Method for detecting internal leakage of nuclear power valve based on time-frequency characteristics of acoustic emission signals

Through the detection method based on the time-frequency characteristics of the acoustic transmission signal, the problem of low leakage rate prediction accuracy and frequent disassembly in the leakage detection of nuclear power valves is solved, remote online detection and high-precision leakage rate prediction are realized, and automation and intelligence are improved level of transformation.

CN119245951APending Publication Date: 2025-01-03HAINAN NUCLEAR POWER CO LTD
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Patent Information

Application Number
CN202411337896.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-09-25
Publication Date
2025-01-03

AI Technical Summary

Technical Problem

The existing leak detection methods in nuclear power valves have problems such as low leakage rate prediction accuracy and frequent valve disassembly inspection and maintenance.

Method used

Using the detection method based on the time-frequency characteristics of acoustic emission signals, multivariate regression is established by collecting the acoustic emission signals during valve leakage, and by extracting the features of the time domain, frequency domain and time-frequency domain, combining support vector regression and backpropagation neural networks. The model predicts leakage rate and leakage level, and uses convolutional neural networks and residual neural networks to train time-frequency images to achieve the prediction of leakage level.

Benefits of technology

Remote online detection of leakage status in the valve is realized, the detection accuracy and safety is improved, the need for frequent disassembly is reduced, the level of automation and intelligence is improved, and the environmental adaptability and computing efficiency is high.

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Abstract

The invention relates to the technical field of valve internal leakage identification, aims to solve the problem of low leakage rate prediction precision in valve internal leakage acoustic emission detection, and discloses a nuclear power valve internal leakage detection method based on acoustic emission signal time-frequency characteristics. Extracting the characteristics of the time domain, the frequency domain and the time-frequency domain of the leakage signal, analyzing the linear relation between the characteristics and the leakage rate of the valve, and predicting the leakage rate and the leakage grade. According to the invention, remote online detection can be carried out on the internal leakage state of the valve, meanwhile, the internal leakage rate of the valve is predicted, the safety of maintenance personnel is guaranteed, the scheme feasibility is high, the measurement is accurate, the applicability is high, the improvement of automation and intelligence levels is facilitated, and good practicability and safety benefits are achieved.
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Description

Technical Field

[0001] The present invention relates to the technical field of valve internal leakage identification, and in particular to a method for detecting internal leakage of nuclear power valves based on time-frequency characteristics of acoustic emission signals. Background Art

[0002] There are a large number of valves in the system of nuclear power plants, whose purpose is to control the fluid transportation in the pipeline and adjust the flow direction, flow rate and pressure of the fluid inside the pipeline.

[0003] In actual applications, systems often experience leakages of varying degrees, among which valve leakage accidents between pipelines occur most frequently. In most cases, valve leakage is caused by long-term erosion of the inside of the valve body by the fluid.

[0004] The existing internal leakage inspection method requires the valve to be disassembled for inspection, which requires the valve to be frequently disassembled. Other non-destructive inspection methods have low prediction accuracy. Summary of the invention

[0005] The main purpose of the present invention is to provide a method for detecting internal leakage of nuclear power valves based on the time-frequency characteristics of acoustic emission signals, so as to solve the problem of low leakage rate prediction accuracy in acoustic emission detection of internal leakage of valves.

[0006] Another object of the present invention is to provide a method for detecting internal leakage of nuclear power valves based on the time-frequency characteristics of acoustic emission signals, so as to solve the problem that the existing detection methods require frequent disassembly of valves for inspection and maintenance.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A method for detecting internal leakage in nuclear power valves based on the time-frequency characteristics of acoustic emission signals. The method collects the acoustic emission signals generated when the valve leaks, extracts the time domain, frequency domain and time-frequency domain characteristics of the leakage signals, analyzes the linear relationship between the characteristics and the valve leakage rate, and predicts the leakage rate and leakage level.

[0009] In some embodiments, the features include: maximum amplitude, root mean square, standard deviation in the time domain, centroid frequency, spectrum kurtosis, root mean square frequency, standard deviation frequency, spectrum area in the frequency domain, third-order cumulant in the time-frequency domain, and wavelet packet information entropy.

[0010] In some embodiments, the method specifically comprises:

[0011] Step 1: Obtain the valve internal leakage acoustic emission signals under different pressures and different leakage rates, analyze and extract the features of the valve internal leakage acoustic emission signals, denoise the data and extract a variety of time-frequency domain features, and analyze the linear relationship between the features and the leakage rate;

[0012] Step 2: Combine the time-frequency domain feature parameters extracted in step 1 with the support vector regression and back propagation neural network methods to establish multivariate regression models between the time-frequency characteristics of the acoustic emission signal and the leakage rate under variable pressure;

[0013] Step 3: According to the valve internal leakage standard, the leakage level is divided according to the valve internal leakage acoustic emission signals collected at different leakage rates, and the leakage level is predicted using three neural networks to determine the leakage amount of the valve internal leakage.

[0014] In some embodiments, in step 1, the internal leakage of the valve is simulated through an experimental environment, and the acoustic emission signals of the internal leakage of the valve under different leakage rates and different pressures are collected. The acoustic emission signals of the internal leakage of the valve are analyzed to determine the frequency band range of the signal to be used, thereby removing excess noise interference.

[0015] In some embodiments, the method for collecting the acoustic emission signal of valve internal leakage includes:

[0016] Build a valve internal leakage simulation experimental environment consisting of an air compressor, pressure vessel, pipeline, valve, pipe, and flow meter;

[0017] Air compressor is used to generate air of a certain pressure and store it in a pressure vessel;

[0018] The gas at a fixed pressure is sent into the valve through the connecting pipe, and the leakage rate is simulated by controlling the valve opening;

[0019] Use the flow meter at the rear end of the valve to record the leakage rate of the valve;

[0020] Attach the acoustic emission sensor to the outer wall of the valve to collect data on leakage acoustic emission signals;

[0021] The leakage is simulated by controlling the air compressor to change the gas pressure in the pressure vessel and the valve opening to collect the acoustic emission signals of valve leakage at different pressures and leakage rates.

[0022] In some embodiments, five features, namely, centroid frequency, spectrum kurtosis, root mean square frequency, standard deviation frequency, and spectrum area, are extracted in the frequency domain, and the calculation formulas thereof are respectively:

[0023]

[0024] Where FC represents the center of gravity frequency, f represents the signal frequency, P(f) represents the power spectrum of the signal; K is the spectral kurtosis, x i is the spectrum amplitude, x is the mean of the amplitude, MSF is the mean square frequency, VF is the frequency standard deviation, and S is the spectrum area.

[0025] In some embodiments, the third-order cumulative amount and wavelet packet information entropy of the leakage acoustic emission signal are feature extracted in the time-frequency domain, and the calculation formulas are:

[0026] c 3x (τ1,τ2)=m 3x (τ1,τ2)=E{x(k)x(k+τ1)x(k+τ2)};

[0027] Where m is the autocorrelation sequence, τ1 and τ2 are offsets;

[0028] The wavelet packet entropy calculation formula is as follows:

[0029]

[0030] where p 4,k =E 4,k / E4, the number 4 represents the node of the fourth layer of wavelet packet decomposition, E 4,k is the energy of the K nodes in the fourth layer, and E4 is the sum of the energy of each node in the fourth layer.

[0031] In some embodiments, in step 2, a feature matrix is ​​constructed for the 10 feature quantities obtained in step 1, and then combined with the front-end pressure of the valve as a model input, and then a verification experiment is carried out on the trained model to verify the adaptability of the model.

[0032] In some embodiments, in step 3, the method for predicting valve leakage level specifically includes:

[0033] To stipulate the maximum leakage volume;

[0034] The internal leakage level of the valve is divided into different levels according to the range of leakage, corresponding to different rated flow rates;

[0035] The acoustic emission signal of valve leakage is converted into a time-frequency image, and the deep features of the image are extracted using a convolutional neural network.

[0036] Convert the leakage signal into a time-frequency image and reduce the amount of computation through a convolutional neural network;

[0037] ResNext50 (32×4d) residual neural network, DenseNet dense connection network and ResNet50 network are used to train time-frequency image data;

[0038] Soft voting is performed on the three trained models, and the class with the largest probability sum among all voting results is taken as the result to predict the leakage level.

[0039] In some embodiments, the levels divided according to the range of leakage include four different levels: extremely small, small, medium, and large, which correspond to less than 0.01% of the rated circulation, 0.01% to 0.05% of the rated circulation, 0.05% to 0.1% of the rated circulation, and greater than 0.1% of the rated circulation, respectively.

[0040] Compared with the prior art, the method for detecting internal leakage of nuclear power valves based on the time-frequency characteristics of acoustic emission signals provided by the present invention has the following beneficial effects:

[0041] The present invention can perform remote online detection of the internal leakage status of the valve and predict the internal leakage rate of the valve to ensure the safety of maintenance personnel. The scheme has high feasibility, accurate measurement, high applicability, helps to improve the level of automation and intelligence, and has good practicality and safety benefits.

[0042] The present invention can be used to determine the internal leakage of the valve, avoid frequent disassembly of the valve for inspection and maintenance, and when leakage occurs, the leakage of the valve can be determined stably and safely, so that maintenance can be carried out in time.

[0043] The present invention adopts a method based on the time-frequency characteristics of acoustic emission signals to detect internal leakage of nuclear power valves, and deep learning is used to predict the leakage rate of valves under different pressures, which has a good effect and strong environmental adaptability.

[0044] The present invention adopts time-frequency images to predict the leakage level, which can reduce the amount of calculation. At the same time, the three-model voting method is adopted to effectively improve the accuracy of model prediction and reduce misjudgment. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for the technical description.

[0046] Figure 1 A flow chart of a method for detecting internal leakage of a nuclear power valve based on the time-frequency characteristics of an acoustic emission signal provided by the present invention;

[0047] Figure 2 A block diagram of the experimental system composition of the nuclear power valve internal leakage detection method based on the time-frequency characteristics of the acoustic emission signal provided by the present invention;

[0048] Figure 3 A schematic diagram of the linear relationship between the standard deviation and the leakage rate provided by the present invention;

[0049] Figure 4 A schematic diagram of the linear relationship between the root mean square and the leakage rate provided by the present invention;

[0050] Figure 5 A schematic diagram of the linear relationship between the maximum amplitude in the time domain and the leakage rate provided by the present invention;

[0051] Figure 6 A schematic diagram of the linear relationship between the center of gravity frequency and the leakage rate provided by the present invention;

[0052] Figure 7 A schematic diagram of the linear relationship between spectrum kurtosis and leakage rate provided by the present invention;

[0053] Figure 8 A schematic diagram of the linear relationship between the root mean square frequency and the leakage rate provided by the present invention;

[0054] Fig. 9 A schematic diagram of the linear relationship between the standard deviation frequency and the leakage rate provided by the present invention;

[0055] Fig.10 A schematic diagram of the linear relationship between the spectrum area and the leakage rate provided by the present invention;

[0056] Fig.11 A schematic diagram of the linear relationship between the third-order cumulative amount and the leakage rate provided by the present invention;

[0057] Fig.12 A schematic diagram of the linear relationship between the wavelet packet information entropy and the leakage rate provided by the present invention. DETAILED DESCRIPTION

[0058] The following is further explained in detail through specific implementation methods.

[0059] like Figure 1 As shown, the present invention provides a method for detecting leakage in nuclear power valves based on the time-frequency characteristics of acoustic emission signals. The method collects the acoustic emission signals generated when the valve leaks, extracts the time domain, frequency domain and 10 time-frequency domain features of the leakage signal, analyzes the linear relationship between the leakage signal and the valve leakage rate, and realizes the prediction of the leakage rate and leakage level. The present invention utilizes that when a leak occurs inside the valve, the internal fluid, under the action of pressure, generates turbulence at the leakage point, generates elastic waves, and the elastic waves are transmitted along the valve body to the valve surface. The acoustic emission sensor collects this signal, and the leakage of the valve can be judged according to the characteristics of the signal.

[0060] The 10 features include: maximum amplitude, root mean square, standard deviation in the time domain, centroid frequency, spectrum kurtosis, root mean square frequency, standard deviation frequency, spectrum area in the frequency domain, third-order cumulant in the time-frequency domain, and wavelet packet information entropy.

[0061] The specific steps include:

[0062] Step 1: Through experimental environment simulation, obtain the valve leakage acoustic emission signals under different pressures and leakage rates, analyze and extract the features of the valve leakage acoustic emission signals, analyze the detected time domain and frequency domain signals, determine the useful signal frequency band range (remove useless signals such as clutter), then denoise the data and extract a variety of time and frequency domain features, and analyze the linear relationship between the features and the leakage rate.

[0063] Step 2: Combine the time-frequency domain feature parameters extracted in step 1 with the support vector regression and back propagation neural network methods to establish multivariate regression models between the time-frequency characteristics of the acoustic emission signal and the leakage rate under variable pressure.

[0064] Step 3: According to the valve internal leakage standard, the leakage level is divided according to the valve internal leakage acoustic emission signals collected at different leakage rates, and the leakage level is predicted using three neural networks to determine the leakage amount of the valve internal leakage.

[0065] As an implementable method, in step 1, the internal leakage of the valve is simulated through an experimental environment, the internal leakage acoustic emission signals of the valve under different leakage rates and different pressures are collected, the internal leakage acoustic emission signals of the valve are analyzed, and the frequency band range of the useful signal is determined, thereby removing unnecessary noise interference.

[0066] As an implementable method, the valve internal leakage acoustic emission signal collection method adopted is as follows:

[0067] Build a valve internal leakage simulation experimental environment consisting of an air compressor, pressure vessel, pipeline, valve, pipeline and flow meter, such as Figure 2 As shown;

[0068] Air compressor is used to generate air of a certain pressure and store it in a pressure vessel;

[0069] The gas at a fixed pressure is sent into the valve through the connecting pipe, and the leakage rate is simulated by controlling the valve opening;

[0070] Use the flow meter at the rear end of the valve to record the leakage rate of the valve;

[0071] Attach the acoustic emission sensor to the outer wall of the valve to collect data on leakage acoustic emission signals;

[0072] The leakage is simulated by controlling the air compressor to change the gas pressure in the pressure vessel and the valve opening to collect the acoustic emission signals of valve leakage at different pressures and leakage rates.

[0073] The feature extraction of the leakage acoustic emission signal under different leakage rates and pressures is performed, and the three features of the maximum amplitude (direct observation), root mean square and standard deviation of the leakage acoustic emission signal are extracted in the time domain. The calculation formulas for the standard deviation and root mean square are:

[0074]

[0075] In the frequency domain, five features including center of gravity frequency, spectrum kurtosis, root mean square frequency, standard deviation frequency and spectrum area are extracted, and the calculation formulas are:

[0076]

[0077] Where FC represents the center of gravity frequency, f represents the signal frequency, P(f) represents the power spectrum of the signal; K is the spectral kurtosis, x i is the spectrum amplitude, x is the mean of the amplitude, MSF is the mean square frequency, VF is the frequency standard deviation, and S is the spectrum area.

[0078] The third-order cumulative amount and wavelet packet information entropy of the leakage acoustic emission signal are extracted in the time-frequency domain, and the calculation formulas are:

[0079] c 3x (τ1,τ2)=m 3x (τ1,τ2)=E{x(k)x(k+τ1)x(k+τ2)};

[0080]

[0081] By extracting these 10 features in the time domain, frequency domain, and time-frequency domain, the linear relationship between different feature quantities and leakage rate is analyzed under the same pressure condition. After analysis, it is found that these 10 feature quantities have a certain correlation with the leakage rate, such as Figures 3 to 12 As shown in the figure, these 10 feature quantities can all be used as features for predicting leakage rate. As an implementable method, in step 2, a feature matrix is ​​first constructed for the 10 feature quantities obtained in step 1, and then the front-end pressure of the valve is combined as the model input; then a verification experiment is carried out on the trained model to verify the adaptability of the model.

[0082] As an implementable method, in step 3, a method for predicting the internal leakage level of a valve is proposed in view of the fact that the valve leakage rate prediction model has a large relative error when predicting a small leakage rate. The method for predicting the valve leakage level specifically includes:

[0083] First, the control valve leakage standard is specified according to the American Fluid Control Society standard, and the maximum leakage is stipulated;

[0084] In combination with the research on valve internal leakage, the valve internal leakage level is divided into four different levels according to the range of leakage: very small, small, medium and large, corresponding to less than 0.01% of the rated flow, 0.01% to 0.05% of the rated flow, 0.05% to 0.1% of the rated flow and greater than 0.1% of the rated flow respectively;

[0085] The acoustic emission signal of valve leakage is converted into a time-frequency image, and the deep features of the image are extracted using a convolutional neural network.

[0086] Convert the leakage signal into a time-frequency image and reduce the amount of computation through a convolutional neural network;

[0087] In order to obtain a higher accuracy, the present invention adopts three neural network voting methods (simultaneously) to predict the leakage level:

[0088] ResNext50 (32×4d) residual neural network, DenseNet dense connection network and ResNet50 network (used simultaneously) are used to train time-frequency image data;

[0089] Soft voting is performed on the three trained models, that is, the class with the largest probability sum among all voting results is taken as the result to predict the leakage level.

[0090] During implementation, a valve internal leakage simulation experimental system is first built to collect leakage acoustic emission signals under different pressures and leakage rates. Then, the leakage acoustic emission signals are analyzed to determine the frequency band range of the useful signal and then perform denoising. Finally, feature extraction is performed on the denoised leakage acoustic emission signal to extract 10 features, including the maximum amplitude, root mean square and standard deviation in the time domain, the centroid frequency, spectrum kurtosis, root mean square frequency, standard deviation frequency and spectrum area in the frequency domain, the third-order cumulant and wavelet packet information entropy in the time-frequency domain, and the linear relationship between the 10 features and the leakage rate is analyzed.

[0091] The feature matrix is ​​constructed, and the neural network model and support vector regression model are trained in combination with the valve front-end pressure to achieve the prediction of leakage rate. In view of the large relative error when predicting small leakage rate, the method for predicting the internal leakage level of the valve proposed in the present invention is adopted, the leakage level is divided according to the international standard, the collected leakage acoustic emission signal is converted into a time-frequency image, and the ResNext50 (32×4d) residual neural network, DenseNet dense connection network and ResNet50 network are used to train the time-frequency image data, and the three trained models are soft-voted, that is, the class with the largest probability sum of all voting results is taken as the result to achieve the prediction of leakage level.

[0092] The present invention can perform remote online detection of the internal leakage state of the valve and predict the internal leakage rate of the valve, thereby ensuring the safety of maintenance personnel, fundamentally improving the level of automation and intelligence, and having good practicality and safety benefits.

[0093] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for detecting internal leakage of nuclear power valves based on the time-frequency characteristics of acoustic emission signals, characterized in that: By collecting the acoustic emission signal generated when the valve leaks, the time domain, frequency domain and time-frequency domain features of the leakage signal are extracted, the linear relationship between the features and the valve leakage rate is analyzed, and the leakage rate and leakage level are predicted.

2. The method for detecting internal leakage of nuclear power valves based on the time-frequency characteristics of acoustic emission signals according to claim 1 is characterized in that: include: Maximum amplitude, root mean square, standard deviation in the time domain, center of gravity frequency, spectrum kurtosis, root mean square frequency, standard deviation frequency, spectrum area in the frequency domain, third-order cumulant in the time-frequency domain, and wavelet packet information entropy.

3. The method for detecting internal leakage of nuclear power valves based on the time-frequency characteristics of acoustic emission signals according to claim 1 or 2, characterized in that: The method specifically includes: Step 1: Obtain the valve internal leakage acoustic emission signals under different pressures and different leakage rates, analyze and extract the features of the valve internal leakage acoustic emission signals, denoise the data and extract a variety of time-frequency domain features, and analyze the linear relationship between the features and the leakage rate; Step 2: Combine the time-frequency domain feature parameters extracted in step 1 with the support vector regression and back propagation neural network methods to establish multivariate regression models between the time-frequency characteristics of the acoustic emission signal and the leakage rate under variable pressure; Step 3: According to the valve internal leakage standard, the leakage level is divided according to the valve internal leakage acoustic emission signals collected at different leakage rates, and the leakage level is predicted using three neural networks to determine the leakage amount of the valve internal leakage.

4. The method for detecting internal leakage of nuclear power valves based on the time-frequency characteristics of acoustic emission signals according to claim 3 is characterized in that: In step 1, the internal leakage of the valve is simulated through an experimental environment, and the acoustic emission signals of the internal leakage of the valve under different leakage rates and different pressures are collected. The acoustic emission signals of the internal leakage of the valve are analyzed to determine the frequency band range of the adopted signal, thereby removing excess noise interference.

5. The method for detecting internal leakage of nuclear power valves based on the time-frequency characteristics of acoustic emission signals according to claim 3 or 4, characterized in that: The methods for collecting acoustic emission signals of valve internal leakage include: Build a valve internal leakage simulation experimental environment consisting of an air compressor, pressure vessel, pipeline, valve, pipe, and flow meter; Air compressor is used to generate air of a certain pressure and store it in a pressure vessel; The gas at a fixed pressure is sent into the valve through the connecting pipe, and the leakage rate is simulated by controlling the valve opening; Use the flow meter at the rear end of the valve to record the leakage rate of the valve; Attach the acoustic emission sensor to the outer wall of the valve to collect data on leakage acoustic emission signals; The leakage is simulated by controlling the air compressor to change the gas pressure in the pressure vessel and the valve opening to collect the acoustic emission signals of valve leakage at different pressures and leakage rates.

6. The method for detecting internal leakage of nuclear power valves based on the time-frequency characteristics of acoustic emission signals according to claim 5 is characterized in that: In the frequency domain, five features including center of gravity frequency, spectrum kurtosis, root mean square frequency, standard deviation frequency and spectrum area are extracted, and the calculation formulas are: Where FC is the center frequency, f is the signal frequency, P(f) is the power spectrum of the signal, K is the spectral kurtosis, and x i is the spectrum amplitude, is the mean of the amplitude, MSF is the mean square frequency, VF is the standard deviation of the frequency, and S is the spectrum area.

7. The method for detecting internal leakage of nuclear power valves based on the time-frequency characteristics of acoustic emission signals according to claim 5 is characterized in that: The third-order cumulative amount and wavelet packet information entropy of the leakage acoustic emission signal are extracted in the time-frequency domain, and the calculation formulas are: c 3x (τ1,τ2)=m 3x (τ1,τ2)=E{x(k)x(k+τ1)x(k+τ2)}; Where m is the autocorrelation sequence, τ1 and τ2 are offsets; The wavelet packet entropy calculation formula is as follows: Among them, p 4,k =E 4,k / E4,E 4,k is the energy of k nodes in the fourth layer, and E4 is the sum of the energy of each node in the fourth layer.

8. The method for detecting internal leakage of nuclear power valves based on the time-frequency characteristics of acoustic emission signals according to claim 3 is characterized in that: In step 2, a feature matrix is ​​constructed for the 10 feature quantities obtained in step 1, and then the front-end pressure of the valve is used as the model input. After that, a verification experiment is carried out on the trained model to verify the adaptability of the model.

9. The method for detecting internal leakage of nuclear power valves based on the time-frequency characteristics of acoustic emission signals according to claim 3 is characterized in that: In step 3, the method for predicting the valve leakage level specifically includes: To stipulate the maximum leakage volume; The internal leakage level of the valve is divided into different levels according to the range of leakage, corresponding to different rated flow rates; The acoustic emission signal of valve leakage is converted into a time-frequency image, and the deep features of the image are extracted using a convolutional neural network. Convert the leakage signal into a time-frequency image and reduce the amount of computation through a convolutional neural network; ResNext50 (32×4d) residual neural network, DenseNet dense connection network and ResNet50 network are used to train time-frequency image data; The three trained models are soft-voted, and the class with the largest probability sum among all voting results is taken as the result to predict the leakage level.

10. The method for detecting internal leakage of nuclear power valves based on the time-frequency characteristics of acoustic emission signals according to claim 9, characterized in that: The levels divided according to the range of leakage include four different levels: extremely small, small, medium and large, which correspond to less than 0.01% of the rated circulation, 0.01% to 0.05% of the rated circulation, 0.05% to 0.1% of the rated circulation, and greater than 0.1% of the rated circulation.

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