Two-phase flow and data assimilation coupled clay settlement curve prediction method

Abstract

The invention relates to a clay settlement curve prediction method based on two-phase flow and data assimilation coupling, and the method comprises the following steps: S1, obtaining settlement interface-time experiment data based on an indoor settlement test; s2, constructing a model initial parameter set; s3, operating two-phase flow simulation by using different parameter combinations to obtain sedimentation interface-time simulation data of clay; s4, logarithmic transformation is carried out on specified model parameters, and statistical characteristics of the specified model parameters are improved; s5, constructing a unified space-time agent model; s6, based on an EnKF data assimilation method, optimizing the unified space-time proxy model trained in the step S5; and S7, outputting and evaluating. According to the method, the parameter distribution of the two-phase flow model suitable for a certain clay can be quickly optimized through the data assimilation method, the proxy models suitable for different concentrations and different heights are output, the settlement curve of the clay is directly predicted, the calculation cost is greatly reduced, and the efficiency and precision of clay settlement prediction are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of settlement prediction, in particular to a clay settlement curve prediction method coupled with two-phase flow and data assimilation. BACKGROUND

[0002] High water content clay (such as dredged sludge, engineering slurry) has a slow settlement and consolidation process under natural conditions. In port sludge treatment, reclamation and environmental governance engineering, it is of great significance to quickly and accurately predict the settlement curve of clay for engineering design and construction optimization. At present, the settlement characteristics mainly rely on indoor settlement test and field monitoring, which has long cycle and high cost. The traditional theoretical model (such as Terzaghi consolidation theory) has strict assumptions and difficult parameter determination, and it is difficult to accurately describe the settlement process of high water content slurry.

[0003] Therefore, in view of the above defects existing in the prior art, it is necessary to develop a high-efficiency settlement curve prediction method combining two-phase flow model and data assimilation method, which has important application value. SUMMARY

[0004] In view of the deficiencies in the background art, the technical problem to be solved by the present application is to provide a clay settlement curve prediction method based on two-phase flow and data assimilation coupling. The method can quickly predict the clay settlement curve through concentration and height, and improve the prediction efficiency.

[0005] The present application is accomplished by adopting the following technical scheme: a clay settlement curve prediction method based on two-phase flow and data assimilation coupling, the steps are as follows: S1. Based on the indoor settlement test, the settlement interface-time experimental data are obtained; S2. A plurality of groups of initial model parameters are generated by using Latin hypercube distribution to construct an initial parameter set of the model; S3. Each group of parameters obtained in S2 is input into the two-phase flow model, and the two-phase flow simulation is run with different parameter combinations to obtain settlement interface-time simulation data, and a complete simulation database is constructed; S4. The specified model parameters in S2 are logarithmically transformed; S5. The logarithmically transformed parameters in S4 and time are taken as joint input, and the settlement height is taken as output to construct a unified space-time proxy model, and the trained unified space-time proxy model is obtained based on the simulation data of S3; S6. The trained unified space-time proxy model in S5 is optimized based on the EnKF data assimilation method, and the steps are as follows: S61. In each iteration of the EnKF data assimilation, an adaptive rescaling strategy based on variance targeting (RTPS) is used to adaptively inflate the state vector, and 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 augmented state sample covariance is calculated. S62. The augmented state sample covariance matrix, the observation operator matrix, and the observation error matrix are used to calculate the Kalman gain matrix K , the augmented state is optimally corrected, and the updated parameter set and the prediction result are obtained. S63. Repeat operations S61-S62 until the root mean square error between the settling curve output by the unified space-time agent model and the experimental data in S1 reaches the preset convergence condition or target accuracy. S7. Output and evaluation.

[0006] Further, in S61, the specific steps of establishing an augmented state set and calculating a sample covariance are as follows: 1) Use the agent model obtained in S5 to calculate the observation vector matrix . 2) After the set is updated, an adaptive rescaling strategy based on variance targeting is used to adaptively inflate the state vector, and adaptive inflation is used to maintain diversity and improve the rank structure of the covariance estimate by scaling up the set disturbance in each iteration. 3) The state vector matrix is concatenated with the calculated observation vector matrix to form an augmented state vector matrix , which allows the state vector and the observation vector to be corrected simultaneously in one update, and an augmented state set is established. 4) Calculate the sample mean of the augmented state set, and then calculate the sample covariance .

[0007] Further, the specific steps of the Kalman update set in S62 are as follows: 1) Use the observation disturbance scheme to generate independent noise for each augmented matrix set, and the observation error matrix is composed of the measurement error covariance matrix and the agent model error covariance matrix. 2) The augmented state sample covariance matrix from S61 is used with the observation operator matrix H and the observation error matrix to determine the Kalman gain matrix, which is used to determine the optimal linear weighting fusion ratio of the predicted state and the observation, so that the updated parameter set optimally matches the observation information.

[0008] Further, the ensemble prediction is to predict each sample in the ensemble by the unified space-time surrogate model in S5 in a virtual time step, wherein the time series data is regarded as a virtual time step, and the formula of the prediction ensemble is represented as:

[0009] is a prediction ensemble matrix, is a surrogate model operator, is a prediction state vector of the i-th ensemble member, j is a state vector ensemble matrix.

[0010] Further, the state vector ensemble provides the initial value for the next round of prediction, which is the ensemble state after the data assimilation of the last round, and the formula is represented as

[0011] is a state vector of the i-th ensemble member after the last analysis iteration, j is a state vector ensemble matrix, is a state vector dimension, is the number of ensemble members. N

[0012] Further, in S61, the state vector adaptive inflation enhances the variance of the prediction ensemble, and the formula is represented as:

[0013] is a state vector ensemble mean, is an adaptive inflation coefficient.

[0014] Further, the augmented state matrix combines the predicted state and the model-predicted observation output to form an augmented state, which provides complete state-observation information for subsequent Kalman update, and is represented as:

[0015] is an observation information output obtained by the surrogate model prediction, is an augmented state matrix, is an observation vector dimension.

[0016] Further, the augmented state sample covariance quantifies the error distribution of the prediction ensemble, including the correlation between the state and the observation, and the formula is represented as:

[0017] is an augmented state ensemble mean,​​ It is the augmented sample covariance.

[0018] Furthermore, the Kalman gain matrix K is expressed as follows:

[0019] 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).

[0020] 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:

[0021] 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.

[0022] 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

[0023] 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. Figure 2 This is a schematic diagram of the clay settlement simulation area; Figure 3 Convergence plot of EnKF estimated parameters; Figure 4 This is a comparison chart of experimental and predicted settlement curves. Detailed Implementation

[0024] 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.

[0025] 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: S1. Obtain the settling interface-time experimental data based on the indoor settling test.

[0026] The indoor settling test comprises: taking a reference clay sample, preparing it into a specified initial concentration and height, conducting a settling test in a transparent cylinder, and recording the change of the settling interface with time through an image acquisition system to obtain the settling curve of the sample, and obtaining the settling interface-time experimental data.

[0027] Specifically, the solid phase concentration (solid volume percentage ) of the sample and the initial liquid level height (denoted as ) are prepared according to the experimental design, and the sample is slowly poured into the transparent cylinder after static and uniform stirring to reduce air entrainment and disturbance. The above-mentioned sample is taken , . A high-resolution camera is used to vertically shoot the side wall of the cylinder to record the settling interface, and finally the settling curve of the sample is obtained. The sampling frequency is preferably designed as: one frame every 60s in the initial rapid stage, and then sparse sampling, one frame every 300s, until the interface is basically stable.

[0028] S2. Construct the initial parameter set of the model.

[0029] The initial values of the parameters are fitted and obtained from the experimental data in S1, and multiple sets of initial model parameters are generated based on the initial values of the parameters using Latin hypercube distribution to construct the initial parameter set of the resistance model. As the input basis of the two-phase flow numerical simulation, it is used to reflect the system behavior under the uncertainty of different parameters. The parameters include A 1、 n 1、 A 2、 n 2, the initial values of the parameters are fitted and obtained from the experimental values: A 1=2.089464e-06; n 1 = -22.104375; A 2=4.666758; n 2=-8.76994.

[0030] The initial parameter set is determined by Latin hypercube sampling to generate efficient and uniformly distributed initial samples in the multi-dimensional parameter space. Specifically, 1) the parameter set of the resistance model controlling the two-phase flow simulation is selected, A 1、 n 1、 A 2、 n 2 are fitting parameters. 2) Latin hypercube sampling (LHS) is used to uniformly generate 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.

[0031] S3. Construct a complete simulation database.

[0032] 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.

[0033] 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.

[0034] 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:

[0035] 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.

[0036] 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.

[0037] 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:

[0038]

[0039] 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.

[0040] S4. Perform a logarithmic transformation on the specified model parameters to improve their statistical properties.

[0041] 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.

[0042] For example, in S2 A 1. 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.

[0043] S5. Construct a unified spatiotemporal proxy model.

[0044] 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.

[0045] The specific steps are as follows: 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.

[0046] 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.

[0047] 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.

[0048] S6. Based on the EnKF data assimilation method, the unified spatiotemporal surrogate model trained in S5 is optimized. In each iteration, the surrogate is first called with the current (inflated) parameter set to make a prediction, the augmented state is assembled, the covariance matrix is calculated, and then the augmented state Kalman gain is used to update the ensemble. The steps are as follows: S61. The augmented state set is established and the sample covariance is calculated.

[0049] In each iteration of EnKF data assimilation, an adaptive scaling strategy based on variance target (RTPS) is used for adaptive inflation of the state vector. The diversity of the ensemble distribution is maintained through adaptive variance inflation. Then the state vector matrix and the observation vector matrix are combined to form the augmented state vector matrix, the augmented state set is established, and the augmented state sample covariance is calculated. In the iteration process of EnKF data assimilation, the observation information is integrated into the predicted state to generate an updated state vector set, and data assimilation is achieved. The iteration formula is expressed as:

[0050] is the j th augmented state vector, is the updated augmented state vector, is the actual observation vector, is the independent observation noise.

[0051] The specific steps of establishing the augmented state set and calculating the sample covariance are as follows: Using the data obtained in S5, form samples, and perform ensemble prediction (forecast) on each sample to obtain the observation vector matrix . The ensemble prediction method is to perform surrogate prediction on each sample in the ensemble through the unified spatiotemporal surrogate model in S5 in an artificial time step to obtain the observation vector , wherein the time series data is regarded as an artificial time step. The formula for the predicted ensemble is: The formula for the predicted ensemble is:

[0052] is the predicted ensemble matrix, is the surrogate model operator, is the predicted state vector of the j th ensemble member, is the state vector ensemble matrix.

[0053] Among them, the state vector ensemble provides the initial value for the next round of prediction, which is the ensemble state after the last round of data assimilation, and the formula is expressed as:

[0054] is the state vector of the last analysis iteration of the ensemble member, j is the state vector of the last analysis iteration of the ensemble member, is the state vector of the last analysis iteration of the ensemble member, is the state vector of the last analysis iteration of the ensemble member, N is the state vector of the last analysis iteration of the ensemble member.

[0055] The prediction ensemble method may collapse after repeated updates, resulting in ensemble collapse, causing filter divergence or underestimating uncertainty. Therefore, after the ensemble prediction update, the adaptive scaling strategy based on variance target (RTPS) is used for adaptive inflation, which maintains diversity and improves the rank structure of covariance estimation by scaling up the ensemble perturbation at each iteration.

[0056] wherein the state vector adaptive inflation enhances the variance of the prediction ensemble, prevents variance collapse, improves sample diversity, and ensures filter stability, and the formula is expressed as:

[0057] is the analysis ensemble mean, is the adaptive inflation coefficient.

[0058] The state vector matrix is concatenated with the calculated observation vector matrix to form the augmented state vector matrix , which allows the state vector (estimated parameters) and the observation vector (predicted interface-time data) to be corrected simultaneously in one update, establishing an augmented state ensemble.

[0059] The augmented state matrix combines the predicted state with the model-predicted observation output, forming an augmented state matrix that provides complete state-observation information for subsequent Kalman updates, expressed as:

[0060] is the observation information output predicted by the proxy model, is the augmented state matrix, is the observation vector dimension.

[0061] 4) Calculate the sample mean of the augmented state ensemble , and then calculate the sample covariance , which provides the basis for subsequent Kalman gain calculation.

[0062] 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:

[0063] It is the mean of the augmented set of states. It is the augmented sample covariance.

[0064] S62. Kalman Update.

[0065] 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.

[0066] Specific steps: 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 the variance.

[0067] 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:

[0068] 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).

[0069] S63. Iterative optimization and convergence determination.

[0070] Referring to Figure 3 As shown, the operations S61-S62 are repeated until the root mean square error between the settlement curve output by the unified space-time surrogate model and the experimental data reaches a preset convergence condition or target accuracy, and an optimized unified space-time surrogate model is obtained. The stop criterion is preferably that the RMSE curve tends to be flat, and when the RMSE improves by less than a threshold (such as 1E-3) for a plurality of consecutive (for example, 10) iterations.

[0071] S7. Output and evaluation.

[0072] Referring to Figure 4 As shown, the two-phase flow model parameter distribution optimized by data assimilation and the finally predicted clay settlement curve are output by the optimized unified space-time surrogate model in S6, and a model error index is calculated to comprehensively evaluate the prediction accuracy.

[0073] Specifically, after the optimized unified space-time surrogate model, the final parameter set in the logarithmic space is inversely transformed back to the physical space to derive the final estimated parameter set, the parameter convergence history, and the experimental-predicted comparison data in S1, and the optimized unified space-time surrogate model is evaluated. When predicting, only the concentration and height need to be input into the unified space-time surrogate model, and the settlement curve of the clay slurry at different concentrations and different heights can be predicted.

[0074] The above is only a preferred embodiment of the present application, and does not limit the present application in any form. Although the present application has been disclosed as above with a preferred embodiment, it is not intended to limit the present application. Any person skilled in the art can make some changes or modifications to the above disclosed technical content to obtain equivalent embodiments with equivalent changes, without departing from the scope of the technical solution of the present application. Any simplification, modification, equivalent change and modification of the above embodiments made according to the technical essence of the present application, as long as it does not deviate from the technical solution of the present application, still belongs to the scope of the technical solution of the present application.

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. Obtain the settlement interface-time experimental data based on the indoor settlement test; S2. Generate multiple sets of initial model parameters using Latin hypercube distribution to construct the initial parameter set of the model; S3. Input each set of parameters obtained in S2 into the two-phase flow model for numerical calculation to obtain the settlement interface-time simulation data and construct a complete simulation database; S4. Perform logarithmic transformation on the specified model parameters in S2; S5. Construct a unified space-time surrogate model with parameters and time as joint inputs and settlement height as output, and train the trained unified space-time surrogate model based on the simulation data in S3; S6. Optimize the trained unified space-time surrogate model in S5 based on the data assimilation method, as follows: S61. In each iteration of EnKF data assimilation, use the adaptive scaling strategy based on variance target to perform adaptive inflation of the state vector, then combine the state vector matrix and the observation vector matrix to form an augmented state vector matrix, establish an augmented state set, and calculate the augmented state sample covariance; S62. Calculate the Kalman gain matrix K using the augmented state sample covariance matrix, the observation operator matrix, and the observation error matrix to optimally correct the augmented state and obtain the updated parameter set and the prediction result; S63. Repeat operations S61-S62 until the root mean square error between the settlement curve output by the unified space-time surrogate model and the experimental data in S1 reaches the preset convergence condition or the target accuracy; S7. Output and evaluate, Output the two-phase flow model parameter distribution optimized by data assimilation and the final predicted clay settlement curve, calculate the model error index, and comprehensively evaluate the prediction accuracy.

2. The method according to claim 1, characterized in that: In S61, the specific steps of establishing the augmented state set and calculating the sample covariance are as follows: 1) Compute the observation vector matrix using the surrogate model obtained with S5 ; 2) After set prediction update, use the adaptive scaling strategy based on variance target to perform adaptive inflation of the state vector, which maintains diversity and improves the rank structure of covariance estimation by scaling up the set disturbance by a certain proportion in each iteration; 3) concatenating the state vector matrix with the computed observation vector matrix to form an augmented state vector matrix such that it allows to correct both the state vector and the observation vector simultaneously in one update, establishing an augmented state set; 4) Compute sample mean of augmented state set Recalculate sample covariance .

3. The method according to claim 1 or 2, characterized in that: The specific steps of Kalman update set in S62 are: 1) Adopt an observed-perturbation scheme to generate independent noise for each augmented matrix set , the observation error matrix is composed of the measurement error covariance matrix and the proxy model error covariance matrix; 2) Augmented state sample covariance matrix from S61 with observation operator matrix H and observation error matrix for determining a Kalman gain matrix, the Kalman gain being used for determining the optimal linear weighting fusion scale of the predicted state with the observation, so that the updated parameter set optimally matches the observation information.

4. The method according to claim 2, characterized in that: Set prediction is to predict each sample in the set through the unified space-time surrogate model in S5 in an artificial time step, wherein the time series data is regarded as an artificial time step, and the formula of the predicted set is: is a prediction ensemble matrix, is a proxy model operator, is a predicted state vector of the j th ensemble member, is a state vector ensemble matrix.

5. The method for predicting clay settling curve based on two-phase flow and data assimilation coupling according to claim 4, characterized in that: The state vector set provides the initial value for the next round of prediction, which is the set state after the last round of data assimilation, and the formula is: is the state vector of the last analysis iteration of the j th set member, is the set matrix of state vectors, is the dimension of the state vector, N is the number of set members.

6. The method for predicting clay settling curve based on two-phase flow and data assimilation coupling according to claim 4, characterized in that: In S61, the adaptive inflation of the state vector enhances the variance of the prediction set, and the formula is: is the state vector set mean, is the adaptive dilation coefficient.

7. The method according to claim 2, wherein the method is characterized by: The augmented state matrix combines the predicted state and the observed output predicted by the model to form an augmented state, which provides complete state-observation information for subsequent Kalman update, and is represented as: is the observation information output predicted by the proxy model, is the augmented state matrix, is the dimension of the observation vector.

8. The clay settling curve prediction method based on two-phase flow and data assimilation coupling according to claim 1 or 2, characterized in that: The augmented state sample covariance quantifies the error distribution of the prediction set, including the correlation between the state and the observation, and the formula is: is the augmented state set mean, is the augmented state sample covariance.

9. The method for predicting clay settling curve based on two-phase flow and data assimilation coupling according to claim 3, characterized in that: The formula of the Kalman gain matrix K is: is the Kalman gain matrix, is the observation operator matrix, is the observation error covariance matrix (including the surrogate model error and measurement error).

10. The method for predicting clay settling curve based on two-phase flow and data assimilation coupling according to claim 7, characterized in that: In S6, the iteration process of EnKF data assimilation integrates the observation information into the predicted state to generate an updated state vector set, realizes data assimilation, and the iteration formula is: is the (k + 1)th augmented state vector, j is the (k + 1)th updated analysis vector, is the (k + 1)th updated analysis vector, is the (k + 1)th actual observation vector, is the (k + 1)th independent observation noise.

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