SNMR signal parameter estimation method based on local Capon estimation

Abstract

The present invention discloses a method for estimating SNMR signal parameters based on local Capon estimation, which belongs to the field of surface nuclear magnetic resonance technology. The present invention constructs a mixed signal model including SNMR signals and power frequency harmonic noise, constructs a Capon spectrum, introduces a local Fourier matrix into the Capon spectrum, and the obtained local Capon spectrum is a function whose independent variables are frequency and relaxation time; a peak search is performed on the function, and the coordinates corresponding to the peak correspond to the SNMR signal relaxation time and Larmor frequency; combined with the least squares method, the initial amplitude, relaxation time, Larmor frequency and initial phase of the SNMR signal can be obtained. Compared with previous methods, the present method does not need to consider the influence of power frequency harmonic noise in the collected signal, but regards it as part of the signal. Therefore, when the signal is in a low signal-to-noise ratio and a large noise situation, the precision and accuracy of the SNMR signal parameter estimation are higher.

Description

Technical Field

[0001] The present invention relates to the field of surface nuclear magnetic resonance technology, and more particularly to a method for estimating SNMR signal parameters based on local Capon estimation. Background Art

[0002] Surface nuclear magnetic resonance (SNMR) technology is currently the only method that can directly estimate water content and pore structure below 100 meters below the surface. Over the past few decades, with the development and maturity of measurement and data processing technologies, SNMR technology has been widely used in groundwater resource surveys and hydrogeological assessments. SNMR signals collected by nuclear magnetic resonance water exploration instruments in the field are susceptible to noise, primarily power frequency harmonics and random noise. Determining the relevant parameters of the SNMR signal model from this noisy signal is a key aspect of SNMR technology.

[0003] The current main method is to remove the two types of noise in turn, such as using the harmonic modeling method to remove the power frequency harmonic noise, then using the superposition method to suppress random noise, and finally obtaining the parameters of the SNMR signal through the fitting method.

[0004] However, the prior art has the following shortcomings:

[0005] (1) If traditional methods are used to obtain parameters of SNMR signals, the SNMR signals may be distorted during the noise removal process, resulting in large errors in the final parameter estimation.

[0006] (2) Power frequency harmonic noise is the noise that has the greatest impact on SNMR signals. Some methods require prior analysis of power frequency harmonics, such as harmonic modeling. Some high-resolution algorithms also require obtaining the number of power frequency harmonic components in advance. Summary of the Invention

[0007] In response to the problems existing in the prior art, the purpose of the present invention is to propose a SNMR signal parameter estimation method based on local Capon estimation. This method does not need to consider the influence of power frequency harmonic noise in the acquired signal, but regards it as part of the signal. Therefore, when the signal is in a low signal-to-noise ratio and large noise situation, the precision and accuracy of SNMR signal parameter estimation are higher.

[0008] To achieve the above object, the present invention adopts the following technical solution: a SNMR signal parameter estimation method based on local Capon estimation, the method comprising:

[0009] Step S1: constructing a mixed signal model including SNMR signal and power frequency harmonic noise;

[0010]

[0011] In the mixed signal model, x(n) is the data sequence of the collected signal, K is the number of signal components, k = 1, 2, ..., K, E k 、 f k and T k They correspond to the amplitude, phase, frequency and relaxation time of the kth signal component, j is an imaginary unit, and ω(n) is random noise;

[0012] Convert the data sequence x = [x(1), x(2), ..., x(L)] of the collected signal into an M × N dimensional Hankel matrix X:

[0013]

[0014] x(M), x(N), and x(L) are the Mth, Nth, and Lth points in the data sequence, respectively. The three have the following relationship:

[0015] L=M+N-1,M <N;

[0016] And calculate the X covariance matrix R:

[0017] R=XX H

[0018] Step S2: Construct the Capon spectrum, introduce the local Fourier matrix F into the Capon spectrum, and obtain a function with the independent variables of frequency f and relaxation time T

[0019] ① The constructed Capon spectrum is:

[0020]

[0021] Where R is the covariance matrix of X in step S1, s M and s N are one-dimensional column vectors of length M and N respectively, For s M The conjugate transpose of

[0022] s M (f,T)=[1 e -1 / T+j2πf … e (-1 / T+j2πf)(M-1) ] H

[0023] s N (f,T)=[1 e (-1 / T+j2πf) … e (-1 / T+j2πf)(N-1) ] H

[0024] Among them, f and T are frequency independent variables and time independent variables respectively;

[0025] ②Introduce the local Fourier matrix in the Capon spectrum and define the M×(2P+1)-dimensional local Fourier matrix F:

[0026]

[0027] In the local Fourier matrix F, f is the frequency independent variable, with f as the center and P adjacent frequency points on both sides, and the interval between each frequency is N f is the sampling frequency.

[0028] After introducing the local Fourier matrix F The autocorrelation matrix becomes:

[0029]

[0030] Therefore, the Capon spectrum is rewritten as:

[0031]

[0032] Is a function of f and T, by Perform peak search, where the peak coordinates correspond to the Larmor frequency f of the SNMR signal L and relaxation time

[0033] Step S3: using the least squares method to obtain the initial amplitude and phase of the SNMR signal;

[0034] Construct a one-dimensional vector z of length L:

[0035]

[0036] Substitute z and x into the estimator obtained by the least squares method

[0037]

[0038] The initial amplitude E0 of the SNMR signal and the initial phase of the SNMR signal It is obtained by the following formula:

[0039]

[0040] Furthermore, the process of constructing a mixed signal model including SNMR signal, power frequency harmonic noise and random noise in step S1 is as follows:

[0041] ①The mathematical model of the signal collected by the receiving coil is:

[0042]

[0043] in, Corresponding SNMR signal, corresponds to the power frequency harmonic noise and ω(n) corresponds to the random noise, E0 is the initial amplitude of the SNMR signal; is the average relaxation time of the SNMR signal; f L is the local Larmor frequency of the SNMR signal, and the receiving frequency of the SNMR signal is the same as the local Larmor frequency; is the initial phase of the SNMR signal; B is the number of harmonic components of the power frequency harmonic noise; b=1,2,…,B; f0 is the fundamental frequency of the power frequency harmonic noise; A b and They correspond to the amplitude and phase of the bth power frequency harmonic component respectively;

[0044] ② Convert the mathematical model of the signal collected by the receiving coil into a complex signal model:

[0045]

[0046] ③Build a mixed signal model including SNMR signal, power frequency harmonic noise and random noise,

[0047]

[0048] In the mixed signal model, x(n) is the data sequence of the collected signal, K is the number of signal components, k = 1, 2, ..., K, E k 、 fk and T k corresponds to the amplitude, phase, frequency, and relaxation time of the kth signal component, j is an imaginary unit, and ω(n) is random noise.

[0049] Of the K signal components in a mixed noise model, only the signal component corresponding to the SNMR signal has a relaxation time constant, while the signal component corresponding to the power frequency harmonics has an infinite relaxation time. Therefore, after introducing the Capon spectrum for this mixed noise model, when searching for peaks along frequency and relaxation time, the peak corresponding to the power frequency harmonics will not appear. The only peak that can be found must correspond to the SNMR signal. This method can effectively remove the influence of power frequency harmonic noise.

[0050] Through the above-mentioned design scheme, the present invention can bring the following beneficial effects: The present invention proposes a SNMR signal parameter estimation method based on local Capon estimation. This method, combined with the least squares method, can obtain the initial amplitude, relaxation time, Larmor frequency, and initial phase of the SNMR signal. Compared with previous methods, this method does not need to consider the influence of power frequency harmonic noise in the acquired signal, but instead regards it as part of the signal. Therefore, when the signal is in a low signal-to-noise ratio and the noise is large, the precision and accuracy of the SNMR signal parameter estimation are higher. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The accompanying drawings herein are used to provide a further understanding of the present invention and constitute a part of the present application. The exemplary embodiments of the present invention and their descriptions are used to understand the present invention and do not constitute improper limitations of the present invention. In the accompanying drawings:

[0052] Figure 1 SNMR signal parameter estimation flow chart in an embodiment of the present invention;

[0053] Figure 2 is the Capon spectrum of the SNMR signal in the embodiment of the present invention. DETAILED DESCRIPTION

[0054] To make the objects, features, and advantages of the present invention more apparent and understandable, the technical solutions of the present invention are described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the present invention is not limited to the following embodiments, and specific implementation methods can be determined based on the technical solutions of the present invention and actual conditions. To avoid obscuring the essence of the present invention, well-known methods, processes, and procedures are not described in detail.

[0055] The present invention proposes a method for estimating SNMR signal parameters based on local Capon estimation, comprising:

[0056] 1. SNMR signal model:

[0057] The mathematical model of the data sequence x(n) of the signal collected by the receiving coil is shown as follows:

[0058]

[0059] Formula (1) consists of three parts, corresponding to SNMR signal, power frequency harmonic noise and random noise respectively. SNMR signal has four parameters, namely E0, f L and There are four parameters of power frequency harmonic noise, namely B, f0, A b and ω(n) is random noise.

[0060] E0 is the initial amplitude of the SNMR signal, which is positively correlated with the groundwater content in the detected area;

[0061] is the relaxation time of the SNMR signal, which is related to the geological lithology and underground pore density of the underground aquifer in the detected area. Different aquifers have different corresponding relaxation times.

[0062] f L is the local Larmor frequency of the SNMR signal. The Larmor frequency is related to the latitude of the detected area. The receiving frequency of the nuclear magnetic resonance signal should be the same as the local Larmor frequency.

[0063] It is the initial phase of the SNMR signal and is related to the electrical conductivity of the underground aquifer and other related hydrological information.

[0064] B is the number of harmonic components of the power frequency harmonic noise. Theoretically, the number of harmonic components of the power frequency harmonic noise is an unknown quantity.

[0065] f0 is the fundamental frequency of the power frequency harmonic noise, which is usually 50 Hz or 60 Hz, but may deviate in practice.

[0066] A b and They correspond to the amplitude and phase of the bth power frequency harmonic component respectively.

[0067] Convert the real signal model shown in formula (1) to the complex signal model shown in formula (2):

[0068]

[0069] The complex model is further simplified, and a mixed signal model including SNMR signal and power frequency harmonic noise is constructed.

[0070]

[0071] The mixed signal model shown in formula (3) is the number of signal components, E k 、 f k and T k Corresponding to the amplitude, phase, frequency and relaxation time of the k-th signal component, j is an imaginary unit.

[0072] In order to obtain the parameters of the SNMR signal, the Capon spectrum is introduced, and the spectrum peak search is performed with frequency and relaxation time as independent variables. Since only the SNMR signal has relaxation time, and the relaxation time of the power frequency harmonic noise is infinite, when performing peak search within a certain range, there is only one peak corresponding to the SNMR signal, and its coordinates are the Larmor frequency and relaxation time of the SNMR signal.

[0073] 2. Local Capon Parameter Estimation Process

[0074] The data sequence x = [x(0), x(1), ..., x(L)] of the collected signal is converted into an M × N dimensional Hankel matrix, as shown in formula X:

[0075]

[0076] x(M), x(N) and x(L) are the Mth, Nth and Lth sampling points of the data sequence x respectively. The three have the following relationship: L = M + N - 1, M <N。

[0077] The corresponding Capon spectrum is obtained as follows:

[0078]

[0079] Where R is the covariance matrix of X, which can be obtained by R=XX H Get;s M and s N are one-dimensional column vectors of length M and N respectively, s N With s M resemblance, For s M The conjugate transpose of; f and T are the frequency and relaxation time variables respectively; where s M As shown in formula (6).

[0080] s M (f,T)=[1 e -1 / T+j2πf … e (-1 / T+j2πf)(M-1) ] H (6)

[0081] In order to improve the effect of Capon estimation, the present invention introduces a local Fourier matrix into the Capon spectrum to improve the resolution of parameter extraction.

[0082] Define the local Fourier matrix F of M×(2P+1) dimensions:

[0083]

[0084] In the local Fourier matrix F, f is the frequency independent variable, and there are P adjacent frequency points on both sides of the frequency independent variable f as the center, and the interval between each frequency is N f is the sampling frequency.

[0085] After introducing the local Fourier matrix F The autocorrelation matrix becomes:

[0086]

[0087] The Capon spectrum in formula (8) can be rewritten as:

[0088]

[0089] Through a Capon Peak search, peak coordinates f, T correspond to the Larmor frequency f of the SNMR signal L and relaxation time

[0090] After the relaxation time and Larmor frequency of the SNMR signal are obtained, the initial amplitude and phase can be calculated using the least squares method.

[0091] Construct a one-dimensional vector z of length L:

[0092]

[0093] Substitute z and x into the estimator obtained by the least squares method

[0094]

[0095] E0 and It is obtained by the following formula:

[0096]

[0097] 3. Experimental Verification

[0098] Experimental conditions: In order to verify the feasibility of the above method, the SNMR signal was simulated and its parameters were set as: E0 = 200nV, f L =2360Hz, Then, random noise and power frequency harmonic noise are added to the simulation signal, and the signal-to-noise ratio of the SNMR signal and the random noise is set to 0dB; the fundamental frequency of the added power frequency harmonic noise is 50Hz, the frequency is between 1000Hz and 2000Hz, the amplitude is randomly distributed between 0 and 400nV, and the fundamental frequency is 50Hz.

[0099] Figure 2 The Capon spectrum of the SNMR signal under the above noise conditions is shown. The SNMR signal parameters obtained using the grid method are:

[0100] f L =2360.000000Hz;

[0101] Finding the relaxation time and the Larmor frequency f L Then, combined with the least squares method, we can obtain:

[0102] E0=198.6423nV,

[0103] Under this condition, the SNMR signal parameter estimation method based on local Capon estimation proposed in the present invention can achieve error-free estimation of the relaxation time and Larmor frequency of the SNMR signal, so the method proposed in the present invention is feasible.

[0104] The present invention proposes to form a mixed noise model with power frequency harmonic noise and SNMR signal, and use local Capon estimation based on the properties of the mixed noise model to obtain the relaxation time and Larmor frequency of the SNMR signal. The SNMR signal is a sinusoidal decay signal, and the power frequency harmonic noise is the superposition of multiple sinusoidal signals. Based on the signal characteristics of the two, they are constructed into a mixed noise model, thereby ignoring the influence of the power frequency harmonics as noise on the SNMR signal. The mixed noise model can be regarded as the superposition of multiple sinusoidal decay signals. In the mixed noise model, the attenuation factor of the SNMR signal is the inverse of the relaxation time, and the component attenuation factor of the power frequency harmonic noise is 0. When the relaxation time and frequency are used as the horizontal and vertical coordinates for peak search, there should be only one peak and its coordinates correspond to the relaxation time and Larmor frequency of the SNMR signal.

[0105] The main advantages of the present invention are: 1. Compared with traditional methods, this method does not require the removal or suppression of power frequency harmonic noise and random noise, thus avoiding the impact on the SNMR signal during the denoising process. 2. Other high-resolution algorithms, such as multiple signal classification (MUSIC) and rotation invariant technology (ESPRIT), must be based on the premise that the number of information sources is known. However, in practical applications, the number of power frequency harmonic components is unknown, and the estimation of their number of components is somewhat difficult. Capon spectroscopy can also be used when the number of signal components is unknown.

Claims

1. A SNMR signal parameter estimation method based on local Capon estimation, characterized in that: The method includes: Step S1: constructing a mixed signal model including SNMR signal and power frequency harmonic noise; In the mixed signal model, x(n) is the data sequence of the collected signal, K is the number of signal components, k = 1, 2, ..., K, E k 、 f k and T k They correspond to the amplitude, phase, frequency and relaxation time of the kth signal component, j is an imaginary unit, and ω(n) is random noise; Convert the data sequence x = [x(1), x(2), ..., x(L)] of the collected signal into an M × N dimensional Hankel matrix X: x(M), x(N), and x(L) are the Mth, Nth, and Lth points in the data sequence, respectively. The three have the following relationship: L=M+N-1,M <N; And calculate the X covariance matrix R: R=XX H Step S2: Construct the Capon spectrum, introduce the local Fourier matrix F into the Capon spectrum, and obtain a function with the independent variables of frequency f and relaxation time T ① The constructed Capon spectrum is: Where R is the covariance matrix of X in step S1, s M and s N are one-dimensional column vectors of length M and N respectively, For s M The conjugate transpose of s M (f,T)=[1 e -1 / T+j2πf … e (-1 / T+j2πf)(M-1) ] H s N (f,T)=[1 e (-1 / T+j2πf) … e (-1 / T+j2πf)(N-1) ] H ②Introduce the local Fourier matrix in the Capon spectrum and define the M×(2P+1)-dimensional local Fourier matrix F: In the local Fourier matrix F, f is the frequency independent variable, and there are P adjacent frequency points on both sides of the frequency independent variable f as the center, and the interval between each frequency is N f is the sampling frequency; After introducing the local Fourier matrix F The autocorrelation matrix becomes: Therefore, the Capon spectrum is rewritten as: Is a function of f and T, by Perform peak search, where the peak coordinates correspond to the Larmor frequency f of the SNMR signal L and relaxation time Step S3: using the least squares method to obtain the initial amplitude and phase of the SNMR signal; Construct a one-dimensional vector z of length L: Substitute z and x into the estimator obtained by the least squares method The initial amplitude E0 of the SNMR signal and the initial phase of the SNMR signal It is obtained by the following formula:

2. The SNMR signal parameter estimation method based on local Capon estimation according to claim 1, characterized in that: The process of constructing a mixed signal model including SNMR signal, power frequency harmonic noise and random noise in step S1 is as follows: ①The mathematical model of the signal collected by the receiving coil is: in, Corresponding SNMR signal, corresponds to the power frequency harmonic noise and ω(n) corresponds to the random noise, x(n) is the data sequence of the acquired signal; E0 is the initial amplitude of the SNMR signal; is the relaxation time of the SNMR signal; f L is the local Larmor frequency of the SNMR signal, and the receiving frequency of the SNMR signal is the same as the local Larmor frequency; is the initial phase of the SNMR signal; B is the number of harmonic components of the power frequency harmonic noise; b=1,2,…,B; f0 is the fundamental frequency of the power frequency harmonic noise; A b and They correspond to the amplitude and phase of the bth power frequency harmonic component respectively; ② Convert the mathematical model of the signal collected by the receiving coil into a complex signal model: ③Build a mixed signal model including SNMR signal, power frequency harmonic noise and random noise, In the mixed signal model, x(n) is the data sequence of the collected signal, K is the number of signal components, k = 1, 2, ..., K, E k 、 f k and T k They correspond to the amplitude, phase, frequency and relaxation time of the kth signal component respectively, j is the imaginary unit, and ω(n) is random noise.

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