A method and system for analyzing consolidation process of multi-pore geotechnical medium based on KAN

Abstract

The application discloses a kind of based on KAN's multiple pore rock-soil medium consolidation process analysis method and system, belong to the field of soil consolidation analysis.This method includes: obtaining the data including time, depth and each pore system pore water pressure in the consolidation process of multiple pore rock-soil medium, establishes data set and carries out pre-processing;KAN is trained to obtain the control equation describing the consolidation process of multiple pore rock-soil medium by inversion;PiKAN based on physical information is constructed, the control equation and the initial condition and boundary condition of consolidation process are used as physical constraint, and embedded in loss function;PiKAN is trained using the pre-processed data set, and the pore water pressure of each pore system of multiple pore rock-soil medium at different times and depths is solved.The KAN based on physics and data driving can quickly and effectively obtain the pore water pressure of multiple pore rock-soil medium with less test data, and provide technical support for related engineering stability evaluation.

Description

Technical Field

[0001] This invention relates to the field of soil consolidation analysis, and more specifically to a method and system for analyzing the consolidation process of multi-porous soil media based on Kolmogorov-Arnold Networks (KAN). Background Technology

[0002] Multiporous media, such as blocky soil mounds and fractured rock masses, are widely present in nature and engineering. These media typically exhibit heterogeneous, multi-scale pore systems, such as micropores within soil blocks and macropores between soil blocks. This dual or multi-pore structure significantly alters the evolution of pore water pressure, thereby affecting the consolidation, settlement, and engineering stability of soil and rock media. Accurately predicting the spatiotemporal evolution of pore water pressure in multiporous media under load is crucial for assessing the safety and long-term service performance of related projects, such as embankment projects, dams, and geological disaster prevention projects.

[0003] Traditional prediction methods primarily rely on laboratory experiments and field monitoring. These methods are costly, time-consuming, and limited in the number of measurement points, making it difficult to obtain complete information across the entire field. In recent years, machine learning methods have offered new insights into consolidation analysis. However, traditional purely data-driven models, such as support vector machines, random forests, and neural networks, are essentially black-box models driven by data. Their performance is highly dependent on the scale and quality of the training data, and their application is limited when data is difficult to obtain. To reduce dependence on data volume while ensuring prediction accuracy, existing physical constraints (such as Terzaghi's consolidation theory) can be embedded as constraints into the loss function, making the prediction results approximate the governing equations. However, for multiporous media, their unique pore structure often makes the governing equations complex and difficult to predetermine, limiting their application in complex geotechnical problems where the governing equations are unknown or uncertain.

[0004] Therefore, there is an urgent need for an efficient, accurate, and data-intensive intelligent analysis method for the consolidation process of multi-porous media. Summary of the Invention

[0005] In view of the above problems, the present invention is proposed to provide a KAN-based method and system for analyzing the consolidation process of multiporous soil and rock media, which overcomes or at least partially solves the above problems. It aims to solve the technical difficulties of existing methods in analyzing the consolidation process of multiporous soil and rock media, which have strong data dependence or require prior knowledge of precise control equations.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, embodiments of the present invention provide a method for analyzing the consolidation process of multi-porous soil and rock media based on KAN, comprising the following steps:

[0008] Data preprocessing steps: Obtain data including time, depth, and pore water pressure of each pore system during the consolidation process of multi-porous soil media, establish a dataset, and preprocess it;

[0009] Control equation inversion steps: Based on the preprocessed dataset, train KAN to invert and obtain the control equations describing the consolidation process of the multi-porous soil and rock media;

[0010] Model construction steps: Construct a PiKAN based on physical information, and use the inverted governing equations and the initial and boundary conditions of the consolidation process of the multi-porous soil and rock medium as physical constraints, and embed them into the loss function of the PiKAN.

[0011] The steps for solving pore water pressure are as follows: PiKAN is trained using the preprocessed dataset, and the pore water pressure of each pore system in the multi-porous soil medium at different times and depths is solved based on the trained PiKAN.

[0012] Preferably, the data preprocessing step includes:

[0013] The first part of the data was generated using the analytical solution of the consolidation process of multi-porous soil media.

[0014] The second part of the data on the consolidation of multi-porous soil media is obtained through field monitoring or indoor tests.

[0015] The first part of the data and the second part of the data are fused and preprocessed to form the final dataset for training; the dataset includes: time, depth and pore water pressure data of each pore system during the consolidation process of multi-porous soil media.

[0016] Preferably, the preprocessing includes:

[0017] Calculate the first and second partial derivatives of the pore water pressure with respect to depth;

[0018] Calculate the first partial derivative of the pore water pressure with respect to time;

[0019] The data on pore water pressure and its partial derivatives are normalized.

[0020] Preferably, the governing equation inversion step specifically includes:

[0021] The normalized pore water pressure data and its first-order partial derivatives with respect to time and depth are used as inputs to KAN, and the second-order partial derivatives of pore water pressure with respect to depth are used as outputs.

[0022] Through stepwise training, pruning, and symbolic regression, the final structure and activation function of the KAN network are determined, and its input-output relationship is characterized as the governing equation for the consolidation process of the multi-porous soil and rock medium.

[0023] Preferably, in the model building step, the loss function is represented as a weighted sum of multiple error terms:

[0024]

[0025] in, L 1 represents the mean square error between the predicted pore water pressure and the measured data, ensuring that the model prediction results closely approximate the measured data. L 2 represents the mean square error of the control equations determined by KAN, ensuring that the model satisfies the determined control equations; L 3 and L 4 represents the mean square error of the boundary conditions and initial conditions corresponding to the consolidation process of multi-porous soil media, to ensure that the model meets the boundary conditions and initial conditions; w 1, w 2, w 3, w 4 represents the weighting coefficients for each error term, used to balance the contribution of each error term to the final total error; L This represents the total error.

[0026] Preferably, the input variables of the PiKAN network are the time and depth of the consolidation process in the multi-porous soil medium; the output variable is the pore water pressure of each pore system.

[0027] Secondly, embodiments of the present invention provide a KAN-based system for analyzing the consolidation process of multi-porous soil and rock media, comprising:

[0028] The data preprocessing module is used to import data including time, depth, and pore water pressure of each pore system during the consolidation process of multi-porous soil media, establish a dataset, and preprocess it.

[0029] The control equation inversion module is used to train KAN based on the preprocessed dataset to invert the control equations describing the consolidation process of the multi-porous soil and rock media.

[0030] The model building module is used to construct a PiKAN based on physical information. It uses the inverted governing equations and the initial and boundary conditions of the consolidation process of the multi-porous soil and rock media as physical constraints and embeds them into the loss function of the PiKAN.

[0031] The pore water pressure solution module is used to train the PiKAN using the preprocessed dataset and to use PiKAN to solve the pore water pressure of each pore system in a multi-porous soil medium at different times and depths.

[0032] Thirdly, embodiments of the present invention provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the KAN-based method for analyzing the consolidation process of multi-porous soil media as described in any one of the first aspects.

[0033] Fourthly, embodiments of the present invention provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the KAN-based method for analyzing the consolidation process of multi-porous soil and rock media as described in any one of the first aspects.

[0034] The beneficial effects of the above-described technical solutions provided in the embodiments of the present invention include at least the following:

[0035] 1. Deep Integration of Data and Physics: This invention employs a two-step approach using KAN (Knowledge-Agent Relationship). The first step learns physical laws from a limited dataset to derive the inverted governing equations. The second step embeds these inverted governing equations as physical constraints into the model error function, enabling rapid prediction of pore water pressure in slabs at different times and depths. This invention deeply integrates data-driven and physics-driven approaches, reducing reliance on massive training data while ensuring strict physical consistency of the prediction results.

[0036] 2. Solving the problem of unknown governing equations: For consolidation problems of multiporous media with complex or unknown governing equations, this invention provides a universal solution. Without pre-defining the equation form, KAN can directly deduce the implicit governing equations from the data, overcoming the limitations of the traditional PINN method.

[0037] 3. High accuracy and strong generalization ability: By introducing physical constraints, the method of this invention can still obtain high-accuracy and generalizable prediction results even with small sample sizes, which is significantly better than pure data-driven models and is particularly suitable for data-scarce scenarios in geotechnical engineering.

[0038] 4. End-to-end intelligent analysis system: This invention constructs a complete analysis system from data preprocessing, equation inversion, model building to pressure solution, realizing integrated, automated intelligent analysis of the consolidation process of multi-porous media, which greatly improves the efficiency and reliability of engineering analysis. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0040] Figure 1 This is a flowchart of the KAN-based method for analyzing the consolidation process of multi-porous soil and rock media provided in this embodiment of the invention.

[0041] Figure 2 This is a graph showing the inversion error of the control equation versus the number of iterations provided in this embodiment of the invention.

[0042] Figure 3 This is a graph showing the error loss versus the number of iterations provided in an embodiment of the present invention.

[0043] Figure 4a This is a diagram showing the predicted pore water pressure within a soil block based on the analytical solution data provided in this embodiment of the invention.

[0044] Figure 4b This is a diagram showing the predicted pore water pressure between soil blocks based on the analytical solution data provided in this embodiment of the invention.

[0045] Figure 5 This is a diagram showing the predicted pore pressure within soil blocks using PiKAN after training, as provided in this embodiment of the invention.

[0046] Figure 6 This is a diagram showing the predicted pore pressure between soil blocks using PiKAN after training, as provided in this embodiment of the invention.

[0047] Figure 7 This is a block diagram of the KAN-based consolidation process analysis system for soil and rock media provided in this embodiment of the invention.

[0048] Figure 8 This is a structural diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] Example 1:

[0051] This invention discloses a method for analyzing the consolidation process of multi-porous soil and rock media based on KAN, such as... Figure 1 As shown, it includes the following steps S1~S4:

[0052] S1. Data preprocessing steps: Obtain data including time, depth and pore water pressure of each pore system during the consolidation process of multi-porous soil media, establish a dataset and preprocess it.

[0053] In this embodiment, the method of the present invention is verified by the block soil consolidation process. The block soil has a dual pore structure, and its pore system includes the pore system inside the soil block and the pore system between soil blocks.

[0054] First, a large amount of data was generated using the analytical solution of block soil consolidation. Simultaneously, combined with field or laboratory experimental measurements, a time-inclusive framework was established. t ,depth x pore water pressure within the soil block p 1. Pore water pressure between soil blocks p 2 databases.

[0055] Secondly, after generating data using analytical solutions from the data obtained through the above two methods, the first 10% and the last 10% of the data can be removed, and the middle 80% of the data can be used to build a basic database. Then, the data can be combined with field or indoor test data to form the final database.

[0056] Then, based on the established database, p 1 and p 2 pairs x and t Find the first and second partial derivatives, including p 1,x , p 2,x , p 1,t , p 2,t , p 1,xx and p 2,xx ;

[0057] in, p 1,x , p 2,x They represent p 1 and p 2 pairs of depth x The first derivative of each of them reflects the rate of change of pore water pressure along depth;

[0058] p 1,xx and p2,xx They represent p 1 and p 2 pairs of depth x The second-order partial derivative;

[0059] p 1,t and p 2,t They represent p 1 and p 2 pairs of time t The first-order partial derivative reflects the rate of change of pore water pressure over time.

[0060] Finally, all pore water pressures and their partial derivatives are normalized using a min-max normalization method to eliminate errors caused by data scaling. The specific formula is as follows:

[0061] 1) Pore water pressure within the soil block p Normalization of 1:

[0062]

[0063] in, p 1,max , p 1,min and They are respectively p The maximum and minimum values ​​of 1, as well as the normalized data, are calculated using a similar formula for the normalization of other partial derivative terms.

[0064] 2) Pore water pressure between soil blocks p Normalization of 2:

[0065]

[0066] in, p 2,max , p 2,min and They are respectively p The maximum and minimum values ​​of 2, and the normalized data.

[0067] 3) p 1 pair of depths x first derivative p 1,x Normalization:

[0068]

[0069] in, p 1,x max , p 1,x min and They are respectively p1,x The maximum value, minimum value, and normalized data.

[0070] 4) p 2 pairs of depth x first derivative p 2,x Normalization:

[0071]

[0072] in, p 2,x max , p 2,x min and They are respectively p 2,x The maximum value, minimum value, and normalized data.

[0073] 5) p 1 pair of time t First-order partial derivatives p 1,t Normalization:

[0074]

[0075] in, p 1,t max , p 1,t min and They are respectively p 1,t The maximum value, minimum value, and normalized data.

[0076] 6) p 2 pairs of time t First-order partial derivatives p 2,t Normalization:

[0077]

[0078] in, p 2,t,max , p 2,t,min and They are respectively p 2,t The maximum value, minimum value, and normalized data.

[0079] 7) p 1 pair of depths x The second derivative p 1,xx Normalization:

[0080]

[0081] in, p 1,xx max , p 1,xx min and They are respectively p 1,xx The maximum value, minimum value, and normalized data.

[0082] 8) p 2 pairs of depth x Second-order partial derivatives p 2,xx Normalization:

[0083]

[0084] in, p 2,xx,max , p 2,xx,min and They are respectively p 2,xx The maximum value, minimum value, and normalized data.

[0085] After normalization, the values ​​of all data are scaled to the range of [0, 1], which can eliminate the impact of differences in the dimensions and orders of magnitude of different physical quantities on the model performance.

[0086] S2. Control equation inversion step: Based on the preprocessed dataset, train KAN to invert and obtain the control equations describing the consolidation process of the multi-porous soil and rock medium.

[0087] The normalized pore water pressure data and its first-order partial derivatives with respect to time and depth are used as inputs to the KAN, and the second-order partial derivatives of pore water pressure with respect to depth are used as outputs; that is, the partial derivatives of time and depth are used as the inputs and outputs of the KAN, in the following form:

[0088]

[0089]

[0090] Relevant hyperparameters were determined through trial and error, followed by stepwise training, pruning, and symbolic regression to determine the final structure and activation function of the KAN. The input-output relationship represents the governing equations for the consolidation process of the multi-porous soil and rock media. The final determined governing equations are as follows:

[0091] Among them, the governing equations include p 1,xx and p 2,xxThe two governing equations are related to the minimum and maximum values ​​of the partial derivative terms, indicated by the subscripts min and max.

[0092] S3. Model Construction Steps: Constructing a PiKAN based on physical information The inverted governing equations, as well as the initial and boundary conditions of the consolidation process of the multi-porous soil medium, are used as physical constraints and embedded into the PiKAN loss function.

[0093] The initial condition refers to the time at the start of the consolidation process. t When = 0, this represents the initial distribution of the two types of pore water pressure throughout the entire soil mass. Boundary conditions refer to the conditions underway during the consolidation process. t >0 represents the physical constraints that the pore water pressure or its gradient at the top and bottom boundaries of the soil mass must satisfy. Initial conditions define the state at the start of the consolidation process, while boundary conditions define the constraint rules of the soil boundaries during consolidation. The governing equations, initial conditions, and boundary conditions are embedded as key physical constraints into the loss function of the physical information PiKAN, ensuring that the prediction results of the trained model comply with basic physical laws.

[0094] Specifically, the governing equations determined in step S2 above are used as physical constraints, and combined with the initial and boundary conditions of the consolidation process of multi-porous soil media, a loss function of PiKAN is constructed, which is expressed as follows:

[0095]

[0096] in, L 1 represents the mean square error between the predicted pore water pressure and the measured data, ensuring that the model prediction results closely approximate the measured data. L 2 represents the mean square error of the control equations determined by KAN, ensuring that the model satisfies the determined control equations; L 3 and L 4 represents the mean square error of the boundary conditions and initial conditions corresponding to the consolidation process of multi-porous soil media, to ensure that the model meets the boundary conditions and initial conditions; w 1, w 2, w 3, w 4 represents the weighting coefficients for each error term, used to balance the contribution of each error term to the final total error; L The mean squared error is expressed as follows: The mean squared error of each term is represented by the following formula:

[0097]

[0098]

[0099]

[0100]

[0101] Among them, subscript a and p These represent the actual value and the measured value of the data, respectively. N Indicates the size of the dataset. p 10 and p 20 These represent the initial values ​​of pore water pressure within and between soil blocks, respectively. h Indicates the thickness of the soil layer in the block-shaped soil mound; N This represents the total amount of data in the dataset, where subscripts 1, 2, 3, and 4 represent data items, governing equation items, boundary condition items, and initial condition items, respectively. C 11 - C 24 All parameters are derived from the consolidation control equations for blocky soil mounds determined by KAN, and can be calculated using the following formula:

[0102] , , , ;

[0103] , , , ;

[0104] in, γ w The specific gravity of water; a =1 / ( λ +2 G ), λ Let Lamé constant be . G Shear modulus; k 1 and k 2 represents the permeability coefficient within and between soil blocks, respectively; α 1 and α 2 represents the compressibility coefficient of water within and between soil blocks, respectively; β 1 and β 2 represents the contribution of strain rate within and between soil blocks to the total strain rate, respectively; w This is a fluid transport parameter used to describe the ease with which water can be exchanged within and between soil blocks.

[0105] The input variable for PiKAN is the time of the consolidation process in multi-porous soil media. t and depth x The output variable is the pore water pressure of each pore system, including the pore water pressure within the soil block.p 1. Pore water pressure between soil blocks p 2.

[0106] S4. Pore water pressure solution steps: Train the PiKAN network using the preprocessed dataset, and solve the pore water pressure of each pore system in the multi-porous soil medium at different times and depths based on the trained physical information PiKAN network.

[0107] The hyperparameters of the established PiKAN were determined using a trial-and-error method, and the model was then trained to converge based on the established dataset.

[0108] PiKAN's input is spatiotemporal coordinates ( x , t The output is the predicted pore water pressure. p 1, p 2) Train the network using the dataset prepared in S1, minimizing the loss function using an optimizer such as L-BFGS. L Once training converges, the trained PiKAN can be used as a surrogate model, inputting any spatiotemporal coordinates ( x , t This allows for the rapid calculation of the corresponding pore water pressure within the soil block. p 1. Pore water pressure between soil blocks p 2.

[0109] In this embodiment, by using time and depth as input variables of KAN, it employs a combination of automatic differentiation and backpropagation to calculate the derivative terms in the control equation, and embeds the control equation, initial conditions, and boundary conditions into the loss function to establish a PiKAN based on physical data dual-drive, and trains iteratively to solve the pore water pressure inside soil blocks and between soil blocks at different locations and times.

[0110] Specifically, the hyperparameters of KAN used to determine the governing equations and PiKAN used to solve the pore water pressure include network width, network depth, spline function order and number of meshes, and optimizer. These can be adjusted to ensure the network's fitting ability and computational efficiency.

[0111] Specifically, for porous structures (including microporous, mesoporous, and macroporous systems), the KAN input term can be expanded to the pore water pressure partial derivative term of each porous system. The consolidation control equation of the porous system is inverted through the same multi-step training strategy, and then embedded into the PiKAN loss function to solve the pore water pressure of the porous system.

[0112] Example 2:

[0113] In this embodiment, taking one-dimensional consolidation of a soil mound as an example, analytical solutions are used to generate data. The soil mound depth is 18m, the preload is 100kPa, and the consolidation time is 20 days. Soil mound stiffness... E Compared to Poisson ν The values ​​are 1000 kPa and 0.33 respectively, and the specific gravity of water is 10 kN / m³. 3 Subscripts 1 and 2 represent the intra- and inter-block systems, respectively. Permeability coefficient. k 1 and k 2 are 6.18×10 - 10 m / s and 2.47×10 -6 m / s, the compressibility constant of water α 1 and α 2 are 1.35×10 -7 Pa -1 and 5.40×10 -7 Pa -1 The ratio of the strain rate within and between soil blocks to the total strain rate. β 1 and β 2 are 0.6 and 0.4 respectively. The governing equations for soil consolidation determined by the analytical method are:

[0114]

[0115]

[0116] The analytical solution generated 2500 sets of data (including data from 50 time points and 50 depths). The six inputs to the KAN used for inverting the governing equations include: pore water pressure between soil blocks. p 1. Pore water pressure between soil blocks p 2 and the corresponding derivative terms ( p 1,x , p 2,x , p 1,t , p 2,t The output is p 1,xx and p 2,xx .in p 1,t express p 1 pair of time t The first derivative, p 1,xx express p 1 pair of depths xThe second derivative of , and other meanings are similar. The established network structure is [6, 3, 1], with a spline function order and a grid number of 3. The optimizer uses L-BFGS, and each training iteration is 50 steps. Stepwise training and pruning are performed to determine the final effective input as ( p 1. p 2. p 1,t , p 2,t Then training continues until all activation functions in KAN are determined. Figure 2 for p 1,xx and p 2,xx The error curves all show a rapid decrease followed by asymptotic convergence, verifying the effectiveness of the model structure and training strategy. The final inverted control equation is:

[0117]

[0118]

[0119] The obtained governing equations are consistent with those determined by the analytical method, and the error exists only in the parameters. The parameter-related relative error RE is calculated using the following formula:

[0120]

[0121] in n Indicates the number of parameters. C The subscript represents the parameter of each term in the governing equation. a and p The values ​​represent the actual and predicted values ​​of the parameters, respectively. The average percentage errors of the parameters in the two governing equations compared to those determined by the analytical method are 5.73% and 11.90%, respectively, verifying the feasibility of using the KAN-based block soil consolidation process analysis method of this invention for governing equation inversion.

[0122] Embedding the obtained governing equations into the KAN loss function, and combining the initial and boundary conditions, the final loss function is:

[0123]

[0124] In this embodiment, the weighting parameter w All values ​​are set to 1. The final PiKAN is constructed with time and depth as inputs and outputs as the inter-block pore water pressure and the inter-block pore water pressure. p 1 and p2). The network structure is [2, 5, 5, 2], with spline function order of 5 and grid number of 10. The optimizer is L-BFGS, and the model converges after 400 training steps. The error curve is shown below. Figure 3 As shown, the different error terms all exhibit a convergence trend. Finally, the pore water pressure between soil blocks and between soil blocks at different times and depths is obtained as follows: Figure 4a and Figure 4b As shown, the model prediction results and analytical solution results under different time and depth conditions basically coincide, verifying the reliability of the soil consolidation process analysis method proposed in this invention.

[0125] Example 3:

[0126] In this embodiment, a centrifuge model test was used. The model chamber's length, width, and height were 0.3m, 0.21m, and 0.37m, respectively, with an acceleration of 100g. The soil sample was equivalent to a site with length, width, and height of 30m, 21m, and 18m, respectively, and a load of 120kPa. The model establishment method and hyperparameter settings used for inversion and solving the governing equations were similar to those in Embodiment 2. After KAN was progressively trained and pruned, the post-inverted governing equations were:

[0127]

[0128]

[0129] Embedding it as a constraint into the PiKAN residual term, the trained PiKAN prediction results are as follows: Figure 5 , Figure 6 As shown, the predicted pore water pressure between soil blocks and between soil blocks is basically consistent with the experimental results, with an error of approximately ±15%, further verifying the feasibility and effectiveness of the method proposed in this invention in the consolidation analysis of soil piles.

[0130] Example 4:

[0131] This invention also provides a KAN-based system for analyzing the consolidation process of multi-porous soil and rock media, referring to... Figure 7 As shown, it includes:

[0132] The data preprocessing module is used to import data including time, depth, and pore water pressure of each pore system during the consolidation process of multi-porous soil media, establish a dataset, and preprocess it.

[0133] The control equation inversion module is used to train KAN based on the preprocessed dataset to invert the control equations describing the consolidation process of the multi-porous soil and rock media.

[0134] The model building module is used to construct a PiKAN based on physical information. It uses the inverted governing equations and the initial and boundary conditions of the consolidation process of the multi-porous soil and rock media as physical constraints and embeds them into the loss function of the PiKAN.

[0135] The pore water pressure solution module is used to train the PiKAN using the preprocessed dataset and to use PiKAN to solve the pore water pressure of each pore system in a multi-porous soil medium at different times and depths.

[0136] The storage module is used to store imported data and the data obtained after calculation.

[0137] This system realizes a complete process of integrated, automated, and intelligent analysis of the consolidation process of multi-porous soil media, forming an end-to-end solution that significantly improves the efficiency and reliability of engineering analysis and reduces the complexity of manual modeling and calculation.

[0138] Example 5:

[0139] Based on the same inventive concept, the present invention also provides a computer device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;

[0140] Memory, used to store computer programs;

[0141] When the processor executes the program stored in the memory, it is able to implement the KAN-based method for analyzing the consolidation process of multi-porous soil and rock media as described in any one of Embodiments 1.

[0142] like Figure 8 As shown, the electronic device may include: a processor 10, a communication interface 20, a memory 30, and a communication bus 40, wherein the processor 10, the communication interface 20, and the memory 30 communicate with each other via the communication bus 40. The processor 10 can call logical instructions in the memory 30 to execute a KAN-based method for analyzing the consolidation process of multi-porous soil media, which includes:

[0143] S1. Data preprocessing steps: Obtain data including time, depth and pore water pressure of each pore system during the consolidation process of multi-porous soil media, establish a dataset and preprocess it.

[0144] S2. Control equation inversion step: Based on the preprocessed dataset, train KAN to invert and obtain the control equations describing the consolidation process of the multi-porous soil and rock medium.

[0145] S3. Model construction steps: Construct a PiKAN based on physical information, and use the inverted control equations and the initial and boundary conditions of the consolidation process of the multi-porous soil and rock medium as physical constraints, and embed them into the loss function of the PiKAN.

[0146] S4. Pore water pressure solution steps: Train PiKAN using the preprocessed dataset, and solve the pore water pressure of each pore system in the multi-porous soil medium at different times and depths based on the trained PiKAN.

[0147] This device enables the deployment and application of the aforementioned intelligent analysis methods in real-world engineering scenarios. By executing relevant programs through a processor, it can combine limited on-site monitoring data with physical laws, quickly and accurately outputting pore water pressure prediction results at different locations and times, providing a powerful computational tool for real-time stability assessment and decision-making at engineering sites.

[0148] Example 6:

[0149] This invention also provides a computer-readable storage medium containing a program for executing the KAN-based consolidation process analysis method for multi-porous soil media described in Embodiment 1 above. This program can be executed on a processor.

[0150] Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0151] The program stored on this medium is loaded into the processor's memory and executed to complete various functions. By connecting to hardware devices, this storage medium enables the computer to perform the aforementioned data preprocessing steps, control equation inversion steps, model building steps, and pore water pressure solution steps. This medium allows the core algorithms and processes of this invention to be persistently stored, easily distributed, and copied. Any device containing a processor, after acquiring this medium and reading the program, can obtain the aforementioned consolidation analysis capabilities, greatly promoting the dissemination, portability, and reuse of this technology, and ensuring the consistency and inheritability of the technical solution.

[0152] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0153] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for analyzing the consolidation process of multi-porous soil and rock media based on KAN, characterized in that, Includes the following steps: Data preprocessing steps: Obtain data on time, depth, and pore water pressure of each pore system during the consolidation process of multi-porous soil media, establish a dataset, and preprocess it. Control equation inversion steps: Based on the preprocessed dataset, train KAN to invert and obtain the control equations describing the consolidation process of the multi-porous soil and rock media; Model construction steps: Construct a PiKAN based on physical information, and use the inverted governing equations and the initial and boundary conditions of the consolidation process of the multi-porous soil and rock medium as physical constraints, and embed them into the loss function of the PiKAN. The steps for solving pore water pressure are as follows: PiKAN is trained using the preprocessed dataset, and the pore water pressure of each pore system in the multi-porous soil medium at different times and depths is solved based on the trained PiKAN. The data preprocessing steps include: The first part of the data was generated using the analytical solution of the consolidation process of multi-porous soil media; Acquire the second part of the data on the consolidation of multi-porous soil media; The first and second parts of the data are fused and preprocessed to form the final training dataset. The dataset includes: time, depth, and pore water pressure data of each pore system during the consolidation process of multi-porous soil media. The preprocessing includes: calculating the first and second partial derivatives of the pore water pressure with respect to depth; calculating the first partial derivative of the pore water pressure with respect to time; and normalizing the pore water pressure data and its partial derivatives. The governing equation inversion step specifically includes: The normalized pore water pressure data and its first-order partial derivatives with respect to time and depth are used as inputs to KAN, and the second-order partial derivatives of pore water pressure with respect to depth are used as outputs. Through stepwise training, pruning, and symbolic regression, the final structure and activation function of the KAN are determined, and its input-output relationship is characterized as the governing equation for the consolidation process of the multi-porous soil medium.

2. The method according to claim 1, characterized in that, In the model building step, the loss function is represented as a weighted sum of multiple error terms: in, L 1 represents the mean square error between the predicted pore water pressure and the measured data, ensuring that the model prediction results closely approximate the measured data. L 2 represents the mean square error of the control equations determined by KAN, ensuring that the model satisfies the determined control equations; L 3 and L 4 represents the mean square error of the boundary conditions and initial conditions corresponding to the consolidation process of multi-porous soil media, to ensure that the model meets the boundary conditions and initial conditions; w 1, w 2, w 3, w 4 represents the weighting coefficients for each error term, used to balance the contribution of each error term to the final total error; L This represents the total error.

3. The method according to claim 1, characterized in that, The input variables of PiKAN are the time and depth of the consolidation process of multi-porous soil media, and the output variable is the pore water pressure of each pore system.

4. A KAN-based system for analyzing the consolidation process of multi-porous soil and rock media, characterized in that, For implementing the KAN-based method for analyzing the consolidation process of multi-porous soil and rock media as described in any one of claims 1 to 3, the system comprises: The data preprocessing module is used to import data including time, depth, and pore water pressure of each pore system during the consolidation process of multi-porous soil media, establish a dataset, and preprocess it. The control equation inversion module is used to train KAN based on the preprocessed dataset to invert the control equations describing the consolidation process of the multi-porous soil and rock media. The model building module is used to construct a PiKAN based on physical information. It uses the inverted governing equations and the initial and boundary conditions of the consolidation process of the multi-porous soil and rock media as physical constraints and embeds them into the loss function of the PiKAN. The pore water pressure solution module is used to train the PiKAN using the preprocessed dataset and to use PiKAN to solve the pore water pressure of each pore system in a multi-porous soil medium at different times and depths.

5. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the KAN-based method for analyzing the consolidation process of multi-porous soil and rock media as described in any one of claims 1 to 3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the KAN-based method for analyzing the consolidation process of multi-porous soil and rock media as described in any one of claims 1 to 3.

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