A method for calculating correction frequency band in in-situ calibration of vortex-shedding generator permanent magnet sodium flowmeter

Abstract

A method for calculating the correction frequency band in situ calibration of vortex-shedding generator permanent magnet sodium flowmeter, using the amplitude-frequency characteristics of cross power spectral density, more accurately calculates the correction frequency band, including the maximum frequency and the starting frequency of the correction frequency band; The theoretical calculation formula and specific steps are given. The signals in the correction frequency band are used to calculate the cross correlation, and the cross correlation flow under each flow calculated is close to the standard flow, thereby reducing the nonlinear error in the in situ calibration of vortex-shedding generator permanent magnet sodium flowmeter.

Description

Technical Field

[0001] This invention relates to the field of flow detection, and in particular to a method for calculating the correction frequency band during in-situ calibration of a permanent magnet sodium flow meter without vortex generator. Background Technology

[0002] Sodium-cooled fast reactors (SLFRs) are currently among the cleanest and safest fourth-generation advanced nuclear reactors in the world, capable of increasing uranium resource utilization to 60%-70%. SLFRs typically employ a sodium-sodium-water triple loop design. High-performance liquid metallic sodium is used as the coolant and heat transfer agent in the reactor core. To ensure the safe operation of the fast reactor, permanent magnet sodium flow meters based on Faraday's law of electromagnetic induction are used to monitor the sodium flow rate in the primary and secondary loops. The measuring electrodes of the permanent magnet sodium flow meter are installed at both ends of the pipe cross-section, perpendicular to the diameter of the magnetic field. It picks up the induced electromotive force generated by the conductive fluid cutting magnetic field lines; the amplitude of this electromotive force is directly proportional to the flow rate. Where D is the pipe inner diameter, B is the magnetic flux density, and k is the instrument coefficient. Since the temperature of liquid sodium remains between 250-550℃ year-round, the permanent magnet sodium flow meter operates in this high-temperature environment for extended periods. This causes demagnetization of the permanent magnet, resulting in a decrease in magnetic flux density and causing the measured flow rate to deviate from the standard value. Therefore, the permanent magnet sodium flow meter must be calibrated periodically to eliminate this deviation. However, the permanent magnet sodium flow meter installed in the stack is not removable, so in-situ calibration is necessary. To achieve this, additional electrodes (called cross-correlation electrodes) are added to the permanent magnet sodium flow meter, and the cross-correlation method is used to achieve in-situ calibration.

[0003] The core of the cross-correlation method is signal time delay estimation. Cross-correlation electrodes collect AC signals generated by fluid velocity fluctuations. By estimating the similarity of these signals, the time it takes for the fluid to travel between the preceding and following cross-correlation electrodes (two pairs of signal electrodes on the same sensor or two pairs of signal electrodes arranged on separate preceding and following sensors) is used to reflect the average velocity of the fluid. In the formula, L is the distance between the two pairs of cross-correlation electrodes, and τ is the signal delay (passage time or delay time).

[0004] The specific in-situ calibration methods differ depending on the diameter of the permanent magnet sodium flow meter. For smaller diameter permanent magnet sodium flow meters, a vortex generator is often installed in the flow tube to enhance the disturbance signal, which is beneficial for implementing cross-correlation methods.

[0005] For large-diameter permanent magnet sodium flow meters (e.g., DN150, DN200, DN300), the flow rate within the pipeline is typically high. Adding obstructions to enhance fluid turbulence would cause significant pressure loss and pose a risk of obstruction detachment. Therefore, in-situ calibration can only be performed using the internal fluid turbulence; this is known as in-situ calibration of vortex-free permanent magnet sodium flow meters. However, when the magnetic field of a vortex-free permanent magnet sodium flow meter is short, the Lorentz force distorts the magnetic field, causing deformation of the fluid velocity distribution across the pipe cross-section and resulting in severe nonlinearity in its measurement characteristics.

[0006] To achieve in-situ calibration of vortex-free permanent magnet sodium flow meters, the problem of large nonlinear errors must be addressed. A Chinese invention patent discloses a nonlinear correction method for in-situ calibration of permanent magnet sodium flow meters based on signal frequency band selection (Xu Kejun, Yu Xinlong, Huang Ya, Wu Wenkai. A nonlinear correction method for in-situ calibration of permanent magnet sodium flow meters based on signal frequency band selection, application number: 202011085046.X, application date: 2020.10.12). Addressing the nonlinear characteristics between the cross-correlation flow rate and the standard flow rate (also known as the reference flow rate) that occur during in-situ calibration of large-diameter vortex-free permanent magnet sodium flow meters in long straight pipe sections, the influence of the magnetic field on the flow field is theoretically analyzed, resulting in an "M-shaped" velocity distribution within the pipe cross-section. Based on the phase frequency characteristics of the cross-power spectral density of the two signals, the cross-correlation flow distribution of each frequency signal is calculated, leading to a turbulence distribution model for the pipe cross-section. The model shows that the cross-correlation flow of signals in certain frequency bands is close to the standard flow. Therefore, a nonlinear correction method based on frequency band selection is proposed, which uses signals in different frequency bands to perform cross-correlation calculations under different flow rates, thereby achieving the correction of nonlinear characteristics.

[0007] In other words, the physical model of the "M-shaped" average velocity indicates that signals of different frequencies represent the cross-correlation flow rates of different regions of the pipe cross-section. Low-frequency signals mainly characterize the turbulent flow near the pipe wall, with cross-correlation flow rates greater than or equal to the standard flow rate. High-frequency signals mainly characterize the turbulent flow near the pipe center, with cross-correlation flow rates less than or equal to the standard flow rate. When the fluid velocity changes, the average velocity distribution of the turbulence within the magnetic field also changes accordingly; the higher the velocity, the more pronounced the "M-shaped" average velocity distribution. However, regardless of the velocity change, there is always a region on the pipe cross-section where the sodium flow velocity is close to the standard velocity, and the corresponding signal frequency band always has a cross-correlation flow rate close to the standard flow rate. Therefore, a nonlinear correction method based on signal frequency band selection is proposed. Summary of the Invention

[0008] However, the Chinese invention patent mentioned above determines the frequency band (called the correction band) entirely by manually observing the phase frequency characteristics of the cross power spectral density of the two signals and calculating the cross-correlation flow distribution diagram of each frequency signal, without providing the theoretical formula and specific steps for the calculation.

[0009] The technical solution of this invention is as follows:

[0010] This invention provides a method for calculating the correction frequency band for in-situ calibration of a vortex-free permanent magnet sodium flow meter. Utilizing the amplitude-frequency characteristics of the cross-power spectral density, the correction frequency band, including its maximum and starting frequencies, is calculated relatively accurately. The theoretical calculation formula and specific steps are provided. By using the signal from the correction frequency band for cross-correlation calculations, the calculated cross-correlation flow rates at various flow rates are close to the standard flow rates, thereby reducing nonlinear errors in the in-situ calibration of the vortex-free permanent magnet sodium flow meter.

[0011] The advantages of this invention are:

[0012] The present invention provides a method for calculating the correction frequency band for in-situ calibration of a permanent magnet sodium flow meter without vortex generator. This method can calculate the correction frequency band more accurately without relying on manual observation and trial and error, thereby improving accuracy and efficiency. Attached Figure Description

[0013] Figure 1 These are cross-sectional and side views of the sensor for a permanent magnet sodium flow meter without vortex generators.

[0014] Figure 2(a) shows the standard flow rate of 100 m³ / h. 3 Cross-correlation flow curves of signals at various frequencies at / h;

[0015] Figure 2(b) shows the standard flow rate of 150 m³ / h. 3 Cross-correlation flow curves of signals at various frequencies at / h;

[0016] Figure 2(c) shows the standard flow rate of 200 m³ / h. 3 Cross-correlation flow curves of signals at various frequencies at / h;

[0017] Figure 2(d) shows the standard flow rate of 232 m³ / h. 3 Cross-correlation flow curves of signals at various frequencies at / h;

[0018] Figure 2(e) shows the standard flow rate of 280 m³ / h. 3 Cross-correlation flow curves of signals at various frequencies at / h;

[0019] Figure 3(a) shows the standard flow rate of 100 m³ / h. 3 Signal spectrum at / h;

[0020] Figure 3(b) shows the standard flow rate of 150 m³ / h. 3 Signal spectrum at / h;

[0021] Figure 3(c) shows the standard flow rate of 200 m³ / h. 3 Signal spectrum at / h;

[0022] Figure 3(d) shows the standard flow rate of 232 m³ / h. 3 Signal spectrum at / h;

[0023] Figure 3(e) shows the standard flow rate of 280 m³ / h. 3 Signal spectrum at / h;

[0024] Figure 4(a) shows the standard flow rate of 100 m³ / h. 3 Normalized cross-power spectrum at / h;

[0025] Figure 4(b) shows the standard flow rate of 150 m³ / h. 3 Normalized cross-power spectrum at / h;

[0026] Figure 4(c) shows the standard flow rate of 200 m³ / h. 3 Normalized cross-power spectrum at / h;

[0027] Figure 4(d) shows the standard flow rate of 232 m³ / h. 3 Normalized cross-power spectrum at / h;

[0028] Figure 4(e) shows the standard flow rate of 280 m³ / h. 3 Normalized cross-power spectrum at / h;

[0029] Figure 5 This is the derivation diagram of the starting frequency point f0 of the correction band, and it is also the flow rate of 280m³ / h. 3 The cross-power spectrum normalized to its maximum value at / h;

[0030] Figure 6 It is the frequency band where the cross-correlation flow under each flow is close to the standard flow (reference flow). Specific implementation methods

[0031] The invention will now be further described with reference to the accompanying drawings.

[0032] 1. Structural components of a vortex-free permanent magnet sodium flowmeter

[0033] The sensor of the vortex-free permanent magnet sodium flow meter uses a cast aluminum-nickel-cobalt permanent magnet alloy with high magnetic energy, high stability, high temperature resistance, and radiation resistance as the permanent magnet. Electromagnetic pure iron is used for the yoke and poles, and the surface is treated with anti-oxidation. The pole face length of the permanent magnet is 2D (D is the inner diameter of the pipe). A schematic diagram of the cross-correlation electrode arrangement for in-situ calibration in the vortex-free permanent magnet sodium flow sensor is shown below. Figure 1 As shown.

[0034] Electrodes 1-1 and 1-2 are a pair of cross-correlation electrodes (hereinafter referred to as electrode C1; other electrodes are similar), measuring one signal. The combination of electrodes C1 and C2 is used for cross-correlation measurement, hereinafter referred to as electrode group C1&2; other electrode combinations are similar. These cross-correlation electrodes are positioned at a 45° angle to the flow tube (within...). Figure 1 The horizontal line in the right-hand diagram (serving as the reference line for the angle) is vertically welded to the pipe wall, mainly because the signal strength is greater at 45°. Electrode C1 is located 50mm upstream of the center line of the magnet, and C2 is located 75mm downstream of C1. Electrodes C2, C3, C4, and C5 are evenly distributed with a spacing of 37.5mm.

[0035] 2. Existing patented technical solutions

[0036] Since the phase-frequency characteristic of the cross-power spectral density (CPSD) of two cross-correlated signals represents the phase difference between the two cross-correlated signals at various frequencies, and the phase difference reflects the transit time between the two signals, the cross-correlation flux (also known as the correlation flux) can be calculated using the transit time. Therefore, in in-situ calibration based on the cross-correlation method, the cross-correlation flux at various frequencies can be obtained using the phase-frequency characteristic of the cross-power spectral density.

[0037] The cross-power spectral density function of the two cross-correlated signals x(t) and y(t) is the Fourier transform of their cross-correlation function, i.e.:

[0038]

[0039] In the formula, G xy (f) is the one-sided cross-power spectral density, 0 ≤ f < ∞, R xy (τ) is the cross-correlation function of the two signals. Since signal y(t) is the time delay of signal x(t), then we have y(t) = x(t-τ). f ), where τ f Let G be the transit time at each frequency. xy (f) can be expressed as:

[0040]

[0041] The phase frequency characteristic of the cross power spectral density is:

[0042] θ xy (f)=-2πfτ f (3)

[0043] The transit time τ at each frequency is calculated using formula (3). f Then, based on the distance L between the two pairs of cross-correlated electrodes, the average flow velocity v of the fluid passing through this distance is calculated:

[0044] v=Lτ f (4)

[0045] Based on the pipe diameter D, the cross-correlation flow rate corresponding to different frequency signals at this flow velocity can be obtained as follows:

[0046]

[0047] Based on the phase frequency response curve of the cross power spectral density, the values ​​of electrode group C2&5 at 100m were calculated when the sodium temperature was 400℃. 3 / h, 150m 3 / h、200m 3 / h、232m 3 / h and 280m 3 The cross-correlation flow curves of signals at various frequencies at five flow points per hour, as shown below. Figure 2(a) , 2(b) As shown in 2(c), 2(d) and 2(e).

[0048] Figure 2 illustrates the basis for frequency band selection in the aforementioned patent. Specifically, the aforementioned patent employs manual observation, selecting and determining the correction frequency band based on the overlapping or very close regions of the two curves (cross-correlation flow and standard flow (horizontal line)) in these figures.

[0049] Theoretically, when the standard flow rate is low, the cross-correlation flow rates within the pipeline are generally close to the standard flow rate. However, the observed standard flow rate is 100 m³ / h. 3 / h and 150m 3 The cross-correlation flow curves of different frequency signals at a flow rate of 100 m³ / h revealed that signals above 20 Hz exhibited variations between lower and higher than the standard flow rate. This anomaly is due to the narrow signal bandwidth at low flow rates, with virtually no signal above 20 Hz. Therefore, calculation errors occur when using phase-frequency characteristics to calculate the cross-correlation flow rate, as shown in Figure 3(a), where the standard flow rate is 100 m³ / h. 3 The spectrum at / h and the standard flow rate in 3(b) is 150m³ 3The spectrum is shown at / h. When calculating the signal spectrum, an FFT is performed every 32768 points, covering 16384 points each time. Since signals at frequencies of 20Hz and above are very weak, their contribution to the cross-correlation flux is relatively small. Even if errors occur in the cross-correlation flux calculation, their impact on the final result is minimal and can be ignored. However, this conclusion was reached through manual analysis and judgment.

[0050] 3. Technical solution of the present invention

[0051] 1) Calculate the correction band using the amplitude-frequency response of the cross-power spectral density.

[0052] Based on the Wiener-Khinchin theorem, this invention expresses the cross-power spectral density and cross-correlation function as a Fourier transform pair, and converts the cross-correlation function into the form of cross-power spectral density:

[0053]

[0054] In the formula, |G xy (f) represents the amplitude-frequency response of the cross-power spectral density. This represents the phase frequency characteristic. According to formula (6), the transit time obtained through cross-correlation is the result of weighting the transit times at each frequency by the amplitude of the cross-power spectral density, i.e.

[0055]

[0056] In the formula, τ f These are the transit times at various frequencies, and τ is the transit time over the entire cross-section. f The weighted average, G xy (f) N It is G xy (f) The result after normalizing the maximum value. According to the "M-type" average velocity model, the flow velocity is not uniform across the cross-section. The flow velocity is high near the pipe wall, mainly generating low-frequency signals with large amplitude and short delay time; the flow velocity is low near the center of the pipe, mainly generating high-frequency signals with small amplitude and long delay time.

[0057] 2) Calculate the maximum value of the correction frequency band.

[0058] According to the signal spectrum in Figure 3, the signal amplitude decays rapidly as the frequency increases. Therefore, it can be assumed that when the frequency exceeds a certain value f... max After that, the signal amplitude contributes almost nothing to the transit time, therefore:

[0059]

[0060] In the formula, f maxThe value can be determined by the attenuation of the cross-power spectral density to a certain value. When the power attenuation is 1000 times, the signal can be considered to have been completely attenuated. Therefore, we use a power attenuation of 1000 times as a benchmark, that is, the power spectral density attenuation to -30dB as the lower limit to calculate f. max .

[0061] The amplitude-frequency characteristics of the cross-power spectral density (CPSD) were estimated using the "cpsd" function in Matlab. Specifically, a Hanning window was used to truncate the signal, and a Fast Fourier Transform (FFT) was performed every 65536 points, shifting the signal by 32768 points each time. The CPSD was normalized using the function 10·lg(|G|max(|G|)). It should be noted that this normalization was performed to convert the signal to decibels for better observation of the signal attenuation factor. This differs from the normalization mentioned earlier, which used the maximum value for normalization, resulting in a value between 0 and 1. In this invention, only this step involves normalization to decibels; all other steps use the maximum value for normalization, normalizing the results to between 0 and 1. At a sodium temperature of 400°C, various flow rates (100m³) were... 3 / h, 150m 3 / h、200m 3 / h、232m 3 / h、280m 3 The normalized cross-power spectrum under (h) is shown in Figure 4.

[0062] When the cross-power spectral density is -30dB, at various flow rates f max The values ​​are 15Hz, 20Hz, 28Hz, 31Hz, and 35Hz, respectively.

[0063] 3) Calculate the starting frequency of the correction band.

[0064] According to the "M-type" average velocity model, the cross-correlation flow rate calculated from the low-frequency signal is greater than the standard flow rate, while the cross-correlation flow rate calculated from the high-frequency signal is close to the standard flow rate. Therefore, assuming there exists a frequency point f0 that can distinguish between the low-frequency and high-frequency regions, this f0 is the boundary point between the high and low-frequency regions and also the starting frequency point of the correction band. In the range 0 ≤ f = f l Within the range ≤f0, the cross-correlation flow is greater than the standard flow, f l It is the frequency variable within this region; in f0 ≤ f = f h ≤f max Within the region, the cross-correlation flow equals the standard flow (reference flow), f h It is a frequency variable within this region; its transit time For the standard value τ s The standard transit time τ heres From standard flow Q s According to the formula τ s =πD 2 L / (4Q s The result is obtained by calculation. Therefore, equation (8) can be derived.

[0065]

[0066] The derivation of equation (8) utilizes the characteristics of the cross-power spectral density to simplify equation (8) in order to obtain the formula for calculating f0. This characteristic can be found in [reference needed]. Figure 5 The curve represents the amplitude of the cross-power spectral density, which first increases and then decreases. Here, we mainly utilize its attenuation part. Equation (9) will be explained in detail below.

[0067] The first line of equation (9) shows the relationship between the transit time on the cross section and the transit time at different frequencies, that is, the transit time on the cross section is the weighted average of the transit times at each frequency and the cross-power spectral density amplitude. This frequency range is 0 ≤ f ≤ f max The second line of equation (9) indicates that, taking f0 as the dividing point, the cross-power spectral density after normalization to the maximum value is divided into two parts: a low-frequency region and a high-frequency region; then, for τ... f Perform a weighted summation. In the third row of equation (9), due to the high-frequency region... equal to or close to τ s Therefore, it is considered to be a constant.

[0068] The first term in the fourth row of equation (9) will be discussed below.

[0069] Depend on Figure 5 It can be seen that the cross-power spectral density decreases exponentially with increasing frequency. According to Figure 2(e), the lowest frequency at which the cross-correlation flow rate approaches the standard flow rate is at least 15 Hz; the cross-correlation flow rate below 15 Hz is greater than the standard flow rate. According to the formula... Transit time and cross-correlation flow Q cfl They are inversely proportional; the smaller the frequency, the higher the Q. cfl The larger, The smaller it is. Therefore, the cross-power spectral density |G xy (f l )| N Rather than crossing time Having opposite rates of change, this invention focuses on equation (9). The value of .

[0070] When the flow rate is 280m 3 At / h, the cross-power spectral density, normalized to its maximum value, is as follows: Figure 5The curve shown.

[0071] Depend on Figure 5 It can be seen that the cross-power spectral density at 15 Hz is approximately 0.05, which is attenuated by at least 20 times compared to the maximum value. At the maximum cross-power spectral density, the cross-correlation flux is approximately 5 times the standard flux, i.e. It decreases to 1 / 5 of the standard value. Looking at the direction of gradually increasing frequency... The increase is much smaller than |G xy (f l )| N The degree of reduction, therefore, Located at the maximum frequency f0, therefore,

[0072] The second term in the fourth row of equation (9) will be discussed below.

[0073] (|G xy (f h )| N ) min The minimum value is located at the maximum frequency f. max Therefore, (|G xy (f h )| N ) min =|G xy (f max )| N .

[0074] Based on the above analysis, equation (9) can be simplified to:

[0075] τ≥|G xy (f0)| N ·τ s ·f0+τ s ·|G xy (f max )| N ·(f max -f0) (10)

[0076] Furthermore:

[0077]

[0078] Since the transit time is inversely proportional to the cross-correlation flux, therefore τ / τ s =Q s / Q c ,but

[0079]

[0080] In the formula, Q cThe cross-correlation flux is calculated using the signal across the entire frequency band.

[0081] Equation (12) assumes f0 ~ f max The cross-correlation flow rate at point f is close to the standard flow rate; therefore, the frequency is located between f0 and f1. max Equation (12) holds true for all intervals. In equation (12), the only variables are f0 and its cross-power spectral density value |G. xy (f0)| N According to the critical state of equation (12)

[0082]

[0083] f0 is solved by the amplitude-frequency characteristics of the cross-power spectral density.

[0084] The specific solution steps are as follows:

[0085] Based on the amplitude-frequency characteristics of the cross-power spectral density, solve for each frequency f. i down f i (|G xy (f i )| N -|G xy (f max )| N )+f max |G xy (f max )| N The value, and with Q s / Q c The values ​​are compared, and if they are close, the frequency at that value is f0. If multiple values ​​are close, the closest one should be selected. Even if the closest one is not selected, the frequency difference will not be significant. It is important to note that the rising segment of the signal near 0Hz should be removed; that is, the calculation should start from the frequency corresponding to the maximum amplitude value and search in the falling segment.

[0086] When the sodium temperature is 400℃, the electrode C2&5 has a 100m... 3 / h, 150m 3 / h、200m 3 / h、232m 3 / h and 280m 3 The f0 values ​​for the five flow points are 4Hz, 7Hz, 10Hz, 12Hz, and 15.5Hz. At each flow rate, the cross-correlation flow rates are close to the frequency bands of the standard flow rates, i.e., the correction frequency bands are [4-15Hz], [7-20Hz], [10-28Hz], [12-31Hz], and [15.5-35Hz], respectively. Figure 6 As shown, this is consistent with the results observed in Figure 2.

Claims

1. A method for calculating the correction band in the in-situ calibration of a vortex-shedding-generator-free permanent-magnet sodium flowmeter, characterized in that: the amplitude-frequency characteristic of the cross-power spectral density is used to calculate the correction band; the cross-power spectral density and the cross-correlation function are a pair of Fourier transforms of each other, and the cross-correlation function is expressed in the form of the cross-power spectral density; the amplitude-frequency characteristic of the cross-power spectral density is estimated using the "cpsd" function in Matlab; specifically, the signal is truncated using a Hanning window, and a fast Fourier transform is performed every 65536 points, with a shift of 32768 points each time.

2. The method for calculating the correction band in the in-situ calibration of a vortex-shedding-generator-free permanent-magnet sodium flowmeter according to claim 1, characterized in that: the maximum value of the correction band is calculated.

3. The method for calculating the correction band in the in-situ calibration of a vortex-shedding-generator-free permanent-magnet sodium flowmeter according to claim 1, characterized in that: the starting frequency f0 of the correction band is calculated according to formula (4) and the amplitude-frequency characteristic of the cross-power spectral density: where |G xy (f) | is the amplitude-frequency characteristic of the cross-power spectral density, is the phase-frequency characteristic; it can be seen from equation (1) that the transit time obtained by cross-correlation is the result of weighting the transit times at each frequency by the amplitude of the cross-power spectral density, i.e. In the formula, τ f These are the transit times at various frequencies, and τ is the transit time over the entire cross-section. f The weighted average, |G xy (f)| N It is by |G xy (f)| Obtained after normalization of the maximum value; According to the "M-type" average velocity model, the flow velocity is not uniform on the cross section. The flow velocity is high near the pipe wall, mainly generating low-frequency signals with large signal amplitude and small delay time; the flow velocity is low near the center of the pipe, mainly generating high-frequency signals with small signal amplitude and large delay time. ​ ​ ​ The signal amplitude decays rapidly with increasing frequency, so that it can be assumed that when the frequency exceeds a certain value f max After that, the signal amplitude contributes little to the transit time, so that In the formula, f max The f can be determined by the mutual power spectral density decay to a certain value; when the power decays 1000 times, it can be considered that the signal has been completely attenuated, and therefore, the power decay 1000 times is taken as the reference, and the power spectral density decay to -30dB is taken as the lower limit to calculate f max . ​ ​ where Q s is the standard flow, Q c is the cross-correlation flow calculated using the signal of the entire frequency band, |G xy (f) | is the amplitude-frequency characteristic of the cross-power spectral density, |G xy (f) | N is the maximum value of |G xy (f) |, f max is the maximum value of the correction frequency band, and f0 is the starting frequency of the correction frequency band. The specific solving steps are: according to the amplitude-frequency characteristic of the cross power spectral density, the value of each frequency f i f i xy i N xy max N max xy max N s c The value of f0 is obtained by comparing the value of f0 with the value of Q / Q, if they are close, the frequency under the value is f0; if there are multiple values close, the closest value should be selected; even if the selected one is not the closest, the frequency difference is not much; it should be noted that the rising section of the signal near 0 Hz should be removed, that is, the calculation should start from the frequency corresponding to the maximum amplitude, and the search should be performed in the descending section.​​​​​​​​​​​​

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