A tokamak plasma boundary identification and shape reconstruction method

Abstract

The application provides a tokamak plasma boundary identification and shape reconstruction method. First, the EAST plasma boundary is identified by using a U-Net full convolutional neural network, then boundary points are selected, and finally, the pixel coordinates of the boundary points are fitted with EFIT through an XGBoost model. The application can convert the boundary from the image plane to the tokamak polar surface, and realize the plasma shape reconstruction based on a monocular visible light camera. According to the experimental results, the algorithm has high reconstruction accuracy, and the average error on the test set is only 7.36 mm.

Description

Technical Field

[0001] This invention belongs to the field of plasma boundary identification and configuration reconstruction, and specifically relates to a method for tokamak plasma boundary identification and configuration reconstruction. Background Technology

[0002] Real-time reconstruction of the plasma configuration of a tokamak device is of great significance for optimizing operating parameters, controlling the thermal load and particle deposition on the vacuum chamber walls and divertor target plates, and reducing damage to vacuum chamber components. Modern tokamak devices typically employ magnetic measurement methods, with EFIT primarily used on EAST to estimate the position and shape of the plasma. However, due to the influence of magnet disturbances on the plasma, which randomly disrupt magnetic field lines, and the integral drift phenomenon inherent in this measurement (see: Dickinson D, Roach CM, Saarelma S, et al. Microtearing modes at the top of the pedestal[J]. Plasma Physics & Controlled Fusion, 2013, 55(7):69-78.), this measurement method is not suitable for long-term operation of future tokamak devices.

[0003] Therefore, to meet the needs of long-term operation of future tokamak devices, it is essential to develop new plasma configuration reconstruction algorithms. From images captured by the visible light camera on EAST, this invention can clearly show the plasma boundaries. Extracting the plasma boundaries from the images and performing configuration reconstruction can avoid the problems encountered in magnetic measurements.

[0004] Hao LUO et al. proposed a boundary reconstruction method that does not require camera calibration (Luo H, Luo ZP, Chao X U, et al. Optical plasma boundary reconstruction based on least squares for EAST Tokamak[J]. Frontiers of Information and Electronic Engineering: English Edition, 2018, 19(9):11.). The algorithm aims to minimize the distance between the optical reconstruction result and the EFIT data, achieving an error of 1-2 cm on EAST discharge experiments and EFIT data. However, its edge extraction algorithm requires manual setting of the ROI region, making it difficult to extract the outer plasma boundary, and the fitted data exhibits horizontal drift.

[0005] In the past, the EAST team used the adaptive Canny edge detection algorithm (Xue E, Luo J, Shu S, et al. Plasma Edge Detection and Tracking in the EAST Superconducting Tokamak Discharge[C] / / Third International Conference on Measuring Technology & Mechatronics Automation.IEEE,2011.) and the Snake active contour method based on image energy theory for plasma boundary extraction. However, experimental results showed that both algorithms could only extract edges in a relatively dark vacuum chamber. When the vacuum chamber of the EAST device was bright, both algorithms would produce a large number of erroneous edges. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes a tokamak plasma boundary recognition and configuration reconstruction method. This method is a boundary extraction algorithm based on image segmentation using a U-Net network. It extracts plasma boundaries from the entire image without requiring manual ROI region setting, effectively extracting outer plasma boundaries. Furthermore, based on an XGBoost-based optical reconstruction algorithm, it achieves an average error of 7.36 mm. To better extract plasma boundaries during operation, this invention employs a deep learning-based image segmentation method, using a U-Net network for plasma boundary extraction. Experiments show that the U-Net-based image segmentation method achieves significant results in plasma boundary extraction on EAST.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A method for tokamak plasma boundary identification and configuration reconstruction includes the following steps:

[0009] Step 1, Plasma Boundary Recognition: A deep learning-based image segmentation method is used, and a U-Net network is employed to extract the plasma boundary;

[0010] The loss function used is cross-entropy loss, as shown in the following formula:

[0011]

[0012] Where M represents the number of categories; y c The value can be 0 or 1; it is 1 when the category is the same as the true category, and 0 otherwise. c The predicted value represents the probability that the sample belongs to category c;

[0013] The plasma boundary region was selected from the images through manual annotation and used as the real segmentation image during network training; the resulting model was then used to predict image data outside the training set.

[0014] Step 2, Configuration Reconstruction:

[0015] The XGBoost model was used for fitting; the XGBoost model is defined as follows:

[0016]

[0017] Among them, f k (x) represents the k-th decision tree, x i This represents the input feature vector. This represents the predicted value; the model contains K trees.

[0018] The model's objective function Obj consists of a loss function L and a regularization term Ω. The loss function L is used to evaluate the difference between the predicted value and the true value y. i The error is controlled by the regularization term Ω, which controls the complexity of the model and avoids overfitting.

[0019] The objective function of XGBoost is defined as follows:

[0020]

[0021] The regularization term Ω is defined as follows:

[0022]

[0023] Where γ and λ are modifiable parameters, T is the number of leaves, ω is the weight score of the leaf node, and f represents the decision tree model;

[0024] The model in round s can be defined as:

[0025]

[0026] Where s is the iteration round number, and the model in the s-th round is equal to the model in the (s-1)-th round plus the new model f(x). i ), where f(x) i This minimizes the objective function Obj.

[0027] Rewrite the objective function Obj:

[0028]

[0029] in, For the (s-1)th round model, the sample x i The predicted value, f s (x i) represents the predicted value of the new model trained in the s-th round;

[0030] Taylor expansion of the objective function Obj:

[0031]

[0032] Among them, g i h is the first derivative of the loss function. i This is the second derivative of the loss function;

[0033] Remove constant terms that do not affect the optimization of the objective function. This will not affect the optimization of the objective function, and will also affect Ω(f). s Substituting into the formula, the objective function Obj can be written as:

[0034]

[0035] Among them, I j For all samples falling on leaf node j;

[0036] make And the weight score ω of leaf node j j Find the partial derivatives such that the partial derivatives equal to 0, and we get:

[0037]

[0038]

[0039] Based on the objective function Obj of the optimal solution (s) Split sample data.

[0040] Beneficial effects:

[0041] This invention provides an algorithm for optical plasma boundary reconstruction, which mainly consists of boundary extraction using a U-Net network and boundary reconstruction based on XGBoost. The U-Net-based image segmentation algorithm requires no preprocessing of the original image or manual setting of the ROI region. Compared with traditional edge detection algorithms, this invention's method can extract boundaries better and avoids a large number of false boundaries. In the absence of camera calibration, this invention proposes a method for selecting pixel coordinate label values ​​and implements plasma boundary reconstruction based on XGBoost, converting the image plane into the tokamak's poloidal surface. Experimental results show that the average reconstruction error on the test set is 7.36 mm. Compared with the algorithm of Hao LUO et al., this invention's algorithm has higher accuracy and does not suffer from horizontal drift. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the U-Net network structure of the present invention;

[0043] Figure 2a , Figure 2b , Figure 2c The plasma boundary identification result for gun #110790 at 6.9 seconds; among which, Figure 2a This is the original image. Figure 2b The gray area represents the identified boundary region. Figure 2c To obtain the boundary center point;

[0044] Figure 3a , Figure 3b Fitting curves for the EFIT data at 2.61 seconds for gun #110790; where, Figure 3a To plot the EFIT data and the scaled image coordinates in the same coordinate system; Figure 3b How to select the label values ​​for image coordinates;

[0045] Figure 4a , Figure 4b , Figure 4c , Figure 4d EFIT and optical reconstruction coordinate diagrams for different gun numbers at different times; among them... Figure 4a For gun #110793, at 1.02 seconds... Figure 4b At 6.12 seconds, for gun #110793 Figure 4c At 3.16 seconds, for gun #110790 Figure 4d It is the 10.09th second of gun #110790. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0047] The tokamak plasma boundary identification and configuration reconstruction method of the present invention includes two aspects: plasma boundary identification and micro-reconstruction.

[0048] Step 1, Plasma Boundary Identification:

[0049] To better extract plasma boundaries during operation, this invention employs a deep learning-based image segmentation method and uses a U-Net network to extract plasma boundaries. Experiments show that the U-Net-based image segmentation method is highly effective in extracting plasma boundaries on EAST.

[0050] In the past two years, deep convolutional networks have performed well in many computer vision tasks. For example, the FCN network (Long J, Shelhamer E, Darrell T. Fully Convolutional Networks for Semantic Segmentation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015, 39(4):640-651.) is an improvement on convolutional neural networks and performs pixel-level classification of images. The Deep Lab V3+ network (Long J, Shelhamer E, Darrell T. Fully Convolutional Networks for Semantic Segmentation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2015, 39(4):640-651.) achieved an MIoU of 89% on the Pascal VOC 2012 dataset. The U-Net network has also achieved good results in medical image segmentation.

[0051] U-Net is a semantic segmentation network based on FCN, which achieved excellent results in the ISBI 2012 EM segmentation challenge and is also very fast, performing well even on small datasets. Since the plasma boundary image data annotated in this invention is limited, the U-Net network model was chosen.

[0052] The overall structure of the U-Net network is to first encode (downsample) and then decode (upsample) to obtain pixel classifications of the same size as the original image. This invention appropriately modifies the feature map sizes of each layer of the U-Net network so that the output image is the same size as the input image, facilitating the analysis and research of experimental results. The structure of the U-Net network of this invention is as follows: Figure 1As shown, the Unet network is a fully convolutional network improved from FCN. Its structure consists of a contraction path and a dilation path. The left side represents the contraction path, where each layer consists of two 3×3 convolutional layers and a 2×2 max-pooling layer, using ReLU activation. Each layer doubles the number of feature channels. The right side represents the dilation path, where each layer first uses deconvolution to halve the number of feature channels, then concatenates with the feature maps from the corresponding contraction path, and then passes through two 3×3 convolutional layers. The last layer of the dilation path uses a 1×1 convolutional kernel, resulting in only 1 feature channel. The Sigmoid function restricts the output range to [0,1]. The output segmentation image represents the probability that each pixel belongs to an ELMs filamentary structure. Pixels with a probability greater than 0.5 are ultimately considered to belong to an ELMs filamentary structure.

[0053] In machine learning, training data is used to minimize a loss function to determine the values ​​of the parameters. The loss function measures the difference between the actual variable values ​​and the predicted values; the smaller the loss value, the more accurate the prediction.

[0054] The loss function used is cross-entropy loss, as shown in the following formula:

[0055]

[0056] Where M represents the number of categories, and in this invention, M is set to 2. c The value can be 0 or 1. It takes the value 1 when the category is the same as the true category, and 0 otherwise. c The predicted value represents the probability that the sample belongs to category c.

[0057] Plasma boundary regions were manually labeled in the images and used as the ground truth segmentation images for network training. Before model training, the image size was adjusted to 512×512, and data augmentation was performed to prevent overfitting. The resulting model then predicted image data outside the training set. Figure 2a , Figure 2b , Figure 2c This represents the identification results from the U-Net network. Figure 2a This is the original image. Figure 2b The gray area represents the identified boundary region. Figure 2c To obtain the boundary center point.

[0058] Experimental results show that the U-Net-based image segmentation algorithm can still perform well in a bright vacuum chamber, with almost no erroneous edges, demonstrating high recognition accuracy. To facilitate subsequent configuration reconstruction of the plasma boundary, this invention selects multiple center points of the plasma boundary regions as experimental data for later stages.

[0059] Step 2, Configuration Reconstruction:

[0060] Plasma configuration reconstruction aims to find a functional relationship between the image plane and the poloidal plane. Machine learning can fit a functional model of configuration reconstruction from the data. Therefore, this invention uses the XGBoost model for fitting.

[0061] XGBoost consists of multiple CART (Classification and Regression Tree) decision trees. These trees work together to make decisions, and the results are summed to obtain the final result. It employs the Boosting ensemble approach, integrating multiple weak learners into a single strong learner to improve the overall model performance.

[0062] The XGBoost model can be defined as:

[0063]

[0064] Among them, f k (x) represents the k-th decision tree, x i This represents the input feature vector. This represents the predicted value; the model contains K trees. This represents the space of the regression tree.

[0065] The objective function Obj of the model consists of a loss function L and a regularization term Ω. The loss function L is used to evaluate the predicted value. Compared with the true value y i The error is quantified by the regularization term Ω, which controls the complexity of the model and avoids overfitting.

[0066] The objective function of XGBoost is defined as follows:

[0067]

[0068] The regularization term Ω is defined as follows:

[0069]

[0070] Where γ and λ are modifiable parameters, T is the number of leaves, ω is the weight score of the leaf node, and f represents the decision tree model.

[0071] The model in round s can be defined as:

[0072]

[0073] Where s is the iteration round number, and the model in the s-th round is equal to the model in the (s-1)-th round plus the new model f(x). i ), where f(x) iThis minimizes the objective function Obj. Rewrite the objective function Obj:

[0074]

[0075] in, For the (s-1)th round model, the sample x i The predicted value, f s (x i ) represents the predicted value of the new model trained in the s-th round.

[0076] Taylor expansion of the objective function Obj:

[0077]

[0078] Among them, g i h is the first derivative of the loss function. i It is the second derivative of the loss function.

[0079] Due to the constant term It does not affect the optimization of the objective function, so it can be removed, and Ω(f) can be removed. s Substituting into the formula, the objective function Obj can be written as:

[0080]

[0081] Among them, I j Let be all samples falling on leaf node j. And the weight score ω of leaf node j j Find the partial derivatives such that the partial derivatives equal to 0, and we get:

[0082]

[0083]

[0084] Based on the objective function Obj of the optimal solution (s) Split sample data.

[0085] The experiments and results of this invention are as follows:

[0086] This invention selects data from gun numbers #110790, #110792, and #110793 for processing and analysis. First, boundary recognition is performed on the EAST plasma images captured by the camera. The Unet network is used to segment the images to obtain the plasma boundaries. Multiple boundary points are selected for each image, and the pixel coordinates (u,v) are recorded.

[0087] The pixel coordinates (u,v) are scaled and translated to obtain (u',v'). This coordinate system is then aligned with the EFIT data, ensuring that the geometric center of the plasma boundary coincides with the geometric center of the EFIT data image. Figure 3a , Figure 3b As shown, it is the EFIT data fitting curve of gun #110790 at 2.61 seconds, and the set of pixel coordinates (u',v') at the same time. The left figure is the EFIT data curve and the set of (u',v'), and the right figure shows that by connecting the geometric center with the (u',v') point and extending the straight line to intersect the EFIT curve, the corresponding label value (r,z) can be obtained.

[0088] Connect the center point to the pixel coordinates (u', v'), and extend the straight line to intersect the EFIT fitting curve, obtaining the intersection point coordinates (r, z). Use (r, z) as the label value. The selection of the label value can be seen as a functional mapping relationship with the pixel coordinates, and the XGBoost model can fit the function through training. The same processing is performed on the EFIT data and image data of all gun numbers at the same time. The (u', v') and (r, z) sets obtained from gun numbers #110792 and #110793 are used as the training set, and the (u', v') and (r, z) sets obtained from gun number #110790 are used as the test set.

[0089] This invention trains two XGBoost models, model_R and model_Z, to fit the r and z values, respectively. The input to model_R is the (u', v') set of the training set, and the true value is the r-coordinate of the training set. The input to model_Z is the (u', v') set of the training set, and the true value is the z-coordinate of the training set. The mean squared error of model_R obtained from the training set is 3.5149 × 10⁻⁶. -5 m 2 The mean squared error of model_Z is 1.4034 × 10⁻⁶. -5 m 2 The mean squared error of model_R obtained on the test set is 3.7119 × 10⁻⁶. -5 m 2 The mean squared error of model_Z is 1.7045 × 10⁻⁶. -5 m 2 Therefore, the average distance error between the (r, z) coordinates predicted by the model on the test set and the label value is 7.36 mm. (As shown from...) Figure 4a , Figure 4b , Figure 4c , Figure 4d We can see the model's predicted values ​​compared to the EFIT data.

[0090] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method of tokamak plasma boundary identification and shape reconstruction, characterized in that, Comprising the following steps: Step 1, plasma boundary recognition: first, the EAST plasma image taken by the camera is recognized, the Unet network is used for image segmentation, the plasma boundary is obtained, a plurality of boundary points of each image are selected, and the pixel coordinates (u, v) are recorded; The pixel coordinates (u, v) are scaled and translated to obtain (u', v'), which is in the same coordinate system as the EFIT data, and the geometric center of the plasma boundary is coincided with the geometric center of the EFIT data figure, the straight line connecting the geometric center and the (u', v') point is extended and intersected with the EFIT curve to obtain the corresponding label value (r, z); the center point and the pixel coordinates (u', v') are connected, and the straight line is extended and intersected with the EFIT fitting curve to obtain the intersection coordinates (r, z), which is taken as the label value; The selection of the label value is a function mapping relationship with the pixel coordinates, and the XGBoost model is fitted by training; the EFIT data and the image data at the same time for all shot numbers are processed in the same way, and the training set and the test set are set; Two XGBoost models model_R and model_Z are trained to fit r and z values; The input value of the model model_R is the (u', v') set of the training set, and the real value is the r coordinate of the training set; The input value of the model model_Z is the (u', v') set of the training set, and the real value is the z coordinate of the training set; An image segmentation method based on deep learning is adopted, and a U-Net network is used to extract the plasma boundary; The loss function adopts cross-entropy loss, and the formula is as follows: where M represents the number of classes; is 0 or 1, and is 1 when the class is the same as the true class, otherwise is 0; is the predicted value, representing the probability that the sample belongs to class c. The image is manually labeled to select the plasma boundary region as the real segmentation image during network training; The obtained model is used to predict the image data outside the training set; Step 2, shape reconstruction: The XGBoost model is used for fitting; the XGBoost model is defined as: wherein, denotes the kth decision tree, denotes the input feature vector, denotes the predicted value, the model comprising K trees; The objective function Obj of the model is composed of a loss function L and a regularization term Ω, the loss function L is used to evaluate the error between the predicted value and the true value , and the regularization term Ω is used to control the complexity of the model to avoid overfitting; The objective function of XGBoost is defined as shown below: Wherein, the definition of the regularization term Omega is: wherein, and are modifiable parameters, T is the number of leaves, is the weight fraction of the leaf node; f denotes the decision tree model; The s-th round model can be defined as: wherein s is the iteration round number, the model of the s-th round is equal to the model of the (s-1)-th round plus the new model wherein such that the objective function Obj is minimized; Rewrite the objective function Obj: wherein, is the prediction value of the sample by the model of the s-1th round of training, is the prediction value of the sample by the model of the s-1th round of training, is the prediction value of the sample by the new model of the sth round of training; Taylor expansion is performed on the objective function Obj: wherein, is a first derivative of the loss function, is a second derivative of the loss function; Removing constant terms that do not affect the optimization of the objective function and substituting into the equation, the objective function Obj is written as: ​ wherein, is all samples falling in leaf node j; Let , , and take the partial derivative of the weight score of the leaf node j with respect to the weight w, set the partial derivative equal to zero, and solve for w: Objective function according to optimal solution Splitting sample data.

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