A method for constructing a bearing capacity prediction model of a flexible photovoltaic support composite cable-stayed foundation

Abstract

The application provides a bearing capacity prediction model construction method of a flexible photovoltaic support composite cable-stayed foundation, and belongs to the technical field of photovoltaic support detection. The application establishes a soil fractional order viscoelastic plasticity constitutive database, and obtains equivalent macroscopic constitutive parameters by using a multi-scale homogenization algorithm of a variational asymptotic method. In combination with a symplectic geometry structure-preserving dynamics integration algorithm, the coupling relationship between cable force and displacement is iteratively calculated, multi-working-condition bearing capacity simulation calculation is performed to obtain foundation settlement, cable force distribution and soil plastic zone range. Pretreated simulation data is input into a fractional order memory enhancement model to perform bearing capacity prediction. Iterative optimization is performed according to the deviation rate of the limit bearing capacity prediction value and the design bearing capacity, so that the technical problem of insufficient accuracy of the bearing capacity prediction of the flexible photovoltaic support composite cable-stayed foundation under the coupling action of soil long-term creep and cable force is solved.

Description

Technical Field

[0001] This invention belongs to the field of photovoltaic support testing technology, and specifically relates to a method for constructing a bearing capacity prediction model for a flexible photovoltaic support composite cable-stayed foundation. Background Technology

[0002] Flexible photovoltaic (PV) support systems, forming a load-bearing structure through stay cables and composite foundations, are widely used in the field of new energy power generation. Traditional methods for predicting bearing capacity employ linear elastic constitutive models to describe soil behavior and calculate the ultimate bearing capacity of the foundation through static finite element analysis. However, this method simplifies the soil as an instantaneous elastic material, neglecting the creep deformation and stress relaxation characteristics of the soil under long-term loads. Furthermore, it fails to accurately characterize the large displacement geometric nonlinearity of the stay cables and the force-displacement coupling relationship, leading to significant deviations in prediction results under multi-field coupled conditions. Traditional methods use simple parameter averaging when dealing with layered soils, failing to reflect the influence of microscopic pore structures on macroscopic mechanical properties. Moreover, the accumulated dissipation errors during numerical integration cause the phase trajectory of long-term simulations to diverge, and the prediction model lacks the ability to characterize the viscoelastic-plastic memory effect of the soil. In other words, existing technologies suffer from insufficient accuracy in predicting the bearing capacity of flexible PV support composite stay foundations under the combined effects of long-term soil creep and cable force. Summary of the Invention

[0003] In view of this, the present invention provides a method for constructing a bearing capacity prediction model for a flexible photovoltaic support composite cable-stayed foundation, which can solve the technical problem of insufficient accuracy in the bearing capacity prediction of flexible photovoltaic support composite cable-stayed foundation under the long-term creep of soil and the coupling effect of cable force in the prior art.

[0004] This invention is implemented as follows: It provides a method for constructing a bearing capacity prediction model for a flexible photovoltaic support composite cable-stayed foundation. This includes collecting initial geometric parameters of the cable-stayed system and soil stratification data; establishing a fractional-order viscoelastic-plastic constitutive database of the soil; using a multi-scale homogenization algorithm based on variational asymptotic method to process microscopic soil structural parameters to obtain equivalent macroscopic constitutive parameters; constructing the cable-stayed geometric stiffness matrix in a cooperative rotating coordinate system; iteratively calculating the coupling relationship between cable force and displacement using a symplectic geometric-preserving structure dynamic integral algorithm; adaptively generating a finite element mesh; performing multi-condition bearing capacity simulation calculations to record foundation settlement, cable force distribution, and soil plastic zone range; inputting the preprocessed simulation data into a fractional-order memory-enhanced model for bearing capacity prediction; and iteratively optimizing based on the deviation rate between the predicted ultimate bearing capacity and the design bearing capacity.

[0005] Among the steps of collecting the initial geometric parameters and soil layer data of the cable-stayed system, the initial geometric parameters include cable length, cable inclination angle, and anchor point coordinates, and the soil layer data includes the thickness, density, water content, and initial void ratio of each soil layer.

[0006] The step of establishing a fractional-order viscoelastic-plastic constitutive database for soil involves conducting triaxial creep tests and consolidation tests on each soil layer and recording the stress-strain-time curves throughout the entire process.

[0007] Among them, the multi-scale homogenization algorithm of the variational asymptotic method is based on the principle of energy variation to separate the micro-periodic structure of soil into macro-slowly varying fields and micro-fastly varying fields through asymptotic expansion. It solves the micro-boundary value problem in representative volume elements to obtain localized deformation modes, and derives the anisotropic equivalent stiffness tensor and damping tensor through the volume average theorem.

[0008] Among them, the symplectic geometry-preserving dynamic integration algorithm constructs a numerical integration scheme on a symplectic manifold based on Hamilton's canonical equations to preserve the invariance of the phase space volume. It derives an implicit symplectic Runge-Kutta discrete scheme through the generating function method, thus preserving the symplectic second-form invariance and generalized energy conservation of the system.

[0009] In the iterative calculation of the coupling relationship between cable force and displacement, the initial value of the load increment step size is set to 0.05 times the design load based on the arc length method. When the iterative residual is less than Record the convergence state parameters at regular intervals.

[0010] Among them, the adaptive generation of finite element mesh uses an octree hierarchical algorithm to establish the initial mesh, with a mesh size ranging from 0.1 to 0.8 m. Mesh refinement is driven by a stress gradient error estimator, and local refinement is triggered when the element stress gradient exceeds the critical gradient threshold by 1.5 times.

[0011] When performing multi-condition bearing capacity simulation calculations, the load conditions include combinations of static load, wind load, temperature load, and seismic load. The foundation settlement, cable force distribution, and soil plastic zone range are input into the feature extraction preprocessing module.

[0012] The input layer of the fractional-order memory enhancement model receives a 68-dimensional feature vector. After passing through the feature normalization layer, it enters the fractional-order memory convolution module. The fractional-order memory convolution module contains a hybrid structure of 4 layers of Caputo fractional derivative operators and long short-term memory units, with the fractional order ranging from 0.3 to 0.9.

[0013] The fractional-order memory enhancement model includes a multi-head attention fusion layer with 8 attention heads. It calculates the long-range dependencies between features through query matrix, key matrix, and value matrix. The fused feature vector passes through a 3-layer fully connected neural network with 256, 128, and 64 hidden layer neurons, respectively.

[0014] Among them, the fractional-order memory enhancement model adopts a critical slowing structure. The critical detection gating unit calculates the Mahalanobis distance between the current feature vector and the centroid of the training domain. When the Mahalanobis distance exceeds 0.85 times the radius of the training domain, the slowing mechanism is activated. Through the time delay feedback loop, the neuron state update rate is reduced to 0.3 times the normal rate.

[0015] Among them, the training dataset of the fractional-order memory enhancement model was established by using Latin hypercube sampling to generate 5,000 combinations of soil parameters and load conditions in a 23-dimensional parameter space. Finite element simulation calculations were performed on each combination until convergence, and the bearing capacity-displacement full curve was extracted as label data. Stress field, displacement field, and plastic strain field at 10 time nodes were extracted from the simulation process as feature data.

[0016] The fractional-order memory enhancement model training adopts an adaptive moment estimation optimization algorithm, with an initial learning rate set to 0.0003. A cosine annealing learning rate scheduling strategy is introduced, with 800 training epochs and a batch size of 64. The loss function is a weighted combination of mean squared error loss and quantile loss with a weight ratio of 7:3.

[0017] The dynamic weight adjustment function calculates the weight correction factor based on three dimensions: model prediction uncertainty, feature space coverage, and iteration convergence rate. It dynamically adjusts the contribution of each layer's feature fusion through backpropagation.

[0018] Specifically, during iterative optimization, the iteration is terminated and the final bearing capacity prediction result is output when the deviation rate is between 0% and 5%. When the deviation rate is between 5% and 15%, the initial value of the load increment step size is adjusted and reduced to 0.6 times the original initial value of the load increment step size. When the deviation rate is greater than 15%, the mesh density is increased to 1.8 times the original mesh density.

[0019] Among them, the arc length method controls the incremental path of load and displacement by introducing an arc length parameter. In each incremental step, the load factor and displacement increment are solved simultaneously, so that the iterative process passes through the extreme points of the load-displacement curve.

[0020] This invention establishes a fractional-order viscoelastic-plastic constitutive database of soil and employs a multi-scale homogenization algorithm using variational asymptotic methods to process microscopic soil structural parameters. This achieves cross-scale information transfer from the pore scale to the macroscopic continuous medium, accurately capturing the contribution of particle contact and cementation states to bearing capacity. The introduction of a symplectic geometrically preserved dynamic integral algorithm strictly maintains the phase space volume invariance of the Hamiltonian system, eliminating dissipation errors in traditional numerical methods and ensuring the computational stability of the cable-force-displacement coupling relationship under large displacement conditions. The constructed fractional-order memory enhancement model captures the power-law decay characteristics of soil creep through the Caputo fractional derivative operator. Combined with a critically slowed structure, it automatically reduces the information propagation speed under abnormal conditions to enhance prediction robustness, achieving accurate characterization of the viscoelastic-plastic memory effect of soil. In summary, this invention solves the technical problem mentioned in the background art of insufficient accuracy in predicting the bearing capacity of flexible photovoltaic support composite cable-stayed foundations under the long-term creep of soil and cable-force coupling. Attached Figure Description

[0021] Figure 1 This is a flowchart of the method of the present invention.

[0022] Figure 2 This is a diagram showing the distribution of cable force and displacement in the convergent state of a cable-stayed system.

[0023] Figure 3 This is a diagram showing the evolution of foundation settlement and plastic zone under multiple load conditions. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below.

[0025] like Figure 1 The diagram shown is a flowchart of a method for constructing a bearing capacity prediction model for a flexible photovoltaic support composite cable-stayed foundation provided by the present invention. This method includes the following steps:

[0026] S01. Collect the initial geometric parameters and soil layer data of the cable-stayed system. The initial geometric parameters include cable length, cable inclination angle, and anchor point coordinates. The soil layer data includes the thickness, density, water content, and initial void ratio of each soil layer.

[0027] S02. Establish a fractional-order viscoelastic-plastic constitutive database of soil. Conduct triaxial creep tests and consolidation tests on each soil layer collected in step S01. Record the stress-strain-time curves throughout the entire process. Use the multi-scale homogenization algorithm of variational asymptotic method to process the microscopic soil structure parameters to obtain equivalent macroscopic constitutive parameters.

[0028] S03. Construct the cable geometric stiffness matrix in the cooperative rotating coordinate system. Based on the cable length, cable inclination angle, anchor point coordinates and arc length method collected in step S01, set the initial value of the load increment step size to 0.05 times the design load. Use the dynamic integral algorithm of symplectic geometric preservation structure to iteratively calculate the coupling relationship between cable force and displacement. When the iteration residual is less than the preset threshold, record the convergence state parameters.

[0029] S04. Perform adaptive generation of finite element mesh. Use the octree hierarchical algorithm to establish an initial mesh for the soil-foundation-cable system corresponding to the equivalent macroscopic constitutive parameters obtained in step S02. The mesh size ranges from 0.1 to 0.8 m. Drive mesh refinement according to the stress gradient error estimator. When the element stress gradient exceeds 1.5 times the critical gradient threshold, local refinement is triggered.

[0030] S05. Perform multi-condition bearing capacity simulation calculation, set load conditions including static load, wind load, temperature load, and seismic load combination, record foundation settlement, cable force distribution, and soil plastic zone range under each load condition, and input the foundation settlement, cable force distribution, and soil plastic zone range into the feature extraction preprocessing module.

[0031] S06. Input the simulation data preprocessed in step S05 into the fractional-order memory enhancement model to predict the bearing capacity. The fractional-order memory enhancement model outputs the predicted value of the ultimate bearing capacity and the safety factor. Adjust the internal feature fusion weight of the fractional-order memory enhancement model according to the weight correction factor calculated by the dynamic weight adjustment function.

[0032] S07. Based on the deviation rate between the predicted ultimate bearing capacity and the design bearing capacity predicted in step S06, perform iterative optimization. When the deviation rate is within [0, 5%], terminate the iteration and output the final bearing capacity prediction result. When the deviation rate is within (5%, 15%), adjust the initial value of the load increment step size in step S03 to 0.6 times the original initial value of the load increment step size and return to step S03 to recalculate. When the deviation rate is greater than 15%, increase the mesh density in step S04 to 1.8 times the original mesh density and return to step S04 to remodel.

[0033] The preset threshold is .

[0034] The multi-scale homogenization algorithm of the variational asymptotic method is based on the energy variational principle. It separates the micro-periodic structure of soil into macroscopic slow-changing fields and micro-fast-changing fields through asymptotic expansion. It obtains the localized deformation mode by solving the micro-boundary value problem in the representative volume element. It rigorously derives the anisotropic equivalent stiffness tensor and damping tensor through the volume average theorem. It uses the fast Fourier transform to transform the partial differential equations of the periodic element into a system of algebraic equations to improve computational efficiency. It combines adaptive multi-scale basis functions to capture the localization of strain and the evolution of shear bands, realizing cross-scale information transfer from micro-porous structure to macro-continuous medium. The multi-scale homogenization algorithm of the variational asymptotic method ensures the accurate mapping of the influence of microstructure on macroscopic performance through rigorous mathematical derivation, avoiding the error accumulation caused by the simplification assumptions in traditional homogenization methods. This allows the equivalent macroscopic constitutive parameters to truly reflect the contribution of microscopic mechanisms such as particle contact, pore distribution, and cementation state to bearing capacity. In particular, the influence of soil microstructure evolution on macroscopic mechanical response under long-term loading is accurately characterized, providing a physically well-defined parameter input for the fractional-order viscoelastic-plastic constitutive database of soil, and significantly improving the reliability and applicability of bearing capacity prediction under complex soil conditions.

[0035] The proposed symplectic geometry-preserving dynamic integration algorithm constructs a numerical integration scheme on a symplectic manifold based on Hamilton's canonical equations, preserving the invariance of the phase space volume. It derives an implicit symplectic Runge-Kutta discrete scheme through the generating function method, strictly preserving the symplectic second-form invariance and generalized energy conservation of the system. It employs Lie series expansion techniques to control the local truncation error within the range of high-order small quantities, eliminating the inherent numerical dissipation and dispersion errors of traditional numerical integration methods. It introduces variational integrator techniques to handle constraints, ensuring that the phase trajectory does not diverge and that energy drift is suppressed within the theoretical limit during long-term integration. The proposed symplectic geometry-preserving dynamic integral algorithm addresses the geometric nonlinearity of large displacements and the force-displacement coupling relationship in cable-stayed systems. By preserving the geometry of the Hamiltonian system, it achieves a fundamental improvement in numerical stability, avoiding the divergence failure of traditional Newton-Raphson iterations under extreme load conditions. This ensures that the dynamic response analysis maintains the physical rationality of the phase space trajectory even after thousands of iterations. It plays a decisive role in capturing nonlinear dynamic behaviors such as parametric resonance and internal resonance of the cable system, ensuring the computational robustness of finite element simulations under combined load conditions, and providing high-fidelity training data support for fractional-order memory-enhanced models.

[0036] The structure of the fractional-order memory enhancement model is as follows: the input layer receives a 68-dimensional feature vector, which includes the spatial distribution sequence of foundation settlement, the temporal rate of change of cable force distribution, and the density distribution of soil plastic strain energy. After passing through a feature normalization layer, it enters a fractional-order memory convolution module. This module contains a hybrid structure of four layers of Caputo fractional derivative operators and long short-term memory units, with the fractional order ranging from 0.3 to 0.9. It is used to capture the power-law decay characteristics of soil creep and stress relaxation. The output temporal features enter a multi-head attention fusion layer, which has eight attention heads. It calculates the long-range dependencies between features through learnable query matrices, key matrices, and value matrices. The fused feature vector passes through a three-layer fully connected neural network with 256, 128, and 64 hidden layer neurons, respectively. The activation function uses a parameterized modified linear unit. Finally, the output layer generates the ultimate bearing capacity prediction value and the uncertainty quantification range. The fractional-order memory enhancement model also includes residual connection paths and layer normalization modules to alleviate the gradient vanishing problem.

[0037] The fractional-order memory enhancement model employs a critical slowing structure. The principle of this structure is based on the phenomenon of system response time divergence near the critical point of a phase transition in statistical physics. In the neural network, critical slowing behavior is simulated by dynamically adjusting the activation threshold of neurons. When the statistical moments of the input features approach the boundary of the training set distribution, the critical slowing structure automatically reduces the information propagation speed and enhances the stability of feature representation. The critical slowing structure is implemented by inserting a critical detection gating unit between the multi-head attention fusion layer and the fully connected neural network. This critical detection gating unit calculates the Mahalanobis distance between the current feature vector and the centroid of the training domain. When the Mahalanobis distance exceeds 0.85 times the radius of the training domain, the slowing mechanism is activated. By introducing a time-delay feedback loop, the neuron state update rate is reduced to 0.3 times the normal rate, while the temperature parameter of the attention weights is increased to 1.8 times to enhance feature smoothness. The critical slowing structure enables the fractional-order memory enhancement model to automatically enter a highly robust state when faced with extreme working conditions outside the training set, avoiding prediction distortion caused by parameter space extrapolation. By simulating the fluctuation suppression mechanism of the physical system at the phase transition critical point, it significantly improves the generalization ability of bearing capacity prediction under rare load combinations and abnormal soil layer distribution conditions. The critical slowing structure achieves an adaptive balance between prediction accuracy and stability by dynamically adjusting the information processing speed. In particular, it provides an intrinsic fault-tolerant mechanism for the sensitivity of parameter perturbations in multi-field coupled nonlinear problems, making the entire prediction scheme exhibit stronger reliability and safety margin when facing uncertainties in engineering applications.

[0038] The specific steps for establishing the training dataset of the fractional-order memory enhancement model include: performing Latin hypercube sampling to generate 5000 combinations of soil layer parameters and load conditions in the parameter space. The parameter space has a dimension of 23, including the fractional-order viscoelastic parameters of each soil layer, the geometric parameters of the cable system, the load amplitude and loading rate. Finite element simulation calculations are run on each combination of soil layer parameters and load conditions until convergence. The bearing capacity-displacement full curve is extracted as label data. The stress field, displacement field and plastic strain field at 10 time nodes are extracted as feature data from the simulation process. Principal component analysis is performed on the feature data to reduce the dimension to 68. Samples that have not converged or have mesh distortion are removed. Finally, 4763 effective training samples are obtained, which are divided into training set, validation set and test set in an 8:1:1 ratio.

[0039] The specific training steps of the fractional-order memory augmentation model include: adopting an adaptive moment estimation optimization algorithm, setting the initial learning rate to 0.0003, introducing a cosine annealing learning rate scheduling strategy, setting the number of training epochs to 800, the batch size to 64, and using a loss function consisting of a weighted combination of mean squared error loss and quantile loss with a weight ratio of 7:3. The quantile loss is used to optimize the uncertainty quantization interval. The prediction error is evaluated on the validation set after every 50 training epochs. An early stopping mechanism is triggered when the prediction error on the validation set fails to decrease for 5 consecutive times. Data augmentation techniques are applied during training, adding Gaussian-distributed noise to the input features with a noise standard deviation of 5% of the feature value standard deviation. Gradient clipping is used to prevent gradient explosion, with a clipping threshold set to 2.0. The total number of parameters in the fractional-order memory augmentation model is 1,870,000. After training, the generalization performance is verified on the test set.

[0040] The dynamic weight adjustment function calculates weight correction factors based on three dimensions: model prediction uncertainty, feature space coverage, and iteration convergence rate. First, it calculates the model prediction uncertainty index as the ratio of the uncertainty quantification interval width to the predicted ultimate bearing capacity value. Then, it calculates the feature space coverage as the normalized minimum Euclidean distance between the current input feature and the training set features. Next, it calculates the iteration convergence rate as the ratio of the current iteration residual to the previous iteration residual. After normalizing the model prediction uncertainty index, feature space coverage, and iteration convergence rate to the 0-1 interval, they are summed using a weighting coefficient of 4:3:3 to obtain the comprehensive evaluation index. When the evaluation index is in the range [0, 0.25), the weight correction factor is set to 1.2 to enhance the weight of the fractional-order memory convolution module. When the comprehensive evaluation index is in the range [0.25, 0.6), the weight correction factor is set to 1.0 to maintain the current weight configuration. When the comprehensive evaluation index is in the range [0.6, 0.85], the weight correction factor is set to 0.75 to reduce the weight of the multi-head attention fusion layer. When the comprehensive evaluation index is greater than 0.85, the weight correction factor is set to 0.5 and a model retraining warning is triggered. The weight correction factor dynamically adjusts the contribution of each layer's feature fusion through backpropagation to adapt to the prediction needs of different load conditions.

[0041] The critical gradient threshold is determined based on the coupling relationship between the plastic hardening modulus of the soil material and the size of the grid cell. The calculation formula is as follows: the stress gradient modulus of the current cell divided by the ratio of the reference stress value to the reference stress value, multiplied by the ratio of the characteristic length of the grid cell divided by the reference length. The reference stress value is taken as the yield stress of the soil, and the reference length is set to 1m. When the dimensionless gradient index exceeds 1.5, it is determined that the grid needs to be refined.

[0042] The deviation rate is calculated by subtracting the design bearing capacity from the predicted ultimate bearing capacity, dividing by the design bearing capacity, and finally multiplying by 100% to convert it into a percentage, used to quantify the degree of conformity between the prediction result and the design target. The arc length method introduces an arc length parameter to control the incremental path of load and displacement, simultaneously solving for the load factor and displacement increment in each incremental step, allowing the iterative process to traverse the extreme points of the load-displacement curve, avoiding the numerical divergence problem of traditional load control methods after the bearing capacity peak. The cooperative rotating coordinate system continuously updates the cable geometric stiffness matrix with element deformation, eliminating stiffness calculation errors caused by large rotations. The octree hierarchical algorithm achieves adaptive mesh generation by recursively subdividing a three-dimensional spatial cube. The initial cube covers the entire computational domain, and is subdivided into 8 sub-cubes based on geometric boundaries and material interfaces. Sub-cubes requiring refinement are further recursively subdivided until the mesh size requirements are met. The octree hierarchical algorithm automatically maintains topological consistency between mesh levels. The cable force-displacement coupling relationship is the interdependence between the cable force and displacement of the stay cable established through a geometric nonlinear equation. This cable force-displacement coupling relationship is solved iteratively using a symplectic geometry-preserving dynamic integral algorithm. The convergence state parameters include the final cable force distribution, nodal displacement field, foundation reaction force distribution, and soil stress-strain state, used for the multi-condition bearing capacity simulation calculation in step S05. The stress gradient error estimator calculates the difference between the unit stress gradient and the nodal smooth stress gradient based on the superconvergence patch recovery technique. This difference is used to evaluate local mesh errors and drive mesh refinement. The feature extraction preprocessing module performs spatial interpolation and time series standardization on the foundation settlement, cable force distribution, and soil plastic zone range to generate a 68-dimensional feature vector, which is then input into the fractional-order memory augmentation model. The centroid of the training domain is the arithmetic mean of all feature vectors in the training set, and the radius of the training domain is the maximum Mahalanobis distance between the feature vectors in the training set and the centroid of the training domain. The slowing mechanism reduces the neuron state update rate and increases the attention weight temperature parameter, enabling the fractional-order memory augmentation model to maintain output stability when faced with abnormal inputs. The initial value of the load increment step size is the initial parameter controlling the load application rate in the arc-length method. Adjusting the initial value of the load increment step size directly affects the iteration convergence and calculation accuracy. The grid density is the number of grid cells per unit volume, and the increase in grid density is achieved by reducing the grid size.

[0043] Optionally, the present invention also provides a method for forming a bearing capacity prediction system for a flexible photovoltaic support composite cable-stayed foundation by means of a computer. The computer is provided with a readable storage medium, which stores program instructions. When the program instructions are run in the computer, they execute the above-mentioned method for constructing the bearing capacity prediction model of the flexible photovoltaic support composite cable-stayed foundation.

[0044] The specific implementation methods of the above steps are described in detail below.

[0045] The specific implementation of step S01 is as follows: First, the initial geometric parameters of the cable-stayed system are collected using on-site surveying equipment. This includes measuring the cable length using a laser rangefinder, determining the cable inclination angle using an inclination sensor, and determining the three-dimensional coordinates of the anchor points using a total station. These geometric parameters directly determine the initial stress state and deformation mode of the cable-stayed system. Simultaneously, the soil at the construction site is explored in layers. Physical and mechanical parameters of each soil layer are obtained through borehole sampling, including determining the soil layer thickness using a standard penetration test, measuring the soil density using a ring cutter method, determining the moisture content using an oven-drying method, and obtaining the initial void ratio using a consolidation apparatus test. This layered soil data provides the basic parameter input for the subsequent establishment of the constitutive model, ensuring the consistency between the boundary conditions of the finite element simulation calculation and the actual engineering conditions.

[0046] The specific implementation of step S02 is to conduct indoor triaxial creep tests on the soil samples collected in step S01, apply constant loads under different confining pressures and deviatoric stress levels and continuously record the evolution curve of strain over time, and at the same time conduct consolidation tests to determine the compression deformation characteristics of the soil under progressive loading to obtain the stress-strain-time curve of the whole process. A multi-scale homogenization algorithm based on variational asymptotic methods was used to process experimental data. This algorithm, based on the principle of energy variation, separates the microscopic periodic structure of soil into macroscopic slowly varying fields and microscopic rapidly varying fields through asymptotic expansion techniques. A numerical model of the microscopic boundary value problem was established within a representative volume element. The stress-strain distribution at the microscale was obtained by solving the localized deformation mode. The anisotropic equivalent stiffness tensor and damping tensor were rigorously derived using the volume-average theorem. The partial differential equations of the periodic element were transformed into a system of algebraic equations using fast Fourier transform to significantly improve computational efficiency. Combined with adaptive multi-scale basis functions, the strain localization and shear band evolution phenomena were accurately captured, realizing cross-scale information transfer from microscopic pore structure to macroscopic continuous medium. Finally, a fractional-order viscoelastic-plastic constitutive database of soil was established. This database can realistically reflect the contribution of microscopic mechanisms such as particle contact, pore distribution, and cementation state to macroscopic bearing capacity. In particular, the influence of soil microstructure evolution on macroscopic mechanical response under long-term loading was accurately characterized.

[0047] The specific implementation of step S03 is as follows: a cooperative rotation coordinate system is constructed based on the cable length, cable inclination angle, and anchor point coordinates collected in step S01. This coordinate system is continuously updated as the element deforms, thereby eliminating stiffness calculation errors caused by large rotations. The arc length method is used to set the initial value of the load increment step size to 0.05 times the design load. The arc length method introduces the arc length parameter to simultaneously control the increment path of load and displacement, enabling the iteration process to traverse the extreme points of the load-displacement curve, avoiding the numerical divergence problem that occurs after the peak bearing capacity in traditional load control methods. A symplectic geometry-preserving dynamic integral algorithm is employed to iteratively calculate the coupling relationship between cable forces and displacements. This algorithm constructs a numerical integration scheme on a symplectic manifold based on Hamiltonian canonical equations, preserving the volume invariance of the phase space. An implicit symplectic Runge-Kutta discretization scheme is derived using the generating function method, strictly preserving the system's symplectic second-order invariance and generalized energy conservation. Lie series expansion techniques are used to control local truncation errors within a high-order small range, eliminating the inherent numerical dissipation and dispersion errors of traditional numerical integration methods. Variational integrator techniques are introduced to handle constraints, ensuring that the phase trajectory does not diverge and energy drift is suppressed within the theoretical limit during long-term integration. When the iterative residual is less than... The calculation is determined to be converged and the convergence state parameters are recorded, including the final cable force distribution, nodal displacement field, foundation reaction force distribution, and soil stress-strain state. These parameters provide reliable initial conditions for subsequent multi-condition bearing capacity simulation calculations.

[0048] The specific implementation of step S04 involves using an octree hierarchical algorithm to establish an initial mesh for the soil foundation cable system corresponding to the equivalent macroscopic constitutive parameters obtained in step S02. This algorithm achieves adaptive mesh generation by recursively subdividing a three-dimensional spatial cube. The initial cube covers the entire computational domain. Based on the geometric boundaries and material interfaces, the cube is subdivided into 8 sub-cubes. The sub-cubes requiring refinement are further recursively subdivided until the mesh size requirements are met. The mesh size range is set from 0.1 to 0.8 m to balance computational accuracy and efficiency. Mesh refinement is driven by a stress gradient error estimator. This estimator uses superconvergent patch recovery technology to calculate the difference between the element stress gradient and the node smoothed stress gradient, and uses this difference to evaluate local mesh errors. The critical gradient threshold is determined based on the coupling relationship between the plastic hardening modulus of the soil material and the size of the mesh element. The stress gradient modulus of the current element is divided by the ratio of the reference stress value to the reference stress value, and then multiplied by the ratio of the characteristic length of the mesh element to the reference length. The reference stress value is taken as the yield stress of the soil, and the reference length is set to 1m. When the dimensionless gradient index exceeds 1.5, local refinement is triggered. The octree hierarchical algorithm automatically maintains the topological coordination between mesh levels, ensuring the convergence and accuracy of the finite element calculation.

[0049] The specific implementation of step S05 involves setting multiple combinations of load conditions, including static load, wind load, temperature load, and seismic load. Finite element simulation calculations are performed for each load condition. The convergence state parameters obtained in step S03 are used as initial conditions. The adaptive mesh model established in step S04 is employed to record the spatial distribution pattern of foundation settlement, extract the rate of change of cable force distribution over time, and define the range and expansion trend of the soil plastic zone. These foundation settlement, cable force distribution, and soil plastic zone ranges are input into a feature extraction preprocessing module. This module performs spatial interpolation and time series standardization on the data, extracting stress field, displacement field, and plastic strain field at 10 time nodes from the simulation process. Principal component analysis is performed on these feature data to reduce the dimensionality to 68 dimensions, generating a 68-dimensional feature vector. This feature vector includes the spatial distribution sequence of foundation settlement, the time history rate of change of cable force distribution, and the soil plastic strain energy density distribution, providing high-fidelity training data support for the subsequent fractional-order memory enhancement model.

[0050] The specific implementation of step S06 is as follows: the simulation data preprocessed in step S05 is input into a fractional-order memory-enhanced model for bearing capacity prediction. The input layer of this model receives a 68-dimensional feature vector, which, after passing through a feature normalization layer, enters a fractional-order memory convolution module. This module contains a hybrid structure of four layers of Caputo fractional derivative operators and long short-term memory units, with the fractional order ranging from 0.3 to 0.9, used to capture the power-law decay characteristics of soil creep and stress relaxation. The output temporal features enter a multi-head attention fusion layer, which sets up eight attention heads. It calculates the long-range dependencies between features through learnable query matrices, key matrices, and value matrices. The fused feature vector passes through three layers of fully connected neural networks, with the number of hidden layer neurons being 256, 128, and 64, respectively. The activation function uses a parameterized modified linear unit. Finally, the output layer generates the predicted value of the ultimate bearing capacity and the uncertainty quantization range. The model integrates a critical slowing structure, inserting a critical detection gating unit between the multi-head attention fusion layer and the fully connected neural network. This unit calculates the Mahalanobis distance between the current feature vector and the centroid of the training domain. The centroid of the training domain is the arithmetic mean of all feature vectors in the training set, and the radius of the training domain is the maximum Mahalanobis distance between the feature vector in the training set and the centroid of the training domain. When the Mahalanobis distance exceeds 0.85 times the radius of the training domain, the slowing mechanism is activated. By introducing a time-delayed feedback loop, the neuron state update rate is reduced to 0.3 times the normal rate. At the same time, the temperature parameter of the attention weights is increased to 1.8 times to enhance feature smoothness, enabling the model to automatically enter a highly robust state when faced with extreme input conditions outside the training set. The weight correction factor is calculated based on the dynamic weight adjustment function, which is based on three dimensions: model prediction uncertainty, feature space coverage, and iterative convergence rate. First, the model prediction uncertainty index is calculated as the ratio of the uncertainty quantification interval width to the predicted ultimate bearing capacity value. Then, the feature space coverage is calculated as the normalized minimum Euclidean distance between the current input feature and the training set features. Finally, the iterative convergence rate is calculated as the ratio of the current iteration residual to the previous iteration residual. These three indices are normalized to the 0-1 interval and then summed using a weighting coefficient of 4:3:3 to obtain the comprehensive evaluation index. When the comprehensive evaluation index falls within the 0-1 interval... When the comprehensive evaluation index is in the range of 0.25, the weight correction factor is set to 1.2 to enhance the weight of the fractional-order memory convolution module. When the comprehensive evaluation index is in the range of 0.25 to 0.6, the weight correction factor is set to 1.0 to maintain the current weight configuration. When the comprehensive evaluation index is in the range of 0.6 to 0.85, the weight correction factor is set to 0.75 to reduce the weight of the multi-head attention fusion layer. When the comprehensive evaluation index is greater than 0.85, the weight correction factor is set to 0.5 and a model retraining warning is triggered at the same time. The weight correction factor dynamically adjusts the contribution of feature fusion of each layer through backpropagation to adapt to the prediction needs of different load conditions.

[0051] The specific implementation of step S07 is as follows: Iterative optimization is performed based on the deviation rate between the predicted ultimate bearing capacity and the design bearing capacity obtained in step S06. The deviation rate is calculated as the difference between the predicted ultimate bearing capacity and the design bearing capacity, divided by the design bearing capacity, and then multiplied by 100% to convert it into a percentage. When the deviation rate is within the range of 0% to 5%, it is determined that the degree of conformity between the prediction result and the design target meets the engineering requirements, and the iteration is terminated, outputting the final bearing capacity prediction result. When the deviation rate is within the range of 5% to 15%, it indicates that the accuracy of the cable-displacement coupling calculation is insufficient. The initial value of the load increment step size in step S03 is adjusted to 0.6 times the original initial value, and the process returns to step S03 for recalculation. This adjustment improves the ability of the iteration process to capture the extreme points of the load-displacement curve by reducing the load application rate. When the deviation rate is greater than 15%, it indicates that the finite element mesh resolution cannot fully characterize the stress concentration area. The mesh density in step S04 is increased to 1.8 times the original mesh density, and the process is returned to step S04 to remodel. The increase in mesh density is achieved by reducing the mesh size, which ensures that the stress gradient abrupt change area is fully discretized, thereby significantly improving the reliability and applicability of bearing capacity prediction under complex soil conditions.

[0052] It should be noted that the key technical ideas of this invention include a multi-scale homogenization algorithm based on variational asymptotic methods, a dynamic integral algorithm based on symplectic geometry-preserving structure, and a critical slowing structure for a fractional-order memory-enhanced model. The multi-scale homogenization algorithm based on variational asymptotic methods achieves cross-scale information transfer from microscopic pore structure to macroscopic continuous media through rigorous mathematical derivation. This avoids the error accumulation caused by simplification assumptions in traditional homogenization methods, enabling equivalent macroscopic constitutive parameters to accurately reflect the contribution of microscopic mechanisms such as particle contact, pore distribution, and cementation state to bearing capacity. Compared to traditional empirical constitutive models, it has a stronger physical basis and applicability, especially in accurately characterizing the influence of soil microstructure evolution on macroscopic mechanical response under long-term loading. The symplectic geometry-preserving dynamic integration algorithm fundamentally improves numerical stability by maintaining the geometric structure of the Hamiltonian system. It eliminates the inherent numerical dissipation and dispersion errors of traditional numerical integration methods, avoids the divergence failure of traditional Newton-Raphson iteration under extreme load conditions, and ensures that the dynamic response analysis maintains the physical rationality of the phase space trajectory even after thousands of iterations. This is crucial for capturing nonlinear dynamic behaviors such as parametric resonance and internal resonance in cable systems. The critical slowing structure of the fractional-order memory-enhanced model simulates the fluctuation suppression mechanism of the physical system at the phase transition critical point, enabling the model to automatically enter a highly robust state when faced with extreme inputs outside the training set. This avoids prediction distortion caused by parameter space extrapolation and exhibits stronger generalization ability and safety margin compared to traditional neural network models under rare load combinations and abnormal soil layer distributions. The synergistic effect of these three key technological approaches constitutes a complete technological chain from microscopic soil structure to macroscopic bearing capacity prediction. The variational asymptotic method provides constitutive parameter inputs with a clear physical basis, the symplectic geometric algorithm ensures high-fidelity data support for finite element simulation, and the critical slowing structure enables adaptive robust adjustment of the prediction model. The three work together to form a bearing capacity prediction system that combines physical accuracy, numerical stability, and intelligent adaptability, achieving a significant improvement in prediction reliability and engineering practicality under complex working conditions compared to existing technologies.

[0053] It should be noted that this invention also solves the following technical problem: the problem of computational divergence in traditional finite element simulation under extreme load conditions due to unreasonable meshes. This invention uses an octree hierarchical algorithm to establish the initial mesh, and drives adaptive mesh refinement based on a stress gradient error estimator. When the element stress gradient exceeds 1.5 times the critical gradient threshold, local refinement is triggered to ensure sufficient mesh density in stress concentration areas. By continuously updating the cable-stayed bridge's geometric stiffness matrix through a cooperative rotating coordinate system, stiffness calculation errors caused by large rotations are eliminated. Combined with the arc-length method to control the incremental path of load and displacement, the iterative process can traverse the extreme points of the load-displacement curve, avoiding the numerical divergence problem of traditional load control methods after the peak bearing capacity. This ensures the computational robustness of finite element simulation under combined load conditions and provides high-fidelity training data support for artificial intelligence models.

[0054] Furthermore, this invention addresses the technical problem of insufficient generalization ability of artificial intelligence prediction models when facing extreme conditions outside the training set. The fractional-order memory enhancement model introduces a critical slowing-down structure. A critical detection gating unit calculates the Mahalanobis distance between the current feature vector and the centroid of the training domain. When the Mahalanobis distance exceeds 0.85 times the radius of the training domain, the slowing-down mechanism is activated. A time-delayed feedback loop reduces the neuron state update rate to 0.3 times the normal rate, while simultaneously increasing the temperature parameter of the attention weights to 1.8 times to enhance feature smoothness. A dynamic weight adjustment function calculates weight correction factors based on three dimensions: model prediction uncertainty, feature space coverage, and iteration convergence rate. Through backpropagation, the contribution of feature fusion at each layer is dynamically adjusted, enabling the model to automatically enter a highly robust state under rare load combinations and abnormal soil layer distributions, significantly improving the generalization ability and safety margin of bearing capacity prediction.

[0055] Specifically, the principle of this invention is as follows: This invention uses a multi-scale homogenization algorithm based on variational asymptotic methods to separate the microscopic periodic structure of soil into macroscopic slowly varying fields and microscopic rapidly varying fields. It obtains localized deformation modes by solving the microscopic boundary value problem within representative volume elements. It rigorously derives the anisotropic equivalent stiffness tensor and damping tensor, avoiding the error accumulation caused by the simplification assumptions of traditional homogenization methods. This ensures that the equivalent macroscopic constitutive parameters truly reflect the contribution of microscopic mechanisms to bearing capacity. The symplectic geometry-preserving dynamic integration algorithm constructs a numerical scheme that maintains the invariance of the symplectic second form based on Hamilton's canonical equations. It derives the implicit symplectic Runge-Kutta discrete scheme through the generating function method, rigorously preserving generalized energy conservation, eliminating numerical dissipation and dispersion errors, and ensuring that the phase trajectory does not diverge during long-term integration. The fractional-order memory enhancement model uses a hybrid structure of Caputo fractional derivative operator and long short-term memory unit to capture the power-law decay characteristics of soil creep. The critical slowing structure simulates the response behavior of the critical point of phase transition in statistical physics by dynamically adjusting the activation threshold of neurons. When the input features approach the boundary of the training domain, it automatically reduces the information propagation speed and enhances the stability of features, thus achieving an adaptive balance between prediction accuracy and stability, thereby improving the accuracy of bearing capacity prediction under the long-term creep of soil and the coupling effect of cable force.

[0056] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0057] The specific implementation of step S02 involves using a multi-scale homogenization algorithm based on the variational asymptotic method to process the microscopic soil structure parameters and obtain equivalent macroscopic constitutive parameters. This algorithm is based on the energy variational principle and transforms the displacement field of the soil's mesoscopic periodic structure into... It is represented by asymptotic expansion as a macroscopic slowly varying field. With close observation of rapidly changing fields The superposition, expanded form of which is as follows:

[0058] ;

[0059] In the formula, These are macroscopic coordinates, in meters. For detailed coordinates, the unit is meters. The scale separation parameter, ranging from 0.001 to 0.1, represents the ratio of the mesoscale to the macroscale and is dimensionless. The equivalent stiffness tensor is obtained by solving the mesoscale boundary value problem within a representative volume element. The calculation formula is expressed as follows:

[0060] ;

[0061] In the formula, For detailed observation of the stiffness tensor, the unit is Pa. The volume is a representative unit volume, with units of . , For localized deformation mode functions, dimensionless. The tensor index ranges from 1 to 3, and the integral variable is a volume element. The unit is The stress-strain-time curves were recorded through triaxial creep and consolidation tests. The partial differential equations of periodic elements were transformed into a system of algebraic equations using fast Fourier transform. Adaptive multi-scale basis functions were combined to capture strain localization phenomena, and finally, a fractional-order viscoelastic-plastic constitutive database of soil was established.

[0062] The specific implementation of step S03 involves constructing the cable-stayed cable geometric stiffness matrix in a cooperative rotating coordinate system, and using a symplectic geometry-preserving dynamic integral algorithm to iteratively calculate the coupling relationship between cable force and displacement. This algorithm is based on Hamilton's canonical equations and phase space coordinates. The evolution follows the invariance of the symplectic form, Hamilton function The statement is as follows:

[0063] ;

[0064] In the formula, The equivalent mass of the cable system is expressed in kg. It is a generalized momentum vector, with units of . , This is the potential energy function, in J. The expression is ,in The elastic modulus of the cable material is expressed in Pa. The cross-sectional area of ​​the cable is given in units of 1000 mm. , This is the initial cable length, in meters. Let be a generalized coordinate vector, in meters (m). The iterative formula for the symplectic Runge-Kutta discrete scheme is expressed as follows:

[0065] ;

[0066] ;

[0067] In the formula, For the first The generalized coordinates of the step, in meters. For the first The generalized momentum of a step, with units of 1. , The time step is in seconds. This is the Runge-Kutta level, which defaults to 4. These are weighting coefficients, dimensionless, with empirical values ​​of [value missing]. , These are intermediate-level generalized coordinates, in meters (m). This is intermediate-level generalized momentum, with units of . , The unit is m / s. The unit is N. Cable tension With displacement The coupling relationship is established through geometric nonlinear equations, expressed as follows:

[0068] ;

[0069] In the formula, The tension is measured in N. The angle of inclination is expressed in rad. This represents cable end displacement, in meters (m). The initial load increment step size is set to 0.05 times the design load, and the load factor is controlled using the arc length method. With displacement increment The joint solution yields the arc length constraint equation, which is expressed as follows:

[0070] ;

[0071] In the formula, The load factor increment is dimensionless. This is the displacement increment vector, in meters. This represents the arc length increment, in meters (m), with an empirical value ranging from 0.01 to 0.1. The reference length is 1m. When the iteration residual... Less than The convergence is determined at a certain time, and the residual calculation formula is expressed as follows:

[0072] ;

[0073] In the formula, This is the external load vector, in units of N. This is an internal force vector, with units of N. The Euclidean norm of a vector. The iterative residual is dimensionless.

[0074] The specific implementation of step S04 involves using an octree hierarchical algorithm to establish an initial mesh, with a mesh size ranging from 0.1 to 0.8 μm. Mesh refinement is then driven by a stress gradient error estimator, and the stress gradient modulus is... The critical gradient threshold is obtained by calculating the difference between the element stress gradient and the smoothed nodal stress gradient using the superconvergent plate recovery technique. The calculation formula is expressed as follows:

[0075] ;

[0076] In the formula, This represents the stress gradient modulus of the current element, in Pa / m. The reference stress value is taken as the soil yield stress, in Pa. The feature length of the grid cell, in meters. For reference length, set to 1m. It is a dimensionless gradient index. When the dimensionless gradient index... Local refinement is triggered when the value exceeds 1.5, resulting in a higher mesh density. Defined as the number of mesh cells per unit volume, in units of 1 / 2000. .

[0077] The specific implementation of step S05 is the same as described above, and will not be repeated in detail here.

[0078] The specific implementation of step S06 involves inputting the preprocessed simulation data into the fractional-order memory enhancement model for load-bearing capacity prediction. The fractional-order memory convolution module uses the Caputo fractional derivative operator, and the definition formula of the fractional derivative is as follows:

[0079] ;

[0080] In the formula, For Caputo fractional derivative operators, It is a fractional order, ranging from 0.3 to 0.9, and is dimensionless. For time-dependent functions, For gamma function, The variable is the integral variable, and the unit is seconds (s). The current time is in seconds. For function The first derivative with respect to time. The dynamic weight adjustment function calculates the weight correction factor. Comprehensive evaluation indicators The calculation formula is expressed as follows:

[0081] ;

[0082] In the formula, The width of the uncertainty quantification interval, in kN. This is the predicted ultimate bearing capacity, in kN. The minimum Euclidean distance between the current input features and the training set features is dimensionless. The training domain radius is dimensionless. The residual of the current iteration is dimensionless. The residual from the previous iteration is dimensionless. This is a comprehensive evaluation index, dimensionless. Based on the comprehensive evaluation index... Determine the weight adjustment factor ,when When it falls between 0 and 0.25 The value is 1.2, when When it falls within the range of 0.25 to 0.6 The value is 1.0, when When it falls within the range of 0.6 to 0.85 The value is 0.75, when When greater than 0.85 The value is 0.5. This is a weighting correction factor, dimensionless.

[0083] The specific implementation of step S07 is based on the deviation rate between the predicted ultimate bearing capacity and the design bearing capacity. The deviation rate is calculated using the following formula for iterative optimization:

[0084] ;

[0085] In the formula, The design load-bearing capacity is expressed in kN. This represents the deviation rate, expressed as a percentage. When the deviation rate... The iteration terminates and the final bearing capacity prediction result is output when the deviation rate is between 0% and 5%. If the deviation rate is between 5% and 15%, adjust the initial value of the load increment step to 0.6 times the original value and return to step S03 to recalculate. If the density is greater than 15%, increase the mesh density to 1.8 times the original mesh density and return to step S04 to remodel.

[0086] The fractional-order memory enhancement model training employs an adaptive moment estimation optimization algorithm, with a loss function... The calculation formula is expressed as follows:

[0087] ;

[0088] In the formula, For the sample size, For the first The true labels of each sample are in kN. For the first The predicted value for each sample is in kN. This is the set of quantiles, including the three quantiles of 0.1, 0.5, and 0.9. The quantile loss weight function is defined as follows: ,in To predict residuals, the unit is kN. These are quantile values, dimensionless. For the first The sample at the th The predicted quantile values, in kN. For reference bearing capacity, the value is taken as the design bearing capacity, and the unit is kN. This is the total loss function value, which is dimensionless.

[0089] To better understand and implement this invention, the following is a specific application scenario of this invention, Example 2:

[0090] A technical team undertook the design of a flexible support foundation for a large-scale photovoltaic power station located in the eastern coastal region. The site has complex soil conditions, including alternating layers of silty clay and silt, and the design load needs to consider extreme wind load combinations common in typhoon-prone areas. The team used the bearing capacity prediction model construction method described in this invention to optimize the design of the cable-stayed composite foundation. The team first conducted on-site soil investigation, setting up 12 exploration points within the foundation layout area. Complete soil stratification data were obtained through in-situ sampling and indoor testing. The soil layers, from top to bottom, are: a 2.3m thick plain fill layer, a 5.8m thick silty clay layer, a 4.2m thick silt layer, and a clay layer greater than 10m. The physical and mechanical parameters of each soil layer are shown in Table 1.

[0091] Table 1 Physical and mechanical parameters of the soil layers at the site

[0092]

[0093] The technical team collected the initial geometric parameters of the cable-stayed system, including a front cable length of 18.5m, a rear cable length of 22.3m, a front cable inclination angle of 38 degrees, a rear cable inclination angle of 45 degrees, a front anchorage point coordinate of (0, 0, 0), a rear anchorage point coordinate of (35.2, 0, 0), and a support top anchorage point coordinate of (17.6, 0, 12.8). The team conducted triaxial creep and consolidation tests on the four soil layers collected. The confining pressures were set at three levels: 100kPa, 200kPa, and 300kPa, with a holding time of 72 hours. Complete stress-strain-time curves were recorded. A multi-scale homogenization algorithm using the variational asymptotic method was employed to process the experimental data. A representative volume element size of 0.5 mm was selected, and a three-phase structural model including soil particles, pores, and cement was established at the mesoscale. Through asymptotic expansion, the macroscopic slowly varying field and the mesoscopic rapidly varying field were separated, and the localized deformation mode was obtained by solving the mesoscopic boundary value problem. The Fast Fourier Transform (FFT) transformed the partial differential equations of the periodic element into a system of algebraic equations, improving the computational efficiency to 8.3 times that of the traditional finite element method. The final equivalent macroscopic constitutive parameters obtained include a fractional viscoelastic order of 0.67, a relaxation time of 185 hours, and a long-term modulus of 3.2 MPa for the silty clay layer.

[0094] Based on the collected cable length, inclination angle, and anchorage point coordinates, the technical team constructed a geometric stiffness matrix for the stay cables in a cooperative rotating coordinate system. The initial load increment step size was set to 0.05 times the design load, with a total design load of 450 kN. Iterative calculations were performed using a symplectic geometry-preserving dynamic integral algorithm. The implicit symplectic Runge-Kutta discretization scheme derived through the generating function method maintained the symplectic second-order invariance of the Hamiltonian system. At the 1286th iteration, the iterative residual decreased to [a value missing]. The convergence condition has been met. For example... Figure 2 As shown, in the convergence state, the front cable force is 178.5 kN, the rear cable force is 203.7 kN, the horizontal displacement of the top of the support is 32.5 mm, the vertical displacement is 58.3 mm, the front reaction force of the foundation is 267.8 kN, and the rear reaction force of the foundation is 312.5 kN. The technical team used an octree hierarchical algorithm to establish an initial grid for the soil-foundation-cable system. The computational domain is 50 m long, 30 m wide, and 25 m deep, with an initial grid size of 0.6 m and a total of 187,500 grid cells. According to the calculation results of the stress gradient error estimator, the stress gradient at the interface between the silty clay layer and the silty sand layer reaches 2.8 times the reference stress value, exceeding the critical gradient threshold of 1.5 times and triggering local refinement. After refinement, the grid size in this area is reduced to 0.15 m, and the final total number of grid cells reaches 523,800.

[0095] like Figure 3As shown, the technical team performed multi-condition load-bearing capacity simulation calculations. The load conditions set included static load condition (self-weight plus photovoltaic module dead load), wind load condition (extreme wind speed corresponding to basic wind pressure of 0.75 kPa), temperature load condition (cable force change caused by temperature difference from -20℃ to 60℃), and seismic load condition (seismic acceleration of 0.15g corresponding to a seismic intensity of 7 degrees). Under static load conditions, the foundation settlement was 28.5 mm, the average cable force distribution was 185.3 kN, and the plastic zone of the soil was mainly concentrated within 0.8 m of the bottom of the foundation. Under wind load conditions, the maximum horizontal displacement of the foundation was 45.7 mm, the cable force fluctuation amplitude was ±32.8 kN, and the plastic zone extended downward to a depth of 1.5 m. Under temperature load conditions, the cable force variation range was -18.5 kN to +25.3 kN, and the additional foundation settlement was 5.2 mm. Under seismic load conditions, the peak instantaneous displacement of the foundation was 67.3 mm, the dynamic amplification factor of the cable force was 1.38, and the plastic zone extended to a perimeter of 2.3 m around the foundation. The technical team input the spatial distribution sequence of the foundation settlement, the time history rate of change of the cable force distribution, and the distribution of soil plastic strain energy density into the feature extraction preprocessing module, and generated a 68-dimensional feature vector after spatial interpolation and time series standardization.

[0096] The technical team inputs preprocessed simulation data into a fractional-order memory-enhanced model for bearing capacity prediction. This model's input layer receives a 68-dimensional feature vector, which passes through a feature normalization layer before entering a fractional-order memory convolution module containing a hybrid structure of four layers of Caputo fractional derivative operators and long short-term memory units. The fractional orders are set to 0.45, 0.62, 0.73, and 0.88 to capture the creep power-law decay characteristics of silty clay layers. The output temporal features enter a multi-head attention fusion layer with eight attention heads. The long-range dependency weight distribution between features is calculated using a learnable query matrix, key matrix, and value matrix. The fused feature vector is then processed through a three-layer fully connected neural network with 256, 128, and 64 hidden layer neurons, respectively. The activation function uses a parameterized modified linear unit. The final output layer generates a predicted ultimate bearing capacity of 682.5 kN, with an uncertainty quantization range of [658.3 kN, 706.7 kN] and a safety factor of 1.52. The technical team calculated a weight correction factor of 0.95 based on the dynamic weight adjustment function. This factor is calculated based on three dimensions: model prediction uncertainty index of 0.071, feature space coverage of 0.183, and iteration convergence rate of 0.428. The comprehensive evaluation index is 0.398, which falls within the range of [0.25, 0.6). Therefore, the current weight configuration remains unchanged.

[0097] The technical team calculated and predicted the ultimate bearing capacity of 682.5 kN, with a deviation rate of 5.0% from the design bearing capacity of 650 kN, falling within the range of [0, 5%], thus meeting the termination iteration condition and outputting the final bearing capacity prediction result. Based on the prediction results, the technical team optimized the cable pretensioning values ​​of the cable-stayed system, pretensioning the front cable to 165 kN and the rear cable to 188 kN, ensuring that the settlement of the foundation under the design load was controlled within 22.8 mm, meeting the photovoltaic support's requirements for foundation deformation limitation. This invention achieves cross-scale information transfer from the microscopic pore structure of the soil to the macroscopic continuous medium through a multi-scale homogenization algorithm of the variational asymptotic method, avoiding the error accumulation caused by the simplification assumptions in traditional homogenization methods, and accurately characterizing the long-term creep characteristics of the silty clay layer. The symplectic geometry-preserving dynamic integral algorithm eliminates the dissipation error of traditional numerical integration methods by maintaining the geometry of the Hamiltonian system, ensuring the physical rationality of the phase space trajectory in more than a thousand iterations of the large displacement geometric nonlinear analysis of the cable-stayed system. The critical slowing structure in the fractional-order memory enhancement model enables the model to automatically enter a highly robust state when facing off-training conditions such as extreme typhoon loads. By simulating the fluctuation suppression mechanism of the phase transition critical point in statistical physics, it significantly improves the generalization ability of bearing capacity prediction under rare load combinations, providing reliable technical support for the safe design of flexible photovoltaic support foundations under complex soil conditions.

[0098] It should be noted that the variables involved in this invention are explained in detail in Table 2.

[0099] Table 2 Variable Explanation Table

[0100]

[0101] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for constructing a bearing capacity prediction model for a flexible photovoltaic support composite cable-stayed foundation, characterized in that, The process includes collecting initial geometric parameters of the cable-stayed system and soil stratification data, establishing a fractional-order viscoelastic-plastic constitutive database of the soil, using a multi-scale homogenization algorithm based on variational asymptotic method to process microscopic soil structural parameters to obtain equivalent macroscopic constitutive parameters, constructing the cable-stayed geometric stiffness matrix in a cooperative rotating coordinate system, iteratively calculating the coupling relationship between cable force and displacement using a symplectic geometric-preserving dynamic integral algorithm, adaptively generating finite element meshes, performing multi-condition bearing capacity simulation calculations to record foundation settlement, cable force distribution, and soil plastic zone range, inputting the preprocessed simulation data into a fractional-order memory-enhanced model for bearing capacity prediction, and iteratively optimizing based on the deviation rate between the predicted ultimate bearing capacity and the design bearing capacity.

2. The method for constructing a bearing capacity prediction model for a flexible photovoltaic support composite cable-stayed foundation according to claim 1, characterized in that, In the steps of collecting the initial geometric parameters and soil layer data of the cable-stayed system, the initial geometric parameters include cable length, cable inclination angle, and anchor point coordinates, and the soil layer data includes the thickness, density, water content, and initial void ratio of each soil layer.

3. The method for constructing a bearing capacity prediction model for a flexible photovoltaic support composite cable-stayed foundation according to claim 2, characterized in that, The steps to establish a fractional-order viscoelastic-plastic constitutive database for soil are as follows: conduct triaxial creep tests and consolidation tests on each soil layer and record the stress-strain-time curves throughout the entire process.

4. The method for constructing a bearing capacity prediction model for a flexible photovoltaic support composite cable-stayed foundation according to claim 3, characterized in that, The variational asymptotic method's multi-scale homogenization algorithm, based on the energy variational principle, separates the micro-periodic structure of soil into macroscopic slowly varying fields and micro-fast varying fields through asymptotic expansion. It solves the micro-boundary value problem within a representative volume element to obtain a localized deformation mode, and derives the anisotropic equivalent stiffness tensor and damping tensor through the volume average theorem.

5. The method for constructing a bearing capacity prediction model for a flexible photovoltaic support composite cable-stayed foundation according to claim 4, characterized in that, The symplectic geometry-preserving dynamic integration algorithm constructs a numerical integration scheme on a symplectic manifold based on Hamilton's canonical equations to preserve the invariance of the phase space volume. An implicit symplectic Runge-Kutta discrete scheme is derived through the generating function method, thus preserving the symplectic second-form invariance and the generalized energy conservation of the system.

6. The method for constructing a bearing capacity prediction model for a flexible photovoltaic support composite cable-stayed foundation according to claim 5, characterized in that, When iteratively calculating the coupling relationship between cable force and displacement, the initial value of the load increment step size is set to 0.05 times the design load based on the arc length method. When the iterative residual is less than Record the convergence state parameters at regular intervals.

7. The method for constructing a bearing capacity prediction model for a flexible photovoltaic support composite cable-stayed foundation according to claim 6, characterized in that, The finite element mesh adaptive generation uses an octree hierarchical algorithm to establish the initial mesh, with a mesh size ranging from 0.1 to 0.8 m. Mesh refinement is driven by a stress gradient error estimator, and local refinement is triggered when the element stress gradient exceeds 1.5 times the critical gradient threshold.

8. The method for constructing a bearing capacity prediction model for a flexible photovoltaic support composite cable-stayed foundation according to claim 7, characterized in that, When performing multi-condition bearing capacity simulation calculations, the load conditions include combinations of static load, wind load, temperature load, and seismic load. The foundation settlement, cable force distribution, and soil plastic zone range are input into the feature extraction preprocessing module.

9. The method for constructing a bearing capacity prediction model for a flexible photovoltaic support composite cable-stayed foundation according to claim 8, characterized in that, The input layer of the fractional-order memory enhancement model receives a 68-dimensional feature vector. After passing through the feature normalization layer, it enters the fractional-order memory convolution module. The fractional-order memory convolution module contains a hybrid structure of 4 layers of Caputo fractional derivative operators and long short-term memory units, with the fractional order ranging from 0.3 to 0.

9.

10. The method for constructing a bearing capacity prediction model for a flexible photovoltaic support composite cable-stayed foundation according to claim 9, characterized in that, The fractional-order memory enhancement model includes a multi-head attention fusion layer with 8 attention heads. It calculates the long-range dependencies between features through query matrix, key matrix, and value matrix. The fused feature vector passes through a 3-layer fully connected neural network with 256, 128, and 64 hidden layer neurons, respectively.

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