Industrial quality prediction method and device based on graph attention long-short term memory network

Abstract

The invention relates to an industrial quality prediction method and equipment based on a graph attention long-short term memory network, and the method comprises the steps: obtaining a to-be-predicted data set in an industrial manufacturing process, and carrying out the standardization operation of the data set, and obtaining a standardized data set; obtaining a low-order characteristic variable matrix of the standardized data set through a multi-layer perceptron, and constructing an adjacent matrix; inputting the standardized data set, the adjacent matrix and the low-order characteristic variable matrix into a trained graph attention long-short term memory network model, splicing output time characteristic information and space characteristic information, and obtaining a quality prediction result through a quality predictor; the graph attention long-short-term memory network model comprises a graph attention layer and a long-short-term memory layer which are arranged in parallel and are respectively used for extracting time feature information and space feature information. Compared with the prior art, the method has the advantages of fusing the spatial-temporal characteristics, automatically constructing the adjacent matrix, improving the prediction accuracy and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of product quality prediction, and in particular to an industrial quality prediction method and device based on a graph attention long short-term memory network. Background Art

[0002] With the expansion of production scale and the rapid development of technology, quality control in modern industry has become more and more complex and important. An effective process quality control model can predict the manufacturing quality of products in the early stages of production to improve the process. In the product manufacturing process, quality control is an important means to ensure product quality. Intelligent manufacturing has put forward higher requirements on the real-time and accuracy of product quality information. Advanced information technologies such as industrial big data and artificial intelligence provide new means for real-time quality prediction of industrial process manufacturing products.

[0003] Traditional product quality prediction is mostly based on statistical process control (SPC) research, which predicts the final quality of the product by studying the changing trends of quality parameters in the production process. Most of these SPC-based quality prediction methods rely on the quality information of the important quality parameters of the product manufacturing process itself, and this method relies heavily on the experience and knowledge of quality control experts and is not universal.

[0004] With the rapid development of Internet technology and the Internet of Things (IOT), the amount of data collected is unprecedentedly huge. Due to the limitations of the number of model parameters and operation speed, the traditional SPC-based quality prediction method is not suitable for industrial big data scenarios. In recent years, quality prediction methods based on artificial intelligence algorithm optimization have been proposed. Modeling is carried out for the characteristics of quality data generated by the manufacturing process, and product quality prediction is carried out by analyzing the model results. These artificial intelligence networks use deep hierarchical structures to automatically represent abstract features from process data, and then directly establish the relationship between learning features and target outputs, which can effectively solve the problem of data explosion. Compared with traditional methods, this type of method has a certain degree of optimization in the ability to extract features and predict quality, and has shown significant improvements in quality prediction errors and other aspects. However, most deep learning methods ignore the relationship between data and cannot mine high-level information from the data. In addition, deep learning models are typical "black box models", that is, model training adopts an "end-to-end" decision-making mode. People cannot detect what knowledge the deep model has learned from the data, and it is difficult to understand the impact of the number of network layers, the number of neurons, and the activation function on the results, making the effect of deep learning more dependent on previous engineering experience and parameter adjustment skills.

[0005] In recent years, graph neural networks have gradually become a research hotspot due to their good performance and interpretability, and have been applied to many fields, such as image recognition, point cloud segmentation, recommendation systems, traffic prediction, and chemical structure research. Due to the non-Euclidean characteristics of the data structure, deep learning models cannot extract these features. However, in the graph domain, the geometric structure of the data can provide additional information, including not only the values ​​of the nodes, but also the relationships between them. Therefore, compared with the general data domain, more inter-data information can be provided in the graph domain. However, the application of graph neural networks in large-scale industrial process quality prediction is relatively small.

[0006] After searching, the Chinese invention patent application publication number CN117421580A discloses a method for predicting process quality time series based on graph neural network and transfer learning, including collecting production line process parameters and quality index data through MES system and forming a data set; secondly, mapping all variables to nodes, using the production data corresponding to the variables as node features, mapping the control relationship between process parameters and quality indicators to the edges between nodes, completing the transformation of process relationship to graph data, and using graph neural network to calculate the spatial features in graph data; at the same time, using bidirectional long short-term memory network to calculate the time series features of the quality indicators themselves; finally, splicing the spatial information and time series features to obtain the prediction results, introducing the transfer learning mechanism to realize the update of the model and output the prediction results. This existing patent application directly maps the acquired data by composing, and the process parameters come from expert experience, so there are limitations in input parameters and inaccurate predictions.

[0007] How to achieve accurate prediction of industrial process quality based on graph neural networks has become a technical problem that needs to be solved. Summary of the invention

[0008] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide an industrial quality prediction method and device based on graph attention long short-term memory network.

[0009] The purpose of the present invention can be achieved by the following technical solutions:

[0010] According to one aspect of the present invention, there is provided an industrial quality prediction method based on a graph attention long short-term memory network, the method comprising:

[0011] Step S1, obtaining a data set to be predicted in an industrial manufacturing process, and performing a standardization operation on the data set to obtain a standardized data set;

[0012] Step S2, obtaining a low-order feature variable matrix of the standardized data set through a multi-layer perceptron, and constructing an adjacency matrix;

[0013] Step S3, input the standardized data set, adjacency matrix and low-order feature variable matrix into the trained graph attention long short-term memory network model, and output the temporal feature information and spatial feature information and then pass them through the quality estimator to obtain the quality prediction result;

[0014] The graph attention long short-term memory network model includes a parallel graph attention layer and a long short-term memory layer, which are used to extract temporal feature information and spatial feature information respectively.

[0015] Preferably, after using a multilayer perceptron to obtain the low-order feature variable matrix of the standardized data set in step S2, the K-adjacent algorithm is used to calculate the Euclidean distance or cosine distance, and for each variable feature, the K features with the closest distance are selected as adjacent samples to construct an adjacency matrix, thereby converting the one-dimensional signal data into graph data.

[0016] Preferably, different variable parameters are selected to obtain adjacency matrices with different receptive fields, and spatial features of different receptive fields are fused through feature concatenation operations.

[0017] More preferably, the variable parameters are 1, 2 and 3.

[0018] Preferably, in step S3, the adjacency matrix and the low-order feature variable matrix are input into the graph attention long short-term memory network model to extract spatial feature information; and the standardized data set is input into the graph attention long short-term memory network model to extract temporal feature information.

[0019] Preferably, the calculation process of the long short-term memory layer is specifically as follows:

[0020] i t =σ(W ii d t +b ii +W hi h (t-1) +b hi )

[0021] f t =σ(W if d t +b if +W hf h (t-1) +b hf )

[0022] g t =tanh(W ig d t +b ig +W hg h (t-1) +b hg )

[0023] ot =σ(W io d t +b io +W ho h (t-1) +b ho )

[0024] c t =f t *c (t-1) +i t *g t

[0025] h t =o t *tanh(c t )

[0026] Among them, i t is the input gate, f t is the forget gate, g t is the current input unit state, o t is the output gate, c t is the unit state at the current moment; h t is the hidden state of LSTM, which constitutes the temporal feature H extracted by LSTM t ; W ii , W if , W ig , W io They are the current input gate, forget gate, current input unit and output gate d respectively. t The weight parameter, W hi , W hf , W hg , W ho are the h in the current input gate, forget gate, current input unit and output gate respectively. (t-1) The weight parameter, b ii 、b if 、b ig 、b io They are the current input gate, forget gate, current input unit and output gate d respectively. t The bias value, b hi 、b hf 、b hg 、b ho They are the current input gate, forget gate, current input unit and h in the output gate respectively. (t-1) The bias value, h (t-1) is the hidden state of LSTM at time t-1, d t The data entered at the current moment.

[0027] Preferably, the calculation process of the quality predictor is:

[0028]

[0029] in, Indicates the quality prediction value; FC i represents the i-th fully connected layer, i = 1, 2; Flat is the expansion function, that is, the feature flattening operation; O is the spliced ​​temporal feature information and spatial feature information.

[0030] Preferably, the loss function of the quality predictor is a mean square error function, and the loss function is back-propagated to obtain n features with large weights on the prediction results to update the training parameters of the graph attention long short-term memory network model.

[0031] Preferably, the data set includes manufacturing process data of temperature, pressure, temperature×pressure, material fusion index and material conversion index.

[0032] According to another aspect of the present invention, an electronic device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and the method described above is implemented when the processor executes the program.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] 1) The present invention uses a multi-layer perceptron to obtain the low-order features of the original variables, and then uses the K-adjacent algorithm to calculate and construct the adjacency matrix, converts the one-dimensional process signal into graph data through graph construction technology, and uses a graph attention network to extract spatial features, so as to more fully utilize the correlation between process variables; uses a long short-term memory network to extract time series features to provide more relevant information for the quality prediction of the model, and enhances the richness of feature information after splicing the spatiotemporal features, and outputs the prediction results through a quality estimator, thereby improving the prediction accuracy.

[0035] 2) The present invention uses a multi-layer perceptron to perform feature pre-selection operations, which is equivalent to noise reduction processing, and selects variables containing more feature information. Then, in the part of extracting spatial features in the graph attention network, a network with multiple receptive fields is used to extract feature information with different numbers of neighbors, thereby enriching the feature information in space and enhancing the quality prediction effect.

[0036] 3) The present invention uses the K-neighboring algorithm to calculate the distance. For each variable feature, the nearest K features are selected as neighboring samples according to the distance sorting, and the adjacency matrix is ​​constructed to automatically form spatial correlation features, rather than relying on expert experience to determine the spatial correlation, thereby avoiding the limitations of expert experience and enhancing the adaptability and prediction accuracy of the model.

[0037] 4) The present invention can find several manufacturing parameters with large weights for quality prediction by inferring the attention coefficient, and provide explainable analysis for the prediction process of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flow chart of the industrial quality prediction method based on graph attention long short-term memory network in the present invention;

[0039] Figure 2 Schematic diagram of the architecture of the attention long short-term memory network model in the present invention. DETAILED DESCRIPTION

[0040] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0041] The present embodiment relates to an industrial quality prediction method based on a graph attention long short-term memory network. The method is based on a graph neural network and a long short-term memory network, abandons the model of artificial parameter adjustment, conducts in-depth mining of industrial data, effectively expresses the influence relationship between data, integrates the spatial characteristics and temporal characteristics of manufacturing parameters, improves the accuracy of industrial process quality prediction, and thus performs quality control on the manufacturing process.

[0042] The spatial features of the data are extracted through the graph neural network, and the temporal features of the data are extracted using the long short-term memory network. Finally, a two-layer fully connected layer is used to build a product quality prediction estimator to predict the manufacturing quality of the product, improve the product prediction accuracy of the industrial manufacturing process, and reduce the quality prediction error. At the same time, based on the attention coefficient mechanism of the graph neural network, several manufacturing parameters that are most important for quality prediction are inferred, providing explainable analysis for the model prediction results.

[0043] In order to improve the interpretability of the model, several production parameters with the greatest weight on the final product quality are inferred based on the attention coefficient of the graph neural network, providing an interpretable analysis study for the model's prediction results.

[0044] An industrial quality prediction method based on graph attention long short-term memory network, the method comprises the following steps:

[0045] Step 1: Obtain a sample data set D to be processed, the quality score of the sample data set is Y, and perform a standardization operation on the data set to obtain a standardized data set S(D);

[0046] Step 2: Obtain the low-order feature variable matrix X of the sample through a multi-layer perceptron (MLP), calculate the distance between the feature vectors of each variable in X, and for each variable feature, select the nearest K variable features as adjacent variables to construct the adjacency matrix A;

[0047] Step 3: Input the adjacency matrix A and the feature matrix X into the graph attention network model to extract the spatial feature information Z S ;

[0048] Step 4: Input the original sample data features S(D) after the standardization operation into the long short-term memory network to extract the temporal feature information H of the sample features T ;

[0049] Step 5: Extract the spatial feature information Z from the graph attention network S and the temporal feature information H extracted by the long short-term memory network T The concatenation is used as input features of the final quality estimator;

[0050] Step 6: Substitute the quality prediction scores obtained by the two fully connected layer estimators The quality true score Y is input into the mean square error (MSE) formula to obtain the final loss function.

[0051] Step 7: Update the model training parameters through back propagation of the loss function to improve the quality prediction ability of the model.

[0052] This embodiment also relates to an industrial quality prediction method based on a graph attention long short-term memory network, which is verified in the following experimental environment: the hardware configuration used in the experiment is an Intel(R) Core(TM) i7-12700H processor, a GTX 3050 graphics card, the software environment is CUDA11.3 and cuDNN8.0, and the development environment is Windows 11. The graph attention long short-term memory network model is completed using Pycharm and the open source deep learning framework Pytorch1.12.1.

[0053] The method specifically comprises the following steps:

[0054] Step 1: Use the Kaggle public quality prediction dataset, which mainly contains 5 process control parameters and 1 quality rating score. The control parameters include temperature, pressure, temperature × pressure, material fusion index and material conversion index. The quality rating is divided into percentage values ​​of expert scores. The dataset includes a total of 3958 manufacturing process data. The window size W = 5, the sliding step size S = 1, and the data division of 7:3 are used, that is, 2770 training data and the remaining 1188 are test data. m*n, there are 3958 data in total, each data has 5 process control variables, so m = 3958, n = 5. Standardize the data set to obtain S(D), and the conversion function is:

[0055]

[0056] Among them, d∈D is each data in D, u is the mean of all variables in this data, and σ is the standard deviation of all variables in this data.

[0057] Step 2: Obtain the low-order feature variable matrix X of the sample through a multi-layer perceptron (MLP). The expression of X is:

[0058] X=MLP(D) (2)

[0059] D is the original variable data set, X is the feature data set output by MLP, and the distance (Euclidean distance) between the feature vectors of each variable in X is calculated after standardization:

[0060]

[0061] Among them, x :,i is the i-th variable vector of the special detection matrix X, dist(x :,i ,x :,j ) is the distance between the i-th variable feature data and the j-th variable feature data in X. For each variable feature, select the K sample features with the closest distance as adjacent samples to construct the adjacency matrix A, where K is a variable parameter, A∈R m*m is a 0-1 sparse matrix.

[0062] The distance formula in step 2 can be replaced by the cosine distance:

[0063]

[0064] The cosine distance is not affected by the vector dimension, and can better process the directional information between vectors and extract more spatial feature information.

[0065] Step 3: Input the adjacency matrix A and the feature variable matrix X into the graph attention network (GAT) to extract the spatial feature information Z of the data. S , the expression formula is:

[0066] Z S =GAT(X,A) (5)

[0067] The adjacency matrix A in step 3 is determined by the variable parameter K. In order to more fully extract the spatial feature information, K = 1, 2, 3 is used to extract the feature information of variables with different receptive fields. Finally, the feature concatenation operation is used to obtain the final spatial feature. The formula is:

[0068] Z S,F =⊙{Z S,1 ,Z S,2 ,Z S,3} (6)

[0069] Where Z S,1 ,Z S,2 ,Z S,3 They represent the spatial features extracted when K=1, 2, and 3 respectively.

[0070] Step 4: Input the standardized data S(D) into the long short-term memory network (LSTM) to extract the time series feature H t , the LSTM calculation process is as follows:

[0071] i t =σ(W ii d t +b ii +W hi h (t-1) +b hi ) (7)

[0072] f t =σ(W if d t +b if +W hf h (t-1) +b hf ) (8)

[0073] g t =tanh(W ig d t +b ig +W hg h (t-1) +b hg ) (9)

[0074] o t =σ(W io d t +b io +W ho h (t-1) +b ho ) (10)

[0075] c t =f t *c (t-1) +i t *g t (11)

[0076] h t =o t *tanh (c t) (12)

[0077] Among them, i t is the input gate, f t is the forget gate, g t is the current input unit state, o t is the output gate, c t is the unit state at the current moment; h t is the hidden state of LSTM, which constitutes the temporal feature H extracted by LSTM t ; W ii , W if , W ig , W io are the d in each gate at the current moment t The weight parameter, W hi , W hf , W hg , W ho are h in each gate at the current moment. (t-1) The weight parameter, b ii 、b if 、b ig 、b io are the d in each gate at the current moment t The bias value, b hi 、b hf 、b hg 、b ho are h in each gate at the current moment (t-1) The bias value, h (t-1) is the hidden state of LSTM at time t-1, d t The data entered at the current moment.

[0078] Step 5: Extract the spatial feature information Z from the graph attention network S,F and the temporal feature information H extracted by the long short-term memory network T The concatenation is used as the input feature O of the final quality estimator, and the formula is as follows:

[0079] O=⊙{Z S,F ,H t} (13)

[0080]

[0081] in, Indicates the quality prediction value; FC i represents the i-th fully connected layer; Flat is the expansion function, that is, the feature flattening operation.

[0082] Step 6: Substitute the quality prediction scores obtained by the two fully connected layer estimators The final loss function is obtained by inputting the true quality score Y into the mean square error (MSE):

[0083]

[0084] in, and i They represent the quality prediction value and true value of the i-th sample respectively; N is the number of samples, that is, the number of 2770 training data sets.

[0085] Step 7: Update the model training parameters through the back propagation of the MSE loss function to improve the quality prediction ability of the model. By back propagating the trained model parameters, several features with the greatest weight on the prediction results are obtained, providing explainable analysis for the model's prediction process.

[0086] The electronic device of the present invention includes a central processing unit (CPU), which can perform various appropriate actions and processes according to computer program instructions stored in a read-only memory (ROM) or loaded from a storage unit into a random access memory (RAM). In the RAM, various programs and data required for device operation can also be stored. The CPU, ROM and RAM are connected to each other via a bus. An input / output (I / O) interface is also connected to the bus.

[0087] Multiple components in the device are connected to the I / O interface, including: input units, such as keyboards, mice, etc.; output units, such as various types of displays, speakers, etc.; storage units, such as disks, optical disks, etc.; and communication units, such as network cards, modems, wireless communication transceivers, etc. The communication unit allows the device to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunication networks.

[0088] The processing unit performs the various methods and processes described above. For example, in some embodiments, the method can be implemented as a computer software program, which is tangibly contained in a machine-readable medium, such as a storage unit. In some embodiments, part or all of the computer program can be loaded and / or installed on the device via a ROM and / or a communication unit. When the computer program is loaded into RAM and executed by the CPU, one or more steps of the method described above can be performed. Alternatively, in other embodiments, the CPU can be configured to perform the method in any other appropriate manner (e.g., by means of firmware).

[0089] The functions described above herein may be performed at least in part by one or more hardware logic components. For example, without limitation, exemplary types of hardware logic components that may be used include: field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on chips (SOCs), complex programmable logic devices (CPLDs), and the like.

[0090] The program code for implementing the method of the present invention can be written in any combination of one or more programming languages. These program codes can be provided to a processor or controller of a general-purpose computer, a special-purpose computer or other programmable data processing device, so that the program code, when executed by the processor or controller, enables the functions / operations specified in the flow chart and / or block diagram to be implemented. The program code can be executed entirely on the machine, partially on the machine, partially on the machine as a stand-alone software package and partially on a remote machine, or entirely on a remote machine or server.

[0091] In the context of the present invention, a machine-readable medium may be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, device, or equipment. A machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or equipment, or any suitable combination of the foregoing. A more specific example of a machine-readable storage medium may include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0092] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. An industrial quality prediction method based on graph attention long short-term memory network, characterized in that: The method includes: Step S1, obtaining a data set to be predicted in an industrial manufacturing process, and performing a standardization operation on the data set to obtain a standardized data set; Step S2, obtaining a low-order feature variable matrix of the standardized data set through a multi-layer perceptron, and constructing an adjacency matrix; Step S3, input the standardized data set, adjacency matrix and low-order feature variable matrix into the trained graph attention long short-term memory network model, and output the temporal feature information and spatial feature information and then pass them through the quality estimator to obtain the quality prediction result; The graph attention long short-term memory network model includes a parallel graph attention layer and a long short-term memory layer, which are used to extract temporal feature information and spatial feature information respectively.

2. According to the industrial quality prediction method based on graph attention long short-term memory network described in claim 1, it is characterized in that: After using a multilayer perceptron to obtain the low-order feature variable matrix of the standardized data set in step S2, the K-adjacent algorithm is used to calculate the Euclidean distance or cosine distance. For each variable feature, the K features with the closest distance are selected as adjacent samples to construct an adjacency matrix, thereby converting the one-dimensional signal data into graph data.

3. According to the industrial quality prediction method based on graph attention long short-term memory network described in claim 1, it is characterized in that: Different variable parameters are selected to obtain adjacency matrices with different receptive fields, and the spatial features of different receptive fields are fused through feature concatenation operations.

4. According to the industrial quality prediction method based on graph attention long short-term memory network as described in claim 3, it is characterized in that: The variable parameters are 1, 2 and 3.

5. According to the industrial quality prediction method based on graph attention long short-term memory network described in claim 1, it is characterized in that: In step S3, the adjacency matrix and the low-order feature variable matrix are input into the graph attention long short-term memory network model to extract spatial feature information; and the standardized data set is input into the graph attention long short-term memory network model to extract temporal feature information.

6. The industrial quality prediction method based on graph attention long short-term memory network according to claim 1, characterized in that: The calculation process of the long short-term memory layer is specifically as follows: i t =σ(W ii d t +b ii +W hi h (t-1) +b hi ) f t =σ(W if d t +b if +W hf h (t-1) +b hf ) g t =tanh(W ig d t +b ig +W hg h (t-1) +b hg ) o t =σ(W io d t +b io +W ho h (t-1) +b ho ) c t =f t *c (t-1) +i t *g t h t =o t *tanh(c t ) Among them, i t is the input gate, f t is the forget gate, g t is the current input unit state, o t is the output gate, c t is the unit state at the current moment; h t is the hidden state of LSTM, which constitutes the temporal feature H extracted by LSTM t ; W ii , W if , W ig , W io They are the current input gate, forget gate, current input unit and output gate d respectively. t The weight parameter, W hi , W hf , W hg , W ho are the h in the current input gate, forget gate, current input unit and output gate respectively. (t-1) The weight parameter, b ii 、b if 、b ig 、b io They are the current input gate, forget gate, current input unit and output gate d respectively. t The bias value, b hi 、b hf 、b hg 、b ho They are the current input gate, forget gate, current input unit and h in the output gate respectively. (t-1) The bias value, h (t-1) is the hidden state of LSTM at time t-1, d t The data entered at the current moment.

7. The industrial quality prediction method based on graph attention long short-term memory network according to claim 1, characterized in that: The calculation process of the quality predictor is: in, Indicates the quality prediction value; FC i represents the i-th fully connected layer, i = 1, 2; Flat is the expansion function, that is, the feature flattening operation; O is the spliced ​​temporal feature information and spatial feature information.

8. The industrial quality prediction method based on graph attention long short-term memory network according to claim 1, characterized in that: The loss function of the quality predictor is a mean square error function, and through back propagation of the loss function, n features with large weights on the prediction results are obtained to update the training parameters of the graph attention long short-term memory network model.

9. The industrial quality prediction method based on graph attention long short-term memory network according to claim 1, characterized in that: The data set includes manufacturing process data of temperature, pressure, temperature×pressure, material fusion index, and material conversion index.

10. An electronic device comprising a memory and a processor, wherein a computer program is stored in the memory, wherein: When the processor executes the program, the method according to any one of claims 1 to 9 is implemented.

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