A method and device for identifying overall features of strip shape based on DBSCAN algorithm

Abstract

The present invention provides a method and device for identifying the overall characteristics of strip shape based on the DBSCAN algorithm. The method comprises the following steps: obtaining strip data sets from different layers of a cold rolling mill; processing the strip data sets using the DBSCAN algorithm to obtain cluster centers for each layer of the strip data sets; and obtaining a curve for identifying the overall characteristics of the strip shape based on the cluster centers of each layer of the strip data sets. The present invention accurately identifies the shape characteristics of the rolled strip and determines the difference from the target shape. Based on this information, the adjustment amount of the shape actuator can be accurately set to achieve shape feedback control. Furthermore, by accurately understanding the basic characteristics of the cold rolling mill's rolled strip shape, it can also be used for roll profile optimization, production problem analysis, and other purposes.

Description

Technical Field

[0001] The present invention relates to the field of metallurgical automation and intelligent control technology, and in particular to a method and device for identifying overall characteristics of strip shape based on a DBSCAN algorithm. Background Art

[0002] Flatness feature recognition is a fundamental task in cold rolling strip automatic control systems. Only by accurately identifying the flatness characteristics of the rolled strip can the difference from the target flatness be determined, allowing the adjustment of the flatness actuator to be accurately set, achieving flatness feedback control. Furthermore, accurately understanding the basic characteristics of the cold rolling mill's flatness can also facilitate roll profile optimization and production problem analysis.

[0003] The prior art discloses a method and system for cold-rolled strip shape pattern recognition based on deep autoencoding. This method utilizes the encoder in a deep autoencoding neural network to train large amounts of shape data to achieve feature extraction, ultimately extracting five basic shape patterns. Also disclosed is an online pattern recognition system for cold-rolled strip shape signals, aiming to address the low recognition accuracy, poor real-time performance, and poor stability and robustness of traditional shape pattern recognition systems. Also disclosed is a shape recognition method based on a RBF neural network. This method first uses PCA principal component analysis to reduce the dimension and extract features of the shape stress values ​​detected by a shape meter. A shape recognition model is then established using a genetic algorithm-based RBF neural network, and shape recognition is achieved through network training. Also disclosed is a shape recognition method based on data hypothesis compensation. This method first performs local shape recognition based on shape data hypothesis compensation to prevent the influence of local shape on overall shape recognition. Then, cosine similarity is used to replace the traditional Euclidean distance or Manhattan distance method for overall shape recognition, aiming to improve the recognition accuracy of both global and local shape defects.

[0004] However, the above methods all use appropriate mathematical methods or neural network methods to decompose and identify the plate shape of the frame-by-frame plate shape measurement signals provided by the plate shape meter. This is an identification of the cross-sectional plate shape characteristics of the rolled piece, and cannot reflect the overall characteristics of the plate shape of the cold rolling mill, nor can it provide the overall plate shape characteristics of all steel types, thickness specifications, and width specifications of the strip. There are no reports on the identification and quantitative expression of plate shape characteristics from the tens of thousands of frames of plate shape monitoring signals retained in the control system. In addition, due to the large number of non-steady-state rolling processes in cold rolling production, such as strip biting, dynamic specification change, acceleration and deceleration, and rolling stop and roll change, the rolling parameters fluctuate greatly, which can easily cause strip shape anomalies. These abnormal plate shape signals are stored together with the plate shape signals during steady-state rolling in a time sequence. If they are not processed, the recognition accuracy of the overall plate shape defects will be affected. Summary of the Invention

[0005] The purpose of the present invention is to provide a method and device for identifying the overall characteristics of the strip shape based on the DBSCAN algorithm, which can accurately identify the plate shape characteristics of the rolled strip and obtain the difference from the target plate shape. Based on this, the adjustment amount of the plate shape actuator can be accurately set to achieve the purpose of plate shape feedback control.

[0006] To achieve the above object, the present invention provides a method for identifying overall features of strip shape based on the DBSCAN algorithm, comprising:

[0007] Obtain strip steel datasets at different levels of the cold rolling mill;

[0008] The strip steel data sets of different layers are processed by the DBSCAN algorithm to obtain the cluster center of the strip steel data sets of each layer;

[0009] According to the cluster centers of the steel strip data sets of each layer, a curve for identifying the overall characteristics of the steel strip shape is obtained.

[0010] Optionally, obtain strip datasets for different layers of the cold rolling mill, including:

[0011] Obtain production data sets of the cold rolling mill within a preset time;

[0012] The production data set is divided according to the yield strength, width and thickness of the steel type to obtain strip steel data sets of different layers of the cold rolling mill.

[0013] Optionally, the strip steel datasets of different layers are processed by a DBSCAN algorithm to obtain cluster centers of the strip steel datasets of each layer, including:

[0014] Choose any unlabeled layer-level strip steel dataset;

[0015] Determine whether the ratio of the flatness measurement signals in the unmarked layers to the total flatness measurement signals is greater than a threshold; if so, use Legendre polynomials to perform one-to-one fitting on all flatness measurement signals in the unmarked layers to obtain a set of Legendre polynomial coefficients corresponding to the unmarked layers;

[0016] According to the Legendre polynomial coefficient set corresponding to the unlabeled level, the cluster center of the unlabeled level is obtained by using the DBSCAN algorithm;

[0017] Traverse the remaining unlabeled layers to obtain the cluster centers of the strip steel data sets of each layer.

[0018] Optionally, obtaining the cluster center of the unlabeled level by using a DBSCAN algorithm according to the Legendre polynomial coefficient set corresponding to the unlabeled level includes:

[0019] Inputting the Legendre polynomial coefficient set data corresponding to the unlabeled layer into the DBSCAN algorithm;

[0020] The silhouette coefficient set after cluster analysis is calculated by traversing the free combination of hyperparameters;

[0021] Obtaining a hyperparameter corresponding to a maximum value in the silhouette coefficient set, and dividing the points in the silhouette coefficient set into core points, boundary points, and outliers according to the hyperparameter;

[0022] The cluster center of the unlabeled layer is obtained according to the core points, the boundary points and the abnormal points.

[0023] Optionally, obtaining the cluster center of the unlabeled layer according to the core point, the boundary point, and the abnormal point includes:

[0024] Combining the core points and the boundary points into a new cluster;

[0025] All points in the new cluster are traversed, and the cluster center is calculated based on the Euclidean distance.

[0026] Optionally, obtaining a curve for identifying overall characteristics of the strip shape based on the cluster centers of the strip data sets of each layer includes:

[0027] Performing weighted calculation on the cluster centers of the strip steel data sets of each layer to obtain the overall cluster center;

[0028] Substituting the overall cluster center into the Legendre polynomial, the curve for identifying the overall characteristics of the strip shape is obtained.

[0029] Optionally, the Legendre polynomial is:

[0030]

[0031] Where F is the flatness curve, x is the dimensionless horizontal coordinate, L1, L2, and L4 are the first-order, second-order, and fourth-order coefficients of the Legendre polynomial, respectively.

[0032] The present invention also provides a device for identifying overall characteristics of strip shape based on the DBSCAN algorithm, comprising:

[0033] A data set acquisition unit is used to obtain strip steel data sets of different layers of the cold rolling mill;

[0034] A cluster center obtaining unit is used to process the strip steel data sets of different layers using a DBSCAN algorithm to obtain the cluster center of the strip steel data sets of each layer;

[0035] The curve obtaining unit is used to obtain a curve for identifying the overall characteristics of the strip shape according to the cluster center of the strip data set of each layer.

[0036] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor; the electronic device is characterized in that when the processor executes the program, the method described in any one of the above items is implemented.

[0037] The present invention also provides a readable storage medium having a program or instruction stored thereon, wherein the program or instruction implements any of the above methods when executed by a processor.

[0038] The technical effects and advantages of the present invention are as follows:

[0039] The present invention provides a method for identifying the overall characteristics of strip shape based on the DBSCAN algorithm, comprising: obtaining strip data sets from different layers of a cold rolling mill; processing the strip data sets using the DBSCAN algorithm to obtain cluster centers for each layer of the strip data sets; and, based on the cluster centers for each layer of the strip data sets, obtaining a curve for identifying the overall characteristics of the strip shape. The present invention accurately identifies the shape characteristics of the rolled strip and determines the difference from the target shape. Based on this information, the adjustment amount of the shape actuator can be accurately set to achieve shape feedback control. Furthermore, by accurately understanding the basic characteristics of the cold rolling mill's rolled strip shape, it can also be used for roll profile optimization, production problem analysis, and other purposes.

[0040] Other features and advantages of the present invention will be described in the following description, and in part will become apparent from the description, or will be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Schematic diagram of the overall feature recognition method of strip shape based on DBSCAN algorithm;

[0042] Figure 2 This is the flow chart of overall feature recognition of strip shape based on DBSCAN algorithm;

[0043] Figure 3 This is an example diagram of the yield strength-thickness-width grid division for a cold rolling mill with a width of 1220mm;

[0044] Figure 4 This is a diagram of the DBSCAN hyperparameter optimization process;

[0045] Figure 5 This is the point density map of the #1 layer steel dataset (Layer_1);

[0046] Figure 6This is the flatness cloud diagram after cluster analysis of the #1 layer strip steel dataset (Layer_1);

[0047] Figure 7 Schematic diagram of the device for identifying overall features of strip shape based on the DBSCAN algorithm;

[0048] Figure 8 This is a diagram of an electronic device. DETAILED DESCRIPTION

[0049] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only 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 making creative efforts are within the scope of protection of the present invention.

[0050] Before explaining the present invention, the concept of the present invention is briefly described for ease of understanding.

[0051] The DBSCAN (Density-Based Spatial Clustering of Applications with Noise) algorithm is a density-based spatial clustering algorithm. It can find clusters of arbitrary shapes in noisy spatial data based on the distribution characteristics of the data in the feature space without specifying the cluster division, thereby effectively classifying similar data into the same category. The main idea of ​​the algorithm is to use an area with sufficiently large density as the core and gradually expand the area to eventually form the largest set of density-connected points. It mainly contains two hyperparameters: neighborhood radius (ε) and neighborhood density threshold (Minpts). The sample points in the dataset will be divided into three categories of points according to the selected parameters: core points, boundary points, and outliers. The specific definitions are as follows:

[0052] Let the data space be D. If there exists x∈D that satisfies formula (1), then this point is defined as a core point.

[0053] M(x)≥Minpts,x∈D (1)

[0054] Where M(x) is the number of points in the data space D within the neighborhood radius.

[0055] Points whose number of points within the neighborhood radius is less than Minpts are called boundary points, satisfying formula (2).

[0056] M(x)<Minpts,x∈D (2)

[0057] The remaining points in the dataset are defined as outliers.

[0058] It is worth noting that the Euclidean distance between the core point and the points in its neighborhood is less than ε, satisfying Equation (3).

[0059]

[0060] Where x i ,x j are any two points in the data space; n is the dimension of the space point (input vector).

[0061] Long-term tracking of the strip shape of the cold rolling mill found that strips with similar specifications and yield strengths have similar shapes during the stable rolling stage, and their wave amplitudes and shapes are relatively close. This lays the foundation for the application of the DBSCAN algorithm for cluster analysis and outlier elimination.

[0062] Therefore, the present invention provides a method for identifying the overall characteristics of strip shape based on the DBSCAN algorithm, such as Figure 1 The method includes: obtaining a steel strip dataset of different layers in a cold rolling mill; processing the steel strip dataset of different layers using a DBSCAN algorithm to obtain cluster centers of the steel strip dataset of each layer; and obtaining a curve for identifying overall characteristics of the steel strip shape based on the cluster centers of the steel strip dataset of each layer.

[0063] In order to better understand the present invention, the method is explained in detail below. Figure 2 As shown:

[0064] Step 1: Collect the continuous rolling production data of the cold rolling mill for a long time, including the strip yield strength, thickness, width, plate shape measurement signals and other data to form the original data set (i.e., production data set).

[0065] Step 2: Divide the original data set into different layer strip steel data sets according to the steel grade yield strength (interval A), width (interval B), and inlet thickness (interval C); A is selected as shown in Formula 4, B is the coverage width value of a flatness detection unit on the flatness meter, and C is generally 0.3 mm.

[0066]

[0067] Where σ max and σ min They are the maximum and minimum yield strength of the products rolled in the cold rolling mill, respectively.

[0068] Step 3: Select an unmarked layer-specific strip steel dataset P from the layer-specific strip steel datasets divided in step 2, and determine the flatness measurement signal F within the layer. P Total flatness measurement signal F NIf the judgment condition is met, continue to step 4; if the judgment condition is not met, mark the layer-specific strip steel dataset P and determine whether all layer-specific strip steel datasets have been traversed. If all layer-specific strip steel datasets have been traversed, jump to step 9; otherwise, re-execute step 3.

[0069] Step 4: Use the Legendre polynomials shown in formula (5) to fit all the plate shape measurement signals in the layer one by one to obtain the Legendre polynomial coefficient set L(L1, L2, L4).

[0070]

[0071] Where F is the plate shape curve, x is the dimensionless horizontal coordinate, and L1, L2, and L4 are the first-order, second-order, and fourth-order coefficients of the Legendre polynomial, respectively. In other words, L1 describes the degree of asymmetric plate shape defects, L2 reflects the degree of mid-wave and side-wave defects, and L4 represents the severity of M-wave defects.

[0072] Step 5: Determine the optimal hyperparameters of the DBSCAN algorithm by traversing the hyperparameters, and then divide the points in L(L1, L2, L4) into core points, boundary points, and outliers;

[0073] Step 5.1: Input the dataset L(L1, L2, L4), set the value range of hyperparameters ε and Minpts, generally ε∈(0, 10) and Minpts∈(0, 40);

[0074] Step 5.2: Calculate the silhouette coefficient value after cluster analysis by traversing the free combination of hyperparameters. The silhouette coefficient calculation formula is shown in Equations (6) to (8).

[0075]

[0076]

[0077] b(i)=min(distance(i,j)),i≠j (8)

[0078] In formula (6), N is the total number of samples, a(i) is the average value of the dissimilarity between sample i and other points in the same cluster, b(i) is the minimum value of the dissimilarity between sample i and other points in the same cluster, and the value of SC ranges from -1 to 1. The larger the value, the better the clustering effect. In formula (7), j represents the other sample points in the same cluster as sample i, distance(i,j) represents the Euclidean distance between samples i and j, and n is the total number of samples in the cluster where sample i is located.

[0079] Step 5.3: Divide the points in L into core points, boundary points, and outliers according to the hyperparameters ε and Minpts with the largest silhouette coefficient.

[0080] Step 6: Form a new cluster with the core points and boundary points, traverse all the points in the cluster, and find the point with the smallest Euclidean distance to all points according to formula (9), which is the cluster center l(l1,l2,l4).

[0081]

[0082] Where k is the total number of sample points in the new cluster.

[0083] Step 7: Substitute the cluster center l(l1, l2, l4) into the Legendre polynomial shown in formula (5) to convert it into a flatness signal and obtain the cluster center flatness defect of the strip steel of this layer.

[0084] Step 8: After marking the layer-specific strip steel dataset P, re-execute step 3.

[0085] Step 9: After traversing all the layer-specific strip steel datasets, the number ratio of effective measurement points in each layer-specific strip steel dataset is used as the weighting coefficient to perform weighted calculation on the cluster center of each layer-specific strip steel dataset to obtain the overall cluster center l * (l * 1,l * 2,l * 4), and then substitute it into the Legendre polynomial shown in formula (5) to obtain the overall plate shape characteristics of the cold rolling mill.

[0086] To better illustrate this solution, an example is provided below. This example uses a 1220mm four-stand, six-high HC cold rolling mill as an example. This cold rolling mill is capable of producing chilled coils with a yield strength of 150-450 MPa, a thickness of 0.3-2.5 mm, and a width of 720-1250 mm. The incoming material thickness is 2-5 mm. The overall strip shape feature recognition process based on the DBSCAN algorithm is as follows:

[0087] Step 1: Collect production data from the cold rolling mill for three months of continuous rolling, including 12,402 coils of steel and 2,310,219 plate shape measurement moments, which basically covers all product specifications of the production line.

[0088] Step 2: Divide the data set into different layers according to the steel grade yield strength (interval 30MPa), width (interval 52mm), and thickness (interval 0.3mm). Some of the layers after division are as follows: Figure 3 The numbers in the figure are the number of times the steel strip shape is measured at different layers.

[0089] Step 3: Select the layer strip steel with steel strength between 220 and 250 MPa, entrance thickness between 3.2 and 3.5 mm, and width between 988 and 1040 mm (hereinafter referred to as Layer_1) for plate shape feature analysis. The plate shape measurement time of Layer_1 layer strip steel accounts for 4.59% of the total measurement time.

[0090] Step 4: Use Legendre polynomials to fit all the flatness measurement signals in Layer_1 one by one to obtain the Legendre polynomial coefficient set.

[0091] Step 5: Determine the optimal hyperparameters of the DBSCAN algorithm by traversing the free combination of hyperparameters. The results are as follows: Figure 4 As shown. Figure 4 The results show that the silhouette coefficients in the range of 4.7≤ε≤5.7, 26≤Minpts≤38 are close and optimal. For ε=4.7 and Minpts=26, the silhouette coefficient is 0.785 and the noise ratio is 3.83%. Based on the optimal hyperparameters, the points in this coefficient set are divided into core points, boundary points, and outliers.

[0092] Step 6: Form a new cluster with core points and boundary points, traverse all points in the cluster, and find the point with the smallest Euclidean distance to all points according to formula (9), such as Figure 5 shown.

[0093] Step 7: Substitute the cluster center obtained in step (6) into the Legendre polynomial to obtain the cluster center plate shape defect of this layer, such as Figure 6 shown. Figure 6 This is the flatness distribution cloud map of the Layer_1 strip after removing outliers.

[0094] Step 8: Mark the layer of steel strip and proceed to step 3.

[0095] Step 9: After traversing all the layers of strip steel, use the ratio of the number of effective measurement points of each layer of strip steel data set as the weighting coefficient to perform weighted calculation on the cluster center of each layer of strip steel data set to obtain the overall cluster center l * (l * 1,l * 2,l * 4), and then substitute it into the Legendre polynomial to obtain the overall plate shape characteristics of the cold rolling mill.

[0096] The present invention also provides a device for identifying overall characteristics of strip shape based on DBSCAN algorithm, such as Figure 7The device includes: a data set acquisition unit for acquiring strip steel data sets of different layers of a cold rolling mill; a cluster center acquisition unit for processing the strip steel data sets of different layers using a DBSCAN algorithm to obtain cluster centers of the strip steel data sets of each layer; and a curve acquisition unit for acquiring a curve for identifying the overall characteristics of the strip steel shape based on the cluster centers of the strip steel data sets of each layer.

[0097] Since the content protected by this device is similar to the above method, it will not be introduced in detail here. Please refer to the explanation part of the above method for details.

[0098] The present invention also provides a device, such as Figure 8 As shown. The electronic device includes: at least one processor, at least one communication interface, at least one memory and at least one communication bus; optionally, the communication interface may be an interface of a communication module, such as an interface of a GSM module; the processor may be a processor CPU, or an application-specific integrated circuit ASIC (Application Specific Integrated Circuit), or one or more integrated circuits configured to implement an embodiment of the present invention. The memory may include a high-speed RAM memory, and may also include a non-volatile memory, such as at least one disk memory. The memory stores a program, and the processor calls the program stored in the memory to execute the method provided in the above embodiment of the present application.

[0099] Corresponding to the above-mentioned method of the present application, the present application further provides a computer storage medium. The computer storage medium stores a computer program, which is executed by a processor to execute the method provided in the above-mentioned embodiment of the present application.

[0100] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for identifying overall features of strip shape based on DBSCAN algorithm, characterized in that: include: Obtaining a production data set of a cold rolling mill within a preset time, dividing the production data set according to the yield strength, width, and thickness of the steel type, and obtaining strip steel data sets of different layers of the cold rolling mill; The strip steel data sets of different layers are processed by the DBSCAN algorithm to obtain the cluster center of the strip steel data sets of each layer; Performing weighted calculation on the cluster centers of the strip steel data sets of each layer to obtain an overall cluster center, substituting the overall cluster center into a Legendre polynomial to obtain a curve for identifying overall characteristics of the strip steel shape; Among them, the strip steel data sets of different layers are processed by the DBSCAN algorithm to obtain the cluster center of the strip steel data sets of each layer, including: randomly selecting an unmarked layer strip steel data set; judging whether the ratio of the flatness measurement signal in the unmarked layer to the total flatness measurement signal is greater than a threshold, and if so, using Legendre polynomials to perform one-to-one fitting on all the flatness measurement signals in the unmarked layer to obtain the Legendre polynomial coefficient set corresponding to the unmarked layer; according to the Legendre polynomial coefficient set corresponding to the unmarked layer, the cluster center of the unmarked layer is obtained by the DBSCAN algorithm; and traversing the remaining unmarked layers to obtain the cluster center of the strip steel data sets of each layer.

2. The method for identifying overall features of strip shape based on DBSCAN algorithm according to claim 1, characterized in that: According to the Legendre polynomial coefficient set corresponding to the unlabeled level, the cluster center of the unlabeled level is obtained by using the DBSCAN algorithm, including: Inputting the Legendre polynomial coefficient set data corresponding to the unlabeled layer into the DBSCAN algorithm; The silhouette coefficient set after cluster analysis is calculated by traversing the free combination of hyperparameters; Obtaining a hyperparameter corresponding to a maximum value in the silhouette coefficient set, and dividing the points in the silhouette coefficient set into core points, boundary points, and outliers according to the hyperparameter; The cluster center of the unlabeled layer is obtained according to the core points, the boundary points and the abnormal points.

3. The method for identifying overall features of strip shape based on DBSCAN algorithm according to claim 2, characterized in that: Obtaining the cluster center of the unlabeled layer according to the core point, the boundary point and the abnormal point, including: Combining the core points and the boundary points into a new cluster; All points in the new cluster are traversed, and the cluster center is calculated according to the Euclidean distance.

4. The method for identifying overall features of strip shape based on DBSCAN algorithm according to claim 1, characterized in that: The Legendre polynomial is: in, is the plate curve, is the dimensionless horizontal coordinate, , , are the first-order, second-order, and fourth-order coefficients of the Legendre polynomial respectively.

5. A device for identifying overall characteristics of strip shape based on DBSCAN algorithm for implementing the method according to any one of claims 1 to 4, characterized in that: include: a data set acquisition unit, configured to acquire a production data set of a cold rolling mill within a preset time, divide the production data set according to the yield strength, width, and thickness of the steel type, and acquire strip steel data sets of different layers of the cold rolling mill; A cluster center obtaining unit is used to process the strip steel data sets of different layers using a DBSCAN algorithm to obtain the cluster center of the strip steel data sets of each layer; a curve obtaining unit, configured to perform weighted calculation on the cluster centers of the strip steel data sets of each layer to obtain an overall cluster center, and substitute the overall cluster center into a Legendre polynomial to obtain the curve for identifying the overall characteristics of the strip steel shape; Among them, the strip steel data sets of different layers are processed by the DBSCAN algorithm to obtain the cluster center of the strip steel data sets of each layer, including: randomly selecting an unmarked layer strip steel data set; judging whether the ratio of the flatness measurement signal in the unmarked layer to the total flatness measurement signal is greater than a threshold, and if so, using Legendre polynomials to perform one-to-one fitting on all the flatness measurement signals in the unmarked layer to obtain the Legendre polynomial coefficient set corresponding to the unmarked layer; according to the Legendre polynomial coefficient set corresponding to the unmarked layer, the cluster center of the unmarked layer is obtained by the DBSCAN algorithm; and traversing the remaining unmarked layers to obtain the cluster center of the strip steel data sets of each layer.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor; When the processor executes the program, the method according to any one of claims 1 to 4 is implemented.

7. A readable storage medium having a program or instruction stored thereon, characterized in that: When the program or instruction is executed by a processor, the method according to any one of claims 1 to 4 is implemented.

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