Quantitative detection method of insulator contamination based on unbalanced regression
By adopting an unbalanced regression-based detection method in insulator filth detection, combining error-sensitive loss function and label smoothing algorithm, the problem of uneven data distribution is solved, and the accuracy of the detection model and the ability to prevent and control contaminated flash accidents are improved.
Patent Information
- Application Number
- CN202411807369.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-10
- Publication Date
- 2025-04-04
AI Technical Summary
The existing insulator filth detection method based on deep learning faces the problem of uneven data distribution, which makes it difficult to improve the accuracy of the model and it is difficult to effectively prevent and control the pollution flash accident.
A quantitative detection method for insulator filthiness based on unbalanced regression is adopted. By combining error-sensitive loss function, reweighting method and label smoothing algorithm, an insulator surface filthiness detection model under unbalanced data is established to increase the model's attention to low-density interval samples.
It significantly improves the model's effect on the regression detection task of insulator impurity imbalance data sets, improves the accuracy and generalization capabilities of the model, and effectively prevents and controls flash accidents.
Smart Images

Figure CN119760394A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of insulator contamination degree detection, and in particular, relates to an insulator contamination degree quantitative detection method based on unbalanced regression. Background Art
[0002] Insulators are important insulating tools in electrical equipment systems. They have the functions of support, isolation, and insulation, and can ensure the safe and stable operation of power systems in various regions. Since insulators are generally exposed to open air environments, their surfaces are corroded by various pollutants under long-term action, resulting in a decrease in the lightning resistance and insulation level of the line, which makes it easy to cause accidents such as flashover. Flashover accidents can cause large-scale power outages and cause losses to the social economy. In order to monitor the problems of insulator contamination deposition and flashover discharge in high-voltage transmission systems in various regions, power grid research institutes in various regions of my country need to regularly conduct equivalent salt density method tests on the surface contamination level of insulators in their jurisdiction every year.
[0003] Most of the most advanced non-contact detection methods are based on deep learning. However, this type of method faces a common problem, that is, most of the data sets used to study the contamination degree of insulator surfaces have an imbalanced data distribution, which makes it difficult to improve the accuracy of the model. Research and application of methods for unbalanced data sets can achieve effective use of data sets, improve the accuracy of the model, and effectively prevent and control flashover accidents. Summary of the invention
[0004] In view of the shortcomings of the prior art, the present invention proposes a quantitative detection method for insulator contamination based on unbalanced regression, establishes an insulator surface contamination degree detection model under unbalanced data, improves the influence of prior probability distribution on the model, and increases the model's attention to low-density interval samples, thereby improving the model's effect on the insulator contamination degree unbalanced data set regression detection task; and realizes the quantitative detection of salt and ash values on the insulator surface based on unbalanced data sets.
[0005] The present invention is achieved through the following technical solutions:
[0006] Quantitative detection method of insulator contamination based on unbalanced regression:
[0007] The method specifically comprises the following steps:
[0008] Step 1: Collect the data related to the degree of insulator contamination, count the labels after processing, divide the regions, and obtain the label density;
[0009] Step 2: Select a suitable symmetric kernel and convolve the symmetric kernel with the original label distribution density to extract the kernel smoothed version. Use the symmetric kernel function to convolve the label density distribution of the original data to obtain the label distribution after kernel smoothing.
[0010] Step 3: Randomly initialize the network parameters, including the weights and biases of the feature extraction network and regression layer;
[0011] Step 4: Input the data set into the feature extraction network to extract the pollution feature and obtain the feature vector; input the extracted feature vector into the regression layer for regression training;
[0012] Step 5: Use the error-sensitive loss function to calculate the error between the predicted value and the true label; adjust the sample weight to avoid overfitting;
[0013] Step 6: Back propagation and parameter update: use the Adam optimizer to update the network parameters and accelerate the training process by adjusting the adaptive learning rate so that the regression model can show better prediction performance on the data.
[0014] Step seven, model prediction: the unknown sample to be tested is input into the trained detection model to obtain the detection result, thereby realizing the quantitative detection of the insulator contamination degree.
[0015] Furthermore, in step one,
[0016] Collect data related to the degree of insulator contamination, including but not limited to insulator sample data under different environmental conditions (such as different climate zones, different seasons, and different voltage level lines), and pre-process the collected data;
[0017] All data labels in the data set are counted, divided into equal intervals according to the label range, and the number of samples in the corresponding intervals is calculated to obtain the original label distribution density.
[0018] Further, in step 2, the kernel smoothed version explains the overlap of nearby label data sample information;
[0019] The suitable symmetric kernel must satisfy the condition as shown in formula (1);
[0020]
[0021] According to formula (2), a kernel-smoothed label distribution can be obtained;
[0022]
[0023] Where p(y) is the original label distribution density of the sample; Estimate the density of effective labels for the samples.
[0024] Furthermore, in step three,
[0025] First, we build an overall network architecture that includes a feature extraction network and a regression layer. The feature extraction network consists of multiple convolutional layers, pooling layers, and activation layers, which are used to automatically learn the deep feature representation in the data. The regression layer is usually composed of one or more fully connected layers, which are used to map the feature vector output by the feature extraction network to the final regression prediction result, that is, the pollution degree value of the insulator.
[0026] After the network is built, the parameter initialization operation is performed. For the weight parameters in the feature extraction network and regression layer, a random initialization strategy is adopted; then the data is input into the constructed and initialized network.
[0027] Furthermore, in step 4,
[0028] The data is forward propagated in the feature extraction network according to its network structure. The convolution layer extracts local features of the data, the pooling layer performs feature dimension reduction, and the activation layer introduces nonlinear transformation, thereby obtaining a feature vector that can characterize the relevant characteristics of the insulator contamination degree; the feature vector is then directly input into the regression layer, and a preliminary regression calculation is performed based on the current network parameters to obtain the initial prediction result.
[0029] Furthermore, in step five, the error-sensitive loss function is defined as formula (3);
[0030] In areas close to the predicted values, Huber Loss uses MSE loss, which is less sensitive to outliers; in areas far from the predicted values, Huber Loss uses MAE loss, which can better adapt to outliers;
[0031]
[0032] Where N is the number of samples involved in the model evaluation; y i is the true value of the label of the i-th sample; is the label estimate of the model for the i-th sample;
[0034] Square root inverse frequency weighting (SQINV) is used to reduce the weight of extreme minority class samples by using the square root of the sample effective label estimation density to avoid over-weighting and adjust the sample weight more balanced. Therefore, it is more robust to unbalanced data sets. Its expression is shown in formula (4);
[0035]
[0036] After obtaining the sample weights, multiply the loss term of each sample by the corresponding weight to adjust its importance in the training process, as shown in formula (5);
[0037]
[0038] Furthermore, in step seven, the unknown sample to be tested is input into the trained detection model; the unknown sample first passes through the feature extraction network to extract the feature vector related to the insulator contamination degree, and then the feature vector is input into the regression layer, and the regression layer outputs the prediction result of the insulator contamination degree of the unknown sample according to the learned parameters and model structure, thereby realizing the quantitative detection of the insulator contamination degree.
[0039] Furthermore, the data are divided into three levels: high-density interval, medium-density interval, and low-density interval. When evaluating the performance of the model, the mean absolute error and geometric mean error are used to evaluate the indicators of different sample density intervals and the overall sample.
[0040] An electronic device comprises a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above method when executing the computer program.
[0041] A computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the steps of the above method are implemented.
[0042] Beneficial effects of the present invention
[0043] The present invention adopts a solution combining an error-sensitive loss function, a reweighting method and a label smoothing algorithm, which can significantly improve the accuracy of the residual network model in the unbalanced regression task when facing the key indicator detection of insulator contamination degree, and is feasible in the detection of key indicators of insulator contamination degree for unbalanced data sets. BRIEF DESCRIPTION OF THE DRAWINGS
[0044] Figure 1 This is a flowchart of label normalization of the present invention.
[0045] Figure 2 The original distribution of salt content and the distribution after label smoothing, where (a) is the original label distribution of salt content, and (b) is the Gaussian kernel (l, σ) = (5, 2).
[0046] Figure 3 The MAE comparison diagram of the detection model, where (a) is the MAE comparison of salt content detection, and (b) is the MAE comparison of ash content detection. DETAILED DESCRIPTION
[0047] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings 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.
[0048] The methods used in the following examples are conventional methods unless otherwise specified. The materials, reagents, methods and instruments used are conventional materials, reagents, methods and instruments in the art unless otherwise specified, and can be obtained by those skilled in the art through commercial channels.
[0049] A quantitative detection method for insulator contamination based on unbalanced regression, the method specifically comprises the following steps:
[0050] Step 1: Collect the data related to the degree of insulator contamination, count the labels after processing, divide the regions, and obtain the label density;
[0051] Collect data related to the degree of insulator contamination, including but not limited to insulator sample data under different environmental conditions (such as different climate zones, different seasons, and different voltage level lines), and pre-process the collected data;
[0052] All data labels in the data set are counted, divided into equal intervals according to the label range, and the number of samples in the corresponding intervals is calculated to obtain the original label distribution density.
[0053] Step 2: Select a suitable symmetric kernel and convolve the symmetric kernel with the original label distribution density to extract the kernel smoothed version. Use the symmetric kernel function to convolve the label density distribution of the original data to obtain the label distribution after kernel smoothing.
[0054] In step 2, the kernel smoothing version explains the overlap of information of nearby labeled data samples;
[0055] The suitable symmetric kernel must satisfy the condition as shown in formula (1).
[0056]
[0057] According to formula (2), a kernel-smoothed label distribution can be obtained.
[0058]
[0059] Where p(y) is the original label distribution density of the sample; Estimate the density of effective labels for the samples.
[0060] Step 3: Randomly initialize the network parameters, including the weights and biases of the feature extraction network and regression layer;
[0061] First, we build an overall network architecture that includes a feature extraction network and a regression layer. The feature extraction network consists of multiple convolutional layers, pooling layers, and activation layers, which are used to automatically learn the deep feature representation in the data. The regression layer is usually composed of one or more fully connected layers, which are used to map the feature vector output by the feature extraction network to the final regression prediction result, that is, the pollution degree value of the insulator.
[0062] After the network is built, the parameter initialization operation is performed. For the weight parameters in the feature extraction network and regression layer, a random initialization strategy is adopted; then the data is input into the constructed and initialized network.
[0063] Step 4: Input the data set into the feature extraction network to extract the pollution feature and obtain the feature vector; input the extracted feature vector into the regression layer for regression training.
[0064] The data is forward propagated in the feature extraction network according to its network structure. The convolution layer extracts local features of the data, the pooling layer performs feature dimension reduction, and the activation layer introduces nonlinear transformation, thereby obtaining a feature vector that can characterize the relevant characteristics of the insulator contamination degree; the feature vector is then directly input into the regression layer, and a preliminary regression calculation is performed based on the current network parameters to obtain the initial prediction result.
[0065] Step 5: Use the error-sensitive loss function to calculate the error between the predicted value and the true label; adjust the sample weight to avoid overfitting;
[0066] The error-sensitive loss function Huber Loss is a compromise between MSE Loss and MAE Loss, and its definition is as shown in formula (3).
[0067] In areas close to the predicted values, Huber Loss uses MSE loss, which is less sensitive to outliers; in areas far from the predicted values, Huber Loss uses MAE loss, which can better adapt to outliers.
[0068]
[0069] Where N is the number of samples involved in the model evaluation; y i is the true value of the label of the i-th sample; is the label estimate of the model for the i-th sample.
[0071] Square root inverse frequency weighting (SQINV) is used to reduce the weight of extreme minority class samples by using the square root of the sample effective label estimation density to avoid over-weighting and adjust the sample weight more balanced. Therefore, it is more robust to unbalanced data sets. Its expression is shown in formula (4).
[0072]
[0073] After obtaining the sample weights, the loss term of each sample is multiplied by the corresponding weight to adjust its importance in the training process, as shown in formula (5). This design allows not only the hard label of each sample to be considered when calculating the loss, but also the probability weight of each sample interval, which can reduce the overfitting of the model to a certain interval in the training data, thereby improving the generalization ability of the model.
[0074]
[0075] Step 6: Back propagation and parameter update: use the Adam optimizer to update the network parameters and accelerate the training process by adjusting the adaptive learning rate so that the regression model can show better prediction performance on the data.
[0076] Step 7: Model prediction: The unknown sample to be tested is input into the trained detection model to obtain the detection result, thereby realizing the quantitative detection of the insulator contamination degree.
[0077] In step seven, the unknown sample to be tested is input into the trained detection model; the unknown sample first passes through the feature extraction network to extract the feature vector related to the insulator contamination degree, and then the feature vector is input into the regression layer. The regression layer outputs the prediction result of the insulator contamination degree of the unknown sample according to the learned parameters and model structure, thereby realizing the quantitative detection of the insulator contamination degree.
[0078] The present invention also includes sample density interval classification: after the model training is completed, it is used to evaluate the performance of the model under different sample densities. After the model prediction, this classification is used to analyze in detail the performance of the model under different data richness levels (high density interval, medium density interval, low density interval).
[0079] In order to better evaluate the ability of each imbalanced technique to handle different sample densities, the data is divided into three levels: high-density intervals, intervals with more than 10 training samples; medium-density intervals, intervals with 4 to 10 training samples; and low-density intervals, intervals with no more than 4 training samples. This classification aims to analyze the performance of the model under different data richness levels in detail and evaluate its overall performance.
[0080] The present invention also includes model performance evaluation indicators: when evaluating model performance, this embodiment uses mean absolute error and geometric mean error to evaluate indicators of different sample density intervals and overall samples.
[0081] (1) Mean Absolute Error (MAE), calculated as follows (7).
[0082]
[0083] (2) Geometric Mean Error (GME), which is calculated as shown in formula (8):
[0084]
[0085] Where N is the number of samples participating in the model evaluation;
[0086] y i is the true value of the label of the i-th sample; is the label estimate of the model for the i-th sample.
[0087] In the embodiment, the data set is divided into a training set and a validation set in a ratio of 7:3. The model training rounds are set to 250, and the Adam optimizer is used. The stepLR scheduler is used, and the initial learning rate is set to 0.001, which decays to the original 0.8 every fifty rounds of training.
[0088] In step 2 of the embodiment, the Gaussian kernel is selected as the smoothing kernel, and the calculation formula is as follows (9).
[0089]
[0090] Where σ is the standard deviation. A larger σ means a wider Gaussian function curve.
[0091] y – offset from the center point. A larger kernel window size means more neighborhood points are considered.
[0092] The smoothing effect of taking kernel bandwidth l = 5 and standard deviation σ = 2 is compared. Figure 2
[0093] In step seven, the hyperparameter is set according to the requirements, and in the present invention, it is set to δ=1.
[0094] Table 1 Comparison of salt detection effects
[0095]
[0096] Table 2 Comparison of ash volume detection effects
[0097]
[0098] The final implementation results are shown in Table 1 and Table 2. The MAE visualization comparison is as follows: Figure 3As shown in the figure, it can be found that for unbalanced data, combined with the label smoothing algorithm, the model is trained using the heavily weighted Huber Loss, which shows better fitting effects in both high, medium and low density intervals. Compared with the baseline model, this method maintains the prediction performance in the high-density interval and significantly improves the prediction performance in the medium-density interval and the low-density interval, thereby improving the overall fitting effect.
[0099] An electronic device comprises a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above method when executing the computer program.
[0100] A computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the steps of the above method are implemented.
[0101] The memory in the embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory, ROM, a programmable read-only memory, PROM, an erasable programmable read-only memory, EPROM, an electrically erasable programmable read-only memory, EEPROM, or a flash memory. The volatile memory may be a random access memory, RAM, which is used as an external cache. By way of example but not limitation, many forms of RAM are available, such as static random access memory static RAM, SRAM, dynamic random access memory dynamic RAM, DRAM, synchronous dynamic random access memory synchronous DRAM, SDRAM, double data rate synchronous dynamic random access memory double data rate SDRAM, DDR SDRAM, enhanced synchronous dynamic random access memory enhanced SDRAM, ESDRAM, synchronous link dynamic random access memory synchlink DRAM, SLDRAM, and direct memory bus random access memory direct rambus RAM, DR RAM. It should be noted that memory of the methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.
[0102] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented by software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from a website site, computer, server or data center through a wired method such as coaxial cable, optical fiber, digital subscriber line digital subscriber line, DSL or wireless such as infrared, wireless, microwave, etc. to another website site, computer, server or data center. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or data center that includes one or more available media integrated. The available medium can be a magnetic medium such as a floppy disk, a hard disk, a tape, an optical medium such as a high-density digital video disc digital video disc, DVD, or a semiconductor medium such as a solid state hard disk solid state disc, SSD, etc.
[0103] In the implementation process, each step of the above method can be completed by an integrated logic circuit of hardware in a processor or an instruction in the form of software. The steps of the method disclosed in conjunction with the embodiment of the present application can be directly embodied as a hardware processor for execution, or a combination of hardware and software modules in a processor for execution. The software module can be located in a storage medium mature in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in a memory, and the processor reads the information in the memory and completes the steps of the above method in conjunction with its hardware. To avoid repetition, it is not described in detail here.
[0104] It should be noted that the processor in the embodiment of the present application can be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method embodiment can be completed by an integrated logic circuit of hardware in the processor or an instruction in the form of software. The above processor can be a general-purpose processor, a digital signal processor DSP, an application-specific integrated circuit ASIC, a field programmable gate array FPGA or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components. The methods, steps and logic block diagrams disclosed in the embodiments of the present application can be implemented or executed. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The steps of the method disclosed in the embodiment of the present application can be directly embodied as a hardware decoding processor to perform, or the hardware and software modules in the decoding processor can be combined to perform. The software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in a memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware.
[0105] The above is a detailed introduction to the quantitative detection method for insulator contamination based on unbalanced regression proposed in the present invention, and the principles and implementation methods of the present invention are explained. The description of the above embodiments is only used to help understand the method of the present invention and its core idea; at the same time, for those skilled in the art, according to the idea of the present invention, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as limiting the present invention.
Claims
1. A quantitative detection method for insulator contamination based on unbalanced regression, characterized in that: The method specifically comprises the following steps: Step 1: Collect the data related to the degree of insulator contamination, count the labels after processing, divide the regions, and obtain the label density; Step 2: Select a suitable symmetric kernel and convolve the symmetric kernel with the original label distribution density to extract the kernel smoothed version. Use the symmetric kernel function to convolve the label density distribution of the original data to obtain the label distribution after kernel smoothing. Step 3: Randomly initialize the network parameters, including the weights and biases of the feature extraction network and regression layer; Step 4: Input the data set into the feature extraction network to extract the pollution feature and obtain the feature vector; input the extracted feature vector into the regression layer for regression training; Step 5: Use the error-sensitive loss function to calculate the error between the predicted value and the true label; adjust the sample weight to avoid overfitting; Step 6: Back propagation and parameter update: use the Adam optimizer to update the network parameters and accelerate the training process by adjusting the adaptive learning rate so that the regression model can show better prediction performance on the data. Step seven, model prediction: the unknown sample to be tested is input into the trained detection model to obtain the detection result, thereby realizing the quantitative detection of the insulator contamination degree.
2. The method according to claim 1, characterized in that: In step one, Collect data related to the degree of insulator contamination, including but not limited to insulator sample data under different environmental conditions (such as different climate zones, different seasons, and different voltage level lines), and pre-process the collected data; All data labels in the data set are counted, divided into equal intervals according to the label range, and the number of samples in the corresponding intervals is calculated to obtain the original label distribution density.
3. The method according to claim 2, characterized in that: In step 2, the kernel smoothing version explains the overlap of information of nearby labeled data samples; The suitable symmetric kernel must satisfy the condition as shown in formula (1); According to formula (2), a kernel-smoothed label distribution can be obtained; Where p(y) is the original label distribution density of the sample; Estimate the density of effective labels for the samples.
4. The method according to claim 3, characterized in that: In step three, First, we build an overall network architecture that includes a feature extraction network and a regression layer. The feature extraction network consists of multiple convolutional layers, pooling layers, and activation layers, which are used to automatically learn the deep feature representation in the data. The regression layer is usually composed of one or more fully connected layers, which are used to map the feature vector output by the feature extraction network to the final regression prediction result, that is, the pollution degree value of the insulator. After the network is built, the parameter initialization operation is performed. For the weight parameters in the feature extraction network and regression layer, a random initialization strategy is adopted; then the data is input into the constructed and initialized network.
5. The method according to claim 4, characterized in that: In step four, The data is forward propagated in the feature extraction network according to its network structure. The convolution layer extracts local features of the data, the pooling layer reduces the dimension of the features, and the activation layer introduces nonlinear transformation, so as to obtain the feature vector that can characterize the related features of the insulator contamination degree. The feature vector is then directly input into the regression layer, where a preliminary regression calculation is performed based on the current network parameters to obtain the initial prediction result.
6. The method according to claim 5, characterized in that: In step five, The error-sensitive loss function is defined as formula (3); In areas close to the predicted values, Huber Loss uses MSE loss, which is less sensitive to outliers; in areas far from the predicted values, Huber Loss uses MAE loss, which can better adapt to outliers; Where N is the number of samples involved in the model evaluation; y i is the true value of the label of the i-th sample; is the label estimate of the model for the i-th sample; Square root inverse frequency weighting (SQINV) is used to reduce the weight of extreme minority class samples by using the square root of the sample effective label estimation density to avoid over-weighting and adjust the sample weight more balanced. Therefore, it is more robust to unbalanced data sets. Its expression is shown in formula (4); After obtaining the sample weights, multiply the loss term of each sample by the corresponding weight to adjust its importance in the training process, as shown in formula (5); 7. The method according to claim 6, characterized in that: In step seven, the unknown sample to be tested is input into the trained detection model; the unknown sample first passes through the feature extraction network to extract the feature vector related to the insulator contamination degree, and then the feature vector is input into the regression layer. The regression layer outputs the prediction result of the insulator contamination degree of the unknown sample according to the learned parameters and model structure, thereby realizing the quantitative detection of the insulator contamination degree.
8. The method according to claim 7, characterized in that: The data is divided into three levels: high-density interval, medium-density interval, and low-density interval. When evaluating the performance of the model, the mean absolute error and geometric mean error are used to evaluate the indicators of different sample density intervals and the overall sample.
9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.
10. A computer-readable storage medium for storing computer instructions, characterized in that: When the computer instructions are executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.