A method for predicting clay settlement curves by coupling two-phase flow and data assimilation

Abstract

This invention relates to a method for predicting clay settlement curves based on the coupling of two-phase flow and data assimilation. The steps are as follows: S1. Obtain settlement interface-time experimental data based on indoor settlement tests; S2. Construct an initial parameter set for the model; S3. Run two-phase flow simulations with different parameter combinations to obtain settlement interface-time simulation data of clay; S4. Perform logarithmic transformation on the specified model parameters to improve their statistical properties; S5. Construct a unified spatiotemporal surrogate model; S6. Optimize the unified spatiotemporal surrogate model trained in S5 based on the EnKF data assimilation method; S7. Output and evaluation. This method can quickly optimize the parameter distribution of a two-phase flow model suitable for a certain type of clay through data assimilation, output a surrogate model suitable for different concentrations and heights, directly predict the settlement curve of clay, significantly reduce computational costs, and improve the efficiency and accuracy of clay settlement prediction.

Description

Technical Field

[0001] This invention relates to the field of settlement prediction technology, and in particular to a method for predicting clay settlement curves by coupling two-phase flow with data assimilation. Background Technology

[0002] High-moisture-content clays (such as dredged silt and engineering waste slurry) settle and consolidate slowly under natural conditions. In projects such as port silt treatment, land reclamation, and environmental remediation, rapid and accurate prediction of clay settlement curves is crucial for optimizing engineering design and construction. Currently, settlement characteristics mainly rely on indoor settlement tests and field monitoring, which are time-consuming and costly. Traditional theoretical models (such as Terzaghi consolidation theory) make stringent assumptions, have difficult parameter determination, and struggle to accurately describe the settlement process of high-moisture-content clay slurry.

[0003] Therefore, in view of the above-mentioned defects in the existing technology, it is necessary to develop an efficient sedimentation curve prediction method that combines two-phase flow model and data assimilation method, which has important application value. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the technical problem to be solved by the present invention is to provide a method for predicting clay settlement curves based on the coupling of two-phase flow and data assimilation. This method can quickly predict clay settlement curves directly through concentration and height, thereby improving prediction efficiency.

[0005] This invention is achieved by the following technical solution: a method for predicting clay settlement curves based on the coupling of two-phase flow and data assimilation, comprising the following steps:

[0006] S1. Based on indoor settlement tests, obtain settlement interface-time experimental data;

[0007] S2. Use the Latin hypercube distribution to generate multiple sets of initial model parameters and construct the initial parameter set of the model;

[0008] S3. Input the parameters obtained in S2 into the two-phase flow model, run the two-phase flow simulation with different parameter combinations, obtain the settling interface-time simulation data, and build a complete simulation database;

[0009] S4. Perform a logarithmic transformation on the model parameters specified in S2;

[0010] S5. Using the parameters after logarithmic transformation in S4 and time as joint inputs, and settlement height as output, construct a unified spatiotemporal proxy model, and train it based on the simulated data in S3 to obtain the trained unified spatiotemporal proxy model.

[0011] S6. Based on the EnKF data assimilation method, optimize the unified spatiotemporal proxy model trained in S5. The steps are as follows:

[0012] In each iteration of S61.EnKF data assimilation, an adaptive scaling (RTPS) strategy based on variance objective is used to adaptively expand the state vector. Then, the state vector matrix and the observation vector matrix are combined to form an augmented state vector matrix, an augmented state set is established, and the sample covariance of the augmented state is calculated.

[0013] S62. Calculate the Kalman gain matrix using the augmented-state sample covariance matrix, observation operator matrix, and observation error matrix. K The augmented state is optimally corrected to obtain the updated parameter set and prediction results.

[0014] S63. Repeat S61-S62 until the root mean square error between the settlement curve output by the unified spatiotemporal proxy model and the experimental data in S1 reaches the preset convergence condition or target accuracy.

[0015] S7. Output and Evaluation.

[0016] Furthermore, in step S61, the specific steps for establishing the augmented state set and calculating the sample covariance are as follows:

[0017] 1) Calculate the observation vector matrix using the surrogate model obtained from S5. ;

[0018] 2) After the set prediction is updated, an adaptive scaling strategy based on variance objective is adopted to adaptively expand the state vector. The adaptive expansion maintains diversity and improves the rank structure of covariance estimation by proportionally amplifying the set perturbation in each iteration.

[0019] 3) Convert the state vector matrix The calculated observation vector matrix Concatenate them to form an augmented state vector matrix. This allows for the simultaneous modification of the state vector and observation vector in a single update, thus establishing an augmented state set.

[0020] 4) Calculate the sample mean of the augmented state set. Then calculate the sample covariance. .

[0021] Furthermore, the specific steps of the Kalman update set in S62 are as follows:

[0022] 1) An observation perturbation scheme is adopted to generate independent noise for each augmented matrix set. Observation error matrix It consists of the measurement error covariance matrix and the surrogate model error covariance matrix;

[0023] 2) Obtain the augmented state sample covariance matrix from S61. With the observation operator matrix H and observation error matrix The Kalman gain is used to determine the optimal linear weighted fusion ratio between the predicted state and the observations, so that the updated parameter set best matches the observation information.

[0024] Furthermore, ensemble prediction involves performing a surrogate prediction for each sample in the ensemble using the unified spatiotemporal surrogate model in S5 within an artificial time step. Here, the time-series data is considered as an artificial time step. The formula for the predicted ensemble is expressed as:

[0025]

[0026] It is a prediction set matrix. It is a proxy model operator. It is the first j The predicted state vector of each set member, It is a set matrix of state vectors.

[0027] Furthermore, the set of state vectors provides the initial values ​​for the next round of prediction; it is the set of states after data assimilation in the previous round, expressed by the formula:

[0028]

[0029] It is the first j The state vector of each set member after the last analysis iteration It is a set matrix of state vectors. It is the dimension of the state vector. N It is the number of members in the set.

[0030] Furthermore, in S61, the variance of the state vector adaptive expansion enhancement prediction set is expressed by the formula:

[0031]

[0032] It is the mean of the set of state vectors. It is an adaptive expansion coefficient.

[0033] Furthermore, the augmented state matrix combines the predicted state with the observed output predicted by the model to form the augmented state, providing complete state-observation information for subsequent Kalman updates, as shown below:

[0034]

[0035] It is the output of the observation information predicted by the surrogate model. It is an augmented state matrix. It is the dimension of the observation vector.

[0036] Furthermore, the error distribution of the augmented state sample covariance quantization prediction set, including the correlation between states and observations, is expressed by the following formula:

[0037]

[0038] It is the mean of the augmented set of states. It is the augmented sample covariance.

[0039] Furthermore, the Kalman gain matrix K is expressed as follows:

[0040]

[0041] It is the Kalman gain matrix. It is the observation operator matrix. It is the observation error covariance matrix (including surrogate model error and measurement error).

[0042] Furthermore, in S6, the iterative process of EnKF data assimilation integrates observation information into the predicted state, generating an updated set of state vectors to achieve data assimilation. The iterative formula is expressed as follows:

[0043]

[0044] It is the first j An augmented state vector, It is the updated analysis vector. It is the actual observed vector. It is independent observation noise.

[0045] In this invention, the method utilizes data assimilation to establish an efficient prediction model, which is then coupled with a two-phase flow model to obtain clay settlement curves. By accurately locating the model parameter range through data assimilation and two-phase flow coupling, complex assumptions are avoided, resulting in high prediction accuracy and wide applicability. This solves the technical problem that traditional consolidation theories have many limiting assumptions and are difficult to accurately reflect the settlement law of high-water-content clay. Attached Figure Description

[0046] Figure 1 This is a flowchart illustrating a method for predicting clay settlement curves based on the coupling of two-phase flow and data assimilation.

[0047] Figure 2 This is a schematic diagram of the clay settlement simulation area;

[0048] Figure 3 Convergence plot of EnKF estimated parameters;

[0049] Figure 4 This is a comparison chart of experimental and predicted settlement curves. Detailed Implementation

[0050] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0051] Reference Figures 1-4 As shown, this invention provides a method for predicting clay settlement curves based on the coupling of two-phase flow and data assimilation, the steps of which are as follows:

[0052] S1. Based on indoor settlement tests, obtain settlement interface-time experimental data.

[0053] The indoor settlement test includes: taking a reference clay sample, preparing it to a specified initial concentration and height, conducting a settlement test in a transparent graduated cylinder, and recording the change of the settlement interface over time through an image acquisition system to obtain the settlement curve of the sample and obtain the settlement interface-time experimental data.

[0054] Specifically, the sample solid concentration (solid volume percentage) ) and the initial liquid level height (denoted as Prepare the samples according to the experimental design. After static and uniform stirring, slowly pour the samples into a transparent graduated cylinder to reduce air entrainment and disturbance. Take the above samples... , A high-resolution camera was used to vertically photograph the sidewall of the graduated cylinder to record the settling interface, ultimately obtaining the settling curve of the sample. The sampling frequency was preferably designed as follows: one frame was taken every 60 seconds in the initial rapid phase, followed by sparse sampling, one frame was taken every 300 seconds, until the interface was basically stable.

[0055] S2. Construct the initial parameter set for the model.

[0056] Initial values ​​of the parameters were obtained by fitting experimental data from S1. Based on these initial values, multiple sets of initial model parameters were generated using a Latin hypercubic distribution, constructing a set of initial parameters for the drag model. These parameters serve as the input basis for the two-phase flow numerical simulation, reflecting the system behavior under different parameter uncertainties. The parameters include... A 1. n 1. A 2. n 2. Obtain initial values ​​of the parameters by fitting experimental values: A 1 = 2.089464e-06; n 1 = -22.104375; A2 = 4.666758; n 2 = -8.76994.

[0057] The set of initial parameters is determined by Latin hypercube sampling to generate efficient and uniformly distributed initial samples in the multidimensional parameter space. Specifically, 1) the set of parameters for the drag model controlling the two-phase flow simulation is selected. A 1. n 1. A 2. n 2 are both fitting parameters. 2) Latin hypercube sampling (LHS) is used to generate uniformly within a specified range. A parameter vector is used to ensure that EnKF can learn the uncertainty of the system response from a wide range of candidate parameters in the initial stage. The Latin hypercube sampling step includes: firstly, dividing the range of values ​​for each parameter into... Divide the data into several equally probable subintervals, and randomly select a value from each subinterval. Then, extract values ​​from different parameter dimensions... The values ​​are randomly paired and combined to form 10 multidimensional sample points. Following the principle of "the more, the more accurate," but in order to balance computational precision and computational cost, we take... The upper and lower limits can be set freely according to the reliability of the sample, with a range of 0.1 being preferred.

[0058] S3. Construct a complete simulation database.

[0059] Input the parameters obtained in S2 into the two-phase flow model, run the two-phase flow simulation with different parameter combinations, obtain the settling interface-time simulation data, and build a complete simulation database.

[0060] Reference Figure 2 As shown, in the sedimentation simulation, gravity was used as the driving force. The bottom of the sample was set as an impermeable boundary, the sidewalls as symmetrical boundaries, and the top was allowed to drain freely to ensure the accuracy of the sedimentation process. The correspondence between the position of the sedimentation interface and time was obtained through batch processing, resulting in complete sedimentation curves for all two-phase flow examples.

[0061] The specific steps are as follows: 1) Calculate The resistance term, where the model described in S2 is a resistance model, has the following specific formula:

[0062]

[0063] In the formula and These are the velocities of the liquid and solid terms. A 1. n 1.A 2. n 2 are the model parameters that need to be determined. e It is a natural constant.

[0064] 2) Substitute into S2 to obtain Group drag coefficient parameters, for different concentrations ( Group) and height ( Two-phase flow simulation was performed on clay slurry (group) to generate... Simulation data of the settling interface-time were used to construct a complete simulation database. The viscosity of the two-phase flow was taken as... The density of water is taken as 1000 kg / m³, the density of particles is taken as 2650 kg / m³, and the simulation time step is [missing information]. Boundary conditions are attached. Figure 2 Substitute this into the initial settings for two-phase flow to solve the Navier-Stokes equations.

[0065] The two-phase flow model is solved using the Navier-Stokes equations, along with the mass and momentum equations. The Navier-Stokes equations are as follows:

[0066]

[0067]

[0068] In the formula and It represents the volume fraction of solids and liquids. It refers to the density of soil and water; It is the gravitational constant; and These represent liquid and solid pressures, respectively. and Representing shear stress in liquids and solids, respectively. This represents the resistance term.

[0069] S4. Perform a logarithmic transformation on the specified model parameters to improve their statistical properties.

[0070] Logarithmic transformation is performed on the specified model parameters in S2 to improve their statistical distribution characteristics and enhance the stability of subsequent data assimilation. Specified model parameters refer to model parameters with a large range; specifically, when a model parameter differs from other parameters by three orders of magnitude or more, it is considered a model with a large range and requires logarithmic transformation to bring the parameters within a similar order of magnitude, preventing instability or computational divergence during the training of the surrogate model and data assimilation.

[0071] For example, in S2 A1. If the magnitude of the parameter differs too much from other parameters, direct use in statistical processing and data assimilation (EnKF) can lead to extremely large sample variance or skewed distribution, thus affecting the stability of Kalman gain estimation and updates. Logarithmic transformation can reduce scaling differences and make the parameter distribution closer to a normal distribution, which is beneficial to the Gaussian approximation assumption of EnKF.

[0072] S5. Construct a unified spatiotemporal proxy model.

[0073] By using logarithmically transformed model parameters as input and settlement height as output, a unified spatiotemporal surrogate model is trained to characterize the mud settling process. This surrogate model, built on S3 data, can rapidly generate complete settlement time series without rerunning numerical solutions, transforming the prediction process from discrete, costly multi-round simulations to continuous, efficient inference. In subsequent EnKF iterations, the surrogate model can return simulation results for any parameter combination at extremely low time cost, replacing the traditional iterative computation mode of "re-executing CFD after parameter updates" with a lightweight process of "machine learning prediction combined with Kalman updates." With this alternative mechanism, the data assimilation process no longer relies on repeated two-phase flow solutions, but achieves rapid convergence through efficient model inference, significantly improving overall computational efficiency and meeting the real-time requirements of iterative optimization.

[0074] The specific steps are as follows:

[0075] S51. All generated by S3 The data sets are aggregated into a spatiotemporal point dataset (preferably 100 sets of data) and trained into a unified spatiotemporal proxy model.

[0076] S52. Use the Python module sklearn to import Gaussian Process Regression (GPR) and Random Forest (RF) surrogate models. Specifically: 1) The kernel function for GPR is Constant * RBF + WhiteKernel, and the length_scale of RBF can be adaptively optimized for each dimension. GPR provides both the prediction mean and uncertainty (return_std=True), facilitating the inclusion of surrogate uncertainty into the observation error matrix (the observation error matrix consists of the measurement error covariance matrix and the surrogate model error covariance matrix). When using GPR, the mean of the surrogate prediction variance is used to construct a diagonal matrix, which is then added to the measurement error matrix to obtain the total observation error. This process explicitly incorporates surrogate uncertainty into the Kalman gain calculation, thereby reducing the misleading effect of surrogate error on the assimilation results. 2) RF can use GridSearchCV to find the optimal combination of n_estimators, max_depth, min_samples_leaf, etc.

[0077] S53. Obtained from S3 The simulated data was divided into training, validation, and test sets in an 8:1:1 ratio. After cross-validation on the training set, the RMSE was calculated on the validation set as an early indicator. Finally, the entire dataset was used to train the final model, resulting in the trained unified spatiotemporal proxy model.

[0078] S6. Based on the EnKF data assimilation method, optimize the unified spatiotemporal surrogate model trained in S5. In each iteration, the surrogate prediction is first called using the current (inflated) parameter set, the augmented state is assembled, the covariance matrix is ​​calculated, and then the set is updated using the augmented state Kalman gain. The steps are as follows:

[0079] S61. Establish the augmented state set and calculate the sample covariance.

[0080] In each iteration of EnKF data assimilation, a variance-based adaptive scaling (RTPS) strategy is employed to adaptively dilate the state vectors, maintaining the diversity of the set distribution through adaptive variance dilation. The state vector matrix and the observation vector matrix are then combined to form an augmented state vector matrix, establishing an augmented state set, and the sample covariance of the augmented states is calculated. The iterative process of EnKF data assimilation incorporates observation information into the predicted state, generating an updated state vector set, thus achieving data assimilation. The iterative formula is expressed as:

[0081]

[0082] It is the first j An augmented state vector, It is the updated augmented state vector. It is the actual observed vector. It is independent observation noise.

[0083] The specific steps for establishing the augmented state set and calculating the sample covariance are as follows:

[0084] Using the data obtained from S5, form For each sample, perform ensemble forecasting to obtain the observation vector matrix. The ensemble prediction method performs surrogate prediction on each sample in the ensemble using the unified spatiotemporal surrogate model in S5 within an artificial time step, obtaining the observation vector. In this context, time-series data is considered as a single artificial time step. The formula for the prediction set is expressed as:

[0085] The formula for the aforementioned prediction set is expressed as follows:

[0086]

[0087] It is a prediction set matrix. It is a proxy model operator. It is the first j The predicted state vector of each set member, It is a set matrix of state vectors.

[0088] The state vector set provides the initial values ​​for the next round of prediction; it is the set of states after data assimilation in the previous round, expressed by the formula:

[0089]

[0090] It is the first j The state vector of each set member after the last analysis iteration It is a set matrix of state vectors. It is the dimension of the state vector. N It is the number of members in the set.

[0091] The prediction ensemble method may suffer from ensemble collapse after repeated updates, leading to filter divergence or underestimation of uncertainty. Therefore, after the ensemble prediction is updated, an adaptive scaling (RTPS) strategy based on variance objective is adopted for adaptive expansion. Adaptive expansion maintains diversity and improves the rank structure of covariance estimation by scaling up the ensemble perturbation in each iteration.

[0092] Among them, adaptive expansion of the state vector enhances the variance of the prediction set, prevents variance collapse, improves sample diversity, and ensures filter stability. The formula is expressed as:

[0093]

[0094] It is to analyze the mean of the set. It is an adaptive expansion coefficient.

[0095] The state vector matrix The calculated observation vector matrix Concatenate them to form an augmented state vector matrix. This allows for the simultaneous correction of the state vector (estimated parameters) and the observation vector (prediction interface-time data) in a single update, thus establishing an augmented state set.

[0096] The augmented state matrix combines the predicted state with the observed output predicted by the model to form an augmented state matrix, providing complete state-observation information for subsequent Kalman updates, and is represented as:

[0097]

[0098] It is the output of the observation information predicted by the surrogate model. It is an augmented state matrix. It is the dimension of the observation vector.

[0099] 4) Calculate the sample mean of the augmented state set. Then calculate the sample covariance. This provides a basis for subsequent Kalman gain calculations.

[0100] The error distribution of the augmented state sample covariance quantization prediction set, including the correlation between states and observations, provides a basis for Kalman gain calculation. (Sample covariance) The formula is expressed as:

[0101]

[0102] It is the mean of the augmented set of states. It is the augmented sample covariance.

[0103] S62. Kalman Update.

[0104] The Kalman gain matrix K is calculated using the augmented state sample covariance matrix, observation operator matrix, and observation error matrix. The augmented state is then optimally corrected to obtain the updated parameter set and prediction results.

[0105] Specific steps:

[0106] 1) To maintain the statistical consistency of the analysis set, an observation perturbation scheme is adopted to generate independent noise for each augmented matrix set. Observation error matrix It consists of two parts: the measurement error covariance matrix and the surrogate model error covariance matrix. The measurement error covariance matrix is ​​a constant (empirical value), preferably 0.2. The surrogate model error covariance matrix is ​​composed of the observation vector matrix. Obtained by calculating variance.

[0107] 2) Obtain the augmented state sample covariance matrix from S61. With the observation operator matrix H and observation error matrix Used to determine the Kalman gain matrix K Among them, the observation operator matrix H From the observation vector matrix The transformation yields the Kalman gain, which is used to determine the optimal linear weighted fusion ratio between the predicted state and the observations, ensuring that the updated parameter set optimally matches the observation information. The formula is expressed as:

[0108]

[0109] It is the Kalman gain matrix. It is the observation operator matrix. It is the observation error covariance matrix (the observation error covariance matrix includes the surrogate model error covariance matrix and the measurement error covariance matrix. The former is obtained by transforming the observation vector matrix, and the latter is a constant value used to characterize the data processing error during experimental or simulation post-processing).

[0110] S63. Iterative optimization and convergence determination.

[0111] Reference Figure 3 As shown, repeat operations S61-S62 until the root mean square error between the settlement curve output by the unified spatiotemporal surrogate model and the experimental data reaches the preset convergence condition or target accuracy, thus obtaining the optimized unified spatiotemporal surrogate model. The preferred stopping criterion is: the RMSE curve flattens out, and the RMSE improvement is less than a threshold (e.g., 1E-3) after several consecutive iterations (e.g., 10).

[0112] S7. Output and Evaluation.

[0113] Reference Figure 4 As shown, the two-phase flow model parameter distribution and the final predicted clay settlement curve are output by the unified spatiotemporal proxy model optimized in S6 after data assimilation optimization, and the model error index is calculated to comprehensively evaluate the prediction accuracy.

[0114] Specifically, after optimizing the unified spatiotemporal surrogate model, the final parameter set in logarithmic space is inversely transformed back to physical space to derive the final estimated parameter set, parameter convergence history, and experimental-prediction comparison data in S1, thus evaluating the optimized unified spatiotemporal surrogate model. When using it for prediction, simply input the concentration and height into the unified spatiotemporal surrogate model to predict the settling curves of clay slurry at different concentrations and heights.

[0115] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for predicting clay settlement curves based on the coupling of two-phase flow and data assimilation, characterized by the following steps: as follows: S1. Based on indoor settlement tests, obtain settlement interface-time experimental data; S2. Multiple sets of initial model parameters are generated using the Latin hypercube distribution to construct the initial parameter set of the model; S3. Input the parameters obtained in S2 into the two-phase flow model, perform numerical calculations, obtain the settlement interface-time simulation data, and construct a complete simulation database. S4. Perform a logarithmic transformation on the model parameters specified in S2; S5. Using parameters and time as joint inputs and settlement height as output, construct a unified spatiotemporal proxy model and train it based on the simulation data in S3 to obtain the trained unified spatiotemporal proxy model. S6. Based on the data assimilation method, optimize the unified spatiotemporal proxy model trained in S5. The steps are as follows: In each iteration of S61.EnKF data assimilation, an adaptive scaling strategy based on variance objective is used to adaptively expand the state vector. Then, the state vector matrix and the observation vector matrix are combined to form an augmented state vector matrix, an augmented state set is established, and the sample covariance of the augmented state is calculated. S62. Calculate the Kalman gain matrix K using the augmented state sample covariance matrix, observation operator matrix and observation error matrix, perform optimal correction on the augmented state, and obtain the updated parameter set and prediction results; S63. Repeat S61-S62 until the root mean square error between the settlement curve output by the unified spatiotemporal proxy model and the experimental data in S1 reaches the preset convergence condition or target accuracy. S7. Output and Evaluation The system outputs the parameter distribution of the two-phase flow model after data assimilation and optimization, as well as the final predicted clay settlement curve. It also calculates the model error index and comprehensively evaluates the prediction accuracy.

2. The method for predicting clay settlement curves based on the coupling of two-phase flow and data assimilation as described in claim 1, characterized in that: In step S61, the specific steps for establishing the augmented state set and calculating the sample covariance are as follows: The observation vector matrix is ​​calculated using the surrogate model obtained from S5. ; After the set prediction is updated, an adaptive scaling strategy based on variance objective is used to adaptively expand the state vector. The adaptive expansion maintains diversity and improves the rank structure of covariance estimation by proportionally amplifying the set perturbation in each iteration. 3) Convert the state vector matrix The calculated observation vector matrix Connected together, forming an augmented state matrix This allows for the simultaneous modification of both the state vector and the observation vector in a single update, thus establishing an augmented state set. 4) Calculate the sample mean of the augmented state set. Then calculate the sample covariance. .

3. The method for predicting clay settlement curves based on the coupling of two-phase flow and data assimilation as described in claim 1 or 2, characterized in that: The specific steps for Kalman update of the set in S62 are as follows: 1) An observation perturbation scheme is adopted to generate independent noise for each augmented matrix set. Observation error covariance matrix R total It consists of the measurement error covariance matrix and the surrogate model error covariance matrix; 2) Obtain the augmented state sample covariance matrix from S61. With the observation operator matrix H and observation error matrix R total The Kalman gain is used to determine the optimal linear weighted fusion ratio between the predicted state and the observations, so that the updated parameter set best matches the observation information.

4. The method for predicting clay settlement curves based on the coupling of two-phase flow and data assimilation according to claim 2, characterized in that: Ensemble prediction involves performing a surrogate prediction for each sample in the ensemble using the unified spatiotemporal surrogate model in S5 within an artificial time step. Here, the time series data is considered as an artificial time step. The formula for ensemble prediction is expressed as follows: It is a state vector matrix. It is a proxy model operator. It is the first The predicted state vector of each set member, It is a set matrix of state vectors.

5. The method for predicting clay settlement curves based on the coupling of two-phase flow and data assimilation according to claim 4, characterized in that: The set of state vectors provides the initial values ​​for the next round of prediction; it is the set of states after data assimilation in the previous round, expressed by the formula: It is the first The state vector of each set member after the last analysis iteration It is the set matrix of state vectors after the last analysis iteration. It is the dimension of the state vector. N It is the number of members in the set.

6. The method for predicting clay settlement curves based on the coupling of two-phase flow and data assimilation according to claim 4, characterized in that: In S61, the variance of the state vector adaptive expansion enhancement prediction set is expressed by the formula: It is the mean of the set of state vectors. It is an adaptive expansion coefficient.

7. The method for predicting clay settlement curves based on the coupling of two-phase flow and data assimilation according to claim 2, characterized in that: The augmented state matrix combines the predicted state with the observed output predicted by the model to form the augmented state, providing complete state-observation information for subsequent Kalman updates, and is represented as: It is the output of the observation information predicted by the surrogate model. It is an augmented state matrix. It is the dimension of the observation vector.

8. The method for predicting clay settlement curves based on the coupling of two-phase flow and data assimilation according to claim 1 or 2, characterized in that: The error distribution of the augmented state sample covariance quantization prediction set, including the correlation between states and observations, is expressed by the following formula: It is the mean of the augmented set of states. It is the augmented sample covariance matrix.

9. The method for predicting clay settlement curves based on the coupling of two-phase flow and data assimilation according to claim 3, characterized in that: The Kalman gain matrix K is expressed as follows: It is the Kalman gain matrix. It is the observation operator matrix. It is the observation error covariance matrix.

10. The method for predicting clay settlement curves based on the coupling of two-phase flow and data assimilation according to claim 7, characterized in that: In step S6, the iterative process of EnKF data assimilation integrates observation information into the predicted state, generating an updated set of state vectors to achieve data assimilation. The iterative formula is expressed as follows: It is the first An augmented state vector, It is the updated analysis vector. It is the actual observed vector. It is independent observation noise.

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