An electromagnetic vortex flowmeter signal processing method based on mutual information

Abstract

The application is a kind of electromagnetic vortex flowmeter signal processing method based on mutual information, which is used for detecting whether the steam generator leaks or not, and ensuring the safe operation of the whole nuclear power plant. By calculating the amplitude range of a time domain signal, the amplitude range is equally divided into 150 segments, the time domain signal is divided into two groups of data in time sequence, the probability of the amplitude distribution of the two groups of data in each segment is calculated, and the probability of the two groups of data in the same amplitude of each segment is calculated, then the mutual information of the signal in the segment is calculated, the mutual information results of multiple signals are processed by sliding median filtering, and the final result is compared with the threshold value to determine whether the steam generator leaks or not.

Description

Technical Field

[0001] The invention belongs to the technical field of steam generator leakage detection in fast reactors, and particularly relates to a method for detecting whether flowing liquid metallic sodium contains hydrogen generated by steam generator leakage based on an electromagnetic vortex flowmeter. Background Art

[0002] Energy is a vital material foundation for human survival and development. It plays a crucial role in industry, agriculture, national defense, transportation, and other sectors, and holds a crucial position in international competition. Fourth-generation nuclear power technology, fast neutron reactors (abbreviated as "fast reactors"), will increase uranium resource utilization from the current 1% to over 60%, significantly improving uranium resource utilization. Based on the world's currently proven natural uranium reserves, it is estimated that the uranium resources required for fast reactors will be sustainable for over 3,000 years. Liquid sodium metal is a common coolant in fast reactors. Heat exchange between liquid sodium and water occurs in the steam generator, making it a key component of fast reactors. However, due to long-term operation under harsh conditions of high temperature and high pressure, steam generators can crack or damage, leading to medium leaks. A sodium bubble detector, based on the vortex electromagnetic induction principle, is one of the instruments used to monitor steam generator leaks. It detects bubbles in flowing liquid sodium and offers high accuracy, high sensitivity, and ease of use.

[0003] Existing literature “Peak-to-peak standard deviation based bubble detection method in sodium flow with electromagnetic vortex flowmeter” (Xu W, Review of Scientific Instruments, 2019, Vol. 90). Starting from the amplitude of the sensor output signal, this paper selects a certain time length as the calculation period, and judges whether the steam generator is leaking based on the size of the peak-to-peak standard deviation of the signal of multiple calculation periods. Existing literature “Bubble detection in sodium flow using EVFM and correlation coefficient calculation” (Xu W, Annals of Nuclear Energy, 2019, Vol. 129). This paper uses the spectrum transformation method to calculate the frequency of the signal, calculates the data length of a signal period based on the frequency, selects the data of the two latest adjacent period signals, calculates the correlation coefficient, filters and averages multiple correlation coefficients, compares them with the threshold, and judges whether the steam generator is leaking. Existing literature “Signal processing methodbased on energy ratio for detecting leakage of SG using EVFM” (Xu W, Nuclear Engineering and Technology, 2020, Vol. 52). This paper calculates the upper and lower envelopes of the primary instrument signal, averaging them to determine the output signal baseline. This baseline is then removed from the primary signal to obtain the flow signal. The energy of the flow signal and the energy of the primary instrument output signal are then calculated separately. The energy ratio is calculated, using the flow signal energy as the numerator and the primary instrument output signal energy ratio as the denominator. This energy ratio is compared with a set threshold to determine whether the steam generator is leaking.

[0004] The existing literature, "Signal processing method of bubble detection in sodium flow based on inverse Fourier transform to calculate energy ratio" (Xu W, Annals of Nuclear Energy, 2019, Vol. 129), uses fast Fourier transform to calculate the frequency of the primary instrument output signal. This paper rationally selects the signal length used for the fast Fourier transform to expand the frequency variation range of the primary instrument output signal when bubbles are present in sodium. This paper establishes a relationship between frequency resolution and frequency conversion range, and uses this relationship to determine whether a steam generator leak is occurring. Summary of the Invention

[0005] The present invention aims to determine whether a steam generator is leaking by detecting bubbles within the steam generator. A threshold is calculated based on existing methods, and when the calculated result of the signal collected by the A / D is less than the set threshold, an alarm signal is issued, indicating that the steam generator is leaking.

[0006] This paper proposes a signal processing method for electromagnetic vortex flowmeter based on mutual information, which can effectively determine whether a steam generator leaks.

[0007] The technical solution of the present invention is as follows: The bubble detector in sodium mainly consists of a primary instrument and a secondary instrument. The output signal of the primary instrument comprises a DC signal and an AC signal. The profile of the primary output signal approximates a sine wave. By analyzing and processing the output signal, it is determined whether the steam generator is leaking. When the liquid sodium contains no bubbles, the output signal of the primary instrument approximates a sine wave signal. When the sodium contains bubbles, the output signal of the primary instrument is distorted and no longer an approximate sine wave signal, and the signal regularity deteriorates. Therefore, based on the characteristics of the signal, the output signal of the primary instrument is processed using a mutual information method to determine whether the steam generator is leaking.

[0008] The specific process of the signal processing method of the electromagnetic vortex flowmeter based on mutual information is as follows:

[0009] 600 data points are selected each time, and the amplitude range of the 600 data points is calculated. The amplitude range is divided into 150 segments. The continuously collected data is divided into two segments according to the time sequence, which are recorded as variables X and Y respectively. The probability P(x i ) and P(y i ), and P(x i ,y i ), and then calculate the mutual information, where the formula for mutual information is as follows:

[0010]

[0011] Where P(x i ) and P(y i ) is a time domain sequence of a signal X(n) = [X(1), X(2), .... X.. N (and Y(n) = [Y(1), Y(2), .... Y(N)]], and the probability of occurrence of each segment of data after segmenting according to the specified number of segments. N is the data length and Z is the total number of segments.

[0012] The calculated data is updated by sliding, discarding the first 300 points of data each time and adding 300 new points at the end. The mutual information is then recalculated. The calculated mutual information results are then subjected to a sliding median filter. Each time, 15 mutual information results are selected and sorted by size. The middle 9 results are averaged as the final output. The 15 selected mutual information results are updated, one point at a time, and the sliding filter result is recalculated. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 Sensor structure diagram of the sodium bubble detector.

[0014] Figure 2 The positional relationship between the vortex that produces the minimum value of the vortex signal and the working electrode.

[0015] Figure 3 The positional relationship between the vortex that produces the maximum value of the vortex signal and the working electrode.

[0016] Figure 4 Sodium flow rate 6.7m 3 Time domain diagram with a time length of 0.6s at / h.

[0017] Figure 5 Sodium flow rate 6.7m 3 Time domain diagram with a time length of 0.6s at / h.

[0018] Figure 6 Flowchart based on mutual information algorithm.

[0019] Figure 7 Sodium flow 3.5m 3 / h based on the mutual information signal processing method.

[0020] Figure 8 Sodium flow 4.5m 3 / h based on the mutual information signal processing method.

[0021] Figure 9 Sodium flow 5.5m3 / h based on the mutual information signal processing method.

[0022] Figure 10 Sodium flow 6.7m 3 / h based on the mutual information signal processing method. DETAILED DESCRIPTION

[0023] The present invention will be further described below with reference to the accompanying drawings.

[0024] The design concept of the present invention is as follows: When the steam generator is leaking and the liquid sodium metal does not contain bubbles generated by the sodium-water reaction, the output signal of the primary instrument of the electromagnetic vortex flowmeter approximates a sinusoidal signal. When the steam generator is leaking, the liquid sodium metal contains bubbles generated by the sodium-water reaction, and the output signal of the primary instrument becomes a gas-liquid two-phase flow signal. By comparing the characteristics of the two output signals, it can be found that when the output signal of the primary instrument becomes a gas-liquid two-phase flow signal, the signal is no longer approximately sinusoidal and its regularity deteriorates. Therefore, based on the concept of mutual information, the amplitude range of a time domain signal is calculated. The amplitude range is divided into 150 equal segments. The time domain signal is divided into two segments according to chronological order. The probability that the amplitude of the two segments is distributed in each segment is calculated, as well as the probability that the amplitude of the two segments is the same in each segment. Then, the mutual information value of the time domain signal is calculated. By comparing the mutual information values ​​when the steam generator is leaking and when the steam generator is leaking, an appropriate threshold is selected as the basis for determining whether the steam generator is leaking, thereby achieving the purpose of determining whether the steam generator is leaking.

[0025] Figure 1 Diagram of the sensor structure of a sodium bubble detector. The sensor is an all-metal structure, primarily consisting of a metal pipe, a permanent magnet, a vortex generator, and electrodes. The permanent magnet generates a magnetic field perpendicular to the paper and oriented inward. The metal pipe is made of non-magnetic stainless steel with an inner diameter of 40 mm. The permanent magnet generates a magnetic field that passes through the liquid sodium pipe and can operate at temperatures up to 600°C. The vortex generator utilizes a trapezoidal columnar structure, which not only generates an AC signal in the conductive liquid under the permanent magnetic field but also effectively prevents stratification of the conductive liquid and gas as they flow through the magnetic field. Electromotive force signals are collected using measuring electrodes (consisting of a reference electrode and a working electrode). The working electrode is located at the center of the permanent magnetic field, 46 mm from the vortex generator. The reference electrode is located upstream of the working electrode, 31 mm from the vortex generator. These electrodes work together to collect eddy current signals. The magnetic field generated by the permanent magnet is parallel to the axis of the vortex generator.

[0026] Figure 2It is the positional relationship between the vortex where the sensor signal produces a minimum value and the working electrode. When the midpoint of the line connecting the centers of two adjacent vortices is directly below the working electrode, and the vortex rotates counterclockwise relative to the plane, the negatively charged particles in the liquid will move toward the working electrode, generating a minimum point of a complete cycle signal. The positional relationship between the working electrode and the vortex is shown in the figure. Figure 2 When the midpoint of the line connecting the centers of two adjacent vortices is directly below the working electrode, and the vortex rotates counterclockwise relative to the plane, the negatively charged particles in the liquid will move toward the working electrode, generating a maximum point of a complete cycle signal. The positional relationship between the working electrode and the vortex is shown in the figure. Figure 3 As shown in Figure 1. The “×” represents a magnetic field pointing inward perpendicular to the paper. The circle represents a vortex, and the arrow represents the direction of the vortex's rotation. The hollow arrow represents the direction of motion of the charged particle.

[0027] When there is no vortex generator, the sensor collects a pure electromagnetic signal. When the magnetic field strength is constant, the collected signal is a DC signal. However, when there are bubbles in the liquid sodium, the DC signal cannot effectively reflect the impact of the bubbles on the DC signal. Compared with the vortex street signal generated by the vortex generator, it can better reflect the impact of bubble noise on the signal, which is convenient for the subsequent study of signal processing methods.

[0028] According to the principle of vortex signal generation, when the flowing liquid flows through the nonlinear cylinder, the relationship between the flow velocity v and the signal frequency f is as follows:

[0029]

[0030] Where Sr is the Strouhal number related to the frequency and velocity of the flowing liquid; v is the velocity of the flowing liquid; d is the width of the nonlinear cylinder's incident cross-section; and m is the ratio of the area on both sides of the nonlinear cylinder to the cross-section on both sides of the pipe.

[0031] Combined with the sensor of the bubble detector in sodium in this article, the vortex generator is the corresponding nonlinear cylinder. Assuming that the inner diameter of the pipe through which the liquid metal sodium flows is D, then the instantaneous flow volume of the fluid is q v , from this we can get the relationship between instantaneous flow and frequency in the sodium bubble detector instrument of this article:

[0032]

[0033] k is the instrument coefficient, which can be obtained through calibration fitting at different flow rates. Therefore, under constant working conditions and when the Reynolds number is within a certain range, the sodium bubble detector instrument can reflect the flow rate changes of the flowing liquid sodium in the pipeline.

[0034] Figure 4 and Figure 5The output signals of the sensors are those with and without gas, respectively. When the steam generator is leak-free, the sensor output signals are more regular than those when leaking. Mutual information is a measure of the correlation between two systems. Therefore, by calculating the mutual information results before and after a certain period of time, we can determine whether the steam generator is leaking.

[0035] Figure 6 Flowchart of the method for processing sodium bubble signals based on mutual information, the specific steps are as follows:

[0036] (1) Select 600 points to obtain the time domain signal. When the length is equal to 600, calculate the amplitude range of the 0.6-second flow signal and divide the amplitude range into 150 equal segments.

[0037] (2) The continuously collected data are divided into two groups according to the time sequence, and the probability that the amplitude of each group of data is distributed in each segment and the probability that the two groups of data have the same amplitude in each segment are calculated.

[0038] (3) Calculate the mutual information of this segment of the signal based on the mutual information formula, where the mutual information calculation formula is as follows

[0039]

[0040] Where P(x i ) is the probability of the amplitude of the first 300 time domain sequences X(n) = [X(1), X(2), ... X(300)] being distributed in each segment, P(y i ) is the probability that the amplitude of the next 300 time domain sequences Y(n)=[Y(1),Y(2),......Y(300)] is distributed in each segment, P(x i ,y i ) is the probability that the amplitude of the two groups of data is the same in each segment. Z is the total number of segments, here Z = 150.

[0041] (4) Perform sliding update on 600 selected data points, i.e. discard the first 300 data points and add 300 data points at the end to reconstruct 600 data points, calculate the mutual information corresponding to the updated data, and save the calculation results into the signal mutual information array.

[0042] (5) Repeat the calculation according to the above steps to obtain the mutual information value of each time period.

[0043] (6) When the number of calculated signal mutual information values ​​is equal to 15, select 15 consecutive mutual information results for sorting, remove the smallest 3 and largest 3 results, calculate the average of the middle 9 mutual information values, and use it as the final signal mutual information calculation result.

[0044] (7) Determine whether the calculated signal mutual information result is less than the set threshold. If it is less than or equal to the threshold, it is determined that the steam generator has leaked and an alarm signal is issued. If the signal mutual information value is greater than the threshold, the 15 selected signal mutual information for sliding average filtering are updated by sliding, that is, the first signal mutual information is discarded and a new signal mutual information is added at the end, and the 15 signal mutual information are recombined for median filtering.

[0045] Figure 7 、 Figure 8 、 Figure 9 、 Figure 10 The following are the results of the electromagnetic vortex flowmeter signal processing method based on mutual information for data at different sodium flow rates. The horizontal axis in the figure represents time (t / s), and the vertical axis represents the result of algorithmic processing of the sensor output signal transmitted from the electromagnetic vortex flowmeter secondary instrument to the upper machine position. The output results show that when there is no leak in the steam generator, the mutual information results are all greater than 0.777. When there is a leak in the steam generator, the mutual information results under different leakage conditions will be less than the threshold. Therefore, when there is no leak in the steam generator, the output signals of different sodium flow rates are collected and processed using the electromagnetic vortex flowmeter signal processing method based on mutual information. A value less than the minimum mutual information result and a certain margin are retained as the threshold for determining whether a leak has occurred. Based on the above method, the threshold is finally determined to be T = 0.777.

Claims

1. A signal processing method for an electromagnetic vortex flowmeter based on mutual information, characterized in that: Calculate the amplitude range of a time domain signal, divide the amplitude range into 150 equal segments, and divide the time domain signal into two segments according to the time sequence. Calculate the probability that the amplitudes of the two segments are distributed in each segment, and the probability that the amplitudes of the two segments are the same in each segment. Then calculate the mutual information value of the time domain signal. The mutual information result of this segment of the signal is calculated based on the mutual information formula. The calculation formula of mutual information is as follows: In the formula For the first 300 time domain sequences The probability of the amplitude being distributed in each segment, For the next 300 time domain sequences The probability of the amplitude being distributed in each segment, is the probability that the two sets of data have the same amplitude in each segment, is the total number of segments, where ; Based on the mutual information results, it is determined whether the steam generator is leaking.

2. The electromagnetic vortex flowmeter signal processing method based on mutual information according to claim 1, characterized in that: (1) Select 600 points to obtain the time domain signal. When the length is equal to 600, calculate the amplitude range of the 0.6-second flow signal and divide the amplitude range into 150 segments. (2) Divide the continuously collected data into two groups according to the time sequence, and calculate the probability that the amplitude of each group of data is distributed in each segment, as well as the probability that the two groups of data have the same amplitude in each segment; (3) Perform sliding update on 600 selected data points, i.e. discard the first 300 data points and add 300 data points at the end to reconstruct 600 data points, calculate the mutual information corresponding to the updated data, and save the calculation results into the signal mutual information array; (4) Repeat the above steps to obtain the signal entropy value of each time period; (5) When the number of calculated signal mutual information values ​​is equal to 15, select 15 consecutive signal entropy results for sorting, remove the smallest 3 and largest 3 results, calculate the average of the middle 9 mutual information values, and use it as the final signal mutual information calculation result; (6) Determine whether the calculated signal mutual information result is less than the set threshold. If it is less than or equal to the threshold, it is determined that the steam generator has leaked and an alarm signal is issued. If the signal mutual information value is greater than the threshold, the 15 selected signal mutual information for sliding average filtering are updated by sliding, that is, the first signal mutual information is discarded, and a new signal mutual information is added at the end, and the 15 signal mutual information are recombined for median filtering.

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