Data envelope analysis method based on machine learning

Abstract

The invention discloses a data envelope analysis method based on machine learning, and the method comprises the steps: dividing data into data with high consistency and data with poor consistency through a two-classification K-means + + algorithm and a threshold value; the method comprises the following steps: firstly, performing data envelope analysis on data with high consistency by using an improved isolated forest method, finding out singular points, decomposing the singular points into each piece of data, and then analyzing the data to obtain which piece of voltage data is relatively good and poor, thereby being beneficial to subsequent equipment health management. And for the data with poor consistency, problem data points in the data can be found out through a 2-classification K-means + + algorithm, and voltage entries with poor consistency are deduced back so as to facilitate subsequent troubleshooting.

Description

Technical Field

[0001] The present invention relates to a data envelopment analysis method based on machine learning, which is mainly used in the field of data analysis. Background Art

[0002] Ground tests on control systems are limited, and the test data available for the product is not much, and the data is small sample data; in addition, there is a lack of effective test data envelopment analysis methods. This method is a very important part of aircraft testing. It determines whether the test is effective, whether the correct conclusion of the test can be given, and whether problems occur during the test.

[0003] The commonly used data envelopment analysis method in aerospace is: a data cluster is obtained from multiple test data of different aircraft with the same control system design (for example, the first 5 sets of good data are used), the maximum and minimum values ​​are counted (as upper and lower envelope values), and each point of the sixth set of data is compared with the maximum and minimum values ​​to draw a conclusion on whether it is an envelope.

[0004] The above methods do not answer or solve the following three major problems: (1) Are multiple sets of test data consistent? (2) How to detect isolated points and manage equipment health for data with strong consistency? (3) How to automatically isolate abnormal data for data with poor consistency? And because the qualified range is too large, it is easy to include abnormal data in the qualified envelope. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art and propose a data envelopment analysis method based on machine learning, which solves the problem of abnormal data being regarded as qualified envelope data and lays the foundation for solving equipment and aircraft problems in advance.

[0006] The technical solution of the present invention is:

[0007] In a first aspect, the present invention proposes a data envelopment analysis method based on machine learning, the steps are as follows:

[0008] (1) Pulse sampling of primary and secondary power supply voltages to form discrete power supply voltage data;

[0009] (2) Using 2-cluster K-means++ machine learning method to cluster each type of power supply voltage data separately to obtain the threshold;

[0010] (3) According to the threshold, if the value is less than the threshold, it is considered that the consistency is weak, that is, a part of the newly added test data is inconsistent with other existing data. The 2-cluster K-means++ machine learning method is continued to be used for cluster analysis to obtain abnormal data, which is used for subsequent system troubleshooting;

[0011] (4) If it is greater than this threshold, it is considered to be highly consistent, that is, this piece of data is consistent with other existing data. The isolation forest machine learning method based on the histogram threshold is used to perform data envelopment analysis on all data to obtain isolated point data, and then the equipment health status analysis is performed based on the isolated point data.

[0012] Furthermore, pulse sampling of the primary and secondary power supply voltages is performed in the period from the ignition of the aircraft to the power failure.

[0013] Furthermore, the 2-cluster K-means++ machine learning method is used to cluster each type of power supply voltage data to obtain a threshold value, specifically:

[0014] (2.1) The cluster identifiers obtained by the 2-cluster K-means++ algorithm include 0 and 1. Then it is necessary to identify 0 and 1 through the 2-cluster K-means++ algorithm, aggregate the clusters with more data into 0 and aggregate the clusters with less data into 1;

[0015] (2.2) Determine the threshold value based on the difference between an abnormal data and all other normal data contained in the data.

[0016] Furthermore, the isolation forest machine learning method based on the histogram threshold improvement is used to perform data envelopment analysis on all data to obtain isolated point data, specifically:

[0017] (4.1) According to the path length h(d) of the test sample point d in each isolated binary tree, the outlier value of d is calculated to evaluate its anomaly; the smaller the path length, the higher the anomaly score of the sample point, and the lower the score after model training;

[0018] (4.2) According to the histogram characteristics of the relevant data and the obvious differences between the isolated points and the normal data histograms, the threshold dividing line between the isolated points and the normal points of the relevant data is determined.

[0019] In a second aspect, the present invention proposes a data envelopment analysis system based on machine learning, comprising:

[0020] Sampling module: performs pulse sampling on the primary and secondary power supply voltages to form discrete power supply voltage data;

[0021] Threshold acquisition module: Use 2-cluster K-means++ machine learning method to cluster each type of power supply voltage data to obtain the threshold;

[0022] Weak consistency data processing module: judge according to the threshold value. If it is less than the threshold value, it is considered that the consistency is weak, that is, a part of the newly added test data is inconsistent with other existing data. The 2-cluster K-means++ machine learning method is continued to be used for cluster analysis to obtain abnormal data; it is used for subsequent system troubleshooting;

[0023] Strong consistency data processing module: If it is greater than this threshold, it is considered to be highly consistent, that is, this piece of data is consistent with other existing data. The isolation forest machine learning method based on the histogram threshold improvement is used to perform data envelopment analysis on all data to obtain isolated point data, and then the equipment health status analysis is performed based on the isolated point data.

[0024] Furthermore, pulse sampling of the primary and secondary power supply voltages is performed in the period from the ignition of the aircraft to the power failure.

[0025] Furthermore, the 2-cluster K-means++ machine learning method is used to cluster each type of power supply voltage data to obtain a threshold value, specifically:

[0026] (2.1) The cluster identifiers obtained by the 2-cluster K-means++ algorithm include 0 and 1. Then it is necessary to identify 0 and 1 through the 2-cluster K-means++ algorithm, aggregate the clusters with more data into 0 and aggregate the clusters with less data into 1;

[0027] (2.2) Determine the threshold value based on the difference between an abnormal data and all other normal data contained in the data.

[0028] Furthermore, the isolation forest machine learning method based on the histogram threshold improvement is used to perform data envelopment analysis on all data to obtain isolated point data, specifically:

[0029] (4.1) According to the path length h(d) of the test sample point d in each isolated binary tree, the outlier value of d is calculated to evaluate its anomaly; the smaller the path length, the higher the anomaly score of the sample point, and the lower the score after model training;

[0030] (4.2) According to the histogram characteristics of the relevant data and the obvious differences between the isolated points and the normal data histograms, the threshold dividing line between the isolated points and the normal points of the relevant data is determined.

[0031] In a third aspect, the present invention proposes a non-volatile storage medium, comprising: a computer program product, which executes the data envelopment analysis method based on machine learning when the computer program product is executed.

[0032] In a fourth aspect, the present invention proposes a computer program product, which implements the data envelopment analysis method based on machine learning when executed by a processor.

[0033] The beneficial effects of the present invention compared with the prior art are:

[0034] (1) The present invention solves the problem of whether multiple sets of test data are consistent.

[0035] (2) The present invention solves the problem of how to detect isolated points on data with strong consistency and perform equipment health management.

[0036] (3) The present invention solves the problem of how to automatically isolate abnormal data with poor consistency to support subsequent troubleshooting.

[0037] (4) The present invention also solves the problem that abnormal data is easily included in the qualified envelope because the qualified range is too large.

[0038] (5) The present invention does not require human participation. By putting the data to be tested into a folder, data envelopment analysis can be automatically completed with one click. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flow chart of the method of the present invention;

[0040] Figure 2 is a schematic diagram of the score histogram;

[0041] Figure 3 This is a schematic diagram of data with strong consistency;

[0042] Figure 4 This is a schematic diagram of data with poor consistency;

[0043] Figure 5 This is the 2-cluster kmeans++ data envelopment analysis diagram of 8 test data of 5V voltage;

[0044] Figure 6 This is the data envelopment analysis diagram of the isolation forest algorithm for 8 data of 5V voltage;

[0045] Figure 7 This is a graph analyzing the accuracy of the Kmeans algorithm for different isolated point data. DETAILED DESCRIPTION

[0046] The specific embodiments of the present invention are further described in detail below with reference to the accompanying drawings.

[0047] The present invention proposes a data envelopment analysis method based on machine learning. First, multiple power supply voltage data of batch aircraft designed with the same control system are judged, and the data are divided into data with strong consistency and data with poor consistency through a two-category K-means++ algorithm and a threshold. Then, a histogram-modified isolated forest method data envelopment analysis is performed on the data with strong consistency to find singular points and decompose them into each data. Then, these data are analyzed to determine which voltage data is relatively good and poor, which is helpful for subsequent equipment health management. For data with poor consistency, the two-category K-means++ algorithm can be used to find the problem data points, and the voltage entries with poor consistency can be inferred for subsequent troubleshooting.

[0048] In summary, this method lays the foundation for solving equipment and aircraft problems in advance, solves the three problems in the background technology section, and solves the problem of abnormal data being regarded as qualified envelope data.

[0049] A data envelopment analysis method based on machine learning comprises the following steps:

[0050] (1) In the period from aircraft ignition to power failure, pulse sampling of primary and secondary power supply voltages is performed to form discrete power supply voltage data;

[0051] Before the aircraft is ignited, the power supply voltage is unstable and will change due to the load conditions. After ignition, the voltage is relatively stable, and the data can be compared in a common stable stage. Therefore, the stable voltage data samples from after ignition to before power failure are selected for data envelopment analysis.

[0052] (2) Use the 2-cluster K-means++ algorithm to cluster each type of power supply voltage data separately to obtain the threshold;

[0053] (2.1) The cluster identifiers obtained by the 2-cluster K-means++ algorithm include 0 and 1. Then it is necessary to identify 0 and 1 through the 2-cluster K-means++ algorithm, aggregate the clusters with more data into 0 and aggregate the clusters with less data into 1;

[0054] (2.2) Determine the threshold value based on the difference between an abnormal data and all other normal data contained in the data.

[0055] (3) According to the threshold, if the value is less than the threshold, it is considered that the consistency is weak, that is, a part of the newly added test data is inconsistent with other existing data. The 2-cluster K-means++ machine learning method is continued to be used for cluster analysis to obtain abnormal data and find isolated points; this is used for subsequent system troubleshooting;

[0056] (4) If it is greater than this threshold, it is considered to be highly consistent, that is, this piece of data is consistent with other existing data. The isolation forest machine learning method based on the histogram threshold is used to perform data envelopment analysis on all data to obtain isolated point data, and then the equipment health status analysis is performed based on the isolated point data.

[0057] Using the isolation forest machine learning method based on histogram threshold improvement, data envelopment analysis is performed on all data to obtain isolated point data, specifically:

[0058] (4.1) According to the path length h(d) of the test sample point d in each isolated binary tree, the outlier value of d is calculated to evaluate its anomaly; the smaller the path length, the higher the anomaly score of the sample point, and the lower the score after model training;

[0059] (4.2) According to the histogram characteristics of the relevant data and the obvious differences between the isolated points and the normal data histograms, the threshold dividing line between the isolated points and the normal points of the relevant data is determined.

[0060] The specific implementation is given below:

[0061] Part I Algorithm Principle: Basic Principle of K-means++ Algorithm for 2 Classifications:

[0062] 1) Randomly select a point from the sample as the cluster center.

[0063] 2) Calculate the distance from each sample point to the selected cluster center, represented by D(x): the larger D(x), the greater the probability of it being selected as the next cluster center.

[0064] 3) Use the roulette wheel method to select the next cluster center (the larger D(x) is, the greater the probability of being selected as the cluster center)

[0065] 4) Repeat step 2) until 2 cluster centers are selected.

[0066] 5) For any sample point, find its distance to the two cluster centers, and then classify the sample point to the cluster center with the smallest distance until all sample points are classified (clustered into 2 categories).

[0067] 6) Calculate the average value for each cluster, and then use the two means as the new center points of each cluster.

[0068] 7) Repeat steps 5) and 6) until the center point position does not change or changes within the allowable range. The basic principle of the isolation forest machine learning method based on histogram threshold improvement:

[0069] (1) Constructing an Isolation Forest

[0070] 1) Randomly select m sample points from the data set D as the sample set Sd for generating a single isolated binary tree.

[0071] 2) Randomly select a feature f and a cut value p from the sample set Sd. If the maximum and minimum values ​​of all samples contained in the node N under the feature f are f_max and f_min respectively, then p[f_min,f_max].

[0072] 3) If the value of the sample with respect to feature f is less than the cut value p, the sample is divided into the left child of node N. Otherwise, it is divided into the right child.

[0073] 4) Repeat steps 2) and 3) to split the left and right child nodes of node N respectively to generate an isolated binary tree. Stop generating when there are multiple identical data or only one data in the child node or the isolated binary tree has reached the set maximum height.

[0074] (2) Calculate the abnormal score of the test sample point

[0075] According to the path length h(d) of the test sample point d in each isolated binary tree, the outlier value of d is calculated to evaluate its abnormality. The smaller the path length, the higher the outlier score of the sample point. The lower the score after model training.

[0076] (3) Determine outliers based on score histogram analysis

[0077] According to the characteristics of a large number of related data histograms, the obvious differences between isolated points and normal data histograms, the threshold dividing line between isolated points and normal points of the related data is determined, such as Figure 2 Score histogram. In the figure, blue is the score histogram value of normal data, green is the score histogram of isolated points, and the red line is the score histogram threshold line. The score below this line is the score of isolated points, and the score above this line is the normal value score.

[0078] Based on the basic principles of the K-means++ algorithm for the above two classifications and the basic principles of the isolation forest machine learning method based on the histogram threshold improvement, such as Figure 1 As shown, the data envelopment analysis method based on machine learning proposed in the present invention comprises the following steps:

[0079] (1) Pulse sampling of the primary and secondary power supply voltages is performed to form discrete power supply voltage data. The power supply voltage is unstable before the aircraft is ignited and will change due to the load conditions. After ignition, the voltage is relatively stable, and the data can be compared in a common stable stage. Therefore, the stable voltage data samples from after ignition to before power failure are selected for data envelopment analysis. Figure 3 For a data graph with strong consistency, Figure 4 This is a data graph with poor consistency;

[0080] (2) Use the 2-cluster K-means++ algorithm to cluster each type of power supply voltage data separately to obtain the threshold.

[0081] The method of determining the threshold using the 2-cluster K-means++ algorithm in step (2) is specifically as follows:

[0082] (2.1) The cluster identifiers obtained by the 2-cluster K-means++ algorithm include 0 and 1. Then it is necessary to identify 0 and 1 through the 2-cluster K-means++ algorithm, aggregate the clusters with more data into 0 and aggregate the clusters with less data into 1;

[0083] (2.2) Determine the threshold value based on the difference between one abnormal data and all other normal data (generally, there is a huge difference between the average of the percentage of all normal data and the one abnormal data, so the threshold value is easy to determine);

[0084] Take the value table of the proportion of isolated point data to the total data in Table 1 as an example. The 2-classification K-means++ method cluster analysis is performed on 8 data of each of the 7 types of power supply voltage data to obtain the value of the proportion of isolated point data to the total data, as shown in Table 1.

[0085] Table 1

[0086]

[0087] (3) According to the threshold, if the value is less than the threshold, it is considered that the consistency is weak, that is, a part of the newly added test data is inconsistent with other existing data. The 2-cluster K-means++ machine learning method is used for cluster analysis to obtain abnormal data and find isolated points for subsequent system troubleshooting. Figure 5 As shown in the figure, the 2-cluster kmeans++ data envelopment analysis diagram of 8 test data of 5V voltage provides support for subsequent system troubleshooting;

[0088] (4) If it is greater than this threshold, it is considered to be highly consistent, that is, this data is consistent with other existing data. The isolation forest machine learning method based on the histogram threshold is used to perform data envelopment analysis on all data to obtain isolated point data, and then the equipment health status analysis is performed based on the isolated point data;

[0089] The isolation forest machine learning method based on histogram threshold improvement in step (4) is specifically:

[0090] (4.1) According to the path length h(d) of the test sample point d in each isolated binary tree, calculate the outlier value of d to evaluate its anomaly. The smaller the path length, the higher the anomaly score of the sample point. The lower the score after model training;

[0091] (4.2) Based on the histogram characteristics of a large amount of related data and the obvious differences between the histograms of isolated points and normal data, the threshold dividing line between isolated points and normal points of the related data is determined.

[0092] Based on the histogram threshold, the isolation forest algorithm is improved. The threshold is set using the histogram method to count all qualified and unqualified points, and then the positions of these points in each data are determined to locate a single data. Data envelopment analysis is performed on the 8 power supply voltage test data. The consistency of the 8 data is strong, such as Figure 6 As shown in the figure, the data envelopment analysis diagram of the isolation forest algorithm for 8 data of 5V voltage is shown.

[0093] from Figure 6 It can be seen that the red color is qualified envelope data, and the blue color is qualified non-envelope data. It can be seen from the figure that some qualified non-envelope data are considered qualified enveloped, which is the part sandwiched between the blue data in the lower right corner of the image.

[0094] Roll the data back to each original data, draw a summary table of the proportion of each voltage isolated point (qualified non-envelope point) to the total number of points, as shown in Table 2, and convert the summary table of the proportion of each voltage isolated point (qualified non-envelope point) to the conversion table of the proportion of each voltage isolated point (qualified non-envelope point) to the total number of points shown in Table 3 (remove the 0 value after the decimal point).

[0095] Table 2

[0096]

[0097]

[0098] Table 3

[0099] Serial number Battery 1 Battery 2 Battery 3 Battery 4 Battery 5 Battery 6 Battery 7 1. 0.2 0.1 2. 0.1 0.2 0.1 3. 0.1 0.2 4. 0.2 0.1 0.1 0.2 5. 0.1 6. 0.4 0.2 0.1 7. 0.3 0.1 8. 0.6 0.2 0.5 0.2

[0100] in conclusion:

[0101] 1) From the horizontal analysis of the data, it can be seen that the aircraft with the best overall power supply voltage is the aircraft numbered 5.

[0102] 2) From the horizontal analysis of the data, it can be seen that the aircraft with the worst overall power supply voltage is aircraft numbered 8, followed by aircraft numbered 4.

[0103] 3) From the longitudinal analysis of the data, it can be seen that battery 4 and battery 5 are slightly worse.

[0104] Example:

[0105] Verify the correctness of the algorithm:

[0106] (1) Verification of the accuracy of the isolation forest method

[0107] The accuracy test is performed by using random data that is as close to the actual data as possible. Table 4 shows the accuracy table of the improved isolation forest test.

[0108] Table 4

[0109]

[0110] Table 4 Description:

[0111] 1) Taking the table value of sequence number 1 as an example, 28.5, 0.2, 20000, 20, 0.2, 100 represent, with 28.5 as the mean, standard deviation of 0.2, 20000 random numbers (representing normal values), 20 as the mean, 0.2 as the standard deviation, 100 random numbers (representing abnormal values), and others are similar.

[0112] 2) 0.9 is the accuracy of the training set.

[0113] From Table 4, we can conclude that:

[0114] 1) The data accuracy is highest when the signal-to-noise ratio is between 2% and 6%.

[0115] 2) When the data signal-to-noise ratio is between 10% and 14%, the accuracy can easily reach the maximum value.

[0116] 3) It can be seen from the measured data that if one of the eight pieces of data is inconsistent with the other pieces of data, it can be detected very well. That is, a signal-to-noise ratio of 12.5% ​​can detect the inconsistency (non-identity) of the entire piece of data.

[0117] (2) Accuracy verification of Kmeans++ clustering method

[0118] The accuracy test is performed by using random data that is as close to the actual data as possible. Table 5 is the test accuracy table of the Kmeans++ method for 2 clusters.

[0119] Table 5

[0120]

[0121]

[0122] From Table 5, we can conclude that:

[0123] 1) When the standard value is 28.5 and the abnormal value is 29, the clustering ability of the k-means algorithm is low. Otherwise, the algorithm accuracy is close to the maximum value, indicating that the clustering accuracy is extremely high.

[0124] 2) When the standard value is 28.5 and the outlier value is 29, the kmeans algorithm converges to an accuracy of about 0.75 as the number of outlier points increases. Figure 7The accuracy analysis of Kmeans algorithm for different isolated point data is shown in the figure.

[0125] The contents not described in detail in the specification of the present invention belong to the common knowledge of the professionals in this field.

Claims

1. A data envelopment analysis method based on machine learning, characterized in that Here are the steps: (1) Pulse sampling of primary and secondary power supply voltages to form discrete power supply voltage data; (2) Using 2-cluster K-means++ machine learning method to cluster each type of power supply voltage data separately to obtain the threshold; (3) According to the threshold, if the value is less than the threshold, it is considered that the consistency is weak, that is, a part of the newly added test data is inconsistent with other existing data. The 2-cluster K-means++ machine learning method is continued to be used for cluster analysis to obtain abnormal data, which is used for subsequent system troubleshooting; (4) If it is greater than this threshold, it is considered to be highly consistent, that is, this piece of data is consistent with other existing data. The isolation forest machine learning method based on the histogram threshold is used to perform data envelopment analysis on all data to obtain isolated point data, and then the equipment health status analysis is performed based on the isolated point data.

2. The data envelopment analysis method based on machine learning according to claim 1, characterized in that: Pulse sampling of the primary and secondary power supply voltages is performed in the period from aircraft ignition to power failure.

3. The data envelopment analysis method based on machine learning according to claim 1, characterized in that: The 2-cluster K-means++ machine learning method is used to cluster each type of power supply voltage data to obtain a threshold value, specifically: (2.1) The cluster identifiers obtained by the 2-cluster K-means++ algorithm include 0 and 1. Then it is necessary to identify 0 and 1 through the 2-cluster K-means++ algorithm, aggregate the clusters with more data into 0 and aggregate the clusters with less data into 1; (2.2) Determine the threshold value based on the difference between an abnormal data and all other normal data contained in the data.

4. The data envelopment analysis method based on machine learning according to claim 1, characterized in that: The isolated forest machine learning method based on the improved histogram threshold is used to perform data envelopment analysis on all data to obtain isolated point data, specifically: (4.1) According to the path length h(d) of the test sample point d in each isolated binary tree, the outlier value of d is calculated to evaluate its anomaly; the smaller the path length, the higher the anomaly score of the sample point, and the lower the score after model training; (4.2) According to the histogram characteristics of the relevant data and the obvious differences between the isolated points and the normal data histograms, the threshold dividing line between the isolated points and the normal points of the relevant data is determined.

5. A data envelopment analysis system based on machine learning, characterized in that include: Sampling module: performs pulse sampling on the primary and secondary power supply voltages to form discrete power supply voltage data; Threshold acquisition module: Use 2-cluster K-means++ machine learning method to cluster each type of power supply voltage data to obtain the threshold; Weak consistency data processing module: judge according to the threshold value. If it is less than the threshold value, it is considered that the consistency is weak, that is, a part of the newly added test data is inconsistent with other existing data. The 2-cluster K-means++ machine learning method is continued to be used for cluster analysis to obtain abnormal data; it is used for subsequent system troubleshooting; Strong consistency data processing module: If it is greater than this threshold, it is considered to be highly consistent, that is, this piece of data is consistent with other existing data. The isolation forest machine learning method based on the histogram threshold improvement is used to perform data envelopment analysis on all data to obtain isolated point data, and then the equipment health status analysis is performed based on the isolated point data.

6. The data envelopment analysis system based on machine learning according to claim 5, characterized in that: Pulse sampling of the primary and secondary power supply voltages is performed in the period from aircraft ignition to power failure.

7. The data envelopment analysis system based on machine learning according to claim 5, characterized in that: The 2-cluster K-means++ machine learning method is used to cluster each type of power supply voltage data to obtain a threshold value, specifically: (2.1) The cluster identifiers obtained by the 2-cluster K-means++ algorithm include 0 and 1. Then it is necessary to identify 0 and 1 through the 2-cluster K-means++ algorithm, aggregate the clusters with more data into 0 and aggregate the clusters with less data into 1; (2.2) Determine the threshold value based on the difference between an abnormal data and all other normal data contained in the data.

8. The data envelopment analysis system based on machine learning according to claim 5, characterized in that: The isolated forest machine learning method based on the improved histogram threshold is used to perform data envelopment analysis on all data to obtain isolated point data, specifically: (4.1) According to the path length h(d) of the test sample point d in each isolated binary tree, the outlier value of d is calculated to evaluate its anomaly; the smaller the path length, the higher the anomaly score of the sample point, and the lower the score after model training; (4.2) According to the histogram characteristics of the relevant data and the obvious differences between the isolated points and the normal data histograms, the threshold dividing line between the isolated points and the normal points of the relevant data is determined.

9. A non-volatile storage medium, characterized in that: include: A computer program product, which, when executed, performs the data envelopment analysis method based on machine learning as described in any one of claims 1 to 4.

10. A computer program product, characterized in that When the computer program product is executed by a processor, the data envelopment analysis method based on machine learning described in any one of claims 1 to 4 is implemented.

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