Foundation pit water inflow multi-source data intelligent prediction method
By incorporating the physical laws of groundwater seepage and data-driven methods into neural networks, and combining high-precision analytical or numerical solutions, the problems of dependence on a large amount of observation data and violation of physical laws in the prediction of water inflow in foundation pits have been solved, achieving high-precision and rapid prediction of water inflow.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CENT SOUTH UNIV
- Filing Date
- 2026-02-28
- Publication Date
- 2026-05-12
AI Technical Summary
In existing technologies, pure data-driven machine learning models require a large amount of high-quality observation data to predict the water inflow of foundation pits, and the prediction results may violate physical laws, with poor generalization and extrapolation capabilities.
The basic physical laws of groundwater seepage are integrated into the learning process of neural networks. By constructing a deep learning neural network and combining it with low-fidelity data generated from high-precision analytical or numerical solutions, a total loss function containing physical laws is constructed, and an optimization algorithm is used to minimize the loss function to train the neural network.
With limited observational data, accurate prediction of water inflow was achieved, reducing reliance on expensive monitoring data. The prediction results followed physical laws, improving prediction speed and accuracy.
Smart Images
Figure CN121743790B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of underground engineering technology, specifically to an intelligent prediction method for multi-source data on foundation pit water inflow. Background Technology
[0002] Foundation pit engineering is a crucial aspect of urban construction, and groundwater control is essential for safe construction. Accurately predicting the water inflow into the foundation pit is fundamental to developing economical and effective dewatering plans.
[0003] In recent years, purely data-driven machine learning models have been attempted for predicting groundwater inflow. These methods learn the mapping relationship between geological parameters, pit dimensions, and inflow volume solely from historical data, completely ignoring the fundamental physical laws governing groundwater seepage. This results in models requiring large amounts of high-quality observational data for training, and their predictions may violate physical laws, exhibiting poor generalization and extrapolation capabilities.
[0004] Therefore, there is an urgent need in this field for a method to predict the inflow of water into foundation pits that can overcome the above-mentioned shortcomings, so as to provide a scientific basis for optimizing construction parameters and formulating effective dewatering schemes. Summary of the Invention
[0005] This invention aims to overcome the shortcomings of existing technologies and provide an intelligent prediction method for multi-source data on foundation pit water inflow. This method integrates the fundamental physical laws of groundwater seepage into the learning process of a neural network, achieving a complementary advantage between physical laws and data-driven approaches. This invention can integrate low-fidelity data generated based on high-precision analytical or numerical solutions, even with only a limited amount of high-fidelity observational data, to achieve a scientifically accurate prediction of water inflow.
[0006] To achieve the above objectives, this invention provides an intelligent prediction method for multi-source data on foundation pit water inflow, comprising the following steps:
[0007] S1. During the construction of the foundation pit, the depth of dewatering within the foundation pit should be monitored simultaneously. Water level outside the foundation pit Pore water pressure at different depths inside and outside the foundation pit The actual water inflow into the foundation pit is monitored using a flow meter; and the depth of the foundation pit is obtained through engineering geological surveys or field tests. Soil permeability coefficient at the location ;
[0008] S2. Based on the geometric dimensions, excavation depth, and geological survey results of the foundation pit, clarify the calculation area and boundary of the seepage field; determine the governing equations within this area and the constant head and constant flow conditions on all boundaries; at the same time, define the head continuity and flow continuity conditions between the inner and outer areas of the foundation pit below the retaining structure and above the impermeable layer.
[0009] S3. Construct two deep learning neural networks corresponding to the inner and outer sides of the foundation pit, respectively; where the input of the deep learning neural network for the inner side of the foundation pit is spatial coordinates. Depth of water in the foundation pit Depth of impermeable layer Width of the inner side of the foundation pit and soil permeability coefficient The output is the predicted groundwater head value. and inflow For the deep learning neural network outside the foundation pit, its input is spatial coordinates. Water level outside the foundation pit Depth of impermeable layer Calculated width of the outer side of the foundation pit and soil permeability coefficient The output is the predicted groundwater head value. ;
[0010] S4. Construct a total loss function that incorporates physical laws. The total loss function consists of data loss terms. Loss term in the governing equation Boundary condition loss term and regional continuous condition loss terms Weighted linear combination constitutes:
[0011] ;
[0012] S5. Minimize the total loss function using an optimization algorithm. By iteratively updating the network parameters on the inner and outer sides of the foundation pit. This allows the neural network's predictions to fit the observed data while satisfying physical equations, boundary conditions, and regional continuity constraints.
[0013] S6. After training, input the parameters of future working conditions into the trained neural network for prediction to obtain the predicted value of the pit water inflow. .
[0014] Furthermore, the governing equation in step S2 is the groundwater seepage balance equation under steady-state conditions, and its expression is:
[0015]
[0016] in, For the total water head.
[0017] Furthermore, the data loss item Data loss term including neural network head prediction inside the foundation pit Data loss item for predicting water inflow volume from the neural network inside the foundation pit. And the data loss term for neural network head prediction on the outer side of the foundation pit. The data loss term integrates high-fidelity on-site monitoring data and low-fidelity data, and normalizes the errors. The expression is:
[0018] .
[0019] Furthermore, the loss term of the governing equation The loss term of the head control equation, calculated based on automatic differentiation technology, includes the head control equation predicted by the neural network inside the foundation pit. And the loss term of the head control equation predicted by the neural network on the outside of the foundation pit. Its expression is:
[0020] .
[0021] Furthermore, the boundary condition loss term Including the constant head boundary loss term of the neural network inside the foundation pit and constant flow boundary loss term And the neural network constant head boundary loss term outside the foundation pit and constant flow boundary loss term Furthermore, both the constant head boundary loss term and the constant flow boundary loss term were normalized; the boundary condition loss term The expression is:
[0022] .
[0023] Furthermore, the inter-regional continuous conditional loss term This includes the head loss terms of the neural networks inside and outside the foundation pit, located between the permeable layer and the retaining structure of the foundation pit. and flow loss items Furthermore, both the head loss term and the flow loss term have been normalized; the inter-regional continuity condition loss term The expression is:
[0024] .
[0025] Furthermore, the optimization process in step S5 adopts a phased strategy: first, the Adam optimizer is used to achieve rapid initial convergence of the total loss function; then, after the loss decreases slowly, the L-BFGS optimizer is switched to continue fine optimization of the total loss function to obtain a more accurate solution.
[0026] Furthermore, in step S6, the predicted value of the pit water inflow... The calculation formula is:
[0027]
[0028] in, The soil permeability coefficient, To calculate the cross-section, For the water head at The gradient in the direction is also obtained through a trained network and automatic differentiation techniques.
[0029] Compared with the prior art, the present invention has the following beneficial effects:
[0030] (1) By incorporating the control equation and boundary conditions as constraints into the loss function, this invention ensures that the prediction results of the neural network follow physical laws and avoids the physical inconsistencies that may arise from a purely data-driven model.
[0031] (2) This invention integrates a small amount of high-fidelity monitoring data and a large amount of low-fidelity numerical solution data, and uses physical laws as strong prior knowledge, which greatly reduces the dependence on expensive and scarce field monitoring data.
[0032] (3) Once the network training is completed, the prediction of the inflow under the new working condition is only a forward propagation, which is much faster than traditional numerical simulation software and is very suitable for parameter inversion and rapid scheme comparison.
[0033] (4) The loss term of this invention has been normalized to avoid the large difference in magnitude between different loss terms, which would cause the optimizer to favor the dominant term and ignore other important constraints, making the training process more stable and enhancing stability.
[0034] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description
[0035] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:
[0036] Figure 1 This is a flowchart of a multi-source data intelligent prediction method for foundation pit water inflow according to the present invention;
[0037] Figure 2 This is a schematic diagram of the geometric model for calculating the seepage field in the foundation pit in this invention;
[0038] Figure 3This is a schematic diagram of the neural network structure for the physical information of water inflow in the foundation pit in this invention. Detailed Implementation
[0039] The present invention will now be described in detail with reference to the embodiments shown in the accompanying drawings. However, it should be noted that these embodiments are not intended to limit the present invention. Equivalent transformations or substitutions in function, method, or structure made by those skilled in the art based on these embodiments are all within the scope of protection of the present invention.
[0040] Please see Figure 1 This embodiment provides a method for intelligent prediction of foundation pit water inflow from multiple sources, which includes the following steps:
[0041] S1. Automated monitoring will be implemented during the dewatering construction of the foundation pit. Water level observation wells will be installed inside the foundation pit to monitor the dewatering depth. Multiple water level observation wells were installed outside the foundation pit to monitor the static water level outside the pit. Pore water pressure gauges were installed at different depths inside and outside the foundation pit to monitor the water pressure at different depths. The data was then converted into head. A flow meter was installed on the main dewatering well pipe of the foundation pit to monitor the real-time water inflow. Simultaneously, based on the geological survey report, the data was obtained as the depth increased. Variation in soil permeability coefficient .
[0042] S2. When the length of the excavation pit is much greater than the inner width of the excavation pit. When the cross-section is parallel to the width, the seepage field can be approximated as planar seepage. Based on the symmetry of the foundation pit seepage, half of the cross-section is analyzed, as shown in Figure 2.
[0043] According to the geological survey report, the lower boundary of the calculation area is determined to be the depth of the impermeable layer. The outer boundary is taken to a position that is far enough away from the edge of the excavation pit (usually 3-5 times the excavation depth). This is to ensure that the boundary water level is not disturbed by precipitation. In this embodiment, the total head is... Groundwater seepage is considered as steady-state flow, and its governing equation is:
[0044] .
[0045] The water level outside the foundation pit is the constant head boundary, i.e. The water level inside the foundation pit is also a constant head boundary, i.e. The bottom of the excavation pit is an impermeable boundary, and its boundary conditions are as follows:
[0046]
[0047] Ignoring the permeability of the retaining structure, the boundary conditions at the retaining structure above the inner and outer sides of the foundation pit are as follows:
[0048]
[0049] Due to the symmetry of the seepage in the foundation pit, the boundary conditions in the middle of the inner side of the foundation pit are as follows:
[0050]
[0051] The outer boundary of the foundation pit is considered to be an impermeable boundary.
[0052]
[0053] The continuity condition of the area from below the retaining structure to above the bottom impermeable layer, and the area inside and outside the excavation pit, is as follows:
[0054]
[0055]
[0056] in, , These represent the water head inside and outside the foundation pit, respectively.
[0057] S3. Construct two fully connected deep neural networks (DNNs) to simulate the seepage fields on the inner and outer sides of the foundation pit, respectively. For example... Figure 3 As shown, the neural network input layer inside the foundation pit has 5 neurons, each corresponding to a spatial coordinate. Depth of water in the foundation pit Depth of impermeable layer Width of the inner side of the foundation pit and soil permeability coefficient The output layer has two neurons, which output the predicted median head value. and the predicted water inflow of the foundation pit The neural network on the outer side of the foundation pit has 5 neurons, each corresponding to a spatial coordinate. Water level outside the foundation pit Depth of impermeable layer Calculated width of the outer side of the foundation pit and soil permeability coefficient The output layer has one neuron, which outputs the predicted outer head value. Each deep neural network contains 5 hidden layers, with 50 neurons per layer. The activation function is chosen to have a smooth second derivative, such as the tanh function, to facilitate the calculation of the loss term in the control equation. The weights and bias parameters of the neural networks inside and outside the pit are specified. , These are the parameters to be trained.
[0058] S4. To ensure that the predictions of the deep neural network conform to physical laws, construct a total loss function that incorporates physical laws. The loss function consists of four weighted parts: .in, For the data loss term, the normalized mean square error is calculated between the network predictions and the monitoring data (high-fidelity data) and the data generated from high-precision numerical solutions or analytical solutions (low-fidelity data). To determine the loss term in the control equation, a large number of random configuration points are collected within the computational domain. The second-order partial derivative of the predicted head with respect to spatial coordinates is calculated using automatic differentiation techniques, and then substituted into the control equation to calculate the normalized mean square error of the residual. For the boundary condition loss term, point sets are collected on various boundaries, and the normalized mean square error of the predicted head or its normal gradient with respect to the boundary conditions is calculated. For the regional continuous conditional loss term, a set of points is collected at the interface between the inside and outside regions of the foundation pit, and the normalized mean square error between the predicted head value and the normal gradient of the networks on both sides is calculated. , , and These are the weighting coefficients for each loss term.
[0059] Because the numerical ranges of different loss terms can vary significantly, the optimizer may favor the dominant term while ignoring other important constraints. Therefore, this embodiment normalizes the loss terms, specifically:
[0060] (1) Data loss items This includes the data loss term between the water head predicted by the neural network inside the foundation pit and the known observed water head. Data loss term between the water inflow predicted by the neural network on the inner side of the foundation pit and the observed water inflow. And the data loss term between the water head predicted by the neural network on the outside of the foundation pit and the known observed water head. Its expression is:
[0061]
[0062] Considering the limited amount of monitoring data in actual engineering projects, this embodiment uses the monitoring data as high-fidelity data. Data generated using high-precision analytical or numerical solutions is used as low-fidelity data.
[0063] In this embodiment, 20 pore water pressure gauges are installed within the foundation pit, thus providing 20 head observations. For the neural network inside the foundation pit, 100 placement points are randomly generated within the domain to calculate data loss. The data loss term is normalized by calculating the relative error.
[0064] 1) Data loss term between predicted head and known observed head for:
[0065]
[0066]
[0067]
[0068] in, To predict the head value; For high-fidelity head data; Low-fidelity head data; , The weighting coefficients for the error terms of high-fidelity data and low-fidelity data can be set to 0.7 and 0.3, respectively. , These are the normalization coefficients for the head data loss terms in high-fidelity and low-fidelity data, respectively.
[0069] 2) Data loss term between the predicted inflow volume and the observed inflow volume of the neural network inside the foundation pit. for:
[0070]
[0071] in, For high-fidelity head data; This is low-fidelity head data.
[0072] 3) Assume there are 30 pore water pressure gauges within the foundation pit, providing 30 head observations. For the neural network inside the foundation pit, 100 placement points are randomly generated within the domain to calculate data loss. The loss term between the predicted head and the known observed head is... for:
[0073]
[0074]
[0075]
[0076] in, , These are the normalization coefficients for the head data loss terms in high-fidelity and low-fidelity data, respectively.
[0077] (2) Loss term in the control equation Including the loss term of the head control equation predicted by the neural network inside the foundation pit. And the loss term of the head control equation predicted by the neural network on the outside of the foundation pit. Its expression is:
[0078] .
[0079] 1) Randomly select a large number of configuration points within the calculation area, and use automatic differentiation technology to calculate the predicted head at these points. Spatial coordinates The second-order partial derivatives are calculated and substituted into the governing equations to calculate the residuals. For the neural network inside the pit, 1000 placement points are randomly generated within the domain to calculate the physical loss.
[0080]
[0081]
[0082] in, The normalization coefficient is the loss term of the neural network control equation within the foundation pit.
[0083] 2) For the neural network outside the foundation pit, 2000 placement points are randomly generated within the domain to calculate the physical loss:
[0084]
[0085]
[0086] in, The normalization coefficient is the loss term of the control equation of the neural network outside the foundation pit.
[0087] (3) Boundary condition loss terms include the neural network constant head boundary loss term inside the foundation pit. and constant flow boundary loss term And the neural network constant head boundary loss term outside the foundation pit and constant flow boundary loss term Its expression is:
[0088] .
[0089] In one specific implementation, for the neural network inside the foundation pit, 50 points are uniformly selected on the constant head boundary, 50 points are uniformly selected on the bottom boundary, and 100 points are uniformly selected on both side boundaries to calculate the head boundary condition loss.
[0090]
[0091]
[0092]
[0093]
[0094]
[0095] in, The normalization coefficient for the loss term of the neural network head boundary condition within the foundation pit; , These are the normalization coefficients for the bottom boundary conditions and side boundary loss terms of the neural network flow within the foundation pit, respectively.
[0096] In one specific implementation, for the neural network outside the foundation pit, 100 points are uniformly selected on the constant head boundary, 100 points are uniformly selected on the bottom boundary, and 200 points are uniformly selected on both side boundaries to calculate the boundary condition loss. Specifically:
[0097]
[0098]
[0099]
[0100]
[0101]
[0102] in, The normalization coefficient for the loss term of the neural network head boundary condition outside the foundation pit; , These are the normalization coefficients for the bottom boundary conditions and side boundary loss terms of the neural network flow outside the foundation pit, respectively.
[0103] (4) Loss term due to continuity conditions between regions This includes the head loss term for both the inner and outer neural networks of the foundation pit, located between the permeable layer and the retaining structure of the foundation pit. and flow loss items The specific expression is:
[0104]
[0105] In one specific implementation, 200 points are uniformly selected at the boundary of the area below the permeable layer and above the foundation pit retaining structure for calculating the area continuity condition loss term; specifically:
[0106]
[0107]
[0108]
[0109]
[0110] in, , These are the normalization coefficients for the loss terms under continuous conditions of head and flow between regions, respectively.
[0111] S5, using the dewatering depth inside the foundation pit over the past 10 days. Water level outside the foundation pit Water pressure at different depths and actual water inflow The monitoring data is used to train the neural network. Specifically, a phased optimization strategy is adopted: first, the Adam optimizer is used for initial training, leveraging its adaptive learning rate characteristic to achieve rapid convergence; when the loss decreases slowly, the L-BFGS optimizer is switched to perform fine-tuning to obtain a more accurate solution. To prevent overfitting, new configuration points are continuously and randomly sampled in the computational domain and boundaries during training. The training objective is to find a set of optimal network parameters. This results in the total loss function minimize.
[0112] S6. After the training is completed, the planned dewatering depth inside the foundation pit for the following day will be determined. Water level outside the foundation pit By inputting the model, the predicted value of the foundation pit water inflow for the following day can be obtained. The prediction of water inflow is achieved by generating dense integration points on the depth plane at the bottom of the excavation pit. For each integration point, a trained inner neural network is used to obtain the predicted water head. And its vertical gradient is calculated using automatic differentiation techniques. Subsequently, based on Darcy's law, the total flow rate at the bottom of the foundation pit, i.e., the predicted inflow of water into the foundation pit, was calculated through numerical integration. :
[0113]
[0114] in, The soil permeability coefficient, To calculate the cross-section, For the water head at Gradient of direction.
[0115] The present invention provides an intelligent prediction method for multi-source data of foundation pit water inflow, which achieves a deep integration of physical mechanisms and data-driven methods. While ensuring that the prediction results strictly conform to physical laws, it reduces the dependence on a large amount of observation data, improves the accuracy and reliability of prediction, and provides better decision support for foundation pit dewatering design.
[0116] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for intelligent prediction of foundation pit water inflow from multiple sources, characterized in that, Includes the following steps: S1. During the construction of the foundation pit project, the water depth inside the foundation pit, the water level outside the foundation pit, and the pore water pressure at different depths inside and outside the foundation pit are monitored simultaneously, and the actual water inflow of the foundation pit is monitored using a flow meter; and the soil permeability coefficient at the depth of the foundation pit is obtained through engineering geological survey or field test. S2. Based on the geometric dimensions, excavation depth, and geological survey results of the foundation pit, clarify the calculation area and boundary of the seepage field; determine the governing equations within this area and the constant head and constant flow conditions on all boundaries; at the same time, define the head continuity and flow continuity conditions between the inner and outer areas of the foundation pit below the retaining structure and above the impermeable layer. S3. Construct two deep learning neural networks corresponding to the inside and outside of the foundation pit, respectively. For the deep learning neural network inside the foundation pit, the inputs are spatial coordinates, the depth of water level inside the foundation pit, the depth of the impermeable layer, the width of the inside of the foundation pit, and the soil permeability coefficient. The outputs are the predicted groundwater head and the inflow rate. For the deep learning neural network outside the foundation pit, the inputs are spatial coordinates, the water level outside the foundation pit, the depth of the impermeable layer, the calculated width of the outside of the foundation pit, and the soil permeability coefficient. The output is the predicted groundwater head. S4. Construct a total loss function incorporating physical laws. This total loss function is a weighted sum of data loss terms, governing equation loss terms, boundary condition loss terms, and inter-regional continuity condition loss terms; where: The data loss item Data loss term including neural network head prediction inside the foundation pit Data loss item for predicting water inflow volume from the neural network inside the foundation pit. And the data loss term for neural network head prediction on the outer side of the foundation pit. The data loss term integrates high-fidelity on-site monitoring data and low-fidelity data, and normalizes the errors. The expression is: ； The loss term of the governing equation The loss term of the head control equation, calculated based on automatic differentiation technology, includes the head control equation predicted by the neural network inside the foundation pit. And the loss term of the head control equation predicted by the neural network on the outside of the foundation pit. Its expression is: ； The boundary condition loss term Including the constant head boundary loss term of the neural network inside the foundation pit and constant flow boundary loss term And the neural network constant head boundary loss term outside the foundation pit and constant flow boundary loss term Furthermore, both the constant head boundary loss term and the constant flow boundary loss term were normalized. The inter-regional continuous conditional loss term This includes the head loss terms of the neural networks inside and outside the foundation pit, located between the permeable layer and the retaining structure of the foundation pit. and flow loss items Furthermore, both the head loss and flow loss terms were normalized. S5. Minimize the total loss function using an optimization algorithm, and iteratively update the network parameters on the inner and outer sides of the pit. ; S6. After training is completed, the parameters of future working conditions are input into the trained neural network for prediction to obtain the predicted value of the pit water inflow.
2. The intelligent prediction method for multi-source data of foundation pit water inflow according to claim 1, characterized in that, The governing equation in step S2 is the groundwater seepage equilibrium equation under steady-state conditions, and its expression is: in, For the total water head.
3. The intelligent prediction method for multi-source data of foundation pit water inflow according to claim 1, characterized in that, The optimization process in step S5 adopts a phased strategy: first, the Adam optimizer is used to achieve rapid initial convergence of the total loss function; then, after the loss decreases slowly, the L-BFGS optimizer is switched to continue fine optimization of the total loss function.
4. The intelligent prediction method for multi-source data of foundation pit water inflow according to claim 1, characterized in that, In step S6, the predicted value of the pit water inflow... The calculation formula is: in, The soil permeability coefficient, To calculate the cross-section, For the water head at Gradient of direction.