A Tokamak Magnetic Sensor Layout Optimization Design Method

Abstract

This invention provides a tokamak magnetic sensor layout optimization design method, comprising: data preparation, constructing a sensor signal matrix and an objective variable matrix; filtering out sensor signals with low signal-to-noise ratio; constructing an optimization objective function of appropriate form; determining the priority selection order of sensors based on the optimization objective function using a first-order incremental selection method; optimizing the hyperparameters in the optimization objective function using a grid search method to determine the final optimization objective function, the corresponding sensor selection priority order, and the minimum number of sensors; based on the sensor signal sorting results, selecting a type of sensor signal with an incrementally increasing number starting from the minimum number to obtain usable layout schemes; and defining the layout with the minimum total number of sensors among the usable layout schemes that have passed verification testing as the optimal layout. This invention can significantly reduce the number of magnetic sensors while meeting the plasma reconstruction accuracy requirements, and the reconstruction accuracy is significantly higher than that of a uniform distribution with the same number of sensors.

Description

Technical Field

[0001] This invention relates to the field of sensor layout optimization in nuclear fusion magnetic field measurement technology, and specifically to a tokamak magnetic sensor layout optimization design method. Background Technology

[0002] Magnetic diagnostics is one of the most fundamental types of diagnostics required for the operation of tokamak devices. To provide sufficient information for plasma equilibrium reconstruction, mainstream tokamak devices typically install numerous magnetic sensors (including small probes and single-turn loops) on their poloidal cross-sections. For future fusion experimental devices, the device size will increase significantly while the required reconstruction accuracy will not decrease substantially. Furthermore, the device's inner walls will be covered with numerous shielding layers, leaving limited space for installing small probes. If the required plasma reconstruction accuracy can be achieved by deploying fewer magnetic sensors, it will have significant practical implications and application value for improving the reliability and economy of the diagnostic system.

[0003] Currently, research on the layout design of magnetic sensors in tokamak devices mainly considers signal recovery capability and sensitivity to configuration changes. The final layouts are mostly based on expert experience, lacking strong interpretability. The resulting layouts are characterized by a large number of sensors, uniform distribution, and significant redundancy. Summary of the Invention

[0004] To meet the reliability and cost requirements of future fusion experimental devices for magnetic diagnostic systems and to address the problems of existing layout design methods, this invention provides a tokamak magnetic sensor layout optimization design method. This method can significantly reduce the number of magnetic sensors required while meeting plasma reconstruction accuracy requirements, and the reconstruction accuracy is significantly higher than that of a uniform distribution with the same number of sensors.

[0005] To achieve the objectives of this invention, the following technical solution is adopted:

[0006] A method for optimizing the layout of a tokamak magnetic sensor includes the following steps:

[0007] Step S1: Prepare data, define target variables, simulate and generate a large number of plasma equilibrium instances, obtain sensor measurement signals and target variable values ​​under plasma equilibrium instances, and construct sensor signal matrix and target variable matrix;

[0008] Step S2: Filter out sensor signals with low signal-to-noise ratio;

[0009] Step S3: Introduce the distance and measurement direction angle difference between sensors into the redundancy evaluation of the conventional minimum redundancy maximum correlation criterion to solve the problem of overly concentrated overall sensor layout caused by multicollinearity and similarity between sensor signals, and make up for the imbalance between sensor signal and target variable information entropy by normalizing mutual information, and construct an optimization objective function of appropriate form.

[0010] Step S4: Based on the optimization objective function, determine the priority selection order of sensors through a first-order incremental selection method;

[0011] Step S5: Optimize the hyperparameters in the objective function using a grid search method to determine the final objective function, the corresponding sensor selection priority, and the minimum number of sensors.

[0012] Step S6: Based on the sorting results of the sensor signals, select one type of sensor signal and start from the minimum number to increase the number. Use the binary search method to determine the minimum number of another type of sensor signal required to meet the plasma reconstruction verification test, and record the available layout schemes.

[0013] Step S7: Determine the layout with the fewest total number of sensors among the available layout schemes that have passed the verification test as the optimal layout.

[0014] Further, step S1 includes: First, based on the engineering parameters of the tokamak device and the magnetic sensors, a ring of magnetic sensors is uniformly arranged inside the first wall of the tokamak device to form an initial dense distribution of magnetic sensors as a candidate sensor set, wherein the single-turn ring should avoid the window area; Second, the intersection point of the radial line starting from the center of the tokamak device's pole section along a specified direction and the first wall of the tokamak device is defined as the configuration evaluation reference point, and the distance between the outermost magnetic surface and the corresponding configuration reference point in the specified direction is defined as the configuration evaluation basis; A large number of equilibrium instances under plasma configurations are simulated using plasma equilibrium fitting code, and the magnetic sensor measurement values ​​corresponding to the equilibrium instances are read, while the defined distance values ​​are calculated, which respectively constitute the input matrix. Input matrix and target matrix .

[0015] Further, step S2 includes: calculating the average absolute amplitude of the magnetic sensor signal, and by setting a fixed limit, considering signals smaller than the fixed limit as low signal-to-noise ratio signals and removing them from the candidate sensor set.

[0016] Further, step S3 includes:

[0017] Using Mutual Information Measuring the redundancy between sensor signals and the correlation between sensor signals and the target variable, for two discrete random variables. and The formula for calculating the mutual information between the two is as follows:

[0018] (1)

[0019] in, For discrete random variables Pick The probability of the value being true. For discrete random variables Pick The probability of the value being true. For discrete random variables The joint probability;

[0020] The mutual information is normalized using the cross-union-comparison (CUC) method to compensate for the severe imbalance between the information entropy of the sensor signal and the target variable, thus normalizing the mutual information. The definition is as follows:

[0021] (2)

[0022] Among them, random variables Information entropy ,random variable Information entropy When the logarithmic function is base 2, the unit of information entropy is _____. , It is the total number of possible values ​​that a discrete random variable can take. This means taking the first one. indivual, That is, discrete random variables The A possible value; random variable Generally refers to sensor signals and / or target variables. This represents the values ​​of the sensor and / or the target variable in a single equilibrium instance;

[0023] Based on the distance between sensors, an exponential function is used to define the distance discount function. The definition is as follows:

[0024] (3)

[0025] in, This is a hyperparameter, and its value range is... , and For sensors Location coordinate, and For sensors Location coordinate;

[0026] For directional two-dimensional small probe signals, an additional angle difference discount function is introduced. The definition is as follows:

[0027] (4)

[0028] in, For modulo function, These are sensors Angle and sensor for measuring signals when using a small probe The measurement angle when the probe signal is small;

[0029] For the expected installation One sensor, with When there are multiple target variables, the optimization objective function of the improved minimum redundancy maximum correlation criterion is... The following describes the optimization objective function for a single-turn loop signal. Defined as:

[0030] (5)

[0031] in, For the expected number of sensors to be installed, The number of target variables selected. Indicates inclusion A set of candidate sensors, express A set consisting of target variables Representative sensor set The first in One sensor, Represents the set of target variables The first in One target variable, Representative sensor and target variable Mutual information between them For target variable Information entropy For sensors Information entropy;

[0032] For two-dimensional small probe signals, optimize the objective function. Defined as:

[0033] (6).

[0034] Further, step S4 includes: when a hyperparameter is given In this process, the sensor selection priority is determined using a first-order incremental selection method, including: for single-turn loop signals, firstly, the single-turn loop signal with the maximum average weighted mutual information with the target variable is selected as the first selected single-turn loop signal and removed from the candidate single-turn loop signal set; then, based on this, the following steps are performed: When the candidate single-turn loop signal that maximizes the objective function (5) is selected, it is chosen as the second selected single-turn loop signal and removed from the candidate single-turn loop signal set. This process is repeated until all single-turn loop signals are selected. The order of the elements in the set then represents the selection priority of the single-turn loop signals, denoted as . For small probe signals, only the objective function is modified to Equation (6), and the rest of the process is the same as above. The selection priority of small probe signals is denoted as... .

[0035] Further, step S5 includes: in hyperparameters The range of values Within, multiple searchable objects are generated at certain intervals. Values, forming a vector Hyperparameters for small probe signals Search, when hyperparameters Pick First, the selection priority of the small probe signals is obtained according to step S4. Secondly, with the fixed single-turn loop signal selected as the entire set, several balanced instances are chosen as verification cases. A binary search test is used to determine the minimum number of small probe signals required to reconstruct the selected balanced instances within a specified accuracy. This number is denoted as... Let hyperparameters Iterate through all the values ​​to be searched, and finally, The smallest element corresponding The value is the hyperparameter. The optimal value; hyperparameters for single-turn loop signals. During the search, the small probe signal is fixed as the entire sample is selected; the rest of the process is the same as above; hyperparameters While the optimal value is determined, optimize the objective function. Priority vector for selecting single-turn loop signals and small probe signals and and the corresponding minimum number and It is confirmed.

[0036] Further, step S6 includes: first, fixing the layout of the sensor type with the smallest number of sensors in step S5 to the layout corresponding to the smallest number, that is, if The layout of the fixed small probes is as follows: The former If The layout of the fixed single-turn ring is as follows: The former First, combining the binary search method and the balance verification example, test the minimum number of another type of sensor signal required to meet the reconstruction accuracy requirements, and record the total number of sensor signals and the corresponding available layout; then, gradually increase the number of fixed sensor signals, repeatedly search for the minimum number and layout corresponding to the other type of sensor signal, and record it, until the number of fixed sensor signals increases to the minimum value of the currently recorded total number of sensor signals, then stop the search.

[0037] Further, step S7 includes: among the layouts verified through the balance instance recorded in step S6, the layout with the fewest total sensor signals is considered the optimal layout.

[0038] The beneficial effects of this invention are:

[0039] (1) This invention takes into account the imbalance between sensor signals and target variables in terms of information entropy. By introducing the cross-union ratio form to normalize the mutual information, it solves the problem that a single part of the optimization objective function plays a decisive role in the final layout scheme in the conventional minimum redundancy maximum correlation criterion.

[0040] (2) The present invention takes into account the multicollinearity and similarity between signals of the same type of sensors. By increasing the consideration of the distance between sensors and the difference in measurement direction angle, the problem of the overall sensor layout being too concentrated is solved.

[0041] (3) The sensor layout optimization method of the present invention has high computational efficiency. From the layout optimization results, the optimized layout only uses a small number of signals to meet the proposed inversion accuracy requirements. The inversion accuracy of the optimized layout is significantly better than the inversion effect of the uniformly distributed number commonly used in tokamak devices. Attached Figure Description

[0042] Figure 1 This is a flowchart of a tokamak magnetic sensor layout optimization design method according to the present invention;

[0043] Figure 2 This is an example diagram of the initial dense layout of the magnetic sensor of the present invention;

[0044] Figure 3 Example diagram showing the configuration evaluation parameter settings of the present invention;

[0045] Figure 4 This is the optimized layout diagram of the present invention. Detailed Implementation

[0046] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0047] The tokamak magnetic sensors mentioned in this invention include two-dimensional small probes and single-turn loops. These are two types of magnetic sensors, both requiring layout optimization, and the optimization results of both will jointly affect the accuracy of plasma reconstruction. In the following text, when certain descriptions apply to both two-dimensional small probes and single-turn loops, the term "magnetic sensor" or "sensor" will be used; for descriptions applicable only to two-dimensional small probes or single-turn loops, the term "two-dimensional small probe" or "single-turn loop" will be used directly.

[0048] like Figure 1 As shown, the tokamak magnetic sensor layout optimization design method of the present invention includes the following steps:

[0049] Step S1: Prepare data, define target variables, simulate and generate a large number of plasma equilibrium instances, obtain sensor measurement signals and target variable values ​​under plasma equilibrium instances, and construct sensor signal matrix and target variable matrix;

[0050] Step S2: Filter out sensor signals with low signal-to-noise ratio;

[0051] Step S3: Introduce the distance and measurement direction angle difference between sensors into the redundancy evaluation of the conventional minimum redundancy maximum correlation criterion to solve the problem of overly concentrated overall sensor layout caused by multicollinearity and similarity between sensor signals, and make up for the imbalance between sensor signal and target variable information entropy by normalizing mutual information, and construct an optimization objective function of appropriate form.

[0052] Step S4: Based on the optimization objective function, determine the priority selection order of sensors through a first-order incremental selection method;

[0053] Step S5: Optimize the hyperparameters in the objective function using a grid search method to determine the final objective function, the corresponding sensor selection priority, and the minimum number of sensors.

[0054] Step S6: Based on the sorting results of the sensor signals, select one type of sensor signal and start from the minimum number to increase the number. Use the binary search method to determine the minimum number of another type of sensor signal required to meet the plasma reconstruction verification test, and record the layout scheme.

[0055] Step S7: The layout scheme with the fewest total number of sensors among those that pass the verification test is designated as the optimal layout.

[0056] Specifically, step S1 includes: First, generating an initial dense layout of sensors as a candidate sensor set based on the engineering parameters of the tokamak device and the magnetic sensors. Second, defining the intersection of a radial line originating from the center of the tokamak device's pole section along a specified direction with the first wall of the tokamak device as a configuration evaluation reference point, and defining the distance between the outermost magnetic surface and the corresponding configuration reference point in the specified direction as the configuration evaluation criterion. Using EFIT (Plasma Equilibrium Fitting Code) simulation, a large number of equilibrium instances under plasma configurations are generated (an equilibrium instance refers to a single equilibrium generated by simulation), and the magnetic sensor measurements corresponding to the equilibrium instances are read. Simultaneously, the defined distance values ​​are calculated, forming the input matrix. Input matrix and target matrix .

[0057] Specifically, step S2 includes: calculating the average absolute amplitude of the magnetic sensor signal, and by setting a fixed limit, treating signals smaller than the fixed limit as low signal-to-noise ratio signals and removing them from the candidate sensor set.

[0058] Specifically, step S3 includes:

[0059] Using Mutual Information Measuring the redundancy between sensor signals and the correlation between sensor signals and the target variable, for two discrete random variables. and The formula for calculating the mutual information between the two is as follows:

[0060] (1)

[0061] in, For discrete random variables Pick The probability of the value being true. For discrete random variables Pick The probability of the value being true. For discrete random variables The joint probability.

[0062] The mutual information is normalized using the cross-union-comparison (CUC) method to compensate for the severe imbalance between the information entropy of the sensor signal and the target variable, thus normalizing the mutual information. The definition is as follows:

[0063] (2)

[0064] Among them, random variables Information entropy ,random variable Information entropy When the logarithmic function is base 2, the unit of information entropy is _____. , It is the total number of possible values ​​that a discrete random variable can take. This means taking the first one. indivual, That is, discrete random variables The A possible value; random variable Generally refers to sensor signals and / or target variables. This represents the values ​​of the sensor and / or the target variable in a single equilibrium instance;

[0065] Based on the distance between sensors, an exponential function is used to define a distance discount function, which more effectively suppresses redundancy between signals from sensors at greater distances, preventing sensors from being densely distributed in localized areas. Distance discount function The definition is as follows:

[0066] (3)

[0067] in, This is a hyperparameter, and its value range is... , and For sensors Location coordinate, and For sensors Location coordinate.

[0068] For directional two-dimensional probe signals, the additional introduction of an angle difference discount function strongly suppresses redundancy of neighboring probes in nearly perpendicular measurement directions. However, for similar measurement directions, the angle difference discount function has almost no effect. The definition is as follows:

[0069] (4)

[0070] in, For modulo function, These are small probe signals. Angle and small probe signal The angle.

[0071] In summary, regarding the expected installation One sensor, with When there are multiple target variables, the objective function of the improved minimum redundancy maximum correlation criterion is as follows. For a single-turn loop signal, the objective function is defined as:

[0072] (5)

[0073] in, For the expected number of sensors to be installed, The number of target variables selected. Indicates inclusion A set of candidate sensors, express A set consisting of target variables Representative sensor set The first in One sensor, Represents the set of target variables The first in One target variable, Representative sensor and target variable Mutual information between them For target variable Information entropy For sensors Information entropy;

[0074] For a two-dimensional small probe signal, the objective function is defined as:

[0075] (6)

[0076] Specifically, step S4 includes: when a hyperparameter is given In this case, the sensor selection priority can be determined using the following first-order incremental selection method. Taking a single-turn loop signal as an example, firstly, the single-turn loop signal with the maximum average weighted mutual information with the target variable is selected as the first selected single-turn loop signal and removed from the candidate single-turn loop signal set. Then, based on this, the following calculation is performed. When the candidate single-turn loop signal that maximizes the objective function (5) is selected, it is chosen as the second selected single-turn loop signal and removed from the candidate single-turn loop signal set. This process is repeated until all single-turn loop signals are selected. The order of the elements in the set then represents the selection priority of the single-turn loop signals, denoted as . Similarly, for small probe signals, only the objective function is modified to Equation (6), and the remaining steps are the same as above. The selection priority order of small probe signals is denoted as... .

[0077] Specifically, step S5 includes: in hyperparameters The range of values Within, multiple searchable objects are generated at certain intervals. Values, forming a vector Hyperparameters of small probe signals Taking search as an example. When hyperparameters... Pick First, the selection priority of the small probe signals is obtained according to step S4. Secondly, with the fixed single-turn loop signal selected as the entire set, several balanced instances are chosen as verification cases. A binary search test is used to determine the minimum number of small probe signals required to reconstruct the selected balanced instances within a specified accuracy. This number is denoted as... Let hyperparameters Iterate through all the values ​​to be searched, and finally, The smallest element corresponding The value is the hyperparameter. The optimal value. Similarly, for the hyperparameters of a single-turn loop signal. During the search, the small probe signal is fixed as the entire sample selected; the remaining steps are the same as above. Hyperparameters While the optimal value is determined, optimize the objective function. Priority vector for selecting single-turn loop signals and small probe signals and and the corresponding minimum number and It has also been confirmed.

[0078] Specifically, step S6 includes: first, fixing the layout of the sensor type with the smallest number of sensors in step S5 to the layout corresponding to the smallest number, that is, if The layout of the fixed small probes is as follows: The former If The layout of the fixed single-turn ring is as follows: The former Next, combining the binary search method and the balance verification example, test the minimum number of another type of sensor signal required to meet the reconstruction accuracy requirements, and record the total number of sensor signals and the corresponding available layout; then, gradually increase the number of fixed sensor signals, repeatedly search for the minimum number and layout corresponding to the other type of sensor signal, and record it, until the number of fixed sensor signals increases to the minimum value of the currently recorded total number of sensor signals, then stop the search.

[0079] Specifically, step S7 includes: among the layouts recorded in step S6 that can be verified through balancing instances, the layout with the fewest total number of sensor signals is considered the optimal layout.

[0080] Example:

[0081] An embodiment of the present invention provides a tokamak magnetic sensor layout optimization design method, comprising the following steps:

[0082] Step S1: Based on the engineering dimensions of the tokamak device and the minimum space required for the installation and wiring of the magnetic sensor, evenly distribute a ring of 91 two-dimensional small probes and 98 single-turn loops on the inner wall of the device as an initial dense layout, such as... Figure 2 As shown, the left figure shows the initial dense layout of the small probes, and the right figure shows the initial dense layout of the single-turn ring. The two-dimensional small probes used to measure the magnetic field strength in a specified direction at their location are mounted against the wall (the measurement direction of the two-dimensional small probes parallel to the first wall of the tokamak device is shown in the left figure; for ease of illustration, the measurement direction perpendicular to the first wall of the tokamak device and pointing outwards from the center of the cross-section from the poles of the tokamak device is not shown in the figure). The single-turn ring avoids all window areas. Let the total number of small probe signals be... The total number of single-turn loop signals is .

[0083] Based on the EFIT program, a large number of equilibrium instances under plasma configurations that conform to the evolution law of device discharge parameters were simulated. The total number of equilibrium instances generated by the simulation is denoted as . .

[0084] Read the magnetic sensor measurement data corresponding to the balance instance and construct two input matrices. , .matrix The matrix represents the small probe signal. Each column represents the measurement data of the same small probe signal under different equilibrium instances, and each row represents the data of all small probe signals in the same equilibrium instance. The middle section represents the single-turn loop signal. Each column represents the measurement data of the same single-turn loop signal under different balancing instances, and each row represents the data of all single-turn loop signals in the same balancing instance.

[0085] Let the total number of defined target variables be . ,like Figure 3 As shown. The target variable is calculated in the simulation. The values ​​taken from each equilibrium instance constitute the objective variable matrix. Among them, the objective variable matrix Each row represents the distance calculation result of a balanced instance in different reference directions, and each column represents... The distance calculation result of a balanced instance in a certain reference direction.

[0086] Step S2: Because the magnetic field component at the location of some two-dimensional probes is consistently very small in a certain measurement direction, the corresponding signal-to-noise ratio will be very low, and its use should be avoided in practical applications. Therefore, the average absolute amplitude of all probe signals is calculated. ,in, Corresponding to the Small probe signal, This is the index value. The average absolute magnitude is adjusted according to the actual situation. Set appropriate limits, and use small probe signal numbers that are not less than those limits to form a candidate small probe signal set. The candidate single-turn loop signal set is the entire set of single-turn loop signals.

[0087] Step S3: Construct the form of the optimization objective function;

[0088] Step S4: For hyperparameters Given a given set of parameters, the sensor selection priority is determined using a first-order incremental selection method. When analyzing single-turn loop signals, firstly, the single-turn loop signal with the maximum average weighted cross-information with the target variable is selected as the first selected single-turn loop signal and removed from the candidate single-turn loop signal set. Then, based on this, the following calculations are performed... When the candidate single-turn loop signal that maximizes the objective function (5) is selected, it is chosen as the second selected single-turn loop signal and removed from the candidate single-turn loop signal set. This process is repeated until all single-turn loop signals are selected. The order of the elements in the set then represents the selection priority of the single-turn loop signals, denoted as . Similarly, when analyzing small probe signals, only the objective function is modified to Equation (6), and the remaining steps are the same as above. The priority order for selecting small probe signals is denoted as... .

[0089] Step S5: In hyperparameters The range of values Within this scope, 19 search terms are generated at intervals of 0.05. Values, forming a vector Optimal hyperparameters for small probe signals During the search, the layout of the single-turn loops is set to include all signals in the candidate single-turn loop set. When the hyperparameters... Pick First, the selection priority of the small probe signals is obtained according to step S4. Secondly, several balanced instances are selected as verification cases. A binary search test is used to determine the minimum number of small probe signals required to reconstruct the selected balanced instances within a specified accuracy. This number is denoted as... Let hyperparameters Iterate through all the values ​​to be searched, and finally, The smallest element corresponding The value is the hyperparameter. The optimal value. Similarly, the optimal hyperparameter for a single-turn loop signal. During the search, the small probes are arranged to include all signals in the candidate small probe signal set, and the remaining steps are the same as above. Hyperparameters While the optimal value is determined, the optimization objective function for the single-turn loop signal and the small probe signal is... Selecting priority vectors and and minimum number and It has also been confirmed.

[0090] Step S6: First, preset the layout of the sensor type with the smallest number of sensors from step S7 as the layout corresponding to the smallest number of sensors, i.e., if Then the layout of the small probes is pre-set. The former If The single-turn ring layout is then pre-set to... The former Next, combining the binary search method and the balance verification example, we tested the minimum number of signals required for another type of sensor to meet the reconstruction accuracy requirements, and recorded the total number of sensor signals and the corresponding layout. Then, we gradually increased the number of sensor signals with the pre-set layout in the previous text, and repeatedly searched for the minimum number and layout corresponding to the other type of sensor signal, and recorded it, until the number of pre-set sensor signals increased to the minimum value of the currently recorded total number of sensor signals, at which point we stopped the search.

[0091] Step S7: The layout scheme with the fewest total number of sensor signals in the layout that passes the verification test is the optimal layout.

[0092] Figure 4The optimized layout of the magnetic sensor for the tokamak device in the embodiment is presented. The left figure shows the optimized layout of the small probes, with a total of 13 small probes installed, involving 14 small probe signals; the right figure shows the optimized layout of the single-turn loop, with a total of 16 single-turn loops installed.

Claims

1. A method for optimizing the layout of a tokamak magnetic sensor, characterized in that, Includes the following steps: Step S1: Prepare data, define target variables, simulate and generate a large number of plasma equilibrium instances, obtain sensor measurement signals and target variable values ​​under plasma equilibrium instances, and construct sensor signal matrix and target variable matrix; Step S2: Filter out sensor signals with low signal-to-noise ratio; Step S3: Introduce the distance and measurement direction angle difference between sensors into the redundancy evaluation of the conventional minimum redundancy maximum correlation criterion to solve the problem of overly concentrated overall sensor layout caused by multicollinearity and similarity between sensor signals, and make up for the imbalance between sensor signal and target variable information entropy by normalizing mutual information to construct an optimization objective function; Step S4: Based on the optimization objective function, determine the priority selection order of sensors through a first-order incremental selection method; Step S5: Optimize the hyperparameters in the objective function using a grid search method to determine the final objective function, the corresponding sensor selection priority, and the minimum number of sensors. Step S6: Based on the sorting results of the sensor signals, select one type of sensor signal and start from the minimum number to increase the number. Use the binary search method to determine the minimum number of another type of sensor signal required to meet the plasma reconstruction verification test, and record the available layout schemes. Step S7: Determine the layout with the fewest total number of sensors among the available layout schemes that have passed the verification test as the optimal layout.

2. The tokamak magnetic sensor layout optimization design method according to claim 1, characterized in that, Step S1 includes: First, based on the engineering parameters of the tokamak device and the magnetic sensors, a ring of magnetic sensors is uniformly arranged inside the first wall of the tokamak device to form an initial dense distribution of magnetic sensors as a candidate sensor set, wherein the single-turn ring should avoid the window area; Second, the intersection point of the radial line starting from the center of the tokamak device's pole section and along a specified direction with the first wall of the tokamak device is defined as the configuration evaluation reference point, and the distance between the outermost magnetic surface and the corresponding configuration reference point in the specified direction is defined as the configuration evaluation basis; A large number of equilibrium instances under plasma configurations are generated using plasma equilibrium fitting code, and the magnetic sensor measurement values ​​corresponding to the equilibrium instances are read, while the defined distance values ​​are calculated, which respectively constitute the input matrix. Input matrix and target matrix .

3. The tokamak magnetic sensor layout optimization design method according to claim 1, characterized in that, Step S2 includes: calculating the average absolute amplitude of the magnetic sensor signal, and by setting a fixed limit, considering signals smaller than the fixed limit as low signal-to-noise ratio signals and removing them from the candidate sensor set.

4. The tokamak magnetic sensor layout optimization design method according to claim 1, characterized in that, Step S3 includes: Using Mutual Information Measuring the redundancy between sensor signals and the correlation between sensor signals and the target variable, for two discrete random variables. and The formula for calculating the mutual information between the two is as follows: （1） in, For discrete random variables Pick The probability of the value being true. For discrete random variables Pick The probability of the value being true. For discrete random variables The joint probability; The mutual information is normalized using the cross-union-comparison (CUC) method to compensate for the severe imbalance between the information entropy of the sensor signal and the target variable, thus normalizing the mutual information. The definition is as follows: （2） Among them, random variables Information entropy ,random variable Information entropy When the logarithmic function is base 2, the unit of information entropy is _____. , It is the total number of possible values ​​that a discrete random variable can take. This means taking the first one. indivual, That is, discrete random variables The A possible value; random variable Generally refers to sensor signals and / or target variables. This represents the values ​​of the sensor and / or the target variable in a single equilibrium instance; Based on the distance between sensors, an exponential function is used to define the distance discount function. The definition is as follows: （3） in, This is a hyperparameter, and its value range is... , and For sensors Location coordinate, and For sensors Location coordinate; For directional two-dimensional small probe signals, an additional angle difference discount function is introduced. The definition is as follows: （4） in, For modulo function, These are sensors Angle and sensor for measuring signals when using a small probe The measurement angle when the probe signal is small; For the expected installation One sensor, with When there are multiple target variables, the optimization objective function of the improved minimum redundancy maximum correlation criterion is... The following describes the optimization objective function for a single-turn loop signal. Defined as: （5） in, For the expected number of sensors to be installed, The number of target variables selected. Indicates inclusion A set of candidate sensors, express A set consisting of target variables, Representative sensor set The first in One sensor, Represents the set of target variables The first in One target variable, Representative sensor and target variable Mutual information between them For target variable Information entropy For sensors Information entropy; For two-dimensional small probe signals, optimize the objective function. Defined as: （6）。 5. The tokamak magnetic sensor layout optimization design method according to claim 4, characterized in that, Step S4 includes: when a hyperparameter is given In this process, the sensor selection priority is determined using a first-order incremental selection method, including: for single-turn loop signals, firstly, the single-turn loop signal with the maximum average weighted mutual information with the target variable is selected as the first selected single-turn loop signal and removed from the candidate single-turn loop signal set; then, based on this, the following steps are performed: When the candidate single-turn loop signal that maximizes the objective function (5) is selected, it is chosen as the second single-turn loop signal and removed from the candidate single-turn loop signal set. This process is repeated until all single-turn loop signals are selected. The order of the elements in the set is the selection priority of the single-turn loop signals, denoted as . For small probe signals, only the objective function is modified to Equation (6), and the rest of the process is the same as above. The selection priority of small probe signals is denoted as... .

6. The tokamak magnetic sensor layout optimization design method according to claim 5, characterized in that, Step S5 includes: in hyperparameters The range of values Within, multiple searchable objects are generated at certain intervals. Values, forming a vector Hyperparameters for small probe signals Search, when hyperparameters Pick First, the selection priority of the small probe signals is obtained according to step S4. Secondly, with the fixed single-turn loop signal selected as the entire set, several balanced instances are chosen as verification cases. A binary search test is used to determine the minimum number of small probe signals required to reconstruct the selected balanced instances within a specified accuracy. This number is denoted as... Let hyperparameters Iterate through all the values ​​to be searched, and finally, The smallest element corresponding The value is the hyperparameter. The optimal value; hyperparameters for single-turn loop signals. During the search, the small probe signal is fixed as the entire sample is selected; the rest of the process is the same as above; hyperparameters While the optimal value is determined, optimize the objective function. Priority vector for selecting single-turn loop signals and small probe signals and and the corresponding minimum number and It is confirmed.

7. The tokamak magnetic sensor layout optimization design method according to claim 6, characterized in that, Specifically, step S6 includes: first, fixing the layout of the sensor type with the smallest number of sensors in step S5 to the layout corresponding to the smallest number, that is, if The layout of the fixed small probes is as follows: The former If The layout of the fixed single-turn ring is as follows: The former First, combining the binary search method and the balance verification example, test the minimum number of another type of sensor signal required to meet the reconstruction accuracy requirements, and record the total number of sensor signals and the corresponding layout; then, gradually increase the number of fixed sensor signals, repeatedly search for the minimum number and layout of the other type of sensor signal, and record it, until the number of fixed sensor signals increases to the minimum value of the currently recorded total number of sensor signals, then stop the search.

8. The tokamak magnetic sensor layout optimization design method according to claim 1, characterized in that, Step S7 includes: among the layouts verified through the balance instance recorded in step S6, the layout with the fewest total sensor signals is considered the optimal layout.

Images