CN114324972B - Self-adaptive generalized cross-correlation time delay estimation method suitable for fluid cross-correlation speed measurement - Google Patents
Self-adaptive generalized cross-correlation time delay estimation method suitable for fluid cross-correlation speed measurement Download PDFInfo
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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
Technical Field
The invention relates to a time delay estimation method, in particular to a self-adaptive generalized cross-correlation time delay estimation method suitable for fluid cross-correlation speed measurement.
Background
Fluid flow rate measurement is a very important part in the field of fluid parameter measurement, and has important significance for process control, system safety, industrial stability and the like. Especially for complex fluids such as gas-liquid two-phase flow, gas-solid two-phase flow and the like, the measurement of the flow velocity of the fluid is always paid much attention and paid attention. The cross-correlation time delay estimation method is the most widely applied method in flow velocity measurement, and the method is used for calculating the flow velocity according to the distance between the upstream and the downstream by calculating the cross-correlation function of the upstream and the downstream sensing signals and estimating the time delay through peak detection to obtain the transition time of the fluid from the upstream to the downstream. However, in complex fluids such as two-phase flow, strong periodic signals, i.e. electrical impedance signals in small channel slug flow obtained by an electrical sensor as shown in fig. 1, are very easy to appear, and such strong periodic signals show that energy is concentrated in a certain frequency range on a frequency domain, and the amplitude of the frequency range is much larger than that of other frequency ranges. For the strong periodic signals, the problem of unobvious peak value exists when the traditional cross-correlation function is used for time delay estimation, so that the problem of time delay estimation failure by utilizing cross-correlation is caused, and further, a huge error occurs in flow velocity measurement.
The generalized cross-correlation time delay estimation method can improve the time delay estimation precision by processing the signal power spectrum on a frequency domain, and the basic flow of the method is as follows: firstly, Fourier transform is carried out on two paths of time domain signals x (i) and y (i), the time domain signals are respectively converted into X (f) and Y (f) on a frequency domain, and then a cross-power spectral density function G is obtained xy (f) Reintroducing the weighting function
And cross power spectral density function G xy (f) Multiplying, then obtaining a cross-correlation function through inverse Fourier transform, and finally detecting the peak value of the cross-correlation function to determine the time delay. Common weighting functions include HB function, Roth function, SCOT function, and phot function, which can sharpen the peak, however, when the signal has strong periodicity as shown in fig. 1, the effect of calculating the delay by the generalized cross-correlation method is not satisfactory, even under different weighting functions, the peak is not prominent,and the time delay estimation is invalid by utilizing the cross correlation. At this time, a new cross-correlation delay estimation method suitable for a strong periodic fluid signal is urgently needed to be found, and the effect of sharpening the peak value of the cross-correlation function can be achieved on the strong periodic fluid signal, so that the effectiveness of cross-correlation delay estimation is ensured, the delay estimation precision is improved, and finally the flow velocity measurement precision is improved.
Disclosure of Invention
The invention provides a self-adaptive generalized cross-correlation time delay estimation method suitable for fluid cross-correlation speed measurement, which aims at solving the problem that the traditional cross-correlation time delay estimation method and the existing generalized cross-correlation time delay estimation algorithm cannot meet the time delay estimation of a strong periodic fluid signal and therefore cannot meet the fluid flow velocity measurement. The strong periodic signal is characterized by: in the frequency domain, the signal appears to be concentrated in energy in a certain frequency domain. Therefore, the method considers the adverse effect of strong periodicity on the time delay estimation, and aims to achieve the purposes of sharpening the peak value and improving the time delay estimation precision by inhibiting the strong periodicity component in the signal. The basic flow of the method is shown in fig. 2, and the basic steps are as follows:
the method comprises the following steps: obtaining upstream input signals x (i) and downstream input signals y (i) reflecting measured fluid flow information by using upstream sensors and downstream sensors arranged on a fluid flow path at a distance L, respectively, and obtaining frequency spectrums of x (i) and y (i) by discrete Fourier transform, namely X (f) and Y (f), respectively;
step two: analyzing the frequency domain characteristics of X (f) and Y (f) to determine whether the signal is a strong periodic signal;
step three: if the signal is a strong periodic signal, determining the frequency corresponding to the strong periodic component, i.e. the frequency to be suppressed, and then designing a corresponding band-stop filter BSF X (f) And BSF Y (f) To suppress periodic components; if the signal is not a strong periodic signal, then the BSF X (f)＝BSF Y (f)＝1；
After signal processing by band elimination filter, frequency domain signals are respectively converted into X 1 (f) And Y 1 (f)；
Step four: mixing X 1 (f) And Y 1 (f) The conjugate of the cross-power spectrum density function is subjected to multiplication to obtain a cross-power spectrum density function GP xy (f) Then, performing inverse discrete Fourier transform to obtain a cross-correlation function gp xy (i)；
Step five: for cross correlation function gp xy (i) And performing peak detection, calculating the time delay tau between the obtained signal x (i) and the signal y (i), and dividing the distance L between the upstream sensor and the downstream sensor by the upstream time delay and the downstream time delay to determine the flow speed v of the measured fluid, namely the v is L/tau.
Compared with the prior art, the invention has the following beneficial effects:
1) the problem that the peak value is not prominent due to the existence of strong periodic components is eliminated, and the purpose of sharpening the peak value of the cross-correlation function is achieved.
2) According to the frequency domain characteristics of the measured time domain signals, the structure of the band elimination filter can be adaptively adjusted, and the universality of the method is improved.
3) Aiming at strong periodic fluid signals, the problem of large delay estimation error in the traditional cross-correlation and the existing generalized cross-correlation method is solved, and the accuracy and the reliability of delay estimation are improved, so that the flow velocity measurement accuracy is improved.
Drawings
FIG. 1 illustrates a typical strong periodic signal and its frequency spectrum in a small channel slug.
FIG. 2 is a working flow of the adaptive generalized cross-correlation time delay estimation method suitable for fluid cross-correlation velocity measurement.
FIG. 3 is a strong periodic electrical impedance signal upstream and downstream of a small channel slug flow obtained with an electrical sensor.
Fig. 4 is a graph of conventional cross-correlation results.
Fig. 5 is a graph of generalized cross-correlation results based on the Roth weighting function.
Figure 6 shows the cross-correlation results of the proposed new method.
Detailed Description
The invention will be further illustrated and described with reference to specific embodiments. The technical features of the embodiments of the present invention can be combined correspondingly without mutual conflict.
The working flow of the self-adaptive generalized cross-correlation time delay estimation method suitable for fluid cross-correlation speed measurement is shown in figure 2.
First, an upstream input signal x (i) and a downstream input signal y (i) reflecting measured fluid flow information are obtained using two sensors arranged upstream and downstream in the fluid flow path. Then, as shown in formula (1) and formula (2), the corresponding spectral signals x (f) and y (f) are obtained by discrete fourier transform.
In practical applications, the spectral signals x (f) and y (f) may be obtained by Fast Fourier Transform (FFT). By analyzing X (f) and Y (f), two band elimination filters BSF are respectively designed X (f) And HBSF Y (f)。
Analysis of X (f) and Y (f) and band-pass filter BSF X (f) And BSF Y (f) The design steps are as follows:
the method comprises the following steps: determining whether a signal is strongly periodic
According to the amplitude-frequency characteristic, when the signal has strong periodicity, the frequency domain shows that the amplitude is larger at some frequency points and is obviously larger than the amplitudes at other frequency points. In an actual working process, because the similarity x (i) and y (i) of two signals is very high (theoretically, only time delay exists), only one of x (f) and y (f) is analyzed (taking x (f) as an example). Whether the signal has strong periodicity can be determined by equation (3).
X(f max，1 )＞kσ (3)
Wherein, X (f) max，1 ) Is the maximum value in X (f), k is the discrimination coefficient, k > 3 is usually taken, and σ is the variance of the frequency domain signal.
If equation (3) holds, the signal is determined to have strong periodicity, otherwise, the signal does not have strong periodicity.
Step two: determining the frequencies that need to be suppressed
If the signal has strong periodicity, then further determination of the frequency that needs to be suppressed is needed. According to equation (4), all corresponding frequency points with frequency domain amplitude greater than k σ can be extracted.
X(f max，i )＞kσ (4)
Wherein f is max，i Representing all corresponding frequency points with frequency domain amplitude greater than k σ, i ═ 1,2, 3.. n.
Step three: designing a bandpass filter BSF X (f) And BSF Y (f)
If the signal does not have strong periodicity, the BSF is determined in step one X (f)＝BSF Y (f) Otherwise, according to the frequency (f) to be suppressed determined in step two max，i I 1,2,3, 4.. n), for a range of [ (1- α) f in the frequency domain max，i ，(1+α)f max，i ]Inner frequency corresponding amplitude design band stop filter BSF X (f) And BSF Y (f) Eliminating strong periodic components in X (f) and Y (f) to obtain X 1 (f) And Y 1 (f) And recording the frequency point f max，i (ii) a Wherein, α is an empirical coefficient, which can be adjusted according to the amplitude-frequency distribution, and may be usually equal to 0.05;
filter BSF designed by formula (5) X (f) And BSF Y (f)。
Then, X 1 (f) And Y 1 (f) Can be obtained by the formulae (6) and (7).
X 1 (f)＝X(f)BSF X (f) (6)
Y 1 (f)＝Y(f)BSF Y (f) (7)
Cross power spectral density function GP xy (f) Can be obtained by calculation of equation (8).
GP xy (f)＝[X 1 (f)]·[Y 1 (f)] * (8)
Wherein [ 2 ], [ 2 ]] * Representing conjugation. By means of a pair of GP xy (f) Performing Inverse discrete Fourier Transform (in practical applications, the Inverse Fast Fourier Transform (IFFT) can be used for calculation) to obtain the generalized cross-correlation function gp xy (t)。gp xy The time corresponding to the peak value of (t) is the time delay tau between the two signals x (i) and y (i).
The invention takes the strong periodic signal of the section plug flow in the small channel as an example to verify the effectiveness of the invention. First, a strong periodic electrical impedance signal (the actual time delay is 56ms, and the corresponding actual flow rate is 0.536m/s) reflecting the flow of the fluid is obtained from the upstream and downstream two electrical sensors (the distance between the upstream and downstream electrical sensors is 30mm), and the upstream and downstream signals are shown in FIG. 3. If the conventional 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 function is shown in fig. 4 and 5.
In the experimental result based on the conventional cross-correlation, a plurality of peak values appear, and the time delay estimation result corresponding to the maximum cross-correlation function value is as follows: 13ms, the error is large compared to the actual delay. If the flow rate measurement is performed according to the result, the flow rate measurement result is as follows: 2.308m/s, the relative error is up to more than 300%, and the result can not be used for practical application. For the result of the generalized cross-correlation (taking the Roth weighting function as an example), as can be seen from fig. 5, it is difficult to find a meaningful peak, and if only the maximum value of the cross-correlation function is taken as the criterion, the corresponding delay estimation result is: 141ms, the error is large compared to the actual delay. If the flow rate measurement is performed according to the result, the flow rate measurement result is as follows: 0.213m/s, and the relative error is as high as 60% or more, and the result is not practical.
When the cross-correlation function value is calculated by the delay estimation method of the present invention, 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 has an obvious peak value, the time delay corresponding to the peak value is 56ms, and the time delay is consistent with the actual time delay, so that the time delay can be accurately estimated, and the effective flow rate measurement is realized. Therefore, for strong periodic fluid signals, the method provided by the invention ensures the effectiveness of time delay estimation, has higher time delay estimation precision, further improves the fluid flow velocity measurement precision and expands the flow velocity measurement application range.
Claims (2)
1. A self-adaptive generalized cross-correlation time delay estimation method suitable for fluid cross-correlation speed measurement is characterized by comprising the following steps:
the method comprises the following steps: obtaining upstream input signals x (i) and downstream input signals y (i) reflecting measured fluid flow information by using upstream sensors and downstream sensors arranged on a fluid flow path at a distance L, respectively, and obtaining frequency spectrums of x (i) and y (i) by discrete Fourier transform, namely X (f) and Y (f), respectively;
step two: analyzing 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 as follows:
since the time domain signals x (i) and y (i) are only considered to have a time delay, the strong periodicity decision results in x (f) and y (f) are the same, wherein x (f) determines whether the signals have strong periodicity by:
X(f max,1 )>kσ
wherein, X (f) max,1 ) Is the maximum value in X (f), k is the discrimination coefficient, and sigma is the standard deviation of the frequency domain signal;
if the above formula is true, determining that the signal has strong periodicity, otherwise, determining that the signal does not have strong periodicity;
step three: if the signal is a strong periodic signal, determining the frequency corresponding to the strong periodic component, i.e. the frequency to be suppressed, and then designing a corresponding band-stop filter BSF X (f) And BSF Y (f) To suppress the periodic components; if the signal is not a strong periodic signal, then the BSF X (f)＝BSF Y (f)＝1；
After signal processing by band elimination filter, frequency domain signals are respectively converted into X 1 (f) And Y 1 (f)；
In step three, the method for determining the frequency to be suppressed is as follows:
extracting all frequency points satisfying the following formula according to the frequency domain signal X (f):
X(f max,i )>kσ
wherein f is max,i Representing all corresponding frequency points with frequency domain amplitude greater than k σ, i ═ 1,2,3 … n;
the design of the corresponding band elimination filter BSF X (f) And BSF Y (f) The method for inhibiting the periodic components comprises the following specific steps:
according to the determined frequency point f to be suppressed max,i I is 1,2,3,4 … n, and has a range of [ (1- α) f in the frequency domain max,i ，(1+α)f max,i ]Inner frequency corresponding amplitude design band stop filter BSF X (f) And BSF Y (f) Eliminating strong periodic components in X (f) and Y (f) to obtain X 1 (f) And Y 1 (f) And recording the frequency point f max,i (ii) a Wherein alpha is an empirical coefficient and can be adjusted according to amplitude-frequency distribution;
wherein, the filter BSF is designed by the formula (5) X (f) And BSF Y (f)：
Then, X 1 (f) And Y 1 (f) Can be obtained by the formulae (6) and (7):
X 1 (f)＝X(f)BSF X (f) (6)
Y 1 (f)＝Y(f)BSF Y (f) (7)
step four: mixing X 1 (f) And Y 1 (f) The conjugate of the cross-power spectrum density function is subjected to product operation to obtain a cross-power spectrum density function GP xy (f) I.e. GP xy (f)＝X 1 (f)[Y 1 (f)] * Then, inverse discrete Fourier transform is carried out to obtain a cross-correlation function gp xy (i)；
Step five: for cross correlation function gp xy (i) Peak detection is carried out, time delay tau between an upstream input signal x (i) and a downstream input signal y (i) is calculated, and the flow velocity v of the measured fluid can be determined by dividing the distance L between the upstream sensor and the downstream sensor by the time delay between the upstream input signal x (i) and the downstream input signal y (i), namely v is L/tau.
2. The adaptive generalized cross-correlation time delay estimation method suitable for fluid cross-correlation velocity measurement according to claim 1, wherein in step four, the cross-power spectral density function GP xy (f) Obtained by calculation of equation (8):
GP xy (f)＝[X 1 (f)]·[Y 1 (f)] * (8)
wherein, the [ alpha ], [ beta ] -a] * Representing conjugation by means of a pair of GP xy (f) Performing inverse discrete Fourier transform to obtain a generalized cross-correlation function gp xy (i)。
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