CNN-LSTM abnormal power consumption behavior identification method and system based on WGAN data expansion

Abstract

The invention discloses a CNN-LSTM abnormal electricity consumption behavior identification method and system based on WGAN data expansion, and belongs to the field of artificial intelligence electricity stealing prevention. The CNN-LSTM abnormal power consumption behavior identification method based on WGAN data expansion comprises the following steps: acquiring power consumption data, and preprocessing the power consumption data; classifying the preprocessed power consumption data, and expanding an abnormal power consumption sample by using a WGAN (Wide Generation Area Network); inputting the expanded one-dimensional power consumption data into a Bi-LSTM model to extract long-term trend characteristics of the power consumption data; converting the one-dimensional data into two-dimensional data in a weekly form, and inputting the two-dimensional data into a CNN model to extract potential features of the power utilization data; and merging the long-term trend features and the potential features, inputting the merged features into a full-connection neural network for detection, and outputting a detection result.

Description

Technical Field

[0001] The present invention belongs to the field of artificial intelligence anti-electricity theft, and specifically relates to a CNN-LSTM abnormal electricity consumption behavior identification method and system based on WGAN data expansion. Background Art

[0002] Abnormal electricity usage includes electricity theft, meter failure, billing errors, etc. The main source is electricity theft. As my country's electricity demand increases, abnormal electricity usage also occurs from time to time, which not only causes economic losses to power companies, but also threatens residents' personal safety and normal electricity use.

[0003] Traditional methods for identifying abnormal electricity consumption behaviors focus on prevention. It is difficult to effectively identify them based on experience and user reports alone. With the development of science and technology, the methods and means of abnormal electricity consumption behaviors have become more scientific and information-based, which greatly increases their concealment. With the in-depth application of procurement systems and marketing systems, abnormal electricity consumption can be identified by using power big data and artificial intelligence methods. Existing methods based on machine learning and deep learning only extract features using one-dimensional electricity consumption data, which makes it difficult to capture potential features and periodicity, and does not take into account the problem of unbalanced data sets, resulting in poor generalization of the model and low detection accuracy. Summary of the invention

[0004] In view of the deficiencies in the prior art, the purpose of the present invention is to provide a CNN-LSTM abnormal electricity consumption behavior identification method and system based on WGAN data expansion, which solves the problems in the prior art.

[0005] The purpose of the present invention can be achieved through the following technical solutions:

[0006] A CNN-LSTM abnormal power consumption behavior identification method based on WGAN data expansion includes the following steps:

[0007] Acquire electricity consumption data and pre-process the electricity consumption data;

[0008] The preprocessed electricity consumption data is classified, and the abnormal electricity consumption samples are expanded using the WGAN network;

[0009] The expanded one-dimensional electricity consumption data is input into the Bi-LSTM model to extract the long-term trend characteristics of the electricity consumption data; and the one-dimensional data is converted into two-dimensional data in weekly form and input into the CNN model to extract the potential characteristics of the electricity consumption data;

[0010] The long-term trend features and the potential features are combined and input into a fully connected neural network for detection, and the detection results are output.

[0011] Furthermore, the electricity consumption data preprocessing process includes: using linear interpolation to fill missing values ​​of electricity consumption data, using the 3σ criterion to process abnormal values ​​of electricity consumption data, and normalizing the electricity consumption data.

[0012] Furthermore, the steps of expanding the abnormal electricity consumption sample include:

[0013] S21, the preprocessed electricity consumption data is divided into a training set, a validation set and a test set. Let the sample of abnormal electricity users in the training set be X, and its distribution is P r ;

[0014] S22, assuming that the potential noise z satisfies the Gaussian distribution P z , the generator G maps the noise z so that the mapped samples satisfy P r The distribution of the generator G is defined as:

[0015]

[0016] θ G and θ D are the parameters of the generator G and the discriminator D respectively;

[0017] S23, the goal of the discriminator D is to determine the authenticity of the generated abnormal power consumption samples and to maximize the gap between the generated samples and the real samples. The objective function of D is defined as follows:

[0018]

[0019] The generator G and the discriminator D compete with each other to output abnormal electricity usage samples with high similarity;

[0020] S24, the Wasserstain distance is used to replace the JS divergence loss function in the GAN network. The Wasserstain distance formula is:

[0021]

[0022] Among them, γ∈Π(P x ,P z ) is based on P x and P z It is a collection of joint distributions composed of marginal distributions; the true distribution x and generated sample z can be sampled from γ, and the minimum expected distance between x and z is the Wasserstain distance.

[0023] Furthermore, the process of extracting the potential features of electricity consumption data includes: firstly inputting the two-dimensional weekly electricity consumption data into the convolution layer of the CNN model for convolution operation, and outputting the feature map y i ; Then the feature map y is pooled iPerform pooling operation and output the feature map y after maximum pooling dimensionality reduction m ; After that, it passes through the dropout and batch normalization layers to prevent model overfitting and internal covariate shift during neural network training, and then passes through the flatten layer to convert the feature map y m Flattened into a one-dimensional vector and input into the fully connected layer, the final output is the potential feature.

[0024] Furthermore, Bi-LSTM is an extension of the LSTM model, which trains two sub-LSTM models simultaneously from the forward and reverse directions at the same time t; the LSTM model consists of three memory gates: input gate, forget gate, and output gate. The input gate determines the input data to be retained, the forget gate filters important information into the cell state, and the output gate determines the information passed to the next hidden layer.

[0025] Furthermore, the Bi-LSTM model formula is expressed as:

[0026] h t =f(Wx t +Uh t-1 +b)

[0027] h t reverse =f(W reverse x t +U reverse h t+1 +b reverse )

[0028] y t =g(Vh t +V reverse h t reverse )+c

[0029] Among them, h t is the hidden layer state at time t, h t reverse is the reverse hidden layer state at time t, W and U are the weight matrices from the input layer to the hidden layer, and W reverse , U reverse is the reverse weight matrix from the input layer to the hidden layer, V, V reverse are the weights from the hidden layer to the output layer and the reverse weight, respectively. f and g are activation functions. t is the output at time t, b and c are both biases.

[0030] Furthermore, the detection model of the fully connected neural network is:

[0031] NTL det =σ(W NN [h CNN ,h Bi-LSTM]+b NN ) (19)

[0032] Where NTL det is the electricity theft detection result, σ is the sigmoid activation function, W NN and b NN are the weights and biases of the fully connected neural network, respectively.

[0033] A CNN-LSTM abnormal power consumption behavior identification system based on WGAN data expansion, including:

[0034] Data preprocessing module: obtains electricity consumption data and preprocesses the electricity consumption data;

[0035] Sample expansion module: classifies the preprocessed electricity consumption data and uses the WGAN network to expand abnormal electricity consumption samples;

[0036] Feature extraction module: input the expanded one-dimensional electricity consumption data into the Bi-LSTM model to extract the long-term trend characteristics of the electricity consumption data; and convert the one-dimensional data into two-dimensional data in weekly form and input it into the CNN model to extract the potential characteristics of the electricity consumption data;

[0037] And, a detection and identification module: after combining the long-term trend features and the potential features, the long-term trend features and the potential features are input into a fully connected neural network for detection, and the detection results are output.

[0038] A computer storage medium stores a readable program, characterized in that when the program is running, it can execute the above-mentioned CNN-LSTM abnormal power consumption behavior identification method based on WGAN data expansion.

[0039] An electronic device, comprising: a processor, a memory, a communication interface and a communication bus, wherein the processor, the memory and the communication interface communicate with each other through the communication bus;

[0040] The memory is used to store at least one executable instruction, and the executable instruction enables the processor to perform operations corresponding to the above-mentioned CNN-LSTM abnormal power consumption behavior identification method based on WGAN data expansion.

[0041] Beneficial effects of the present invention:

[0042] The beneficial effects of the present invention are as follows: the present invention proposes a data expansion algorithm based on WGAN, which can synthesize credible abnormal electricity consumption data samples for training through the encoder module, and at the same time reconstruct the electricity consumption data into one-dimensional and two-dimensional forms and input them into LSTM and CNN models respectively, so as to capture the potential periodic electricity consumption characteristics and time series electricity consumption characteristics of the electricity consumption data and improve the generalization ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0044] Figure 1 This is a flow chart of the abnormal electricity consumption behavior identification method of the present invention;

[0045] Figure 2 This is a diagram of the power consumption anomaly identification model proposed by the present invention;

[0046] Figure 3 This is the LSTM model structure diagram;

[0047] Figure 4 This is a comparison chart of the detection effect of the model proposed in the present invention and the AUC scores of other models. DETAILED DESCRIPTION

[0048] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are 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 creative work are within the scope of protection of the present invention.

[0049] Example 1

[0050] like Figure 1 and Figure 2 As shown, a CNN-LSTM abnormal power consumption behavior identification method based on WGAN data expansion includes the following steps:

[0051] S1, obtain 96 points of electricity consumption data of users with abnormal electricity consumption labels, with a time granularity of 15 minutes, and pre-process the electricity consumption data;

[0052] The steps for preprocessing electricity consumption data include:

[0053] S11, linear interpolation is used to fill in the missing values ​​of electricity consumption data; the expression is:

[0054]

[0055] Among them, f(x i ) is the power consumption at the i-th time point after filling, x i is the electricity consumption at the i-th time point, and NaN is a missing value.

[0056] S12, using the 3σ criterion to process outliers in electricity consumption data;

[0057]

[0058] Among them, g(x i ) is the power consumption at the i-th time point after processing, x is the actual power consumption vector, is the average value of electricity consumption, and σ is the standard deviation. When the electricity consumption data measured at time i does not satisfy the Gaussian distribution, the measured value at that time is Fill it.

[0059] S13, after processing the outlier and missing value data, the power consumption data is normalized to speed up the convergence of the neural network and avoid the problem of gradient explosion; the expression for normalizing the power consumption data is:

[0060]

[0061] Among them, min(x) and max(x) represent the minimum and maximum power consumption of the user respectively.

[0062] S2, using WGAN network to expand abnormal electricity consumption samples to solve the problem of sample imbalance;

[0063] In this step, considering that there are few samples of abnormal electricity consumption, the problem of data imbalance will have an adverse effect on the performance of the algorithm. Therefore, the WGAN model is selected to simulate the abnormal electricity consumption data and expand it; the expansion steps are:

[0064] S21, the preprocessed electricity consumption data obtained in S1 is divided into a training set, a validation set and a test set; let the sample of abnormal electricity users in the training set be X, and its distribution is P r ;

[0065] S22, assuming that the potential noise z satisfies the Gaussian distribution P z , the generator G maps the noise z so that the mapped samples satisfy P r The distribution of the generator G is defined as follows:

[0066]

[0067] Among them, θ G and θ D are the parameters of the generator G and the discriminator D respectively;

[0068] S23, the goal of the discriminator D is to judge the authenticity of the generated abnormal power consumption samples, that is, to maximize the gap between the generated samples and the real samples. The objective function of D is defined as follows:

[0069]

[0070] The generator G and the discriminator D compete with each other to output abnormal electricity usage samples with high similarity;

[0071] S24, the JS divergence loss function used by the GAN network measures the gap between the generated samples and the real samples, which will cause the problem of gradient disappearance or mode collapse during adversarial training; in view of this, the Wasserstain distance (WD) is used to replace the JS divergence loss function in the GAN network to form a WGAN network to measure the gap between the generated samples and the real samples to make up for the defects of the GAN network; the WD formula is as follows:

[0072]

[0073] Among them, γ∈∏(P x ,P z ) is based on P x and P z It is a collection of joint distributions composed of marginal distributions; the true distribution x and generated sample z can be sampled from γ, and the minimum expected distance between x and z is WD.

[0074] S3, input the expanded one-dimensional electricity consumption data into the Bi-LSTM model to extract the long-term trend characteristics of the electricity consumption data; and convert the one-dimensional data into two-dimensional data in weekly form and input it into the CNN model to extract the potential characteristics of the electricity consumption data;

[0075] The specific steps include:

[0076] S31, the one-dimensional electricity consumption data is arranged by week to obtain two-dimensional weekly electricity consumption data, and the data is input into the CNN model to extract the potential features of the electricity consumption data:

[0077] First, the two-dimensional weekly electricity consumption data is input into the convolution layer of the CNN model for convolution operation, and the feature map y is output. i ; Then the feature map y is pooled i Perform pooling operation and output the feature map y after maximum pooling dimensionality reduction m ; and y m After the dropout and batch normalization layers are processed to prevent model overfitting and internal covariate shift during neural network training, the feature map y is flattened. m Flattened into a one-dimensional vector input to the fully connected layer, and finally output the potential feature h CNN .

[0078] The formula for the convolutional layer of the CNN model is as follows:

[0079] y i =σ i (w i *xi +b i ) (7)

[0080] In the formula, σ i is the sigmoid activation function, x i is the input of the i-th layer. When i=1, it is the two-dimensional weekly electricity consumption data. * is the convolution operation. w i is the weight of the i-th convolutional layer, b i is the bias; output y i Feature map; then perform pooling operation through maximum pooling; the maximum pooling formula is as follows:

[0081] y m =max i,j∈R (y i,j ) (8)

[0082] In the formula, y m is the feature map after dimensionality reduction by the maximum pool, j is the jth neuron in the convolutional layer; by adding dropout and batch normalization layers after the pooling layer to prevent model overfitting and internal covariate shift during neural network training, adding a flatten layer to flatten the feature map into a one-dimensional vector and input it into the fully connected layer. The formula of the fully connected layer is as follows:

[0083]

[0084] In the formula, y f That is, the potential feature h extracted from the two-dimensional weekly electricity consumption data CNN .

[0085] S32, uses the Bi-LSTM model to extract the long-term trend characteristics of one-dimensional electricity consumption data;

[0086] Bi-LSTM is an extension of the traditional LSTM model. It trains two sub-LSTM models from the forward and reverse directions at the same time t.

[0087] like Figure 3 As shown in the figure, the LSTM model consists of three memory gates: input gate, forget gate and output gate. The input gate determines the input data to be retained, the forget gate filters important information into the cell state, and the output gate determines the information passed to the next hidden layer. The formulas for different memory gates are as follows:

[0088] f t =σ z (W f x t +U f h t-1 +b f ) (10)

[0089] i t =σz (W i x t +U i h t-1 +b i ) (11)

[0090] o t =σ z (W o x t +U o h t-1 +b o ) (12)

[0091] a t =σ z (W c x t +U c h t-1 +b c ) (13)

[0092] c t =f t ec t-1 +i t ea t (14)

[0093] h t =o t eσ z (c t ) (15)

[0094] where i t , f t and t Respectively represent the values ​​of the input gate, forget gate and output gate at the current time step, σ z is the sigmoid activation function, W and U represent the input x at time t respectively. t and the hidden layer state value h at time t-1 t-1 The corresponding weight; a t is the value of x at time t t and h t-1 The value of feature extraction, c t is the cell state at time t, and e is the Hadamard product, which is the multiplication of corresponding elements in the matrix.

[0095] The Bi-LSTM model formula is as follows:

[0096] h t =f(Wx t +Uh t-1 +b) (16)

[0097] h treverse =f(W reverse x t +U reverse h t+1 +b reverse ) (17)

[0098] y t =g(Vh t +V reverse h t reverse )+c (18)

[0099] Among them, h t is the hidden layer state at time t, h t reverse is the reverse hidden layer state at time t, W and U are the weight matrices from the input layer to the hidden layer, and W reverse , U reverse is the reverse weight matrix from the input layer to the hidden layer, V, V reverse are the weights from the hidden layer to the output layer and the reverse weight, respectively. f and g are activation functions. t is the output at time t, b and c are biases; by weighted summing the forward LSTM and the reverse LSTM, we can get the output of the Bi-LSTM model, which is the long-term trend characteristics of the one-dimensional electricity consumption data.

[0100] S4, merges the features extracted by CNN and Bi-LSTM networks and inputs them into the fully connected neural network to output the detection results;

[0101] The features h extracted by CNN and Bi-LSTM network CNN and h Bi-LSTM The matrix is ​​spliced ​​together and input into a fully connected neural network for detection. The output is the judgment value of whether the user's electricity consumption is abnormal.

[0102] The detection model is as follows:

[0103] NTL det =σ(W NN [h CNN ,h Bi-LSTM ]+b NN ) (19)

[0104] Where NTL det is the electricity theft detection result, σ is the sigmoid activation function, W NN and b NN are the weights and biases of the fully connected neural network, respectively.

[0105] Example 2

[0106] This embodiment uses the time series data on user electricity consumption provided by the State Grid, and records the electricity consumption records of 42,372 users from January 1, 2014 to October 31, 2016. Among them, 3,615 users were identified as abnormal electricity users through offline staff investigation, and the remaining users were not marked as abnormal electricity users.

[0107] The model uses a confusion matrix for performance evaluation. In the confusion matrix, True Positive (TP) represents the number of samples correctly predicted as positive examples, False Positive represents the number of samples incorrectly predicted as positive examples, False Negative (FN) represents the number of samples incorrectly predicted as negative examples, and True Negative represents the number of samples correctly predicted as negative examples. The ROC curve is a curve with FPR and TPR as axes. The ordinate is the true positive rate TPR = TP / P, where P is the number of positive samples, and the abscissa is the false positive rate FPR = FP / N, where N is the number of true negative samples. The larger the area (i.e. AUC) enclosed by the ROC curve and the FPR axis, the better the classification performance of the model.

[0108] Figure 4 The AUC-ROC scores of the proposed model and the baseline model are shown. It can be seen that the AUC score of the proposed model reaches 0.97, which is the best performance compared with the SVM, LR, RF, WD-CNN and LSTM models, indicating that the proposed model can effectively distinguish between normal and abnormal electricity users.

[0109] The method of the present invention may be implemented in hardware, firmware, or as software or computer code that may be stored in a recording medium (such as a CDROM, RAM, floppy disk, hard disk, or magneto-optical disk), or as computer code that is originally stored in a remote recording medium or a non-temporary machine-readable medium downloaded over a network and will be stored in a local recording medium, so that the method described herein may be stored in such software processing on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as an ASIC or FPGA). It is understood that a computer, processor, microprocessor controller, or programmable hardware includes a storage component (e.g., RAM, ROM, flash memory, etc.) that can store or receive software or computer code, and when the software or computer code is accessed and executed by a computer, processor, or hardware, the method described herein is implemented. In addition, when a general-purpose computer accesses the code for implementing the method shown herein, the execution of the code converts the general-purpose computer into a dedicated computer for executing the method shown herein.

[0110] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. A CNN-LSTM abnormal electricity consumption behavior identification method based on WGAN data expansion, characterized in that: The following steps are involved: Acquire electricity consumption data and pre-process the electricity consumption data; The preprocessed electricity consumption data is classified, and the abnormal electricity consumption samples are expanded using the WGAN network; The expanded one-dimensional electricity consumption data is input into the Bi-LSTM model to extract the long-term trend characteristics of electricity consumption data; The one-dimensional data is converted into two-dimensional data in weekly form and input into the CNN model to extract the potential features of electricity consumption data; The long-term trend features and the potential features are combined and input into a fully connected neural network for detection, and the detection results are output.

2. According to claim 1, a CNN-LSTM abnormal electricity consumption behavior identification method based on WGAN data expansion is characterized in that: The electricity consumption data preprocessing process includes: using linear interpolation to fill missing values ​​of electricity consumption data, using the 3σ criterion to process abnormal values ​​of electricity consumption data, and normalizing the electricity consumption data.

3. According to claim 1, a CNN-LSTM abnormal power consumption behavior identification method based on WGAN data expansion is characterized in that: The steps to expand the abnormal electricity consumption sample include: S21, the preprocessed electricity consumption data is divided into a training set, a validation set and a test set. Let the sample of abnormal electricity users in the training set be X, and its distribution is P r ; S22, assuming that the potential noise z satisfies the Gaussian distribution P z , the generator G maps the noise z so that the mapped samples satisfy P r The distribution of the generator G is defined as: θ G and θ D are the parameters of the generator G and the discriminator D respectively; S23, the goal of the discriminator D is to determine the authenticity of the generated abnormal power consumption samples and to maximize the gap between the generated samples and the real samples. The objective function of D is defined as follows: The generator G and the discriminator D compete with each other to output abnormal electricity usage samples with high similarity; S24, the Wasserstain distance is used to replace the JS divergence loss function in the GAN network. The Wasserstain distance formula is: Among them, γ∈Π(P x ,P z ) is based on P x and P z It is a collection of joint distributions composed of marginal distributions; the true distribution x and generated sample z can be sampled from γ, and the minimum expected distance between x and z is the Wasserstain distance.

4. According to claim 1, a CNN-LSTM abnormal electricity consumption behavior identification method based on WGAN data expansion is characterized in that: The process of extracting the potential features of electricity consumption data includes: firstly inputting the two-dimensional weekly electricity consumption data into the convolution layer of the CNN model for convolution operation, and outputting the feature map y i ; Then the feature map y is pooled i Perform pooling operation and output the feature map y after maximum pooling dimensionality reduction m ; After that, it passes through the dropout and batch normalization layers to prevent model overfitting and internal covariate shift during neural network training, and then passes through the flatten layer to convert the feature map y m Flattened into a one-dimensional vector and input into the fully connected layer, the final output is the potential feature.

5. According to claim 1, a CNN-LSTM abnormal electricity consumption behavior identification method based on WGAN data expansion is characterized in that: Bi-LSTM is an extension of the LSTM model. It trains two sub-LSTM models in the forward and reverse directions at the same time t. The LSTM model consists of three memory gates: input gate, forget gate, and output gate. The input gate determines the input data to be retained, the forget gate filters important information into the cell state, and the output gate determines the information passed to the next hidden layer.

6. According to claim 5, a CNN-LSTM abnormal electricity consumption behavior identification method based on WGAN data expansion is characterized in that: The Bi-LSTM model formula is expressed as: h t =f(Wx t +Uh t-1 +b) Among them, h t is the hidden layer state at time t, is the reverse hidden layer state at time t, W and U are the weight matrices from the input layer to the hidden layer, and W reverse , U reverse is the reverse weight matrix from the input layer to the hidden layer, V, V reverse are the weights from the hidden layer to the output layer and the reverse weight, respectively. f and g are activation functions. t is the output at time t, b and c are both biases.

7. The method for identifying abnormal electricity consumption behavior based on CNN-LSTM with WGAN data expansion according to claim 1 is characterized in that: The detection model of the fully connected neural network is: NTL det =σ(W NN [h CNN ,h Bi-LSTM ]+b NN ) (19) Where NTL det is the electricity theft detection result, σ is the sigmoid activation function, W NN and b NN are the weights and biases of the fully connected neural network, respectively.

8. A CNN-LSTM abnormal electricity consumption behavior identification system based on WGAN data expansion, characterized in that: include: Data preprocessing module: obtains electricity consumption data and preprocesses the electricity consumption data; Sample expansion module: classifies the preprocessed electricity consumption data and uses the WGAN network to expand abnormal electricity consumption samples; Feature extraction module: input the expanded one-dimensional electricity consumption data into the Bi-LSTM model to extract the long-term trend characteristics of electricity consumption data; The one-dimensional data is converted into two-dimensional data in weekly form and input into the CNN model to extract the potential features of electricity consumption data; And, a detection and identification module: after combining the long-term trend features and the potential features, the long-term trend features and the potential features are input into a fully connected neural network for detection, and the detection results are output.

9. A computer storage medium storing a readable program, characterized in that: When the program is running, it can execute the CNN-LSTM abnormal electricity consumption behavior identification method based on WGAN data expansion described in any one of claims 1 to 7.

10. An electronic device comprising: A processor, a memory, a communication interface and a communication bus, wherein the processor, the memory and the communication interface communicate with each other via the communication bus; The memory is used to store at least one executable instruction, and the executable instruction enables the processor to perform operations corresponding to a CNN-LSTM abnormal electricity consumption behavior identification method based on WGAN data expansion as described in any one of claims 1-7.

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