CNN + Transform-based power failure prediction method and system

Abstract

The invention discloses a CNN and Transform-based power failure prediction method, and the method comprises the following steps: 1, screening power data related to a fault terminal when a power failure occurs, and carrying out the screening of the power data, the power data comprises the frequency of the power failure event of the terminal, the type of the terminal, the service life of the terminal, the environmental characteristics two days before the power failure event of the terminal and the current day, and the accumulated power failure times of the terminal. 2, converting the electric power data into feature vectors; and step 3, constructing a CNN-Transform model, and training the model by using the power data related to the historical fault terminal. And step 4, converting power data related to the terminal into a feature vector, inputting the feature vector into the trained CNN-Transform model, and performing power failure prediction on the terminal.

Description

Technical Field

[0001] The present invention relates to the field of power systems, and more specifically, to a CNN+Transformer-based power fault prediction method and system. Background Art

[0002] During long-term use, power equipment is easily affected by various factors, such as natural environment, climate, human intervention and line failure, etc. This may cause damage to power equipment, thus triggering power outages, causing serious losses to economic interests and social life.

[0003] IoT technology has been widely used in the power supply industry. By connecting power equipment and terminal devices with sensors and communication modules, these devices can monitor the operating status in real time and transmit data to cloud servers for processing and analysis. This allows power suppliers to obtain a large amount of data in real time, including voltage, current, temperature, humidity and other information.

[0004] Cloud servers collect and store data from various terminal devices, which constitute a big data pool. Through big data analysis technology, this data can be deeply mined and analyzed to discover potential problems and predict possible power failures. Big data analysis can be used to monitor and analyze the operating status of power equipment. By analyzing historical data, patterns and trends of equipment failures can be identified. This helps to detect possible problems in advance and take maintenance measures, thereby reducing the risk of failures and power outages. Using big data and machine learning algorithms, predictive models can be built to predict future power supply conditions based on real-time and historical data. These models can identify the equipment most likely to experience power outages and issue alarms so that timely measures can be taken. By predicting equipment failures and preventing power outages, economic losses can be significantly reduced, including production interruptions, equipment repair costs, and damaged equipment replacement costs.

[0005] By combining the Internet of Things and big data analysis technologies, power suppliers can monitor the operating status of power equipment in real time and predict possible power outages, thereby reducing losses and improving the reliability of power supply.

[0006] The CNN+Tranformer model can be applied to multivariate time series prediction such as power load, but this model has not yet been applied to the fault prediction process of power terminals. In addition, the results of simply migrating existing models to implement fault prediction and classification for power terminals are not accurate.

[0007] In response to the above problems, there is an urgent need for a power fault prediction method and system based on CNN+Transformer. Summary of the invention

[0008] In order to solve the deficiencies in the prior art, the present invention provides a power fault prediction method and system based on CNN+Transformer, which collects fault information of power terminals and inputs it into a pre-trained model to obtain fault prediction and classification of power terminals.

[0009] The present invention adopts the following technical scheme. The first aspect of the present invention relates to a method for predicting power faults based on CNN+Transformer, which comprises the following steps: collecting fault information of power terminals and constructing feature vectors, inputting the feature vectors into a one-dimensional convolutional neural network and a vector embedding network in sequence to obtain a vector to be predicted; inputting the vector to be predicted into a pre-trained CNN+Transformer model to obtain attention information, and using the model output to obtain a mask matrix; the pre-trained CNN+Transformer model uses a multi-head self-attention mechanism of an offset vector and a mask matrix to extract features from the vector to be predicted; and using MLP+softmax to learn the attention information to obtain a fault prediction result of the power terminal.

[0010] Preferably, fault information of the power terminal is collected and a feature vector is constructed, including: the fault information of the power terminal includes the frequency of power outages at the power terminal, the terminal category, the age of the terminal, the environmental characteristics two days before and on the day of the power outage, and the cumulative number of power outages at the terminal.

[0011] Preferably, the feature vector is sequentially input into a one-dimensional convolutional neural network and a vector embedding network to obtain a vector to be predicted, including: the vector embedding network performs word vector embedding and position embedding on the feature vector.

[0012] Preferably, the vector to be predicted is input into a pre-trained CNN+Transformer model, including: the pre-trained CNN+Transformer model is constructed based on a multi-layer cascaded Conformer module.

[0013] Preferably, the mask matrix is ​​obtained using the model output, including: The matrix size at the time step is The mask matrix is: , is the bit-wise perceptual feed-forward layer, is the activation layer, t is the intercepted time step, f is the size of the input matrix.

[0014] Preferably, the pre-trained CNN+Transformer model uses a multi-head self-attention mechanism of an offset vector and a mask matrix to extract features of the prediction vector, including: the multi-head self-attention mechanism is: , In the formula, , and are the query vector, key vector, and value vector of the multi-head self-attention mechanism, is the word vector dimension, is the relative position of the word vector, and , for No. Locations and No. The relative position offset between the positions, and related, is the mask matrix.

[0015] Preferably, MLP+softmax is used to learn attention information to obtain fault prediction results of the power terminal, including: classifying the power terminal according to the fault prediction results, and dividing the predicted faults of the power terminal into passive power outages and non-passive power outages.

[0016] Preferably, the power terminals are smart meters and smart concentrators.

[0017] The second aspect of the present invention relates to a CNN+Transformer-based power fault prediction system using the method in the first aspect of the present invention, the system comprising an acquisition module, a feature extraction module and a prediction module; wherein the acquisition module is used to collect fault information of a power terminal and construct a feature vector, and input the feature vector into a one-dimensional convolutional neural network and a vector embedding network in sequence to obtain a vector to be predicted; the feature extraction module is used to input the vector to be predicted into a pre-trained CNN+Transformer model to obtain attention information, and obtain a mask matrix using the model output; the pre-trained CNN+Transformer model uses a multi-head self-attention mechanism of an offset vector and a mask matrix to perform feature extraction on the vector to be predicted; the prediction module is used to use MLP+softmax to learn attention information to obtain a fault prediction result for the power terminal.

[0018] A third aspect of the present invention relates to a terminal, comprising a processor and a storage medium; the storage medium is used to store instructions; the processor is used to operate according to the instructions to execute the steps of the method in the first aspect of the present invention.

[0019] A fourth aspect of the present invention relates to a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method in the first aspect of the present invention.

[0020] The beneficial effect of the present invention is that, compared with the prior art, the power fault prediction method and system based on CNN+Transformer in the present invention collects fault information of the power terminal and inputs it into the pre-trained model to obtain fault prediction and classification of the power terminal. The present invention improves the multi-head self-attention mechanism by mask matrix and position offset at the same time, and uses MLP+softmax to classify the extracted attention features, thereby obtaining an accurate prediction effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a flow chart of a method for predicting power failures based on CNN+Transformer of the present invention; Figure 2 This is a schematic diagram of the model structure in a power fault prediction method based on CNN+Transformer of the present invention; Figure 3 A schematic diagram of a fault prediction process in a power fault prediction method based on CNN+Transformer of the present invention; Figure 4 This is a schematic diagram of the module structure of a power fault prediction system based on CNN+Transformer in the present invention. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The embodiments described in the present invention are only embodiments of a part of the present invention, not all embodiments. Based on the spirit of the present invention, all other embodiments not recorded in the present invention obtained by ordinary technicians in this field according to the embodiments recorded in the present invention without making creative work should belong to the protection scope of the present invention.

[0023] Figure 1 The first aspect of the present invention relates to a method for predicting power failures based on CNN+Transformer, and the method includes steps 1 to 3.

[0024] Step 1: Collect the fault information of the power terminal and construct a feature vector, and input the feature vector into the one-dimensional convolutional neural network and the vector embedding network in sequence to obtain the vector to be predicted.

[0025] Due to the limitations of prediction, it is impossible to predict active events, such as planned power outages, so this method mainly predicts passive power outages, such as natural factors, equipment aging, etc. First, the data in the cloud database is feature screened and calculated to obtain the fault information of the power terminal.

[0026] Preferably, the fault information of the power terminal is collected and a feature vector is constructed, including: the fault information of the power terminal includes the frequency of power outages at the power terminal, the terminal category, the terminal service life, the environmental characteristics two days before and on the day of the power outage at the terminal, and the cumulative number of power outages at the terminal. Among them, the environmental characteristics include temperature, humidity, wind force, and wind and snow.

[0027] Terminal categories include smart meter terminal data, smart concentrators, and smart load control data. These terminals upload data to the cloud in real time through the Internet of Things technology.

[0028] Time series big data usually contains a large number of features (or variables). Feature screening is an important data preprocessing step. The purpose is to select the features most relevant to power failures from a large number of features to improve the efficiency and accuracy of time series analysis. Time series data is usually high-dimensional and contains many possible features, but not all features are useful for analysis and modeling. If all features are retained, the model may be too complex and lead to overfitting. Feature screening can help improve the performance of the model. In the context of big data, processing and analyzing a large number of features may require a lot of computing resources and time. Feature screening can reduce computing costs and increase analysis speed. Too many features may make the model difficult to interpret.

[0029] By screening the most important features, the interpretability of the model is easier to understand. Some features in time series data may contain a lot of noise. Feature screening can help remove these noisy features, thereby improving the robustness of the model. Multicollinearity refers to the high correlation between features, which may lead to model instability. Through feature screening, redundant features can be removed and the impact of collinearity can be reduced. In time series analysis, feature engineering is a time-consuming process. Feature screening can reduce the burden of feature engineering and make the modeling process more efficient. Reducing the number of features can make visualizations clearer and easier to understand and interpret. Too many features may cause the model to be sensitive to small fluctuations in the data. Feature screening can improve the stability of the model and make it more practical. The main goals of feature screening for time series big data are to improve the efficiency, accuracy and interpretability of the model, reduce computational costs, and improve the data analysis process. By carefully selecting the most relevant features, analysts can better understand the data and better meet specific analysis and prediction needs.

[0030] Firstly, the time series of power outage data of each terminal is standardized. The maximum-minimum scaling normalization method is used to scale the data to the interval [0,1] to eliminate the dimension of the terminal power outage data characteristics and reduce the characteristic influence caused by the dimension.

[0031] The maximum-minimum scaling is normalized to: , In the formula, is the normalized variable, The fault terminal data is input.

[0032] Step 2: Input the vector to be predicted into the pre-trained CNN+Transformer model to obtain attention information, and use the model output to obtain the mask matrix; the pre-trained CNN+Transformer model uses the multi-head self-attention mechanism of the offset vector and the mask matrix to extract features from the vector to be predicted.

[0033] Convolutional Neural Network (CNN) is a deep learning neural network architecture mainly used for image processing and computer vision tasks. The design of CNN is inspired by biological vision system, and it is specifically targeted at processing data with grid structure, such as images and videos. The core component of CNN is the convolution layer. The convolution layer uses a set of filters (also called convolution kernels) to slide over the input data and perform convolution operations. These filters detect different features in the image, such as edges, textures, and shapes. The convolution operation reduces the number of parameters by sharing weights, thereby reducing the risk of overfitting. Pooling layers are usually followed by convolution layers to reduce the dimensionality of the data, extract the most important information, and increase the robustness of the model. Common pooling operations include max pooling and average pooling, which take the maximum or average value within the pooling window, respectively. After the convolution layer, an activation function such as ReLU (Rectified Linear Unit) is usually applied to introduce nonlinearity. This helps the network learn nonlinear features and increase the expressive power of the model. Parameter sharing in CNN is an important feature of convolution kernels. This means that the same set of convolution kernels share the same weights over the entire input image. This reduces the number of model parameters, speeds up training, and improves the model's generalization ability.

[0034] The Transformer module is a deep learning model structure that was originally designed for natural language processing (NLP) tasks, but has since been widely used in a variety of fields, including computer vision, speech processing, and time series analysis. The core idea of ​​the Transformer module is to use a self-attention mechanism to process sequence data. The core of the Transformer is the self-attention mechanism. It allows the model to establish associations between different positions in the input sequence and capture the dependencies between the inputs. The self-attention mechanism calculates the weighted sum of each position to produce a weighted representation, allowing the model to assign the importance of different positions. Transformer usually consists of an encoder and a decoder, and is suitable for sequence-to-sequence tasks such as machine translation. The encoder is responsible for encoding the input sequence into a context-aware representation, while the decoder translates this representation into a target sequence. Each encoder and decoder contains multiple layers of self-attention mechanisms and feedforward neural networks. Since the self-attention mechanism does not consider the position information in the input sequence, the Transformer module introduces position encodings to represent the relative and absolute position of each position. These encodings are added to the embedding vector of the input to help the model understand the order in the sequence. Multi-head self-attention allows the model to focus on different aspects of the input sequence at the same time. It generates multiple different attention representations by calculating self-attention multiple times, each time using different learned weights. This helps the model capture multiple dependencies at the same time. Each encoder and decoder layer includes a feedforward neural network for further processing of the attention representation. Feedforward neural networks are usually composed of multiple layers of fully connected layers to increase the nonlinear modeling capabilities of the model. Each sublayer in the Transformer module contains residual connections and layer normalization to help gradient propagation and accelerate training. These connections allow information to be passed between different layers, helping to maintain the stability of the gradient.

[0035] The model of the present invention combines a convolutional neural network (CNN) and a Conformer model to better model and predict time series.

[0036] Preferably, the feature vector is sequentially input into a one-dimensional convolutional neural network and a vector embedding network to obtain a vector to be predicted, including: the vector embedding network performs word vector embedding and position embedding on the feature vector.

[0037] During the prediction process, a 1D CNN kernel is used to perform convolution operations on the time series, dividing the time series into local windows and mapping each window into an embedding vector, called a "token". These "tokens" carry the short-term pattern information of the time series. In order to capture the long-term dependencies of the time series, position embedding is also introduced and associated with each "token". In this way, both short-term and long-term information in the time series can be comprehensively considered, resulting in more accurate predictions.

[0038] Preferably, the vector to be predicted is input into a pre-trained CNN+Transformer model, including: the pre-trained CNN+Transformer model is constructed based on a multi-layer cascaded Conformer module.

[0039] Figure 2 The following is a schematic diagram of the model structure of a power fault prediction method based on CNN+Transformer in the present invention. In the present invention, the Conformer (CNN+Transformer) architecture used is as follows: Figure 2 As shown in the figure, each Conformer block is composed of a self-attention module, a convolution module and a macron feed-forward module. The cascade of multiple Conformer blocks constitutes the final Conformer architecture. The convolution module introduced after the multi-head self-attention module extracts local features from the rich self-correlated global data, solving the problem that the traditional Transformer model cannot extract detailed local features.

[0040] The output process of Conformer is as follows: , Among them, FFN is a feedforward network, selfattention is multi-head attention, conv is convolution, and layernorm is layer normalization. In the self-attention module, the output is firstly linearly transformed into Q, K, and V through three parameter matrices, and then the multi-head self-attention mechanism is used to extract features from Q, K, and V.

[0041] Preferably, the pre-trained CNN+Transformer model uses a multi-head self-attention mechanism of an offset vector and a mask matrix to extract features of the prediction vector, including: the multi-head self-attention mechanism is: , In the formula, , and are the query vector, key vector, and value vector of the multi-head self-attention mechanism, is the word vector dimension, is the relative position of the word vector, and , for No. Locations and No. The relative position offset between the positions, and related, is the mask matrix.

[0042] Preferably, the mask matrix is ​​obtained using the model output, including: The matrix size at the time step is The mask matrix is: , is the bit-wise perceptual feed-forward layer, is the active layer.

[0043] The convolution module includes Pointwise convolution, Depthwise convolution, Glu activation layer, and Swish activation layer. BatchNorm is only placed after the convolution layer to help train deep models. The output of the convolution module is normalized after the feedforward network and the residual operation to obtain the output of the Conformer architecture. The final output is further converted into a mask matrix to provide improvements for the self-attention mechanism.

[0044] Compared with the traditional prediction model for power outages caused by terminal faults, the proposed model based on CNN and Transformer can effectively improve the accuracy of prediction. The 1D-CNN is introduced in the Transformer block to overcome the shortcomings of the traditional Transformer model that it cannot identify local detailed features. The Conformer model has some obvious advantages over the traditional time series prediction model. Traditional time series prediction models usually use statistical methods, autoregressive models, exponential smoothing, etc., while the Conformer model is a fusion model based on deep learning. The Conformer model can capture complex nonlinear relationships and high-order dependencies in time series. Traditional models usually assume that data has a linear relationship, while the Conformer can better handle nonlinear data. Traditional time series models usually require manual selection and extraction of features, which can be a time-consuming task. The Conformer model can automatically learn relevant features from the data, reducing the burden of feature engineering. Traditional models usually require fixed-length input sequences, while the Conformer model can adapt to variable-length sequences, which is very important for diverse time series data in practical applications. The Transformer part of the Conformer model has a certain degree of interpretability, which can indicate the decision basis of the model when generating predictions. Traditional models are usually easier to explain, but may be limited when dealing with complex relationships. The architecture of the Conformer model can be customized according to the needs of different time series prediction tasks. Traditional models are often not easy to adapt to different tasks and data. The improved Conformer of the present invention simulates real fault analysis scenarios while considering the position offset of word vectors and the reference degree of information generation time, and improves the self-attention process to ensure that the results are accurate and reliable.

[0045] In summary, the advantages of the Conformer model in the power outage event prediction task include its powerful sequence modeling ability, self-attention mechanism, introduction of convolutional neural network, position encoding, multi-channel input, customizability, generalization ability, high performance and certain interpretability. These characteristics make it a powerful tool for processing time series data of various power outage events, which can improve the accuracy and adaptability of prediction. Despite the advantages of the Conformer model, some factors need to be considered, such as computing resources, data requirements and model complexity. In some cases, traditional time series prediction methods may still be a valid choice. However, with the reduction of hardware costs and the development of cloud technology, the cost of computing resources has gradually decreased, and smart grid systems have been gradually built across the country. Once the national power grid is connected, the daily data throughput will be huge. At that time, the traditional prediction model will not be able to play its simple and efficient role. Therefore, the CNN and Transformer-based models will play a huge role in the future cloud-based power outage event prediction methods.

[0046] Step 3: Use MLP+softmax to learn attention information to obtain the fault prediction results of the power terminal.

[0047] Preferably, MLP+softmax is used to learn the attention information to obtain a fault prediction result of the power terminal, including: classifying the power terminal according to the fault prediction result, and dividing the predicted fault of the power terminal into passive power outages and non-passive power outages.

[0048] Figure 3 The figure is a schematic diagram of the fault prediction process in a power fault prediction method based on CNN+Transformer of the present invention. Figure 3 As shown in the figure, the collected data is subjected to feature screening and feature extraction, and the model is trained after being built. During the model training process, the training data can be manually labeled with the fault type as the initial classification basis of the model. If the training results during the training process meet the error requirements or reach the number of training times, the training is terminated and the model parameters are saved, otherwise the training continues. After the training is completed, the new sample data is used to implement the prediction of the new data to obtain the fault classification prediction results. The prediction results can be verified to obtain the accuracy of the prediction results.

[0049] Figure 4The present invention is a schematic diagram of the module structure of a power fault prediction system based on CNN+Transformer. The second aspect of the present invention relates to a power fault prediction system based on CNN+Transformer using the method in the first aspect of the present invention, the system includes an acquisition module, a feature extraction module and a prediction module; wherein the acquisition module is used to collect fault information of the power terminal and construct a feature vector, and input the feature vector into a one-dimensional convolutional neural network and a vector embedding network in sequence to obtain a vector to be predicted; the feature extraction module is used to input the vector to be predicted into a pre-trained CNN+Transformer model to obtain attention information, and obtain a mask matrix using the model output; the pre-trained CNN+Transformer model uses a multi-head self-attention mechanism of an offset vector and a mask matrix to extract features from the vector to be predicted; the prediction module is used to learn attention information using MLP+softmax to obtain a fault prediction result of the power terminal.

[0050] A third aspect of the present invention relates to a terminal, comprising a processor and a storage medium; the storage medium is used to store instructions; the processor is used to operate according to the instructions to execute the steps of the method according to the first aspect of the present invention.

[0051] A fourth aspect of the present invention relates to a computer-readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the steps of the method in the first aspect of the present invention.

[0052] In summary, the present invention predicts equipment that may experience power outages and issues alarms so that timely measures can be taken. By predicting equipment failures and preventing power outages, economic losses can be significantly reduced.

[0053] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents, and any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A power fault prediction method based on CNN+Transformer, characterized in that: The method comprises the following steps: Collecting fault information of the power terminal and constructing a feature vector, and inputting the feature vector into a one-dimensional convolutional neural network and a vector embedding network in sequence to obtain a vector to be predicted; Inputting the vector to be predicted into the pre-trained CNN+Transformer model to obtain attention information, and using the model output to obtain a mask matrix; the pre-trained CNN+Transformer model uses a multi-head self-attention mechanism of an offset vector and the mask matrix to extract features from the vector to be predicted; The attention information is learned using MLP+softmax to obtain a fault prediction result of the power terminal.

2. The power fault prediction method based on CNN+Transformer according to claim 1, characterized in that: The collecting of fault information of the power terminal and constructing a feature vector comprises: The fault information of the power terminal includes the frequency of power outages occurring at the power terminal, the terminal category, the terminal service life, environmental characteristics two days before and on the day of the power outage, and the cumulative number of power outages at the terminal.

3. The power fault prediction method based on CNN+Transformer according to claim 1, characterized in that: The feature vector is sequentially input into a one-dimensional convolutional neural network and a vector embedding network to obtain a vector to be predicted, including: The vector embedding network performs word vector embedding and position embedding on the feature vector.

4. The power fault prediction method based on CNN+Transformer according to claim 1, characterized in that: The step of inputting the vector to be predicted into the pre-trained CNN+Transformer model comprises: The pre-trained CNN+Transformer model is constructed based on multi-layer cascaded Conformer modules.

5. The power fault prediction method based on CNN+Transformer according to claim 1, characterized in that: The method of obtaining a mask matrix by using the model output includes: The matrix size at the time step is The mask matrix is: , is the bit-wise perceptual feed-forward layer, is the activation layer, t is the intercepted time step, f is the size of the input matrix.

6. The power fault prediction method based on CNN+Transformer according to claim 1, characterized in that: The pre-trained CNN+Transformer model uses the multi-head self-attention mechanism of the offset vector and the mask matrix to extract features from the vector to be predicted, including: The multi-head self-attention mechanism is: ， In the formula, , and are the query vector, key vector, and value vector of the multi-head self-attention mechanism, is the word vector dimension, is the relative position of the word vector, and , for No. Locations and No. The relative position offset between the positions, and related, is the mask matrix.

7. The power fault prediction method based on CNN+Transformer according to claim 1, characterized in that: The using MLP+softmax to learn the attention information to obtain the fault prediction result of the power terminal includes: The fault prediction result classifies the power terminal into faults, and divides the predicted faults of the power terminal into passive power outages and non-passive power outages.

8. The power fault prediction method based on CNN+Transformer according to claim 1, characterized in that: The power terminals are smart meters and smart concentrators.

9. A CNN+Transformer-based power fault prediction system using the method according to any one of claims 1 to 8, characterized in that: The system includes an acquisition module, a feature extraction module and a prediction module; wherein, The acquisition module is used to collect fault information of the power terminal and construct a feature vector, and input the feature vector into a one-dimensional convolutional neural network and a vector embedding network in sequence to obtain a vector to be predicted; The feature extraction module is used to input the vector to be predicted into the pre-trained CNN+Transformer model to obtain attention information, and obtain a mask matrix using the model output; the pre-trained CNN+Transformer model uses the multi-head self-attention mechanism of the offset vector and the mask matrix to extract features from the vector to be predicted; The prediction module is used to use MLP+softmax to learn the attention information to obtain the fault prediction result of the power terminal.

10. A terminal comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is configured to operate according to the instructions to execute the steps of the method according to any one of claims 1-8.

11. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

Images