Foundation pit retaining wall deformation prediction method based on physical information neural network

Abstract

The invention belongs to the technical field of computational mechanics and artificial intelligence crossing in civil engineering, and discloses a foundation pit retaining wall deformation prediction method based on a physical information neural network, and the method comprises the following steps: 1, building a retaining wall physical information neural network agent model based on multi-source data fusion; 2, building a displacement-force inversion model of the retaining wall; and 3, carrying out iterative coupling solution on the support system. According to the method, mixed training is carried out by fusing physical rules and field measured data, so that the physical information neural network agent model follows a basic mechanics principle and can also fit specific engineering practice, the prediction result is more reliable, and compared with traditional finite element analysis, the efficiency is improved by several orders of magnitude; therefore, parameter optimization and real-time safety evaluation based on a large amount of calculation become possible.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of computational mechanics and artificial intelligence in civil engineering, and relates to a deformation prediction method for a foundation pit retaining wall based on a physical information neural network. BACKGROUND

[0002] Mechanical analysis of deep foundation pit supporting structure is the key to engineering safety, but the existing analysis methods have deficiencies in calculation efficiency, accuracy and applicability.

[0003] Traditional numerical simulation techniques such as finite element method discretize the retaining wall, support structure and soil in detail, construct a complex nonlinear model for solving. Although such methods are theoretically perfect, their calculation cost is extremely high. In order to accurately capture the wall-soil interaction and the cooperative working effect of the supporting system, the model often needs a large number of units, resulting in a long time-consuming solution, which makes it difficult to apply to practical engineering scenarios such as design optimization, parameter sensitivity analysis which require rapid iteration.

[0004] In recent years, with the development of artificial intelligence technology, pure data-driven neural network models have been introduced for foundation pit deformation prediction. Such methods avoid physical modeling and completely learn historical data to establish the mapping relationship between input parameters and output responses, so the calculation speed is extremely fast. But such "black box" model lacks physical constraints, its prediction results are easy to be physically distorted outside the training data coverage, the generalization ability is weak, and it cannot be applied to new projects lacking massive historical data

[0005] The emerging physical information neural network (PINN) to some extent combines physical laws, but its existing applications are mostly limited to the solution of single component or simple system. For the complex coupled system composed of retaining wall and internal support, the existing PINN technology still lacks effective means to handle the two-way mechanical interaction between them, and cannot realize efficient and accurate cooperative working analysis.

[0006] Therefore, the existing technology still lacks an effective method that can balance physical accuracy and calculation efficiency and is applicable to the coupled analysis of complex supporting systems. SUMMARY

[0007] The application aims to provide a neural mechanics coupled calculation method and device that can combine physical mechanism and field measurement data and efficiently realize coupled analysis of retaining wall and internal support system, solving the problems that traditional methods cannot use construction process data for model dynamic updating and are difficult to quickly analyze and optimize multiple working conditions.

[0008] The technical scheme of the application:

[0009] A physical information neural network-based foundation pit retaining wall deformation prediction method, the steps are as follows:

[0010] Step 1: Construction of retaining wall physical information neural network agent model based on multi-source data fusion

[0011] (1) Construction of theoretical data set:

[0012] Based on the mechanical control equation and geometric boundary condition of the retaining wall, a parameterized finite element simulation is performed to sample in the load parameter space, generating a set of displacement field data of the retaining wall under multiple load conditions, forming a load-displacement theoretical data set ; wherein, is the load vector, is the corresponding displacement field data, is the total number of load-displacement theoretical data samples in the load-displacement theoretical data set;

[0013] (2) Construction of measured data set:

[0014] In the foundation pit construction site, the visual detection system deployed obtains the displacement images of the preset measuring points on the surface of the retaining wall at each construction stage, and after digital image processing, the measured displacement data corresponding to the earth pressure at each construction stage is recorded, forming a load-displacement measured data set ; wherein, is the load vector obtained by the i-th field measurement, is the displacement vector of the preset measuring point corresponding to , and is the total number of measured load-displacement measured data samples in the load-displacement measured data set, wherein the preset measuring points at least include the connection points of the retaining wall and the internal support and the maximum deformation control points of the retaining wall;

[0015] (3) Construction and mixed training of physical information neural network:

[0016] A deep neural network is established with spatial coordinates (x, z) and load vector f as input, and displacement w corresponding to spatial coordinates as output as a physical information neural network agent model, wherein is the network parameter to be trained;

[0017] The load-displacement theoretical data set and the load-displacement measured data set are used as training samples together to construct a hybrid loss function , the expression of which is , wherein is the physical residual term based on the mechanical control equation, is the measured data mean square error term, and These are the weighting coefficients; the mixed loss function is minimized using the gradient descent algorithm. The physical information neural network proxy model is trained. .

[0018] Step 2: Establishment of the displacement-force inversion model for the retaining wall;

[0019] (1) Generation of inversion dataset:

[0020] Using the physical information neural network surrogate model trained in step one Input a large number of randomly sampled load vectors The displacement field of the corresponding retaining wall is calculated, and the displacement vector at the interface between the retaining wall and the internal support is extracted. This forms a displacement-force paired inversion dataset. ;in, This represents the total number of displacement-force paired inversion data samples in the displacement-force paired inversion dataset.

[0021] (2) Construction and training of displacement-force inversion model:

[0022] Network construction: Establish a displacement vector at the interface between the retaining wall and the internal support. As input, with the corresponding load vector Feedforward neural network for output As a displacement-force inversion model; among which, These are the parameters to be trained for the network;

[0023] Model training: Retrieving datasets using displacement-force pairings Using the mean square error between the predicted load and the actual load as training samples, the feedforward neural network is trained under supervision. Thus, a well-trained displacement-force inversion model is obtained.

[0024] Step 3: Iterative coupling solution of the supporting system;

[0025] (1) Model preparation: Obtain the finite element model of the support system based on the engineering design parameters;

[0026] (2) Initialization: Set the initial displacement vector at the interface between the retaining wall and the support. ;

[0027] (3) Iterative loop: For the k-th iteration:

[0028] a. Displacement-force inversion model evaluation: Evaluate the displacement vector at the interface between the retaining wall and the support in the current iteration step. Input into the displacement-force inversion model trained in step two The reaction force of the retaining wall on the support system was calculated. ;

[0029] b. Support system forward analysis: The reverse value of the reaction force... As a load, it is applied to the finite element model of the support system for mechanical analysis, and the new displacement vector of the support system at the connection interface is obtained by solving the problem. ;

[0030] c. Convergence test: Calculate the new displacement vector With the current displacement vector The relative error between the two results; if the error is less than the preset tolerance, the iteration converges and the current result is output; otherwise, continue to the next step;

[0031] d. Displacement Update: The interface displacement vector is updated using a relaxation algorithm. ;in, ω ∈ ( 0 , 1 ] As a relaxation factor, Let k be the displacement vector at the interface between the retaining wall and the support in the next step; then let k = k + 1, and return to step a for the next iteration.

[0032] An apparatus for implementing the above-described method for predicting the deformation of a retaining wall in a foundation pit based on a physical information neural network, comprising:

[0033] Data acquisition and processing module: This includes a visual inspection system deployed at the foundation pit site, used to acquire displacement image data of the retaining wall surface, and to calculate the measured displacement data of the preset measuring points of the retaining wall through image processing technology, forming a load-displacement measured dataset;

[0034] Data processing and model training module: Consists of a computing server, used for:

[0035] (1) Receive and store the load-displacement theoretical dataset generated by parametric finite element simulation and the load-displacement measured dataset transmitted by the data acquisition and processing module;

[0036] (2) Construct and train a physical information neural network agent model using a hybrid loss function;

[0037] (3) Use the trained physical information neural network proxy model to generate a displacement-force pairing dataset and train the displacement-force inversion model;

[0038] (4) As construction progresses, the physical information neural network proxy model is updated using newly measured data;

[0039] The coupled solution and result output module, implemented by the computation server, is used for:

[0040] (1) Run the iterative coupling solution process of the support system, call the displacement-force inversion model and the finite element model of the support system for iterative calculation until convergence;

[0041] (2) Visualize the final displacement field and internal force distribution results obtained from the solution.

[0042] The beneficial effects of this invention are as follows: By integrating physical laws with on-site measured data for mixed training, this invention enables the physical information neural network proxy model to both follow basic mechanical principles and fit specific engineering realities, resulting in more reliable prediction results. At the same time, it improves efficiency by several orders of magnitude compared to traditional finite element analysis, making parameter optimization and real-time safety assessment based on a large amount of computation possible. Detailed Implementation

[0043] The specific embodiments of the present invention will be further described below in conjunction with the technical solution.

[0044] Consider a typical rectangular deep foundation pit project. The foundation pit has a length of L, a width of B, and an excavation depth of H. e The support structure of the foundation pit includes a four-sided closed reinforced concrete retaining wall with a thickness of t. w The total depth of the wall (including the depth below the bottom of the pit) is H. w .

[0045] The internal support system is equipped with K horizontal supports (K≥1, in this embodiment K=2 is used as an example), with installation depths of z1, z2, ..., z K The cross-sectional dimensions of the supports and walers are determined according to the design requirements.

[0046] The physical and mechanical parameters of the soil, such as cohesion c, internal friction angle ϕ, and elastic modulus E, are described. s The earth pressure is determined based on the actual geological survey report. The nonlinear Winkler foundation model is used for calculation, and the subgrade coefficient is... Related to soil parameters and depth

[0047] Step 1: Construction of the PINN proxy model for retaining wall based on multi-source data fusion

[0048] (1) Theoretical Data Generation: Based on the Kirchhoff-Love plate theory and the principle of minimum total potential energy, a theoretical dataset was generated. Load vector f = [ f 1 , f 2 , . . . , f n ] T Each component within the preset range [ f m i n , f m a x ] N is generated using Latin hypercube sampling. theory Group of samples. The calculation of the total potential energy Π involves the bending stiffness D of the plate:

[0049]

[0050] Where E is the elastic modulus of the wall material, and ν is its Poisson's ratio. The total potential energy functional is:

[0051] Pi [ w ^ ] = U [ w ^ ] − W [ w ^ ]

[0052] in, U [ w ^ ] For strain energy, W [ w ^ ] This is work done by external force.

[0053] (2) Data Acquisition and Processing: During construction, the visual inspection device continuously acquires images, and the displacement of the retaining wall feature points is extracted through image processing algorithms (such as DIC) to form a measured dataset. .

[0054] (3) Hybrid training: Among them, the PINN proxy model This is a deep neural network whose input is normalized spatial coordinates. , and normalized load vector The loss function uses a hybrid loss function:

[0055] Li t o t a l ( theta ) = lambda 1 ⋅ Pi [ phi ( x , z ) ⋅ arrow theta ] + lambda 2 ⋅ 1 N m e a s u r e ∑ i = 1 N m e a s u r e ‖ phi ( x , z ) ⋅ arrow theta ( xi , eta , f delta m e a s i ) − ​ m e a s i ‖ 2

[0056] in, For functions that strictly satisfy geometric boundary conditions, and These are the weighting coefficients. The loss function is minimized using a gradient descent algorithm (such as the Adam optimizer). .

[0057] Step 2: Establishment of the retaining wall displacement-force inversion model

[0058] (1) Generation of inversion dataset: Using the trained PINN surrogate model, a large-scale inversion dataset is generated by sampling.

[0059] (2) Inversion model training: Training a feedforward neural network Its input is a normalized displacement vector. The output is the predicted load vector. The loss function is the mean squared error between the predicted and actual values:

[0060]

[0061] Step 3: Iterative Coupling Solution of the Support System

[0062] (1) Initialization: Set the initial value δ of the displacement vector. (0) , is usually set as the zero vector.

[0063] (2) Iterative solution: For the k-th iteration:

[0064] a. Inversion model evaluation, calculating the load vector for the current iteration: ;

[0065] b. The new displacement is obtained by solving the finite element model applied to the internal support system. ;

[0066] c. Calculate the relative error: If ϵ < τ (τ is the preset tolerance), then the iteration converges and the result is output.

[0067] d. Displacement update: If convergence is not achieved, update the displacement using the relaxation factor ω∈(0,1] and proceed to the next iteration.

Claims

1. A method for predicting the deformation of retaining walls in foundation pits based on physical information neural networks, characterized in that, The steps are as follows: Step 1: Construction of a neural network proxy model for the physical information of retaining walls based on multi-source data fusion; Step 2: Establishment of the displacement-force inversion model for the retaining wall; Step 3: Iterative coupling solution of the supporting system; (1) Model preparation: Obtain the finite element model of the support system based on the engineering design parameters; (2) Initialization: Set the initial displacement vector at the interface between the retaining wall and the support. ; (3) Iterative loop.

2. The method for predicting the deformation of retaining walls in foundation pits based on physical information neural networks according to claim 1, characterized in that, The specific implementation process of step one is as follows: (1) Construction of theoretical dataset: Based on the mechanical governing equations and geometric boundary conditions of the retaining wall, parametric finite element simulation is used to sample within the load parameter space, generating multiple sets of retaining wall displacement field data under various load conditions, thus forming a load-displacement theoretical dataset. ;in, For load vectors, For the corresponding displacement field data, This represents the total number of load-displacement theory data samples in the load-displacement theory dataset. (2) Construction of the actual test dataset: At the foundation pit construction site, a deployed visual inspection system acquires displacement images of preset measuring points on the retaining wall surface at each construction stage. After digital image processing technology is used to calculate and record the measured displacement data corresponding to the earth pressure at each construction stage, forming a load-displacement measured dataset. ;in, Let be the load vector obtained from the i-th field measurement. For corresponding The displacement vector of the preset measuring point, The total number of measured load-displacement data samples in the load-displacement measured data set, where the preset measuring points include at least the connection point between the retaining wall and the internal support, and the maximum deformation control point of the retaining wall; (3) Construction and hybrid training of physical information neural networks: Establish a deep neural network that takes spatial coordinates (x, z) and load vector f as input and displacement w corresponding to the spatial coordinates as output. As a proxy model for physical information neural networks, in which These are the network parameters to be trained. Load-displacement theory dataset With load-displacement measured dataset Using both as training samples, a hybrid loss function is constructed. Its expression is ,in For the physical residual terms based on the mechanical governing equations, This is the mean square error term of the measured data. and These are the weighting coefficients; the mixed loss function is minimized using the gradient descent algorithm. The physical information neural network proxy model is trained. .

3. The method for predicting the deformation of retaining walls in foundation pits based on physical information neural networks according to claim 2, characterized in that, The specific implementation process of step two is as follows: (1) Generation of inversion dataset: Using the physical information neural network surrogate model trained in step one Input a large number of randomly sampled load vectors The displacement field of the corresponding retaining wall is calculated, and the displacement vector at the interface between the retaining wall and the internal support is extracted. This forms a displacement-force paired inversion dataset. ;in, This represents the total number of displacement-force paired inversion data samples in the displacement-force paired inversion dataset. (2) Construction and training of displacement-force inversion model: Network construction: Establish a displacement vector at the interface between the retaining wall and the internal support. As input, with the corresponding load vector Feedforward neural network for output As a displacement-force inversion model; among which, These are the parameters to be trained for the network; Model training: Retrieving datasets using displacement-force pairings Using the mean square error between the predicted load and the actual load as training samples, the feedforward neural network is trained under supervision. Thus, a well-trained displacement-force inversion model is obtained.

4. The method for predicting the deformation of retaining walls in foundation pits based on physical information neural networks according to claim 3, characterized in that, The specific implementation process of step two (3) is as follows: For the k-th iteration: a. Displacement-force inversion model evaluation: Evaluate the displacement vector at the interface between the retaining wall and the support in the current iteration step. Input into the displacement-force inversion model trained in step two The reaction force of the retaining wall on the support system was calculated. ; b. Support system forward analysis: The reverse value of the reaction force... As a load, it is applied to the finite element model of the support system for mechanical analysis, and the new displacement vector of the support system at the connection interface is obtained by solving the problem. ; c. Convergence test: Calculate the new displacement vector With the current displacement vector The relative error between the two results; if the error is less than the preset tolerance, the iteration converges and the current result is output; otherwise, continue to the next step; d. Displacement Update: The interface displacement vector is updated using a relaxation algorithm. ;in, ω ∈ ( 0 , 1 ] As a relaxation factor, Let k be the displacement vector at the interface between the retaining wall and the support in the next step; then let k = k + 1, and return to step a for the next iteration.

5. An apparatus for implementing the deformation prediction method for foundation pit retaining walls based on physical information neural networks as described in any one of claims 1-4, characterized in that, The device includes: Data acquisition and processing module: This includes a visual inspection system deployed at the foundation pit site, used to acquire displacement image data of the retaining wall surface, and to calculate the measured displacement data of the preset measuring points of the retaining wall through image processing technology, forming a load-displacement measured dataset; Data processing and model training module: Consists of a computing server, used for: (1) Receive and store the load-displacement theoretical dataset generated by parametric finite element simulation and the load-displacement measured dataset transmitted by the data acquisition and processing module; (2) Construct and train a physical information neural network agent model using a hybrid loss function; (3) Use the trained physical information neural network proxy model to generate a displacement-force pairing dataset and train the displacement-force inversion model; (4) As construction progresses, the physical information neural network proxy model is updated using newly measured data; The coupled solution and result output module, implemented by the computation server, is used for: (1) Run the iterative coupling solution process of the support system, call the displacement-force inversion model and the finite element model of the support system for iterative calculation until convergence; (2) Visualize the final displacement field and internal force distribution results obtained from the solution.

Images