A method and system for hydroelectric unit fault diagnosis based on multi-receptive field GCN

Abstract

The application discloses a kind of based on multi-receptive field GCN's hydroelectric generating set fault diagnosis method and system, belong to hydroelectric generating set fault diagnosis technical field.The application is by constructing graph structure data, vibration sample is abstracted as node, time domain feature and frequency domain feature of vibration sample are as the attribute of node, and the vibration sample between high correlation degree is abstracted as edge, and correlation degree is as the weight of edge, maximum degree of information in limited vibration sample is utilized.A kind of multi-receptive field graph convolution network model is proposed, graph structure data is effectively handled, the correlation information between samples is utilized, the features of different receptive fields are combined, and the quality of sample features is further improved, so as to effectively improve the precision and real-time performance of hydroelectric generating set fault diagnosis.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of hydroelectric unit fault diagnosis, and more particularly to a hydroelectric unit fault diagnosis method and system based on a multi-receptive field GCN. BACKGROUND

[0002] The safe operation of a hydroelectric unit is crucial to energy security and power grid security. The hydroelectric unit is the core of the energy supply function and economic benefit of a hydropower station, and undertakes multiple tasks such as peak shaving, frequency and phase modulation, and rotating backup. The unit is frequently started and stopped, and factors such as water impact, mechanical failure, and electromagnetic imbalance may induce various faults and accidents such as abnormal vibration, structural fatigue, electrical failure, and operation mode damage, which are extremely harmful. The hydroelectric unit fault data has the problems of fewer available labeled samples and greater difficulty in manual labeling. In the face of the rapid development of deep learning models, an efficient model method that can adapt to few samples is needed to accurately diagnose unit faults.

[0003] The signals used for hydroelectric unit fault diagnosis are mainly vibration signals monitored by sensors during the operation of the unit. For one-dimensional signals, the commonly used feature extraction methods are time domain analysis, frequency domain analysis, and time-frequency domain methods for signal processing. Although this type of feature extraction method is simple, the extracted features have practical significance and can to some extent represent the characteristics of various operating states of the bearing. Common time-frequency domain analysis methods include Short-Time Fourier Transform (STFT), wavelet transform (WT), and Variational Mode Decomposition (VMD). After extracting various features using time-frequency domain methods, it is generally difficult to directly distinguish each operating state, so machine learning methods are often used to further learn the extracted features. Common machine learning algorithms used in fault diagnosis include Random Forest (RF), Support Vector Machines (SVM), and Naive Bayes (NB) classifiers. This method has the characteristics of simple structure and fast classification speed, so it was widely used in the early stage of fault diagnosis development. However, this method is difficult to fit complex fault conditions, and when the number of classes to be identified is large, it is difficult to obtain satisfactory results.

[0004] Deep learning model has end-to-end characteristics, can directly extract signal features to omit the step of extracting features by professional knowledge, has strong model generalization ability, can fit relatively complex data distribution, and has high accuracy. Among them, the deep network such as convolutional neural network (CNN), deep belief network (DBN), autoencoder (AE) is widely used in fault diagnosis field. However, the fault diagnosis model based on deep learning usually needs a large amount of labeled data for training to obtain a relatively satisfactory result, and the labeled data is relatively rare in the real situation, so that the general deep learning method performs poorly in the actual scene.

[0005] Patent CN113324754A discloses a gear transmission system fault recognition method based on multi-receptive field graph convolution, constructs a multi-receptive field graph convolution network composed of two layers of multi-receptive field graph convolution layers and two layers of full connection layers, trains the multi-receptive field graph convolution network through the first associated graph data; the second associated graph data is input into the trained multi-receptive field graph convolution network, and the fault recognition of the unknown fault gear transmission system is realized. However, this method has the following shortcomings and defects:

[0006] 1. The method directly uses the time sequence data of the vibration sample as the node feature. Since the original time sequence data points of the sample are more in order to better represent the complete features of the vibration signal, a large amount of computing memory space is occupied during the training of the graph convolution network, which is not conducive to meeting the real-time requirements of fault recognition in the field.

[0007] 2. The weight of the edge in the associated graph data sample constructed by the method is 1, and the characteristics of different samples are not completely consistent, the correlation between each sample is not the same, and simply defining the weight of the edge as 1 cannot well represent the relationship between the samples, which will have a negative impact on the diagnosis result.

[0008] 3. The multi-receptive field graph convolution network constructed by the method includes two multi-receptive field graph convolution layers, and each layer includes three receptive field graph convolution network modules. Under such a model structure, the time required for model training will increase, which is not conducive to meeting the real-time requirements of fault recognition in the field. SUMMARY

[0009] In view of the defects of the prior art, the purpose of the present application is to provide a hydroelectric generator unit fault diagnosis method and system based on multi-receptive domain GCN, which aims to solve the problem that the existing diagnosis method cannot meet the real-time and accuracy requirements.

[0010] To achieve the above object, in a first aspect, the application provides a method for diagnosing faults of a hydroelectric generating unit based on a multi-receptive field GCN, comprising:

[0011] (1) obtaining vibration data of the hydroelectric generating unit during a period to be diagnosed, dividing the vibration data into a plurality of vibration samples to be measured according to a vibration period, and obtaining a vibration sample set to be diagnosed;

[0012] (2) constructing graph structure data corresponding to the vibration sample set to be diagnosed, and the specific process is as follows:

[0013] (2.1) abstracting each vibration sample as a node; (2.2) calculating time domain features and frequency domain features of each vibration sample as attributes of the node; (2.3) calculating the correlation between each pair of vibration samples, if the correlation is lower than a failure threshold, there is no edge between the two vibration samples, otherwise, there is an edge between the two vibration samples, and the correlation is taken as the weight of the edge;

[0014] (3) inputting the graph structure data corresponding to the vibration sample set to be diagnosed into a trained multi-receptive field graph convolution network model to obtain a fault diagnosis result of each vibration sample to be measured;

[0015] The training process of the multi-receptive field graph convolution network model is as follows:

[0016] obtaining historical vibration data of the hydroelectric generating unit, dividing the historical vibration data into a plurality of vibration samples according to a vibration period, labeling fault types of the vibration samples, and obtaining a training vibration sample set;

[0017] constructing graph structure data corresponding to the training vibration sample set;

[0018] training the multi-receptive field graph convolution network model using the graph structure data corresponding to the training vibration sample set to obtain the trained multi-receptive field graph convolution network model.

[0019] Preferably, the calculation of the time domain features of each vibration sample is as follows:

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] wherein, represents a time sequence signal, i.e. original data of vibration of a hydroelectric generating set, represents the number of data points in the vibration sample.

[0032] It should be noted that the present application proposes 11 time domain features, wherein a part of the features (such as and reflect the amplitude and energy features of the signal in the time domain, and another part of the features (such as and reflect the distribution of the signal in the time sequence, and therefore the time domain feature set can more completely reflect the time domain features of the signal, and is helpful to improve the accuracy of subsequent fault identification.

[0033] Preferably, the calculation of the frequency domain features of each vibration sample is specifically as follows:

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] wherein, represents the first frequency of the frequency spectrum after FFT transformation of the vibration sample, a value, representing the number of spectral lines, representing the frequency value of the th spectral line.

[0047] It should be noted that the present application proposes 12 frequency domain features, part of the features (, , and ) reflect the convergence of the signal spectrum, and the other part of the features (, and ) reflect the distribution of the main frequency in the signal frequency component. The set of frequency domain features can better reflect the characteristics of the signal in the frequency domain, and help to improve the accuracy of subsequent fault diagnosis.

[0048] Preferably, the correlation between each pair of vibration samples is calculated as follows:

[0049]

[0050] wherein, represents the correlation between the th vibration sample and the th vibration sample, represents the spectrum of the th vibration sample, represents the cosine value calculation function, represents the edge failure threshold.

[0051] It should be noted that the present application preferably uses the cosine value to measure the correlation, and when the calculated correlation is less than the threshold, it is set to 0, which can effectively reduce the complexity of the generated graph structure data and further improve the real-time performance of fault detection.

[0052] Preferably, the multi-receptive field graph convolutional network model comprises:

[0053] a first graph convolutional layer for extracting first receptive field graph convolutional features from the graph structure data;

[0054] a second graph convolutional layer for extracting second receptive field graph convolutional features from the first receptive field graph convolutional features after ReLU;

[0055] a concatenation layer for concatenating the node features of the graph structure data, the first receptive field graph convolutional features, and the second receptive field graph convolutional features to obtain concatenated features;

[0056] a Dense fully connected layer for receiving the concatenated features after ReLU and performing full connection;

[0057] a Softmax classifier for receiving the full connection features after ReLU and outputting the probability of each fault occurring.

[0058] It should be noted that the multi-receptive field graph convolutional network model of the present application preferably has the above structure, which has a relatively simple structure. Compared with traditional graph convolutional networks, it hardly increases additional computing space and time, while realizing the aggregation of multi-receptive field features, effectively improving the fault diagnosis accuracy while ensuring the real-time requirement of the model.

[0059] Preferably, the output of the first graph convolutional layer is , and the output of the second graph convolutional layer is ;

[0060] wherein, , , ;

[0061] wherein, represents the output vector of the first graph convolutional layer, represents the input vector of the first graph convolutional layer, represents the weight of the first graph convolutional layer, represents an intermediate variable, represents the output vector of the second graph convolutional layer, represents the weight of the second graph convolutional layer, represents the adjacency matrix of the additional node self-connection, represents the degree matrix of the additional self-connection, A represents the adjacency matrix of the graph structure data, represents the unit matrix.

[0062] To achieve the above-mentioned purposes, in a second aspect, the present application provides a hydroelectric generator unit fault diagnosis system based on multi-receptive field GCN, comprising: a processor and a memory.

[0063] The memory is used to store computer programs or instructions.

[0064] The processor is used to execute the computer programs or instructions in the memory, so that the method of the first aspect is executed.

[0065] Overall, compared with the prior art, the above technical solutions conceived by the present application have the following beneficial effects:

[0066] The application provides a hydroelectric generator unit fault diagnosis method and system based on a multi-receptive field GCN, which maximizes the information in limited vibration samples by constructing graph structure data, abstracting vibration samples as nodes, taking time domain features and frequency domain features of the vibration samples as attributes of the nodes, and abstracting vibration samples with high correlation as edges, and taking correlation as weights of the edges. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 is a hydroelectric generator unit fault diagnosis method flowchart based on a multi-receptive field GCN deep learning model provided by the application;

[0068] Figure 2 is a graph structure data example provided by the application;

[0069] Figure 3 is a multi-receptive field GCN model structure schematic diagram provided by the application;

[0070] Figure 4 is a hydroelectric generator unit fault diagnosis system structure diagram based on a multi-receptive field GCN deep learning model provided by the application. DETAILED DESCRIPTION

[0071] In order to make the purpose, technical scheme and advantages of the application clearer, the application is further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the application and do not limit the application.

[0072] Figure 1 is a hydroelectric generator unit fault diagnosis method flowchart based on a multi-receptive field GCN deep learning model provided by the application. As shown in Figure 1 , the method comprises:

[0073] Step 1: original data preprocessing.

[0074] The original data of the hydroelectric generator vibration is taken as an input sample set S, the sample set S is divided into m group data blocks, in order to contain the periodic information in the original vibration signal, grouping is performed according to one period. Feature extraction is performed on the hydroelectric generator vibration signal, specifically, feature extraction is performed on the original signal from the time domain and the frequency domain. And the model training set, the validation set and the test set are divided according to the proportion.

[0075] Among them, the time domain features include:

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[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] wherein, is a time sequence signal, i.e. the original data of the vibration of the hydroelectric generating set, is the number of data points in the sample.

[0088] wherein, the frequency domain features include:

[0089]

[0090]

[0091]

[0092]

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[0094]

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[0096]

[0097]

[0098]

[0099]

[0100]

[0101] wherein, is the first value of the spectrum, is the frequency domain data obtained by FFT transformation of the original data. K is the number of spectrum lines, is the frequency value of the first k spectrum line.

[0102] Step 2: Construction of graph structure data.

[0103] The corresponding spectrum is obtained by performing FFT transformation on the sample data, and then the cosine value of the sample spectrum is calculated as the attribute value of the edge. The features extracted in step 1 are taken as the node attributes, and the attribute values of the edges in step 2 are combined to construct the vibration diagram structure data of the unit. The correlation can also be measured in other ways.

[0104] Figure 2 A graph structure data example provided by the present application is shown in FIG. 1. Figure 2 As shown in FIG. 1, each sample is a node, and the attributes of the node are the features of the sample, i.e., the time domain and frequency domain features extracted. The edge is the correlation between two samples, and the attribute of the edge is the value calculated by the formula in step 2.2, which is used to represent the similarity between different samples. The specific steps are as follows:

[0105] Step 2.1, performing fast Fourier transform on the vibration signal to obtain the spectrum value of the signal F .

[0106] Step 2.2, calculating the correlation between any two samples to construct the adjacency matrix of the graph structure data A , and the specific calculation formula is as follows:

[0107]

[0108] wherein, represents the correlation between the first i sample and the first j sample, represents the spectrum of the first i sample, represents the cosine value calculation function, is the defined edge invalid threshold, and the value range is When the calculated correlation is less than the threshold, it is set to 0, thereby effectively reducing the complexity of the generated graph structure data.

[0109] Step 2.3, constructing the graph structure data , wherein, N represents the node in the graph, E represents the relationship between two samples.

[0110] Step 3: Hydroelectric unit fault diagnosis based on multi-receptive field graph convolutional network.

[0111] A multi-receptive field graph convolutional network model is established to further extract features from the graph structure data obtained in step 2. The output of each standard graph convolutional layer is recorded, and the output and input data of each layer are spliced to obtain a feature set of multiple receptive fields.

[0112] The structure parameters of the multi-receptive field graph convolutional network constructed in this embodiment are shown in Table 1.

[0113] Table 1

[0114]

[0115] Figure 3 is a multi-receptive field GCN model structure diagram provided by the present application. The forward calculation process of the multi-receptive field graph convolutional network is shown in Figure 3 , the training sample is the node of the graph structure data constructed, and the label is the category of the sample. The multi-receptive field graph convolutional network is used to input the sample features and the processed adjacency matrix of the graph structure data into the network for training and testing. The specific steps are as follows:

[0116] Step 3.1, the output of the first layer of graph convolutional network is , wherein, is the output vector of the first graph convolutional layer, is the input vector of the first graph convolutional layer, is the weight of the first graph convolutional layer, represents an intermediate variable.

[0117] Step 3.2, the output of the k graph convolutional layer is , wherein, is the output vector of the k graph convolutional layer, is the input vector of the k graph convolutional layer, is the weight of the k graph convolutional layer.

[0118] Step 3.3, the multi-receptive field features output by the multi-layer graph convolutional network are , wherein, is the spliced feature output by the multi-receptive field graph convolutional network, is the input vector of the network, is the output vector of the k graph convolutional layer. In the present application, takes a value of 2.

[0119] The stitching features are nonlinearly processed to obtain .

[0120] Step 3.4, the calculation used in the previous step The calculation formula is wherein, is an adjacency matrix with added self-connections, is a degree matrix with added self-connections.

[0121] The calculation formula is wherein, A is an adjacency matrix of the graph structure data, which can be calculated from step 2.2, is an identity matrix.

[0122] The calculation formula is wherein, is the renormalization adjacency matrix calculated in the previous step.

[0123] Step 3.5, the ReLU activation function formula used in the previous step calculation is:

[0124]

[0125] Step 4: Based on the Softmax classifier and the training process.

[0126] After the feature extraction of the network model in step 3, a set of feature vectors can be obtained. The Softmax classifier is selected as the classification method for hydroelectric unit faults to handle the multi-classification problem of hydroelectric units under multiple faults. The reconstructed feature vectors are combined through a fully connected network to obtain a linear combination of features as the input of the Softmax classifier, and the probability of the occurrence of each fault is calculated.

[0127] Step 4.1, use the fully connected layer Dense layer to connect behind the graph convolution layer, and splice the output of the previous graph convolution layer to obtain the feature vector as the input vector for further feature extraction. The activation function of the Dense layer still chooses ReLU to reduce the gradient dispersion problem, and the calculation formula is as follows:

[0128]

[0129] wherein, is the weight, is the bias, is the input, corresponding to the spliced feature vector output by the multi-receptive field graph convolution network.

[0130] Step 4.2, the output feature vector of the Dense layer is classified by a Softmax classifier to obtain a probability output vector. Softmax is a widely used classifier in current neural network learning. Its specific formula is:

[0131]

[0132] wherein, x is the input vector of the Softmax classifier, which is the output of the Dense layer in the model, is the weight matrix of the Softmax classifier, C is the number of categories to be distinguished, represents the probability that the output predicted label is c , and finally forms a probability output vector.

[0133] Step 4.3, using cross-entropy loss function as the loss function of the whole model.

[0134] The cross-entropy function is a commonly used loss function in classification problems, which can effectively measure the difference between the expected output and the actual output. The specific formula is:

[0135]

[0136] wherein, is the loss function, N is the number of samples, represents the true label vector of the th sample, represents the actual prediction vector of the th sample.

[0137] Step 5: Model training process based on Adam optimizer.

[0138] The connection weights of the feature combination network are corrected by minimizing the error function, and the connection weights of the entire network are trained using Adam and back propagation algorithm. The trained model is used to diagnose the test sample to obtain the final diagnosis result.

[0139] Adam optimizer has strong robustness in selecting hyperparameters, and is widely used in current deep learning. The Adam algorithm in the present application is combined with cross-entropy to perform gradient derivation on each weight to obtain the weight change value, and introduce a first moment variable s and a second moment variable r and time step t =0. The specific gradient update steps are as follows:

[0140] Step 5.1, calculate the gradient size, the formula is as follows:

[0141] .

[0142] Step 5.2, update the time step:

[0143] .

[0144] Step 5.3, update the biased first moment estimate:

[0145]

[0146] wherein, is the exponential decay rate of the first moment estimate.

[0147] Step 5.4, update the biased second moment estimate:

[0148]

[0149] wherein, is the exponential decay rate of the second moment estimate.

[0150] Step 5.5, correct the bias of the first moment:

[0151] .

[0152] Step 5.6, correct the bias of the second moment:

[0153] .

[0154] Step 5.7, calculate the weight update increment, the specific formula is as follows:

[0155]

[0156] wherein, is the global learning rate, is a small constant for numerical stability.

[0157] Step 5.8, update the value of the weight by .

[0158] .

[0159] The multi-receptive field graph convolutional network model optimized by training can be used for fault diagnosis of the diagnosis set, specifically, the graph structure data is input into the network, the probability vector of the training set sample obtained is analyzed, if the probability value corresponding to a certain fault is the largest and close to 1, it indicates that the sample has the largest possibility of belonging to the fault.

[0160] Figure 4 is a water turbine unit fault diagnosis system structure diagram based on a multi-receptive field GCN deep learning model provided by the application. As shown in Figure 4 , the system comprises a training data processing module, a graph structure data generation module, a neural network model training module, a reconstructed feature vector generation module and a fault probability calculation module, and the above modules are connected in sequence. Specifically:

[0161] The training data processing module is used to obtain a data set, and a group of data blocks is extracted from the data set, data features are extracted, and a model training set, a validation set and a test set are divided;

[0162] The graph structure data generation module is used to calculate the correlation between samples, construct graph structure data in combination with data features, and use the graph structure data as training data of a multi-receptive field graph convolution network model;

[0163] The neural network model training module is used to establish a multi-receptive field graph convolution network model, and train the multi-receptive field graph convolution network model using the training data to obtain the connection weight of the multi-receptive field graph convolution network model;

[0164] The reconstructed feature vector generation module is used to obtain a group of reconstructed feature vectors according to the multi-receptive field graph convolution network model composed of the connection weight;

[0165] The fault probability calculation module is used to obtain the linear combination of features by passing the reconstructed feature vector through a one-layer fully connected combination network, and use the linear combination as the input of a Softmax classifier to calculate the probability representing the possibility of occurrence of each fault.

[0166] Due to the small number of water turbine unit fault instances, the application uses rolling bearing vibration data, which is also a rotating machine, to conduct experiments to prove the effectiveness of the application. The application conducts 10 repeated bearing fault diagnosis experiments. The method of the application is compared with convolution neural network, standard graph convolution network (GCN), Chebyshev graph convolution network (ChebGCN) and other multi-receptive field graph convolution methods (MRF-GCN). The average value of multiple experimental results is taken as the final result, as shown in Table 2.

[0167] Table 2

[0168]

[0169] As can be seen from the results in Table 2, the method proposed in the application has the highest accuracy, and the time spent in training is less than that of the existing multi-receptive field graph convolution method, which is shorter in time consumption and has obvious advantages.

[0170] Those skilled in the art can easily understand that the above description is only the preferred embodiment of the present application, and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for hydroelectric generator unit fault diagnosis based on multi-receptive field GCN, characterized in that, Comprise: (1) obtain the vibration data of the hydroelectric generating set during the diagnosis period, divide it into a plurality of vibration samples according to the vibration period, and obtain the vibration sample set to be diagnosed; (2) construct the graph structure data corresponding to the vibration sample set to be diagnosed, the specific process is: (2.1) each vibration sample is abstracted as a node; (2.2) calculate the time domain feature and frequency domain feature of each vibration sample as the attribute of the node; (2.3) calculate the correlation between each pair of vibration samples, if the correlation is lower than the failure threshold, there is no edge between the two vibration samples, otherwise, there is an edge between the two vibration samples, and the correlation is used as the weight of the edge; (3) input the graph structure data corresponding to the vibration sample set to be diagnosed into the trained multi-receptive field graph convolution network model to obtain the fault diagnosis result of each vibration sample to be tested; The training process of the multi-receptive field graph convolution network model is: obtaining the historical vibration data of the hydroelectric generating set, dividing it into a plurality of vibration samples according to the vibration period, labeling the fault type of each vibration sample, and obtaining the training vibration sample set; construct the graph structure data corresponding to the training vibration sample set; train the multi-receptive field graph convolution network model using the graph structure data corresponding to the training vibration sample set to obtain the trained multi-receptive field graph convolution network model; The multi-receptive field graph convolution network model comprises: a first graph convolution layer for extracting first receptive field graph convolution features from the graph structure data; a second graph convolution layer for extracting second receptive field graph convolution features from the first receptive field graph convolution features after ReLU; a splicing layer for splicing the node features of the graph structure data, the first receptive field graph convolution features and the second receptive field graph convolution features to obtain splicing features; a Dense fully connected layer for receiving the splicing features after ReLU and performing full connection; a Softmax classifier for receiving the full connection features after ReLU and outputting the probability of each fault possibly occurring; The output of the first graph convolutional layer is The output of the second graph convolutional layer is ; wherein , , ; wherein denotes an output vector of the first graph convolution layer, denotes an input vector of the first graph convolution layer, denotes weights of the first graph convolution layer, denotes an intermediate variable, denotes an output vector of the second graph convolution layer, denotes weights of the second graph convolution layer, denotes an adjacency matrix of the additional node self-connection, denotes a degree matrix of the additional self-connection, A denotes an adjacency matrix of the graph structure data, denotes an identity matrix.

2. The method of claim 1, wherein, The calculation of the time domain feature of each vibration sample is as follows: wherein, represents the time series signal, i.e. the raw data of the hydroelectric unit vibration, represents the number of data points within the vibration sample, represents 11 time domain features.

3. The method of claim 1, wherein, The calculation of the frequency domain feature of each vibration sample is as follows: wherein, represents the i-th value of the spectrum after FFT transformation of the vibration sample, represents the number of spectral lines, represents the frequency value of the i-th spectral line, represent 12 frequency domain features.​​ 4. The method of claim 1, wherein, The correlation between each pair of vibration samples is calculated as follows: wherein, represents a correlation between the first vibration sample and the second vibration sample, represents a frequency spectrum of the first vibration sample, represents a cosine value calculation function, represents an edge failure threshold.

5. A multi-sensory domain GCN-based hydroelectric unit fault diagnosis system, characterized in that, Comprise: A processor and a memory; The memory is used to store computer programs or instructions; The processor is used to execute the computer programs or instructions in the memory, so that the method of any one of claims 1-4 is executed.

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