CN114324972B - Self-adaptive generalized cross-correlation time delay estimation method suitable for fluid cross-correlation speed measurement - Google Patents

Abstract

The invention discloses a self-adaptive generalized cross-correlation time delay estimation method suitable for fluid cross-correlation speed measurement. Aiming at the problem that the existing cross-correlation method cannot effectively realize the time delay estimation of the fluid signal containing the strong periodic component, the method introduces an adaptive filter to realize the time delay estimation of the fluid signal containing the strong periodic component based on the basic idea of the generalized cross-correlation. The invention determines whether strong periodic components exist and the corresponding frequency thereof and designs the corresponding band elimination filter for inhibition by carrying out frequency domain analysis on the input upstream and downstream signals, then calculates the cross-power spectral density after inhibition, obtains a cross-correlation function by Fourier inversion, and finally determines the time delay by peak detection. The method has stronger application universality by adaptively designing and adjusting the band elimination filter. The method inhibits strong periodic components in the measured fluid signal, the time delay estimation is effective and reliable, the flow velocity measurement precision is high, and the flow velocity measurement range is large.

Description

An Adaptive Generalized Cross-correlation Delay Estimation Applicable to Fluid Cross-correlation Velocity Measurement method

technical field

The invention relates to a time delay estimation method, in particular to an adaptive generalized cross-correlation time delay estimation method suitable for fluid cross-correlation velocity measurement.

Background technique

Fluid velocity measurement is a very important part in the field of fluid parameter measurement, which is of great significance to process control, system safety and industrial stability. Especially for complex fluids such as gas-liquid two-phase flow, gas-solid two-phase flow, etc., fluid velocity measurement has been widely concerned and valued. The cross-correlation delay estimation method is the most widely used method in flow velocity measurement. This method calculates the cross-correlation function of the upstream and downstream sensing signals, and estimates the delay through peak detection to obtain the transit time of the fluid from upstream to downstream. The distance between upstream and downstream is calculated to obtain the flow velocity. However, in complex fluids such as two-phase flow, strong periodic signals are very likely to appear, as shown in Figure 1, which is the electrical impedance signal in the small channel slug flow obtained by the electrical sensor. In the domain, the energy is concentrated in a certain frequency range, and the amplitude of this frequency band is much larger than that of other frequency bands. For such strong periodic signals, using the traditional cross-correlation function for time delay estimation will have the problem of insignificant peaks, which leads to the failure of time delay estimation using cross-correlation, and further leads to huge errors in flow velocity measurement.

与互功率谱密度函数G_xy(f)相乘，然后通过傅里叶反变换获得互相关函数，最后检测互相关函数的峰值来确定时延。其中常见的加权函数有HB函数、Roth函数、SCOT函数、PHAT函数等，能起到锐化峰值的效果，然而，当信号如图1所示具有强周期性时，通过广义互相关方法计算时延的效果也不令人满意，即使在不同的加权函数下，也都存在峰值不突出，利用互相关进行时延估计失效的问题。此时，亟待寻求一种新的适用于强周期性流体信号的互相关时延估计方法，能对于强周期性流体信号起到锐化互相关函数峰值的效果，从而保证互相关时延估计的有效性，提高时延估计精度，最终提高流速测量精度。The generalized cross-correlation delay estimation method can improve the accuracy of delay estimation by processing the signal power spectrum in the frequency domain. Fourier transform, respectively converted into X(f) and Y(f) in the frequency domain, then obtain the cross power spectral density function G _xy (f), and then introduce the weighting function

Multiply with the cross-power spectral density function G _xy (f), then obtain the cross-correlation function through inverse Fourier transform, and finally detect the peak value of the cross-correlation function to determine the time delay. Among them, the common weighting functions include HB function, Roth function, SCOT function, PHAT function, etc., which can sharpen the peak value. However, when the signal has strong periodicity as shown in Figure 1, when the generalized cross-correlation method is used to calculate The effect of delay is also unsatisfactory. Even under different weighting functions, there is a problem that the peak value is not prominent, and the use of cross-correlation for delay estimation fails. At this time, it is urgent to find a new cross-correlation delay estimation method suitable for strong periodic fluid signals, which can sharpen the peak value of the cross-correlation function for strong periodic fluid signals, so as to ensure the accuracy of cross-correlation delay estimation. Effectiveness, improve the accuracy of delay estimation, and ultimately improve the accuracy of flow velocity measurement.

SUMMARY OF THE INVENTION

Aiming at the problem that the traditional cross-correlation time delay estimation method and the existing generalized cross-correlation time delay estimation algorithm cannot satisfy the strong periodic fluid signal time delay estimation, and thus cannot satisfy the fluid flow velocity measurement, the present invention is based on the generalized cross-correlation time delay estimation method. Based on the idea of analyzing and processing signals in the frequency domain, an adaptive generalized cross-correlation delay estimation method suitable for fluid cross-correlation velocity measurement is proposed. The characteristics of strong periodic signals are: in the frequency domain, the signal appears as energy concentrated in a certain frequency domain range. Therefore, this method takes into account the adverse effect of strong periodicity on time delay estimation, and intends to achieve the purpose of peak sharpening and improving the accuracy of time delay estimation by suppressing strong periodic components in the signal. The basic flow of the method is shown in Figure 2, and its basic steps are:

Step 1: Using the upstream sensor and the downstream sensor arranged on the fluid flow path with a distance of L, the upstream input signal x(i) and the downstream input signal y(i) reflecting the measured fluid flow information are obtained respectively. Transform to obtain the spectrum of x(i) and y(i), which are X(f) and Y(f) respectively;

Step 2: Analyze the frequency domain characteristics of X(f) and Y(f) to determine whether the signal is a strong periodic signal;

Step 3: If the signal is a strong periodic signal, determine the frequency corresponding to the strong periodic component, that is, the frequency that needs to be suppressed, and then design the corresponding band-stop filters BSF _X (f) and BSF _Y (f) to suppress. Periodic component; if the signal is not a strong periodic signal, then BSF _X (f)=BSF _Y (f)=1;

After signal processing by band-stop filter, the frequency domain signal is converted into X ₁ (f) and Y ₁ (f) respectively;

Step 4: Multiply the conjugate of X ₁ (f) and Y ₁ (f) to obtain the cross-power spectral density function GP _xy (f), and then perform inverse discrete Fourier transform to obtain the cross-correlation function gp _xy ( i);

Step 5: Perform peak detection on the cross-correlation function gp _xy (i), calculate and obtain the time delay τ between the signal x(i) and the signal y(i), divide the upstream and downstream sensor distance L by the upstream and downstream delay, then The flow velocity v of the fluid to be measured can be determined, that is, v=L/τ.

Compared with the prior art, the present invention has the following beneficial effects:

1) Eliminate the problem that the peak value is not prominent due to the existence of strong periodic components, so as to achieve the purpose of sharpening the peak value of the cross-correlation function.

2) According to the frequency domain characteristics of the measured time domain signal, the band-stop filter structure can be adaptively adjusted to improve the universality of the method.

3) For strong periodic fluid signals, the problem of large delay estimation error in traditional cross-correlation and existing generalized cross-correlation methods is solved, and the accuracy and reliability of delay estimation are improved, thereby improving flow velocity measurement accuracy.

Description of drawings

Fig. 1 Strong periodic signal and its spectrum in a typical small channel slug flow.

FIG. 2 is the workflow of the adaptive generalized cross-correlation time delay estimation method suitable for fluid cross-correlation velocity measurement according to the present invention.

Figure 3. Strong periodic electrical impedance signals upstream and downstream of small channel slug flow obtained with electrical sensors.

Figure 4. Traditional cross-correlation result graph.

Figure 5. Graph of generalized cross-correlation results based on Roth weighting function.

Figure 6. Cross-correlation results of the proposed new method.

Detailed ways

The present invention will be further elaborated and described below in conjunction with specific embodiments. The technical features of the various embodiments of the present invention can be combined correspondingly on the premise that there is no conflict with each other.

The workflow of the adaptive generalized cross-correlation time delay estimation method suitable for the fluid cross-correlation velocity measurement of the present invention is shown in FIG. 2 .

First, using two sensors arranged upstream and downstream of the fluid flow path, an upstream input signal x(i) and a downstream input signal y(i) reflecting the measured fluid flow information are obtained. Then, as shown in equations (1) and (2), the corresponding spectral signals X(f) and Y(f) are obtained through discrete Fourier transform.

In practical applications, the spectral signals X(f) and Y(f) can be obtained through a Fast Fourier Transform (Fast Fourier Transform, FFT). By analyzing X(f) and Y(f), two band-stop filters, BSF _X (f) and HBSF _Y (f), are designed, respectively.

The analysis of X(f) and Y(f) and the design steps of the bandpass filters BSF _X (f) and BSF _Y (f) are as follows:

Step 1: Determine whether the signal has strong periodicity

According to the amplitude-frequency characteristics, when the signal has strong periodicity, the frequency domain shows that it has a large amplitude at certain frequency points, and the amplitude is significantly larger than that at other frequency points. In the actual workflow, since the similarity X(i) and Y(i) of the two signals are very high (theoretically there is only a delay), only one of X(f) and Y(f) is analyzed, namely Yes (take X(f) as an example). Whether the signal has strong periodicity can be determined by formula (3).

X(f _{max, 1} )>kσ (3)

Among them, X(f _{max, 1} ) is the maximum value in X(f), k is the discriminant coefficient, usually k>3, and σ is the variance of the frequency domain signal.

If Equation (3) holds, it is determined that the signal has strong periodicity, otherwise, the signal does not have strong periodicity.

Step 2: Determine the frequencies that need to be suppressed

If the signal has strong periodicity, it is necessary to further determine the frequencies that need to be suppressed. According to formula (4), all corresponding frequency points whose amplitudes in the frequency domain are greater than kσ can be extracted.

X(f _{max, i} )>kσ (4)

Among them, f _{max, i} represents all the corresponding frequency points whose amplitude in the frequency domain is greater than kσ, i=1, 2, 3...n.

Step 3: Design Bandpass Filters BSF _X (f) and BSF _Y (f)

According to the judgment in step 1, if the signal does not have strong periodicity, then BSF _X (f)=BSF _Y (f)=1, otherwise, according to the frequency (f _{max, i} , i=1, 2, 3, 4...n), design the corresponding amplitudes for frequencies in the range of [(1-α)f _{max, i} , (1+α) f _{max, i} ] in the frequency domain Band-stop filters BSF _X (f) and BSF _Y (f) eliminate strong periodic components in X(f) and Y(f), get X ₁ (f) and Y ₁ (f), and record the frequency point f _{max, i} ; wherein, α is an empirical coefficient, which can be adjusted according to the amplitude-frequency distribution, usually α=0.05;

The filters BSF _X (f) and BSF _Y (f) are designed by formula (5).

Then, X ₁ (f) and Y ₁ (f) can be obtained by formula (6) and formula (7).

X ₁ (f)=X(f)BSF _X (f) (6)

_Y1 (f)=Y(f)BSF _Y (f)(7)

Then the cross-power spectral density function GP _xy (f) can be calculated and obtained by formula (8).

GP _xy (f)=[X ₁ (f)]·[Y ₁ (f)] ^* (8)

where [] ^* denotes conjugation. The generalized cross-correlation function gp _xy (t) is obtained by performing an inverse discrete Fourier transform on GP _xy (f) (in practical applications, it can be calculated by an inverse fast Fourier transform (IFFT)) . The time corresponding to the peak value of gp _xy (t) is the time delay τ between the two signals x(i) and y(i).

The present invention takes the strong periodic signal of the slug flow in the small channel as an example to verify the effectiveness of the present invention. First, a strong periodic electrical impedance signal reflecting the fluid flow in the upstream and downstream of the small channel is obtained through two upstream and downstream electrical sensors (the distance between the upstream and downstream electrical sensors is 30mm) (the actual time delay is 56ms, and the corresponding actual flow rate is: 0.536m/s ), the upstream and downstream signals are shown in Figure 3. If the traditional cross-correlation and the existing generalized cross-correlation method (taking the Roth weighting function as an example) are used for time delay estimation, the cross-correlation functions are shown in Figures 4 and 5.

Among them, in the experimental results based on traditional cross-correlation, there are multiple peaks, and the delay estimation result corresponding to the maximum value of the cross-correlation function is: 13ms, which has a large error compared with the actual delay. If the flow velocity measurement is carried out according to this result, the flow velocity measurement result is: 2.308m/s, the relative error is as high as 300% or more, and the result cannot be used for practical application. For the results of generalized cross-correlation (taking the Roth weighting function as an example), it can be seen from Figure 5 that it is difficult to find meaningful peaks in this result. If only the maximum value of the cross-correlation function is used as the criterion, the corresponding delay estimation result is: 141ms, which has a large error compared with the actual delay. If the flow velocity measurement is carried out according to this result, the flow velocity measurement result is: 0.213m/s, the relative error is as high as 60% or more, and the result cannot be used in practical applications.

When the time delay estimation method in the present invention is used to calculate the cross-correlation function value, the result is shown in FIG. 6 . Compared with the traditional cross-correlation result and the generalized cross-correlation result based on the Roth weighting function, the cross-correlation function value obtained by the method of the present invention has a prominent peak value, and the delay corresponding to the peak value is 56ms, which is different from the actual time. The delay is consistent, and the delay can be accurately estimated, so as to achieve effective flow rate measurement. It can be seen that for strong periodic fluid signals, the method proposed in the present invention ensures the validity of the time delay estimation, and the time delay estimation accuracy is high, which further improves the fluid velocity measurement accuracy and expands the application range of the velocity measurement.

Claims (2)

1. an adaptive generalized cross-correlation time delay estimation method that is applicable to fluid cross-correlation velocity measurement, is characterized in that, comprises the steps: Step 1: Using the upstream sensor and the downstream sensor arranged on the fluid flow path with a distance of L, the upstream input signal x(i) and the downstream input signal y(i) reflecting the fluid flow information to be measured are obtained respectively. Transform to obtain the spectrum of x(i) and y(i), which are X(f) and Y(f) respectively;

Step 2: Analyze the frequency domain characteristics of X(f) and Y(f) to determine whether the signal is a strong periodic signal; The second step is specifically: Since the time-domain signals x(i) and y(i) are only considered to have time delay, the strong periodicity determination results in X(f) and Y(f) are the same, where X(f) determines whether the signal has a Strong periodicity: X(f _max,1 )>kσ Among them, X(f _max,1 ) is the maximum value in X(f), k is the discrimination coefficient, and σ is the standard deviation of the frequency domain signal; If the above formula holds, it is determined that the signal has strong periodicity, otherwise, the signal does not have strong periodicity; Step 3: If the signal is a strong periodic signal, determine the frequency corresponding to the strong periodic component, that is, the frequency that needs to be suppressed, and then design the corresponding band-stop filters BSF _X (f) and BSF _Y (f) to suppress. Periodic component; if the signal is not a strong periodic signal, then BSF _X (f)=BSF _Y (f)=1; After signal processing by band-stop filter, the frequency domain signal is converted into X ₁ (f) and Y ₁ (f) respectively; In step 3, the method for determining the frequency to be suppressed is as follows: Extract all frequency points that satisfy the following formula according to the frequency domain signal X(f): X(f _max,i )>kσ Among them, f _max,i represents all the corresponding frequency points whose amplitude in the frequency domain is greater than kσ, i=1,2,3...n; The described design of the corresponding band-stop filters BSF _X (f) and BSF _Y (f) to suppress periodic components, specifically: According to the determined frequency points f _max,i to be suppressed, i=1, 2, 3, 4...n, the range in the frequency domain is [(1-α)f _max,i , (1+α)f _{max ,i} ] design band-stop filters BSF _X (f) and BSF _Y (f) to eliminate the strong periodic components in X(f) and Y(f), and obtain X ₁ (f) and Y ₁ (f), and record the frequency point f _max,i ; where α is an empirical coefficient, which can be adjusted according to the amplitude-frequency distribution; Among them, the filters BSF _X (f) and BSF _Y (f) are designed by formula (5):

Then, X ₁ (f) and Y ₁ (f) can be obtained by equations (6) and (7): X ₁ (f)=X(f)BSF _X (f) (6) _Y1 (f)=Y(f)BSF _Y (f)(7) Step 4: Multiply the conjugate of X ₁ (f) and Y ₁ (f) to obtain the cross-power spectral density function GP _xy (f), that is, GP _xy (f)=X ₁ (f)[Y ₁ ( f)] ^* , and then perform inverse discrete Fourier transform to obtain the cross-correlation function gp _xy (i); Step 5: Perform peak detection on the cross-correlation function gp _xy (i), calculate and obtain the time delay τ between the upstream input signal x(i) and the downstream input signal y(i), and divide the upstream and downstream sensor distance L by the upstream The time delay between the input signal x(i) and the downstream input signal y(i) can determine the flow velocity v of the fluid to be measured, that is, v=L/τ. 2. the adaptive generalized cross-correlation time delay estimation method that is applicable to fluid cross-correlation velocity measurement according to claim 1, is characterized in that, in step 4, cross-power spectral density function GP _xy (f) is calculated by formula (8) get: GP _xy (f)=[X ₁ (f)]·[Y ₁ (f)] ^* (8) Among them, [] ^* represents the conjugate, and the generalized cross-correlation function gp _xy (i) is obtained by performing the inverse discrete Fourier transform on GP _xy (f).

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