AEnKPF-based digital twin state and parameter joint estimation implementation method

Abstract

A digital twinborn state and parameter joint estimation implementation method based on AEnKPF comprises the steps that a simulation-based digital twinborn model is constructed for a nuclear reactor system, and after a simulation data set needed by joint estimation is obtained through the digital twinborn model, the simulation data set is used for training an agent model; performing hyper-parameter optimization on the proxy model and retraining the proxy model by using an optimal hyper-parameter; and combining the retrained proxy model with an AEnKPF algorithm, and carrying out joint estimation on the state and parameters of the digital twinborn model to realize optimization simulation. The simulation data and the measurement data of the digital twinborn model are fused through the AEnKPF algorithm, the measurable state and the non-measurable parameters of the digital twinborn model can be estimated, the method is suitable for digital twinborn in any field, and co-evolution of the digital twinborn model and a physical entity can be achieved.

Description

Technical Field

[0001] This invention relates to a technology in the field of nuclear engineering, specifically a method for jointly estimating digital twin states and parameters based on adaptive ensemble Kalman particle filtering (AEnKPF). Background Technology

[0002] Existing digital twins of nuclear reactors based on simulation programs suffer from the problem of unreliable computational accuracy. Furthermore, real-world changes are highly nonlinear and random; as the system operates, the differences between the twin model and the actual entity accumulate and expand, ultimately causing the established digital twin to fail. Summary of the Invention

[0003] To address the aforementioned shortcomings of existing technologies, this invention proposes a joint estimation method for the state and parameters of a digital twin based on AEnKPF. By fusing simulation and measurement data of the digital twin model using the AEnKPF algorithm, it is possible to estimate the measurable state and non-measurable parameters of the digital twin model. This method is applicable to digital twins in any field and can achieve the co-evolution of the digital twin model and the physical entity.

[0004] This invention is achieved through the following technical solution:

[0005] This invention relates to a method for joint estimation of the state and parameters of a digital twin based on AEnKPF. The method involves constructing a simulation-based digital twin model of a nuclear reactor system, obtaining the simulation dataset required for joint estimation from the digital twin model, and using this dataset to train a surrogate model. The surrogate model is then optimized using hyperparameters and retrained with the optimal hyperparameters. Finally, the retrained surrogate model is combined with the AEnKPF algorithm to jointly estimate the state and parameters of the digital twin model, thereby achieving optimized simulation.

[0006] This invention relates to a joint estimation system for the state and parameters of a digital twin model implementing the above-mentioned method, comprising: a surrogate model construction unit, an AEnKPF construction unit, and a joint estimation result evaluation system unit, wherein: the AEnKPF construction unit uses ensemble Kalman filtering (EnKF) to generate a proposal distribution in the prediction-update step of particle filtering (PF) to obtain an EnKPF model, and dynamically adjusts the process noise variance through a process noise adaptive adjustment algorithm with dynamic variance weighting; the surrogate model construction unit extracts and integrates the data generated by the simulation program, obtains a dataset, performs hyperparameter optimization and training on the surrogate model, and saves the parameters of the trained surrogate model; the joint estimation result evaluation system unit evaluates the obtained state estimation and parameter estimation results using power spectral density plots, smoothness, and first-order autocorrelation coefficients, and then verifies the parameter estimation results using a dynamic parameter update method of the digital twin model.

[0007] Technical effect

[0008] This invention targets the entire nuclear reactor system, employing the EnKPF algorithm combined with a dynamically variance-weighted adaptive process noise adjustment algorithm to dynamically adjust the process noise variance, thereby achieving state estimation and parameter estimation for the digital twin model of the nuclear reactor. Compared with existing technologies, this invention can simultaneously estimate both the measurable states and unmeasurable parameters of the digital twin model, and can simultaneously achieve noise reduction of state parameters and adjustment of model parameters, ultimately improving the accuracy of the nuclear reactor digital twin model. Attached Figure Description

[0009] Figure 1 This is a flowchart of the present invention;

[0010] Figure 2 A flowchart for the dynamic parameter update of a digital twin model;

[0011] Figure 3 The result of the joint estimation obtained based on the AEnKPF algorithm is shown in the figure.

[0012] Figure 4 This is a validation graph for the parameter estimation results obtained using the dynamic parameter update method. Detailed Implementation

[0013] like Figure 1 As shown, this embodiment illustrates a method for jointly estimating the state and parameters of a digital twin based on AEnKPF, comprising:

[0014] Step 1: Use the Relap5 system program to simulate the nuclear reactor and obtain the simulation dataset required for joint estimation. This simulation is the digital twin model.

[0015] The simulation dataset was obtained by manually modifying the Relap5 input file multiple times after determining the parameters and states that needed to be estimated.

[0016] Step 2: Divide the simulation dataset, optimize the hyperparameters of the surrogate model, and save the surrogate model. Specifically, this includes:

[0017] 2.1 Using KNN regression as a surrogate model, the dataset obtained in step 1 is divided into a training set and a test set in a 9:1 ratio for training and testing the surrogate model. Specifically, time and the parameters to be estimated are used as inputs to the surrogate model, and the states to be estimated are used as outputs of the surrogate model.

[0018] 2.2 Use Bayesian optimization algorithm to optimize hyperparameters. Specifically, minimize the absolute average error of the test set obtained in step 2.1 as the optimization index, search for the number of leaf nodes, the number of nearest neighbors, the power parameter of the Minkowski metric, and the weight function used for prediction of the surrogate model. When the hyperparameter optimization is completed, the optimal hyperparameters of the surrogate model are obtained.

[0019] 2.3 Retrain the surrogate model using the optimal hyperparameters obtained in step 2.2. After retraining, save the model parameters for joint estimation.

[0020] Step 3: Construct the AEnKPF algorithm. Improve the proposal distribution of the traditional PF using EnKF to obtain the EnKPF model. Use a dynamically weighted process noise adaptive adjustment algorithm to dynamically adjust the process noise variance to obtain the AEnKPF model. Specifically, this includes:

[0021] 3.1 Utilizing EnKF in the prediction-update step of PF to generate the proposal distribution, constructing the EnKPF model, specifically including:

[0022] a) Initialize particles at the initial moment: Assume the custom initial state value is The initial covariance is ,make ,in: For the weight of the particle, For state values, superscript The particle's serial number. For covariance, The number of EnKPF particles, subscript 0 or For a specific moment;

[0023] b) Calculate the first A sample of a set of particles: ,in: ,in: The number of samples in the set is indicated by the superscript. For the current moment, superscript For the previous moment, subscript The index of the sample in the set. For the set of state samples, Assuming a normal distribution, the state transition model is defined as follows: The state transition model describes the state. How to start from the previous moment It evolved from, among which: This is the state transition function. To characterize the uncertainty of the system process noise model;

[0024] c) Calculate the mean and covariance of the ensemble sample: , , ,in: The prior covariance of the observed values. To define the prior covariance of the observation space, the observation model is defined as follows: The observation model describes the state Below, observed values How to generate it? For the observation function, To observe noise and characterize measurement error;

[0025] d) Calculate the Kalman gain: , Kalman gain;

[0026] e) Update the set samples using EnKF: , , ,in: The mean is the number of observations. Sampling from a Gaussian distribution with variance;

[0027] f) Construct the proposal distribution function using the ensemble sample: ,in: For different probability distributions;

[0028] g) Calculate the weight of each particle: ;

[0029] h) Perform weight normalization on all particles: ;

[0030] i) Resample the particles and calculate the expected value of the particles as the result output.

[0031] 3.2 The EnKPF algorithm is dynamically adjusted by using a dynamic variance-weighted process noise adaptive adjustment algorithm to obtain the complete EnKPF algorithm, specifically: as well as ,in: For process noise variance, It is a diagonal matrix; The variance of the state particles, subscript State; The variance of the parameter particles, subscript State; For smoothing coefficients; The noise matrix is ​​based on the process.

[0032] In the AEnKPF algorithm, the current estimated variance reflects the dynamic changes of the short-term fast response, while the fundamental noise matrix ensures the stability of the algorithm on a long-term scale. When the parameters converge, the variance decreases, thus reducing process noise; when the system experiences dynamic abrupt changes, the variance increases, thus amplifying process noise. Finally, matrix symmetry ensures the positive definiteness of the covariance matrix, guaranteeing numerical stability during the joint estimation process.

[0033] 3.3 The surrogate model and the sensor detection data of the estimated state are fused using the AEnKPF algorithm to jointly estimate the state and parameters of the digital twin model in step 1. The AEnKPF algorithm outputs the estimation results of the state and parameters.

[0034] Step 4: Evaluate and verify the results of state estimation and parameter estimation.

[0035] 4.1 After obtaining the joint estimation results, the parameter estimation results are verified using a dynamic parameter update method, specifically as follows: Figure 2 As shown, the average value of the parameter estimates over an initial period is used as the initial parameter value for digital twin model simulation calculations; the smaller the period, the more accurate the results. Upon reaching a new period, the average value of the parameter estimates for that period is used as the parameters for the new period for simulation calculations.

[0036] 4.2 The state estimation and parameter estimation results are evaluated using a joint estimation result evaluation system. Specifically, the state estimation evaluation system includes: power spectral density plot (PSD), smoothness, and first-order autocorrelation coefficient; the parameter estimation evaluation system includes: mean absolute error (MAE), mean relative error (MAPE), maximum absolute prediction error (MaxAE), and coefficient of determination. .

[0037] The power spectrum is a function describing the distribution of signal energy in the frequency domain. It converts the time-domain signal into a frequency-domain signal through Fourier transform, showing the energy distribution of the signal at different frequencies. Therefore, the denoising effect can be qualitatively verified by comparing the PSD before and after denoising.

[0038] The smoothness mentioned above measures data volatility through the variance of the difference, with values ​​between 0 and 1. A higher value indicates a smoother signal. The improvement in signal smoothness after noise reduction directly reflects the noise suppression effect. Specifically... ,in: Indicates smoothness, This represents the first-order difference of the signal. The variance is represented by the autocorrelation coefficient. The autocorrelation coefficient is used to measure the correlation between data at different time points in a time series. By comparing the autocorrelation coefficients of the signals before and after noise reduction, it can be determined whether noise reduction has destroyed the original structure of the signal.

[0039] The first-order autocorrelation coefficient mentioned above is specifically... ,in: This represents the first-order autocorrelation coefficient. The subscript represents the mean of a time series. and Indicates a point in time. express Time series value at any given moment.

[0040] The parameter estimation evaluation system selected includes mean absolute error (MAE), mean relative error (MAPE), maximum absolute prediction error (MaxAE), and coefficient of determination. ,in: , , , , in the formula For quantity, The expected value (this invention uses the actual measured value as the expected value), This is the output value of the digital twin model.

[0041] Based on specific practical experiments, using a test rig of a multi-purpose small light water reactor as the object, the core fluid temperature was selected for state estimation, and the heat transfer coefficient (HTC) of the primary and secondary side thermal components was selected for parameter estimation. HTC values ​​of 5, 6, 7, ..., 40 were collected. The simulation data from the first 4000 seconds of the transient was used as the dataset. The Bayesian optimization of the KNN regression was performed 300 times, resulting in an optimal leaf node count of 44, an optimal nearest neighbor layer count of 4, an optimal Minkowski power parameter of 1, and an optimal weight function for prediction that is the reciprocal of the distance between the weights. The AEnKPF measurement noise standard deviation was set to 1.138, the basic process noise to 2.0, the smoothing coefficient to 0.9, the particle count to 22, the ensemble sample size to 11, and the initial HTC value to 22.5. The covariance is 0.1, and the initial core fluid temperature is 250℃ with a covariance of 0.1. The parameter dynamic update period is set to 100 seconds.

[0042] like Figure 3 As shown, the joint estimation results obtained based on the above parameters are as follows: As can be seen from the figure, the MAE of the KNN regression prediction and the measured value obtained using the parameter estimation results is 1.115, and the MAPE is 0.486%; the MAPE of the state estimation result and the measured value is 0.378%; the autocorrelation coefficient is 0.995; the smoothness is 0.884; and the time for a single joint estimation is approximately 0.106 seconds. Figure 3 (c) is the PSD of the measured value and the parameter estimate, which shows that the method proposed in this invention can effectively reduce the noise of the estimated state value.

[0043] like Figure 4 The figure shows the results obtained through the parameter dynamic update method. As can be seen, the MAE of the simulated values ​​and the measured values ​​of the digital twin model is 2.192; MAPE is 0.976%; and MaxAE is 39.615. It is 0.720.

[0044] The results obtained by the existing joint estimation method are as follows: Based on the traditional PF method, the MAE of the KNN regression prediction is 1.203, and the MAPE is 0.527%; the MAPE of the state estimation result is 0.176%; the autocorrelation coefficient is 0.990; the smoothness is 0.691; and the time for a single joint estimation is approximately 0.112 seconds. The MAE of the digital twin model simulation calculation is 2.274; the MAPE is 1.013%; and the MaxAE is 39.580. It is 0.710.

[0045] Compared with existing technologies, this method improves the MAE and MAPE of KNN regression predictions compared to measured values, autocorrelation coefficient, smoothness, time of single joint estimation, and the MAE, MAPE, and MaxAE of simulated values ​​compared to measured values. Both were improved. Based on the parameter estimates obtained from EnKPF, the MAPE of the calculated and measured values ​​of Relap5 decreased from 29.507% to 0.976%. This indicates that the dynamic parameter update method can effectively adjust the model parameters of Relap5, making the calculated values ​​of the digital twin model closer to the detector measurements. Furthermore, these results also demonstrate that the proposed EnKPF algorithm and the dynamically variance-weighted process noise adaptive adjustment algorithm can achieve state estimation and parameter estimation for nuclear reactor digital twins, effectively improving the simulation accuracy of the digital twin model.

[0046] Therefore, based on Figure 1 Joint estimation framework for state parameters and Figure 2 The proposed dynamic parameter update method significantly improves the simulation accuracy of the Relap5 system program. This method can simultaneously estimate both the measurable states and non-measurable parameters of the digital twin model, achieving both parameter denoising and parameter adjustment. This method can be applied to digital twins in any field, effectively fusing multi-source data and enabling the co-evolution of the digital twin model and the physical entity, thereby improving the accuracy of the digital twin model.

[0047] The above-described specific implementations can be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of the present invention. The scope of protection of the present invention is defined by the claims and is not limited to the above-described specific implementations. All implementation schemes within the scope of the claims are bound by the present invention.

Claims

1. A method for joint estimation of digital twin states and parameters based on AEnKPF, characterized in that, By constructing a simulation-based digital twin model of the nuclear reactor system, the simulation dataset required for joint estimation is obtained from the digital twin model and then used to train the surrogate model. The surrogate model is hyperparameter optimized and retrained using the optimal hyperparameters. The retrained surrogate model is then combined with the AEnKPF algorithm to jointly estimate the state and parameters of the digital twin model, thereby achieving optimized simulation.

2. The joint estimation implementation method according to claim 1, characterized in that, The construction of the digital twin model involves using the Relap5 system program to simulate the nuclear reactor and obtain the simulation dataset required for joint estimation. This simulation dataset is the digital twin model. After determining the parameters and states that need to be estimated, the simulation dataset is obtained by manually modifying the Relap5 input file multiple times.

3. The joint estimation implementation method according to claim 1, characterized in that, The hyperparameter optimization mentioned above refers to the use of the Bayesian optimization algorithm to optimize hyperparameters. Specifically, the absolute mean error of the test set is used as the optimization index to search for the number of leaf nodes, the number of nearest neighbors, the power parameter of the Minkowski metric, and the weight function used for prediction in the surrogate model. The optimal hyperparameters of the surrogate model are obtained when the hyperparameter optimization is completed.

4. The joint estimation implementation method according to claim 1, characterized in that, The combination of the retrained surrogate model and the AEnKPF algorithm refers to: constructing the AEnKPF algorithm, using ensemble Kalman filtering (EnKF) to improve the proposal distribution of the traditional PF to obtain the EnKPF model, and using a dynamic variance weighted process noise adaptive adjustment algorithm to dynamically adjust the process noise variance to obtain the AEnKPF model.

5. The joint estimation implementation method according to claim 1 or 4, characterized in that, The combination of the retrained surrogate model with the AEnKPF algorithm specifically includes: 3.1 Utilizing EnKF in the prediction-update step of PF to generate the proposal distribution, constructing the EnKPF model, specifically including: a) Initialize particles at the initial moment: Assume the custom initial state value is The initial covariance is ,make ,in: For the weight of the particle, For state values, superscript The particle's serial number. For covariance, The number of EnKPF particles, subscript 0 or For a specific moment; b) Calculate the first A sample of a set of particles: ,in: ,in: The number of samples in the set is indicated by the superscript. For the current moment, superscript For the previous moment, subscript The index of the sample in the set. For the set of state samples, Assuming a normal distribution, the state transition model is defined as follows: The state transition model describes the state. How to start from the previous moment It evolved from, among which: This is the state transition function. To characterize the uncertainty of the system process noise model; c) Calculate the mean and covariance of the ensemble sample: , , ,in: The prior covariance of the observed values. To define the prior covariance of the observation space, the observation model is defined as follows: The observation model describes the state Below, observed values How to generate it? For the observation function, To observe noise and characterize measurement error; d) Calculate the Kalman gain: , Kalman gain; e) Update the set samples using EnKF: , , ,in: The mean is the number of observations. Sampling from a Gaussian distribution with variance; f) Construct the proposal distribution function using the ensemble sample: ,in: For different probability distributions; g) Calculate the weight of each particle: ; h) Perform weight normalization on all particles: ; i) Resample the particles and calculate the expected value of the particles as the result output; 3.2 The EnKPF algorithm is dynamically adjusted by using a dynamic variance-weighted process noise adaptive adjustment algorithm to obtain the complete EnKPF algorithm, specifically: as well as ,in: For process noise variance, It is a diagonal matrix; The variance of the state particles, subscript State; The variance of the parameter particles, subscript State; For smoothing coefficients; The noise matrix of the basic process; 3.3 The surrogate model and the sensor detection data of the estimated state are fused using the AEnKPF algorithm to jointly estimate the state and parameters of the digital twin model. The AEnKPF algorithm outputs the estimation results of the state and parameters.

6. The joint estimation implementation method according to claim 5, characterized in that, In the AEnKPF algorithm, the current estimated variance reflects the dynamic changes of the short-term fast response, and the basic noise matrix ensures the stability of the algorithm on a long-term scale. When the parameters converge, the variance decreases, which reduces the process noise. When the system undergoes dynamic changes, the variance increases, which amplifies the process noise. Finally, matrix symmetry ensures the positive definiteness of the covariance matrix and guarantees numerical stability in the joint estimation process.

7. The joint estimation implementation method according to claim 1, characterized in that, The results of the joint estimation are evaluated and verified, including: 4.1 The parameter estimation results are verified using a dynamic parameter update method. Specifically, the average value of the parameter estimates over a certain period is used as the initial value of the parameters for digital twin model simulation calculation. The smaller the period, the more accurate the result. When a new period is reached, the average value of the parameter estimates for that period is used as the parameters for the new period for simulation calculation. 4.2 The results of the obtained state estimation and parameter estimation are evaluated through a joint estimation result evaluation system.

8. The joint estimation implementation method according to claim 7, characterized in that, The evaluation system for the joint estimation results includes: power spectral density plot (PSD), smoothness, first-order autocorrelation coefficient, mean absolute error (MAE), mean relative error (MAPE), maximum absolute prediction error (MaxAE), and coefficient of determination. .

9. A joint estimation system for the state and parameters of a digital twin model implementing the method of any one of claims 1-8, characterized in that, include: The system comprises a proxy model construction unit, an AEnKPF construction unit, and a joint estimation result evaluation system unit. The AEnKPF construction unit uses ensemble Kalman filtering (EnKF) to generate a proposal distribution in the prediction-update step of particle filtering (PF) to obtain the EnKPF model, and dynamically adjusts the process noise variance through a process noise adaptive adjustment algorithm with dynamic variance weighting. The surrogate model construction unit extracts and integrates the data generated by the simulation program, obtains the dataset, performs hyperparameter optimization and training on the surrogate model, and saves the parameters of the trained surrogate model. The joint estimation result evaluation system unit evaluates the obtained state estimation and parameter estimation results using power spectral density plots, smoothness, and first-order autocorrelation coefficients, and then verifies the parameter estimation results using the parameter dynamic update method of the digital twin model.

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