System-level twin data assimilation method based on three-dimensional variation and Gaussian least square

Abstract

The invention belongs to the technical field of fluid network system simulation, and discloses a system-level twinborn data assimilation method based on three-dimensional variation and Gaussian least squares, which comprises the steps of defining problems and inputting, constructing a three-dimensional variation method and a Gaussian weighted least squares linearization observation operator, and combining the Gaussian weighted least squares and the three-dimensional variation to assimilate twinborn data. And analyzing and evaluating a result. According to the method, the modeling parameters of the main steam system of the nuclear power plant are calibrated and optimized, so that the prediction precision of the system-level model is improved. The method aims to fully utilize observation data of the main steam system, and high-precision inversion of key modeling parameters is realized by constructing a residual weighted objective function and fusing a system physical model and multi-source observation information, so that the accuracy and credibility of a simulation model of the main steam system are improved, and the simulation efficiency of the main steam system is improved. And reliable data support and technical basis are provided for subsequent state evaluation, performance prediction and digital twinning application.

Description

Technical Field

[0001] This application belongs to the field of fluid network system simulation technology, and in particular relates to a system-level twin model data assimilation method based on three-dimensional variational and Gaussian weighted least squares method. Background Technology

[0002] In the nuclear energy field, digital twin technology has two main applications: design verification of new reactor types and operation support, analysis, and improvement of existing power plants. Whether for design verification or unit operation and maintenance, the core requirement is a high-precision digital twin model.

[0003] Currently, existing mechanistic and data models have limitations and cannot meet the high accuracy requirements of digital twin models. Furthermore, the performance of actual equipment changes over time. Therefore, most current digital twin models combine mechanistic and data-driven approaches. These models use the mechanistic model as the primary model and correct mechanistic modeling errors using data, effectively addressing the insufficient accuracy of twin models for two-loop systems under varying operating conditions. However, a challenge of this approach is how to integrate the data model with the mechanistic model; data assimilation technology offers an effective solution.

[0004] Data assimilation bridges the gap between fragmented and imprecise observational data and mathematical models of dynamic physical processes. Common data assimilation methods include Kalman filtering, three-dimensional variational methods, four-dimensional variational methods, and ensemble Kalman filtering. These methods combine numerical estimation with real-time observation and are widely used in numerical weather prediction, ocean analysis, hydrology, and remote sensing. Among them, the three-dimensional variational method, due to its real-time performance and ability to handle nonlinearities, has also been applied in many areas of nuclear engineering, such as power distribution optimization, core physics field reconstruction, and burnup distribution calibration. However, existing research mainly focuses on the reconstruction of core physics fields, with relatively little research on nuclear power plant system-level models. Nuclear power plant system-level models typically consist of multiple subsystems and components, exhibiting high coupling and nonlinearity, making them difficult to fully represent through physical equations. Therefore, the observation operators used for data assimilation cannot be directly expressed in matrix form. Summary of the Invention

[0005] The purpose of this application is to provide a system-level twin data assimilation method based on three-dimensional variational and Gaussian least squares to calibrate and optimize the modeling parameters of the main steam system of a nuclear power plant, thereby improving the prediction accuracy of the system-level model. This method aims to fully utilize the observation data of the main steam system, construct a residual-weighted objective function, and fuse the system physical model with multi-source observation information to achieve high-precision inversion of key modeling parameters (such as pipe damping coefficients). This improves the accuracy and reliability of the main steam system simulation model, providing reliable data support and a technical foundation for subsequent state assessment, performance prediction, and digital twin applications.

[0006] To achieve the above objectives, this application provides the following technical solution:

[0007] A system-level twin data assimilation method based on three-dimensional variational and Gaussian least squares includes:

[0008] S1: Input background state x b Observed value y obs And establish the background error covariance matrix B;

[0009] S2: Construct a cost function to minimize the difference between the simulation and the true value, and initialize the background state x. b and observed value y obs Given the background error covariance matrix B and the observation error covariance matrix R, a gradient solution framework is established, and an iterative method is used to approximate the optimal state x. a ;

[0010] S3: Local Latin hypercube sampling, calculate the theoretical observation value for each sample, construct state-observation data pairs, and fit the locally linearized observation operator H;

[0011] S4: Linearize the observation operator H using Gaussian weighted least squares method, update the cost function J(x), and output the optimal state x through three-dimensional variational optimization. a ;

[0012] S5: Output the optimal state x a The root mean square error and relative deviation are evaluated, and the analyzed values, observed values ​​and true values ​​and error trends are compared.

[0013] As one feasible approach, S1 includes:

[0014] S1.1: Input background state x b ;

[0015] S1.2: Input observation value y obs ;

[0016] S1.3: Establish the error covariance matrix B and the observation error covariance matrix R as follows:

[0017] B = B0C

[0018] In the formula, B0 is a suitable scalar variance coefficient, and C is the correlation structure of the background error;

[0019] R = diag(r1, r2, ..., r m )

[0020] In the formula, r i (i = 1, 2, ..., m) represents the standard deviation corresponding to the error of the i-th observation.

[0021] As an feasible approach, sources of observational data include pressure, flow, and temperature parameters generated by running a digital twin system.

[0022] As an feasible approach, the relevant structure C of the background error is:

[0023]

[0024] In the formula, C ij Let x be the specific value of the related structure C in the i-th row and j-th column. i For the i-th grid point, x j Let L be the j-th grid point, L be the scale factor, and e be the natural constant.

[0025] As an implementable approach, S2 includes:

[0026] S2.1: Construct the cost function J(x):

[0027] J(x)=(xx b ) T B -1 (xx b )+(Ηx-Y0) T R -1 (Ηx-Y0)

[0028] In the formula, B is the background error covariance matrix, R is the observation error covariance matrix, H is the observation operator that maps the model state space to the observation space, and Y0 is the observed value.

[0029] S2.2: Initialize background state x b and observed value y obs ;

[0030] S2.3: Define the background error covariance matrix B and the observation error covariance matrix R;

[0031] S2.4: Construct the cost function to solve for the optimal state x a ;

[0032] S2.5: Introduce an iterative solution method, using numerical methods to gradually approximate the optimal state x. a .

[0033] As an feasible approach, in S2.3, the background error covariance matrix B is calculated using a second-order autoregressive model, taking into account the scale factor L of the parameters and the distance between grid points; the observation error covariance matrix R is set, and the standard deviation r of each observation is set according to the uncertainty of the observations. i .

[0034] As an feasible approach, S2.4 establishes a gradient solution framework and uses the gradient method to find the optimal state x. a The gradient formula is:

[0035]

[0036] If the observation operator H performs local linearization at the current state x, then the optimal state x a The solution process is transformed into solving a linear system.

[0037] As an implementable approach, S3 includes:

[0038] S3.1: Sampling the state of the sampling area, using Latin hypercube sampling, sampling is performed within a local region of the current state point;

[0039] S3.2: Use a running digital twin system for each sample x i Calculate the theoretical observation value y i =H(x) i );

[0040] S3.3: Construction State-Observation Data Pair (x i ,y i );

[0041] S3.4: The data pairs are fitted using the weighted least squares method to obtain the locally linearized observation operator H.

[0042] As an implementable approach, S4 includes:

[0043] S4.1: Obtain the linearized H based on the Gaussian weighted least squares method, update the cost function J(x), and solve for the optimal state x using optimization methods. a ;

[0044] S4.2: Initialize background state x b Background error covariance matrix B and observation error covariance matrix R;

[0045] S4.3: Linearize the observation operator H using Gaussian weighted least squares method;

[0046] S4.4. Update the optimal state x using a three-dimensional variational optimization objective function. a .

[0047] As an implementable approach, S5 includes:

[0048] S5.1: Output the updated optimal state x a ;

[0049] S5.2: Evaluate the root mean square error, which measures the deviation between the analyzed value and the true value;

[0050] S5.3: Evaluate the relative deviation, stability, and reliability of the optimal state value;

[0051] S5.4: Visualize the results, compare the analyzed values, observed values, and true values, and show the trend of error over time.

[0052] Compared with existing technologies, the system-level twin model data assimilation method based on three-dimensional variational and Gaussian weighted least squares provided in this application has the following advantages:

[0053] This application utilizes a data assimilation method combining Gaussian-weighted least squares (GLS) and three-dimensional variational (3D-Var) to calibrate and optimize the modeling parameters of a nuclear power plant system-level twin model. This method aims to fully leverage the system's observation data, constructing a residual-weighted objective function to fuse the system's physical model with multi-source observation information. This achieves high-precision inversion and uncertainty constraints on key modeling parameters (such as pipe damping coefficients), thereby improving the accuracy and reliability of the simulation model and providing reliable data support and a technical foundation for subsequent state assessment, performance prediction, and digital twin applications.

[0054] The parameter estimation accuracy of this application is high, such as Figures 2 to 4 As shown, the root mean square error (RMSE) between the analyzed values ​​and the true parameter values ​​is consistently below 0.03, indicating that this method has high estimation accuracy for the model parameters.

[0055] This application exhibits a small relative error. Considering the different value ranges of various parameters, the relative deviation was further calculated. The average relative deviation between the analyzed values ​​and the true values ​​is 0.75%, and the standard deviation is 0.56%, indicating that the method has stable and accurate estimation capabilities across all parameter dimensions.

[0056] This application demonstrates good observational fitting performance and strong noise resistance, such as... Figures 5 to 8As shown, in comparison with actual observations (such as pressure, flow rate, and temperature), the analyzed value curves are highly consistent with the true value curves, significantly outperforming the observed data after noise has been added. This indicates that the method not only effectively approximates the true state of the system but also has strong noise resistance. Attached Figure Description

[0057] To more clearly illustrate the technical solution of this application, the accompanying drawings used in the technical description will be briefly introduced below.

[0058] Figure 1 A flowchart of the system-level twin model data assimilation method based on three-dimensional variational and Gaussian weighted least squares provided in this application;

[0059] Figure 2 A schematic diagram of the state parameter assimilation results provided in this application;

[0060] Figure 3 A schematic diagram of another state parameter assimilation result provided in this application;

[0061] Figure 4 A schematic diagram illustrating the deviation between the assimilation results provided in this application and the actual state;

[0062] Figure 5 A schematic diagram showing the comparison between the assimilation results of the temperature sensor provided in this application and actual observations;

[0063] Figure 6 A schematic diagram showing the comparison between the assimilation results of another temperature sensor provided in this application and actual observations;

[0064] Figure 7 A schematic diagram showing the comparison between the assimilation results of the flow sensor provided in this application and the actual observation results;

[0065] Figure 8 A schematic diagram showing the comparison between the assimilation results of the pressure sensor provided in this application and actual observations. Detailed Implementation

[0066] The following detailed description provides further details on specific implementation methods.

[0067] Currently, the damping coefficient of steam pipelines is usually obtained through numerical simulation. However, due to the inability to directly measure it, and model simplification or insufficient modeling, there are often discrepancies between the simulation results and the actual situation. Therefore, this application proposes a three-dimensional variational and Gaussian weighted least squares method based on observations to calibrate the state parameters of the main steam system. Considering that the main steam system is a highly coupled, nonlinear, and complex system-level model, the Gaussian weighted least squares method is first used to locally linearize the observation operator to establish the relationship between the state parameters and the observations. Then, the three-dimensional variational method is used to estimate the state parameters of the main steam system. In experiments based on a running digital twin system dataset, the root mean square error (RMSE) between the assimilation results and the actual state values ​​remains below 3%. Assimilation makes the twin system output closer to the actual value, indicating that the three-dimensional variational and Gaussian weighted least squares method can effectively correct the state parameters and fit the observations well, thus obtaining accurate state parameters of the main steam system.

[0068] like Figure 1 As shown, this application provides a system-level twin data assimilation method based on three-dimensional variational and Gaussian least squares, including:

[0069] Step 1, Define the problem and input: Input background state x b Observed value y obs And establish the background error covariance matrix B.

[0070] Step 2: Construct a 3D variational method: Construct a cost function to minimize the difference between the simulation and the true value, and initialize the background state x. b and observed value y obs Given the background error covariance matrix B and the observation error covariance matrix R, a gradient solution framework is established, and an iterative method is used to approximate the optimal state x. a .

[0071] Step 3: Gaussian weighted least squares linearization of the observation operator: local Latin hypercube sampling, calculate the theoretical observation value for each sample, construct state-observation data pairs, and fit the locally linearized observation operator H.

[0072] Step 4: Combining Gaussian weighted least squares and three-dimensional variational optimization: Linearize the observation operator H using Gaussian weighted least squares, update the cost function J(x), and output the optimal state x through three-dimensional variational optimization. a .

[0073] Step 5, Result Analysis and Evaluation: Output the optimal state x a It assesses root mean square error and relative bias, and visualizes and compares the analyzed values, observed values, and true values, as well as error trends.

[0074] Step 1 defines the problem and inputs used to estimate the main steam system state parameters (such as pipe damping coefficients) to improve the accuracy of the twin system. Specifically, this includes:

[0075] Step 1.1: Input background state x b .

[0076] Initial estimates are typically provided by historical running data or model simulations. They serve as reference states for assimilation and constrain the optimization problem.

[0077] Step 1.2: Input the observed value y obs .

[0078] The simulation results from the model are mixed with Gaussian noise to simulate measurements under real-world conditions, serving as the basis for relating these measurements to state parameters during the optimization process. The data sources include pressure, flow rate, and temperature parameters generated by the running digital twin system.

[0079] Step 1.3: Establish the error covariance matrix.

[0080] Establish the background error covariance matrix B to describe the background state error, as follows:

[0081] B = B0C

[0082] In the formula, B0 represents a suitable scalar variance coefficient, and C represents the correlation structure of the background error, the correlation of which depends only on the distance between states;

[0083]

[0084] In the formula, C ij This represents the specific value of the related structure C in the i-th row and j-th column, x i x represents the i-th grid point; j Represents the j-th grid point; L represents the scale factor; e represents the natural constant;

[0085] L represents the grid points in the spatial grid, where L is the maximum distance between the main steam pipe modeling parameters. For grid point x... i and x j The values ​​of are used to calculate the distance between parameters based on their positions in the main steam pipeline.

[0086] Therefore, all terms in matrix B are positive and decrease exponentially with increasing distance from the diagonal.

[0087] The observation error covariance matrix R is used to describe the error in the observation data. R is defined as follows:

[0088] R = diag(r1, r2, ..., r m )

[0089] In the formula, r i (i = 1, 2, ..., m) is the standard deviation corresponding to the error of the i-th observation.

[0090] Step 2 specifically includes:

[0091] Step 2.1: Construct the cost function and optimize it to minimize the difference between the simulated and true values. From a mathematical perspective, the data assimilation process is about finding an optimal solution that approximates the true but is unknown. In the three-dimensional variational method, the cost function is used to characterize the difference between the simulated and true values, transforming it into an optimization problem of finding the optimal state.

[0092] The cost function in three-dimensional variational data assimilation is expressed as:

[0093] J(x)=(xx b ) T B -1 (xx b )+(Ηx-Y0) T R -1 (Ηx-Y0)

[0094] In the formula, B represents the background error covariance matrix, R represents the observation error covariance matrix, H represents the observation operator that maps the model state space to the observation space, Y0 represents the observed value, and x b Indicates the background state value.

[0095] Step 2.2, for background state x b and observed value y obs Perform initialization.

[0096] Step 2.3: Set the background error covariance matrix B as follows:

[0097] The background error covariance matrix B is calculated using a second-order autoregressive model, considering the scale factor L of the parameters and the distance between grid points. The observation error covariance matrix R is set, and the standard deviation r of each observation is set according to the uncertainty of the observations. i .

[0098] Step 2.4: Establish a gradient solution framework and find the optimal state using the gradient method.

[0099] Gradient formula:

[0100]

[0101] Wherein, if the observation operator H can be locally linearized at the current state x (x is a variable in the gradient function, and the root of the above equation is the optimal state), then the optimal state x aThe solution process can be transformed into solving a linear system.

[0102] Therefore, this application proposes a local Gaussian weighted least squares method to locally linearize the observation operator, thereby locally constructing the observation operator H.

[0103] Step 2.5: Introduce iterative solution methods, using numerical methods (such as the conjugate gradient method) to gradually approximate the optimal state x. a Since H(x) is nonlinear, local linearization (see step 3) is used to speed up convergence.

[0104] Step 3 specifically includes:

[0105] Step 3.1: Sample the state of the sampling area using Latin hypercube sampling, and sample within a local region of the current state point;

[0106] Step 3.2: Use the running digital twin system to process each sample x i Calculate the theoretical observation value y i =H(x) i );

[0107] Step 3.3: Construct state-observation data pairs (x i ,y i );

[0108] Step 3.4: Fit the data pairs using the weighted least squares method to obtain the locally linearized observation operator H.

[0109] Step 4 specifically includes:

[0110] Step 4.1: Obtain the linearized H based on the Gaussian weighted least squares method, update the cost function J(x), and solve for the optimal state x using optimization methods. a ;

[0111] Step 4.2: Initialize background state x b And the background error covariance matrix B, the observation error covariance matrix R;

[0112] Step 4.3: Linearize the observation operator H using Gaussian weighted least squares method;

[0113] Step 4.4: Update the optimal state x using the three-dimensional variational optimization objective function. a .

[0114] Step 5 specifically includes:

[0115] Step 5.1: Output the updated optimal state x a ;

[0116] Step 5.2: Evaluate the root mean square error, which measures the deviation between the analyzed value and the true value;

[0117] Step 5.3: Evaluate the relative deviation to verify the stability and reliability of the analyzed values;

[0118] Step 5.4: Visualize the results, compare the analyzed values, observed values, and true values, and show the trend of error change over time.

[0119] In step 5, the evaluation indicators are as follows:

[0120] The root-mean-square error (RMSE) is as follows:

[0121]

[0122] In the formula, For the true value, These are the assimilated analytical values.

[0123] Relative deviation: The average relative error and standard deviation between the analyzed value and the true value.

[0124] In step 5, the results are displayed:

[0125] State parameter assimilation results: Figure 1 and Figure 2 For example, the assimilated analytical values ​​fluctuate slightly around the true trajectory, with RMSE remaining below 0.03.

[0126] Comparison of assimilation results and true state: Figure 3 This shows the RMSE deviation between the assimilation results and the true state.

[0127] Comparison of assimilation results and observations: Figures 5-8 The results show that the analytical values ​​obtained by using the three-dimensional variational and Gaussian weighted least squares method are in high agreement with the true values, and can effectively suppress observation noise.

[0128] This application employs Gaussian weighted least squares to locally linearize the observation operator, establishing a complex relationship between the main steam system state parameters and the observed values, and then uses a three-dimensional variational method to estimate the state parameters. To verify the effectiveness of this method, experiments were conducted on a dataset of a nuclear power plant digital twin system, which simulates all dynamic processes of the nuclear power plant except for maintenance conditions. Experimental results show that the method can effectively correct the model state parameters and achieves a high degree of agreement with the observed values.

[0129] Through the above steps, the three-dimensional variational method and the Gaussian weighted least squares method effectively combine the global optimization capability of the three-dimensional variational method and the local linearization capability of the Gaussian weighted least squares method, achieving efficient and accurate data assimilation in complex nonlinear systems.

[0130] This application improves the accuracy of parameter estimation. By utilizing Gaussian weighted least squares to locally linearize the observation operator H, it effectively captures the nonlinear relationship between state parameters and observations in complex physical systems. During data assimilation, the optimal state x... a With the real state x true The root mean square error between them remained at a low level, ensuring the accuracy of parameter estimation.

[0131] This application enhances noise robustness. Even after adding Gaussian noise to the simulated data, the proposed method can still be optimized using a three-dimensional variational cost function, significantly reducing the impact of noise on the analysis results and achieving a high degree of fit to the true values.

[0132] This application efficiently constructs observation operators. By employing the Gaussian weighted least squares method, it avoids the high computational complexity of directly deriving global observation operators for complex physical systems. It improves computational efficiency through local linearization while preserving sensitivity to local features.

[0133] This application improves the representation of background error. It adopts a background error covariance matrix B based on the physical model scale factor L, which reasonably describes the spatial correlation of background error, making the update of state parameters more physically meaningful.

[0134] This application is suitable for modeling complex physical fields. By combining a running digital twin system, the applicability of the three-dimensional variational and Gaussian weighted least squares method was verified in the complex multi-physics coupling environment of the main steam system, and the evolution trajectory of key modeling parameters such as the damping coefficient was successfully constructed.

[0135] This application enhances the stability and safety of system operation. By improving the accuracy of simulation results, it provides reliable support for the condition monitoring and operation optimization of the main steam system in nuclear power plants, thereby improving the system's safety and economy.

[0136] The above description is only a specific embodiment of this application, but the protection scope of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the protection scope of this application.

Claims

1. A system-level twin data assimilation method based on three-dimensional variational and Gaussian least squares, characterized in that, include: S1: Input background state x b Observed value y obs Establish the background error covariance matrix B; S2: Construct a cost function to minimize the difference between the simulation and the true value, and initialize the background state x. b and observed value y obs Given the background error covariance matrix B and the observation error covariance matrix R, an iterative method is used to approximate the optimal state x. a ; S3: Local Latin hypercube sampling, calculate the theoretical observation value for each sample, construct state-observation data pairs, and fit the locally linearized observation operator H; S4: Linearize the observation operator H using Gaussian weighted least squares method, update the cost function J(x), and output the optimal state x through three-dimensional variational optimization. a ; S5: Output the optimal state x a The root mean square error and relative deviation are evaluated, and the analyzed values, observed values ​​and true values ​​and error trends are compared.

2. The system-level twin data assimilation method based on three-dimensional variational and Gaussian least squares according to claim 1, characterized in that, S1 includes: S1.1: Input background state x b ; S1.2: Input observation value y obs ; S1.3: Establish the error covariance matrix B and the observation error covariance matrix R as follows: B = B0C In the formula, B0 is a suitable scalar variance coefficient, and C is the correlation structure of the background error; R=diag(r1,r2,...,r m ) In the formula, r i (i = 1, 2, ..., m) represents the standard deviation corresponding to the error of the i-th observation.

3. The system-level twin data assimilation method based on three-dimensional variational and Gaussian least squares according to claim 2, characterized in that, The sources of the observed data include pressure, flow, and temperature parameters generated by running a digital twin system.

4. The system-level twin data assimilation method based on three-dimensional variational and Gaussian least squares according to claim 2, characterized in that, The specific value of the background error correlation structure C in the i-th row and j-th column is: In the formula, x i For the i-th grid point, x j Let L be the j-th grid point, L be the scale factor, and e be the natural constant.

5. The system-level twin data assimilation method based on three-dimensional variational and Gaussian least squares according to claim 1, characterized in that, S2 include: S2.1: Construct the cost function J(x): J(x)=(x-x b ) T B -1 (x-x b )+(Ηx-Y0) T R -1 (Ηx-Y0) In the formula, B is the background error covariance matrix, R is the observation error covariance matrix, H is the observation operator that maps the model state space to the observation space, and Y0 is the observed value. S2.2: Initialize background state x b and observed value y obs ; S2.3: Define the background error covariance matrix B and the observation error covariance matrix R; S2.4: Construct the cost function to solve for the optimal state x a ; S2.5: Introduce an iterative solution method, using numerical methods to gradually approximate the optimal state x. a .

6. The system-level twin data assimilation method based on three-dimensional variational and Gaussian least squares according to claim 5, characterized in that, In S2.3, the background error covariance matrix B is calculated using a second-order autoregressive model, considering the scale factor L of the parameters and the distance between grid points; the observation error covariance matrix R is set, and the standard deviation r of each observation is set according to the uncertainty of the observations. i .

7. The system-level twin data assimilation method based on three-dimensional variational and Gaussian least squares according to claim 5, characterized in that, In S2.4, a gradient solution framework is established, and the optimal state x is found using the gradient method. a The gradient formula is: If the observation operator H performs local linearization at the current state x, then the optimal state x a The solution process is transformed into solving a linear system.

8. The system-level twin data assimilation method based on three-dimensional variational and Gaussian least squares according to claim 1, characterized in that, S3 include: S3.1: Sampling the state of the sampling area, using Latin hypercube sampling, sampling is performed within a local region of the current state point; S3.2: Use a running digital twin system for each sample x i Calculate the theoretical observation value y i =H(x) i ); S3.3: Construction State-Observation Data Pair (x i ,y i ); S3.4: The data pairs are fitted using the weighted least squares method to obtain the locally linearized observation operator H.

9. The system-level twin data assimilation method based on three-dimensional variational and Gaussian least squares according to claim 1, characterized in that, S4 include: S4.1: Obtain the linearized H based on the Gaussian weighted least squares method, update the cost function J(x), and solve for the optimal state x using optimization methods. a ; S4.2: Initialize background state x b Background error covariance matrix B and observation error covariance matrix R; S4.3: Linearize the observation operator H using Gaussian weighted least squares method; S4.

4. Update the optimal state x using a three-dimensional variational optimization objective function. a .

10. The system-level twin data assimilation method based on three-dimensional variational and Gaussian least squares according to claim 1, characterized in that, S5 include: S5.1: Output the updated optimal state x a ; S5.2: Evaluate the root mean square error, which measures the deviation between the analyzed value and the true value; S5.3: Evaluate the relative deviation and verify the stability and reliability of the optimal state value; S5.4: Visualize the results, compare the analyzed values, observed values, and true values, and show the trend of error over time.

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