An Optimization Method for Tokamak Electromagnetic Measurement Diagnosis Based on Bayesian Uncertainty

Abstract

The present invention relates to the technical field of the control system of a nuclear fusion tokamak device, and particularly relates to an optimization method for tokamak electromagnetic measurement diagnosis based on Bayesian uncertainty. The technical solution includes designing the discharge equilibrium of the tokamak device by using the EFIT program and generating corresponding electromagnetic measurement diagnosis signals of magnetic probes and flux loops; based on the electromagnetic measurement diagnosis signals, constructing a Bayesian equilibrium reconstruction model, and the model associates the posterior probability of the equilibrium parameters with the prior probability and the likelihood probability of the diagnosis through the Bayesian formula. The present invention proposes to use Bayesian uncertainty to optimize the diagnosis of magnetic probes and flux loops in the tokamak device, which can uniformly model different diagnoses, comprehensively consider the influence of different diagnoses in the equilibrium reconstruction, and quantify the information amount provided by the diagnosis by using the uncertainty given by the posterior probability. Based on this information amount, the diagnosis can be efficiently optimized, and has strong universality.

Description

Technical Field

[0001] The invention relates to the technical field of nuclear fusion tokamak device control system, and in particular to a tokamak electromagnetic measurement diagnosis optimization method based on Bayesian uncertainty. Background Art

[0002] In nuclear fusion tokamaks, electromagnetic measurement diagnosis is the core technical means for real-time monitoring of plasma state, achieving equilibrium reconstruction and active control. Diagnostics such as magnetic probes and flux rings provide data support for the identification of key parameters such as plasma boundary shape and current distribution by measuring magnetic field and flux signals. The accurate reconstruction of these parameters directly determines the operating stability and performance optimization of the tokamak device. However, with the development of fusion reactor engineering towards scale and practicality, the structural complexity of the device has increased significantly (such as the introduction of breeder blankets and teleoperation systems), resulting in a significant reduction in the physical window that can be used to deploy electromagnetic diagnosis. At the same time, the strong radiation environment and engineering constraints of fusion reactors have caused a sharp increase in the maintenance and replacement costs of the diagnostic system. In this context, how to optimize the configuration of electromagnetic measurement diagnosis within a limited diagnostic window to balance the accuracy of equilibrium reconstruction and engineering feasibility has become a technical problem that needs to be solved urgently.

[0003] At present, the optimization of electromagnetic measurement diagnostics in tokamaks mainly relies on the singular value decomposition (SVD) method. This method constructs a diagnostic signal matrix, uses singular value analysis to determine the minimum number of diagnostics required to reconstruct plasma parameters, and screens redundant diagnostics through linear combinations. However, the existing technology has the following limitations:

[0004] High data dependence: The SVD method needs to construct a matrix based on a large amount of experimental data under different discharge conditions, while the new device design stage can only rely on simulation data, which limits the reliability of the optimization results;

[0005] Ignoring the complementarity of diagnosis: The SVD method optimizes the magnetic probe and the flux loop separately, without considering the synergistic effect of the two types of diagnosis in terms of signal characteristics and information contribution, which may lead to suboptimal configuration;

[0006] Combinatorial explosion problem: For a tokamak device with dozens of diagnostics (such as the 73 electromagnetic diagnostics of the EAST device), SVD needs to traverse thousands of combinations, which is extremely computationally complex and difficult to apply in practice;

[0007] Insufficient dynamic adaptability: Existing methods do not quantify the dynamic changes in the amount of diagnostic information and cannot adapt to the optimization needs in different discharge stages or abnormal operating conditions.

[0008] In addition, the strong radiation environment and compact engineering layout of future fusion reactors further amplify the above problems. Traditional optimization methods are difficult to reduce the number of diagnostics while ensuring the balance reconstruction accuracy and system robustness, seriously restricting the economy and maintainability of fusion reactors.

[0009] In summary, this application proposes a Tokamak electromagnetic measurement diagnostic optimization method based on Bayesian uncertainty. Summary of the Invention

[0010] The object of the present invention is to address the limitation in the optimization of electromagnetic measurement diagnostics in current Tokamak devices in the background art, and to propose a Tokamak electromagnetic measurement diagnostic optimization method based on Bayesian uncertainty.

[0011] The technical solution of the present invention: A Tokamak electromagnetic measurement diagnostic optimization method based on Bayesian uncertainty, comprising the following steps:

[0012] S1. Use the EFIT program to design the discharge equilibrium of the Tokamak device and generate the corresponding electromagnetic measurement diagnostic signals of magnetic probes and flux loops;

[0013] S2. Based on the electromagnetic measurement diagnostic signals, construct a Bayesian equilibrium reconstruction model, which relates the posterior probability of the equilibrium parameters to the prior probability and the likelihood probability of the diagnostics through Bayes' formula;

[0014] S3. Through the Bayesian equilibrium reconstruction model, quantify the information provided by each electromagnetic measurement diagnostic in the equilibrium reconstruction, and the information is measured by the uncertainty change of the posterior probability;

[0015] S4. Gradually reduce the electromagnetic measurement diagnostics with information content lower than the preset threshold, and verify whether the optimized diagnostic configuration meets the requirements of equilibrium reconstruction accuracy through the Bayesian equilibrium reconstruction model;

[0016] S5. Use the EFIT program to perform cross-validation on the optimized diagnostic configuration to ensure that it meets the plasma control requirements.

[0017] Optionally, the discharge equilibrium designed by the EFIT program in step S1 includes the known plasma boundary shape and magnetic flux distribution, and generates the corresponding magnetic probe and flux loop signals through the Biot-Savart theorem.

[0018] Optionally, in S2, the model relates the posterior probability of the equilibrium parameters to the prior probability and the likelihood probability of the diagnostics through Bayes' formula, which is specifically expressed as:

[0019] where is the number of diagnostics, and the likelihood probability is independently calculated based on the physical relationship between the diagnostic signal and the equilibrium parameters.

[0020] Optionally, the method for quantifying the uncertainty described in step S3 is as follows:

[0021] When retaining all diagnoses, calculate the posterior probability uncertainty of the equilibrium parameter as the reference value;

[0022] Reduce each single diagnosis one by one and recalculate the uncertainty. The difference between it and the reference value is used as the information quantity index of this diagnosis.

[0023] Optionally, the preset threshold described in step S4 is dynamically adjusted according to the control requirements of the tokamak device, and is specifically determined by the trade-off curve between the equilibrium reconstruction error and the number of diagnoses.

[0024] Optionally, the cross-validation described in step S5 includes:

[0025] Input the optimized diagnostic configuration into the EFIT program for equilibrium reconstruction;

[0026] Compare the reconstruction results of the Bayesian model and the EFIT program. If the error is within the allowable range, confirm that the optimization scheme is effective.

[0027] Optionally, the electromagnetic measurement diagnosis includes magnetic probes and flux loops. The Bayesian equilibrium reconstruction model comprehensively models the measurement data of magnetic probes and flux loops through a joint probability distribution to reflect their synergistic effect in equilibrium reconstruction.

[0028] Optionally, in the Bayesian equilibrium reconstruction model, the prior probability of the equilibrium parameter is set as a fixed distribution, and the change in the uncertainty of the posterior probability is only related to the change in the number or position of the electromagnetic measurement diagnoses.

[0029] Optionally, the optimization method can be applied to the design stage or the operation stage of the tokamak device, where:

[0030] In the design stage, optimize the diagnostic configuration based on the simulated discharge data generated by the EFIT program;

[0031] In the operation stage, dynamically adjust the diagnostic configuration based on the electromagnetic measurement diagnostic signals collected in real time.

[0032] Compared with the prior art, the present application includes at least one of the following beneficial technical effects:

[0033] (1) Construct a functional relationship for the information quantity provided by electromagnetic measurement diagnosis in equilibrium reconstruction

[0034] The uncertainty of the parameters reconstructed by using the Bayesian method is given to quantify the amount of information provided by each diagnosis. By fixing the prior probability, it is ensured that the uncertainty given by the posterior probability changes with the change of the likelihood probability based on the diagnosis. The change in uncertainty brought about by reducing one diagnosis at a time can quantitatively reflect the amount of information of the reduced diagnosis in the equilibrium reconstruction.

[0035] (2) Unified modeling of different diagnoses

[0036] The Bayesian method realizes the unified modeling of different diagnoses through the joint probability, and comprehensively considers the information complementarity between different diagnoses.

[0037] (3) Improving the optimization scheme through cross-validation

[0038] For different equilibrium reconstruction models, there are differences in the accuracy of the equilibrium parameters reconstructed under the same diagnosis conditions. Through cross-validation, the problem of insufficient equilibrium reconstruction accuracy caused by the inconsistent requirements of different equilibrium reconstruction models for diagnoses can be effectively avoided.

[0039] The present invention proposes to use Bayesian uncertainty to optimize the magnetic probe and flux loop diagnoses in the tokamak device, which can perform unified modeling on different diagnoses, comprehensively consider the influence of different diagnoses in the equilibrium reconstruction, and use the uncertainty given by the posterior probability to quantify the amount of information provided by the diagnosis. Based on this amount of information, the diagnosis can be efficiently optimized, and it has strong universality. Description of the Drawings

[0040] Figure 1 It is a flow chart of an optimization method for tokamak electromagnetic measurement diagnosis based on Bayesian uncertainty;

[0041] Figure 2 It is a distribution diagram of uncertainty in the experimental verification part of the embodiment. Detailed Embodiment

[0042] The technical solution of the present invention will be further described below with reference to the drawings and specific embodiments.

[0043] Embodiment 1

[0044] As Figure 1 shown, an optimization method for tokamak electromagnetic measurement diagnosis based on Bayesian uncertainty proposed by the present invention will be introduced in detail below.

[0045] The present invention proposes to comprehensively optimize the diagnosis of magnetic probes and flux loops in electromagnetic measurements in a tokamak device based on Bayesian uncertainty. The method first uses EFIT to design the discharge equilibrium and its corresponding electromagnetic measurement diagnostic signals; secondly, a Bayesian equilibrium reconstruction model is constructed based on the electromagnetic measurement diagnosis; then, the diagnosis is optimized according to the diagnostic information quantity quantified by the Bayesian equilibrium reconstruction model, and finally, the optimization scheme is verified. The specific implementation steps are as follows:

[0046] (1) Use EFIT to design the discharge equilibrium and its corresponding electromagnetic measurement diagnosis

[0047] The EFIT program can not only perform equilibrium reconstruction but also design the discharge equilibrium. Using the EFIT program, the discharge equilibrium and the corresponding magnetic probe and flux loop signals can be designed. The designed discharge equilibrium is known, and when optimization is carried out, it can be judged whether the optimization limit is reached through the equilibrium accuracy reconstructed by the Bayesian model.

[0048] (2) Establish a Bayesian inference-based equilibrium reconstruction model

[0049] Bayesian inference is an algorithm specifically for solving inverse problems. This algorithm takes the Bayesian formula as the core, as shown in formula (1):

[0050] (1)

[0051] In the formula, A and B represent two events. Generally, there is a causal relationship between event A and event B. Event A is the cause and event B is the result; represents the prior probability, represents the likelihood probability, represents the posterior probability. represents the evidence term, which can be calculated through marginalization in conditional probability ( ). The evidence term is also called the normalization coefficient, and its magnitude has no relation to the posterior probability taking the maximum value. Therefore, in the process of Bayesian inference, the latter half of formula (1), the non-normalized form, is often used. By replacing event B in the Bayesian formula with electromagnetic measurement diagnosis and replacing event A with the equilibrium parameters to be obtained, we can get:

[0052] (2)

[0053] For multiple diagnostic measurements of the same plasma equilibrium parameter, the Bayesian inference algorithm can also easily achieve unified modeling, as shown in formula (3): (3)

[0054] Since the measurements of each diagnosis are independent systems, and the likelihoods constructed by different diagnoses are independent of each other in probability theory, the likelihood probability in formula (2) can be split into a form of multiplying multiple diagnostic likelihoods. When the posterior probability reaches the maximum value, it is the optimal balance parameter solved by the model. At the same time, after the method quantizes the solution of the balance probability, the model can quantitatively give the uncertainty of the balance parameter at each position. This uncertainty quantitatively reflects the amount of information in the balance reconstruction process. The greater the uncertainty, the less the amount of information. The change in uncertainty brought about by reducing one magnetic probe or flux loop each time confirms the amount of information provided by each diagnosis. By fixing the prior probability to ensure that the change in the uncertainty of the posterior probability is caused by the change in the diagnosis, each diagnosis is sorted based on the amount of information from low to high.

[0055] (3) Optimize electromagnetic measurement diagnosis according to Bayesian uncertainty

[0056] For existing devices, the number and positions of magnetic probes and flux loops have been determined. Under the condition of ensuring that the balance reconstruction accuracy meets the requirements of plasma control, gradually reduce the diagnoses with less information to achieve less diagnoses for balance reconstruction. For the preliminary design of unconstructed devices, arrange magnetic probes densely around the device in a circle, and arrange flux loops as densely as possible while avoiding the window positions of the device. Then, use the same method to gradually optimize and reduce the number of electromagnetic measurement diagnoses. For engineering requirements, the dense arrangement methods of magnetic probes and flux loops can be appropriately adjusted, and then optimization can be carried out. Gradually reduce the diagnoses with less influence on uncertainty, and judge whether the optimal limit is reached through the balance reconstruction accuracy.

[0057] (4) Use the equilibrium reconstruction program EFIT to verify the optimization scheme

[0058] There are differences in principle between the EFIT program and Bayesian equilibrium reconstruction. The EFIT couples the ideal magnetohydrodynamics equation, while Bayesian equilibrium reconstruction is based on the Biot-Savart theorem and couples prior information. There are differences in the requirements for diagnostic information amounts between the two models. Therefore, it is necessary to further verify and optimize the optimization scheme through the EFIT program to meet the plasma control requirements.

[0059] Experimental verification: Use the currently operating Tokamak device to verify the feasibility and innovation of the present invention. A Bayesian-based equilibrium reconstruction program is constructed using magnetic probes and flux loops in electromagnetic measurement, and the uncertainty distribution in equilibrium reconstruction is given, as Figure 2 shown. The left side is the uncertainty under the condition of all magnetic probes and flux loops; the right side is the uncertainty distribution after reducing one magnetic probe diagnosis. Summing the uncertainties in Figure 2 , under the condition of all diagnoses, the uncertainty is , the uncertainty after reducing one magnetic probe diagnosis is . Therefore, the information amount of the reduced diagnosis in the equilibrium reconstruction is measured by the change in uncertainty, which is . Measure the information amount of each diagnosis in the same way. The larger the information amount, the greater the change in uncertainty. Gradually reduce the diagnoses with less information amount through the information amount and perform equilibrium reconstruction until the number of reduced diagnoses cannot meet the accuracy of the equilibrium reconstruction. At this time, the number and position of the optimized diagnoses reach the optimum.

[0060] The above specific embodiments are only several alternative embodiments of the present invention. Based on the technical solution of the present invention and the relevant revelations of the above embodiments, those skilled in the art can make various alternative improvements and combinations to the above specific embodiments.

Claims

1. A method for optimizing the diagnosis of electromagnetic measurements in Tokamak based on Bayesian uncertainty, characterized in that: The following steps are involved: S1. Design the discharge balance of the Tokamak device using the EFIT program and generate the corresponding electromagnetic measurement diagnostic signals of the magnetic probe and flux ring; S2. constructing a Bayesian equilibrium reconstruction model based on the electromagnetic measurement diagnostic signal, wherein the model associates the posterior probability of the equilibrium parameter with the prior probability and the likelihood probability of the diagnosis through a Bayesian formula; S3, quantifying the amount of information provided by each electromagnetic measurement diagnosis in the balance reconstruction through the Bayesian balance reconstruction model, wherein the amount of information is measured by the uncertainty change of the posterior probability; S4, gradually reducing the electromagnetic measurement diagnosis whose information amount is lower than a preset threshold, and verifying whether the optimized diagnostic configuration meets the balanced reconstruction accuracy requirement through the Bayesian balanced reconstruction model; S5. Use the EFIT program to cross-validate the optimized diagnostic configuration to ensure that it meets the plasma control requirements.

2. A method for optimizing the diagnosis of electromagnetic measurements in Tokamak based on Bayesian uncertainty according to claim 1, characterized in that: The discharge balance designed by the EFIT program in step S1 includes the known plasma boundary shape and magnetic flux distribution, and generates corresponding magnetic probe and flux loop signals through the Biot-Saffar theorem.

3. The method for optimizing the diagnosis of electromagnetic measurements in Tokamak based on Bayesian uncertainty according to claim 1, characterized in that: In S2, the model associates the posterior probability of the balance parameter with the prior probability and the likelihood probability of the diagnosis through the Bayesian formula, which is specifically expressed as: in, For diagnostic quantities, the likelihood probabilities are independently calculated based on the physical relationship between the diagnostic signal and the balance parameter.

4. The method for optimizing the diagnosis of electromagnetic measurements in Tokamak based on Bayesian uncertainty according to claim 1, characterized in that: The uncertainty quantification method in step S3 is: When retaining all diagnoses, the posterior probability uncertainty of the balance parameter was calculated as the baseline value; After reducing individual diagnoses one by one, the uncertainty is recalculated, and the difference between it and the reference value is used as an indicator of the information content of the diagnosis.

5. The method for optimizing the diagnosis of electromagnetic measurements in Tokamak based on Bayesian uncertainty according to claim 1, characterized in that: The preset threshold in step S4 is dynamically adjusted according to the control requirements of the tokamak device, and is specifically determined by a trade-off curve that balances the reconstruction error and the number of diagnoses.

6. The method for optimizing the diagnosis of electromagnetic measurements in Tokamak based on Bayesian uncertainty according to claim 1, characterized in that: The cross validation in step S5 includes: The optimized diagnostic configuration is input into the EFIT program for balanced reconstruction; Compare the reconstruction results of the Bayesian model with those of the EFIT program. If the error is within the allowable range, the optimization scheme is confirmed to be effective.

7. The method for optimizing the diagnosis of electromagnetic measurements in Tokamak based on Bayesian uncertainty according to claim 1, characterized in that: The electromagnetic measurement diagnosis includes a magnetic probe and a magnetic flux loop, and the Bayesian equilibrium reconstruction model comprehensively models the measurement data of the magnetic probe and the magnetic flux loop through a joint probability distribution.

8. The method for optimizing the diagnosis of electromagnetic measurements in Tokamak based on Bayesian uncertainty according to claim 1, characterized in that: The prior probability of the balance parameter in the Bayesian balance reconstruction model is set as a fixed distribution.

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