used to screen the optimal servo force solution set, and the globally optimal combination is obtained.

[0043] Specifically, in each generation, the Pareto sorted front solution that balances between deformation loss and servo unloading risk is identified by non-dominated sorting. Since the primary objectives L def have a higher priority in engineering, individuals with smaller deformation loss are preferentially selected, and then the control score is used for secondary screening. From the Pareto solution set, the top N beam candidate solutions with the lowest control risk are selected by beam search to form the path solution set of the current stage. The current multiple candidate solutions will be evolved in parallel in the next stage to preserve the diversity of solutions. After each stage ends, the candidate solution with the lowest control cost will be used as the "attractive center" to guide the search direction of the population in the next stage, and ultimately the globally optimal servo control solution sequence is obtained in the multi-stage collaborative evolution process.

[0044] Embodiment: The effectiveness of the proposed optimization framework is verified through numerical simulation of the servo support of a certain foundation pit project. The project details are as follows: The supporting structure is an underground continuous wall with a thickness of 0.8 m and a depth of 37.6 m. The original support system includes 1 concrete support (C1), 2 conventional steel supports (S1 and S3), and 2 servo-controlled steel supports (S2 and S4). Among them, S1 is 609 mm in diameter, and S2 to S4 are uniformly designed as 800 mm, with a wall thickness of 16 mm. The elastic modulus of concrete and steel is 30×10 6 kN / m² and 205×10 6 ​​kN / m2, and the horizontal spacing between supports is 3 m. The preloading of S1 is 870 kN and S3 is 1080 kN, and considering the stress loss after installation, the actual initial axial force of both is set to 50% of the design value. The target axial force of S2 is 1740 kN (corresponding to the distributed load of 580 kN / m), and that of S4 is 1710 kN (corresponding to the distributed load of 570 kN / m). The concrete supports and conventional steel supports are modeled by "node-node anchor element", and the servo support is modeled by concentrated load. The wall deformation is monitored by setting inclinometer tubes at 0.5 m below the ground surface and every 0.5 m, and the data nodes correspond to the 3rd, 5th, 7th, 9th, 11th and 12th construction stages, respectively. The construction sequence is as follows: first, the underground continuous wall is constructed and pumped to the basement, then excavated to -1.0 m to install C1, and then excavated to -4.4 m, -7.4 m, -10.4 m, -13.0 m and -16.4 m, respectively, and then S1, S2, S3 and S4 are installed in turn at each stage. During the installation of S3 and S4, S2 is adjusted to control the axial force. The numerical simulation is carried out using PLAXIS 2D software, and the hardening soil constitutive model is selected for the soil constitutive model. The input parameters are calibrated by back analysis to match the measured data. All soil layers are assumed to be undrained.

[0045] The proposed multi-objective optimization framework is configured as follows: first, the finite element model sets the value range of the servo axial force to 0-2000 kN / m. Within this range, 1000 labeled samples are generated by Latin hypercube sampling as the support set of the pre-trained TabPFN surrogate model. The servo force at each stage is used as the input of the model, and the output includes the maximum wall deformation (for specification checking) and the minimum wall deformation (for reverse bending judgment). In the optimization method, each stage runs 5 rounds of evolutionary iterations, with a population size of 1000 in each round, balancing global search ability and computational cost control. To prevent falling into local optimum, a global disturbance probability of 3% is introduced. In beam search, the top 20 candidate paths (with a beam width of 20) that control the effect best are retained at each stage.

[0046] As shown in Figure 1 , the TabPFN surrogate model is used for servo control wall deformation prediction in the multi-stage excavation process. At each stage, the model takes the adjustable servo force S( t ) of the current stage as input, and retains the servo force S(1: t-1), thus forming a step-by-step input sequence. The model outputs the maximum and minimum wall deformation values at the current stage. This step-by-step modeling approach can reflect the step-by-step activation process of the four groups of servo supports in multiple preset stages (i.e., stages 5 to 12) and incorporate all historical servo force information in each stage. This input structure highly matches the time accumulation characteristics and causal order dependence in the pre-training task of TabPFN, enabling the model to reason without fine-tuning and achieve fast and stable servo control prediction during the multi-stage excavation process.

[0047] As shown in Figure 2 , the wall deformation curves before and after optimization at each excavation stage are compared. The optimized results are calculated by reloading the selected servo force inputs into the finite element model. S1-S4 represent the four servo-controlled supports. As excavation progresses, the maximum deformation position gradually moves downward. Overall, optimization significantly reduces the maximum wall deformation while maintaining smooth inclinometer curves without sudden changes or reverse bending phenomena. In stage 5, due to the shallow excavation depth, only a small support force of 65.7 kN / m is required for S1 to control the entire deformation curve within the specification limits. As the excavation deepens, lateral displacement gradually increases, and the difference between the pre- and post-optimization curves also significantly expands. 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 about 30%-35%. Throughout the process, the proposed optimization framework searches for the optimal combination of S1-S4 servo forces at each stage in the servo force space, achieving multi-stage coordinated control. Ultimately, the inclinometer curves at each stage meet the specification requirements without any reverse bending phenomena, verifying the effectiveness of the framework in controlling wall deformation over the full depth range.

[0048] As shown in Figure 3 , the search beam search path is displayed. The search starts from S1 = 72 kN / m at stage 5 and grows to 848 kN / m at stage 6. Subsequently, the path branches: S2 is 85 or 89 kN / m at stage 7, and 758 or 785 kN / m at stage 8, and combinations of S2 = 682 or 706 kN / m and S3 = 278 or 327 kN / m appear at stage 9. This "expansion-selection" operation continues until stage 12, resulting in 20 non-dominated global control paths.

[0049] As shown in Figure 4As shown, the total unloading of each path is displayed. Among them, the path No. 8 performs best: its total unloading is 741 kN / m, which is significantly lower than the 792 kN / m of the best local path, while still meeting all deformation control requirements. The results show that the proposed GP-APDE method can further reduce the risk of servo unloading through global path search, and achieve more stable and efficient support control.

[0050] The above is only the preferred embodiment of the present application, not any form of limitation on the present application, although the present application has been disclosed as above with the preferred embodiment, however, not to define the present application, any person skilled in the art, within the scope of the technical scheme of the present application, can make some more changes or modifications of the above disclosed technical content as equivalent embodiments, but as long as it does not deviate from the technical scheme of the present application, according to the technical essence of the present application, any modification, equivalent change and modification of the above embodiments, still belongs to the scope of the technical scheme of the present application.

Claims

1. A foundation pit deformation control method 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, the servo support force servo system is used to construct the servo support-wall deformation data set based on the response data of the wall deformation; S2. Deformation prediction proxy model module, Build and optimize TabPFN model, obtain the optimized deformation prediction proxy model, which can quickly predict the wall deformation caused by foundation pit excavation according to the input servo support force, and obtain the wall deformation prediction result; S3. Cross-stage multi-objective optimization module, Build a multi-objective optimization framework integrating differential evolution algorithm, set multiple objectives, input the wall deformation prediction result obtained in S2 into the multi-objective optimization framework, and cooperatively optimize the wall maximum deformation control and servo force unloading risk to obtain the globally optimal combination.

2. The method according to claim 1, wherein the TabPFN model-based and support axial force servo system-based foundation pit deformation control method is characterized by: The steps of constructing the support-wall deformation data set in S1 are as follows: S11. Based on finite element simulation, use the stage loading strategy to activate multiple preset stages of servo support in turn, in each stage, the newly added adjustable servo force and the support force set in the previous stage jointly constitute the cumulative input of the current stage; S12. Generate multiple sets of input combinations within the design axial force range of each support by Latin hypercube sampling, as the loading boundary conditions of the finite element model; S13. Simulate the maximum and minimum deformation values of the retaining wall in each stage, and construct the servo support-wall deformation data set of input servo force-output wall deformation relationship.

3. The method according to claim 1, wherein the TabPFN model-based and support axial force servo system-based foundation pit deformation control method is characterized by: The steps of optimizing the deformation prediction proxy model include: S21. Synthetic data pre-training module, Obtain the pre-trained TabPFN model by generating synthetic data sets through millions of synthetic tasks generated by structural causal models, and obtain the trained TabPFN model to make the Transformer feature extractor of the TabPFN model learn the structural pattern; S22. Bidirectional mixed sparse attention feature extraction module, Introduce a bidirectional attention mechanism into the Transformer feature extractor of the TabPFN model trained in S21, and based on the bidirectional attention mechanism, introduce a support sample pruning mechanism and a local-global hybrid sparse attention mechanism to obtain an optimized TabPFN model; S23. Small sample inference module, Input the servo support-wall deformation data set in S1 into the optimized Transformer feature extractor in S22 for encoding, and then perform small sample inference to obtain the predicted wall deformation result.

4. The method according to claim 3, wherein the TabPFN model-based and support axial force servo system is characterized by: The steps of generating synthetic data sets in S22 are as follows: 1) Randomly generate a directed acyclic graph (DAG), where each node represents a variable X i , with a nonlinear structure function f i determined, function f i describing how each variable depends on its parents, PA i superimposed Gaussian noise to simulate disturbances and uncertainties in real-world conditions; 2) Variables X i Sampling in topological order of the DAG models the causal structure of soil parameters, support forces, and structural deformations. 3) Randomly select a subset of the intermediate variables as input feature vectors x (j) Randomly select one of the other target variables as 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 , for pre-training the TabPFN model, to obtain the trained TabPFN model.

5. The method according to claim 3, wherein the TabPFN model-based and support axial force servo system-based foundation pit deformation control method is characterized by: The bidirectional attention mechanism in S22 includes intra-sample attention and inter-sample attention, and TabPFN alternately performs intra-sample (row direction) attention and inter-sample (column direction) attention in each encoder to extract the linkage pattern between each support force in a single sample, and the inter-sample attention learns the global importance of features at different positions from multiple samples.

6. The method according to claim 3, wherein the TabPFN model-based and support axial force servo system-based foundation pit deformation control method is characterized by: The steps of using the support sample pruning mechanism in S22 are as follows: 1) Pre-encoding and buffering, all support samples are independently encoded in advance during the TabPFN model loading stage, and the servo-force-deformation feature encoding vector is cached in memory; 2) Top-K screening, in the inference stage, first filter out the Top-K most relevant support samples based on the Euclidean distance between the query sample and the cached support samples; 3) Re-encoding and inference, only input the Top-K samples and the query sample into the Transformer for encoding and inference, avoiding repeated operations on the full support set.

7. The method according to claim 3, wherein the TabPFN model-based and support axial force servo system-based foundation pit deformation control method is characterized by: The local-global hybrid sparse attention mechanism in S22 replaces the original fully connected dot product attention, and the specific steps are as follows: 1) Set a fixed-width local window for each servo force input position, and only perform attention calculation between its adjacent support points to capture the local spatial coupling relationship; 2) Introduce a Top-K dynamic global attention mechanism, according to the preliminary similarity score, filter out the K most influential remote positions from all support positions, and add attention interaction between these positions, taking into account the long-distance linkage effect; 3) The sparse attention mask is used to shield irrelevant positions, effectively compressing the proportion of non-zero elements in the attention weight matrix, reducing the attention calculation complexity from the original O ( n 2 ) to approximately O ( n ).

8. The method for foundation pit deformation control based on the TabPFN model and support axial force servo system according to claim 3 or 4 or 5 or 6 or 7, characterized in that: The specific steps of obtaining the predicted wall deformation result in S23 are as follows: 1) Divide the servo support-wall deformation data set 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 each support sample through attention weight, and identifies the support sample closest in stress-deformation behavior; 2) TabPFN model assigns an attention weight to each support sample according to the similarity between the query sample and each support sample α i , the model weights and integrates the value vectors of the support samples containing the label in the support sample set, and aggregates them into a new vector representation V i Z q ;​ 3) fused expression Z q is fed into a multi-layer perceptron (MLP) for decoding, which maps the vector to a probability distribution over a predefined wall deformation interval { y 1, y 2, … , y M} 4) The probability prediction output in 3) is converted into a continuous deformation expectation value by using the weighted average method of segmented distribution, and the predicted wall deformation result is obtained.

9. The method according to claim 1, wherein the TabPFN model-based and support axial force servo system-based foundation pit deformation control method is characterized by: The optimization objectives of the multi-objective optimization framework include controlling the maximum deformation, suppressing the reverse bending, and minimizing the servo force unloading amount. The control of the maximum deformation and the suppression of the reverse bending are the main objectives, and under the premise of meeting the main objective of deformation control, the minimum servo force unloading amount is introduced as a secondary objective.

10. The method according to claim 1 or 9, wherein the method is characterized in that: The specific steps of obtaining the global optimal combination are as follows: S31. The maximum wall deformation is limited to within 3% of the excavation depth, with an 80% pre-alarm threshold set. H S31. The maximum wall deformation is limited to within 3% of the excavation depth, with an 80% pre-alarm threshold set. S32. Master target loss function L def is defined as follows; S33. After the main objective of S31 and S32 is satisfied, the framework further introduces an unloading penalty term L ctrl , to suppress the unloading amount of the servo force between adjacent excavation stages; S34. The wall deformation prediction result in S2 is input into the multi-objective optimization framework, and the solution set that meets the two main objectives and one secondary objective set in S31-S33 is filtered out, and then the differential evolution algorithm is used to search the population in the multi-stage servo force combination space, and the priority guided beam search method based on Pareto sorting is used to filter the optimal servo force solution set, and the global optimal combination is obtained.

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