CN115235391A - Method for measuring ice thickness based on A0 modal dispersion curve - Google Patents
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- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B17/00—Measuring arrangements characterised by the use of infrasonic, sonic or ultrasonic vibrations
- G01B17/02—Measuring arrangements characterised by the use of infrasonic, sonic or ultrasonic vibrations for measuring thickness
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Abstract
The invention discloses a method for measuring ice thickness based on an A0 modal dispersion curve, which comprises the steps of collecting an A0 modal impact signal excited by knocking an ice surface through an accelerometer; extracting an A0 modal dispersion curve by adopting deconvolution time-frequency analysis; setting an expected sequence d = [ d ] of ice layer thickness according to thickness measurement resolution requirement 1 ,d 2 ,…,d M ]，d i Represents the ith desired ice layer thickness, i =1, 2.., M; solving an expected frequency dispersion curve of the A0 mode corresponding to the thickness of each expected ice layer; calculating a correlation coefficient rho (d) of the expected frequency dispersion curve of the A0 mode corresponding to each expected ice layer thickness respectively by the frequency dispersion curve of the A0 mode i ) (ii) a Obtaining an ice layer thickness measurement D:
invention toolThe device has the advantages of small strength, simple operation, convenient implementation, capability of ensuring the safety of polar region scientific expedition personnel, no need of expensive underwater vehicles and carried acoustic emission sonar, no need of integrated acoustic emission equipment, and more economical efficiency because only the accelerometer is used for collecting natural acoustic signals such as knocking on ice.
Description
Technical Field
The invention belongs to the field of acoustic measurement, relates to a method for measuring the thickness of an ice layer, and particularly relates to a method for measuring the thickness of the ice layer based on an accelerometer to acquire an A0 modal dispersion curve of the ice layer.
Background
The scientific investigation of the north pole is one of the main contents of the north pole strategy in China. As development and utilization of the north pole become more and more realistic, exploring the north pole has important strategic significance. The polar region sea ice structure is an important parameter which has profound influence on global climate, and one leading technical difficulty in the field of global change research is the problem of measuring the thickness of the sea ice.
The in-situ measurement method is a conventional method for researching and obtaining the thickness of the sea ice, is realized by drilling the ice core, has high precision and reliable data, is time-consuming and labor-consuming, and is only suitable for ice section measurement of a thin ice layer. The latest patent of the same technology, namely a parametric array ice layer profile detection underwater robot and an ice layer profile detection method, provides that the problems of measurement of ice thickness by using an underwater vehicle and a carried elevation sonar under ice by using echo, deployment and recovery of the vehicle and positioning and navigation under ice exist at present; the system for detecting the thickness of the polar sea ice proposes a system based on an electromagnetic method to measure the thickness of the ice on the ice, and the equipment is expensive and is easily influenced by the arctic weather and illumination.
Researches find that a strong A0 mode similar to plate wave propagation exists in the ice layer of an ice-covered water area, and the mode has obvious dispersion characteristics in a low frequency band and is sensitive to ice layer thickness parameters.
Disclosure of Invention
Aiming at the prior art, the invention aims to provide a method for measuring the thickness of an ice layer based on an accelerometer to acquire an A0 modal dispersion curve in the ice layer, and the method has the advantages of convenience in arrangement, safety in operation and economy compared with the existing method.
In order to solve the technical problem, the method for measuring the thickness of the ice layer comprises the following steps:
step 1: acquiring an A0 modal impact signal excited by knocking the ice surface at a known distance through an accelerometer;
and 2, step: extracting an A0 modal dispersion curve by adopting deconvolution time-frequency analysis;
and step 3: setting an expected sequence of ice layer thicknesses d = [ d ] according to thickness measurement resolution requirements 1 ,d 2 ,…,d M ]In which d is i Represents the ith desired ice layer thickness, i =1, 2.., M;
and 4, step 4: solving an expected frequency dispersion curve of the A0 mode corresponding to the thickness of each expected ice layer;
and 5: calculating a correlation coefficient rho (d) of the expected frequency dispersion curve of the A0 mode corresponding to each expected ice layer thickness respectively for the frequency dispersion curve of the A0 mode i )；
Step 6: obtaining an ice layer thickness measurement D:
further, the extracting of the A0 modal dispersion curve by deconvolution time-frequency analysis includes:
performing short-time Fourier transform on the A0 modal impact signal to obtain a conventional time-frequency spectrogram B (n, k), wherein n and k are respectively an nth sampling point in a time domain and a kth sampling point in a frequency domain of the spectrogram;
and (3) performing deconvolution operation on B (n, k), solving by a Bayesian iterative method, and expressing as:
in the formula, P m (n, k) is a spectrogram after the mth iteration optimization based on a deconvolution method, m represents the iteration times,
a two-dimensional correlation operation is represented,
representing a two-dimensional convolution operation, P when m =1 m (n, k) = B (n, k), S (n, k) is a point scattering function, satisfying:
in the formula, T is the number of rectangular window function points of short-time Fourier transform, and N is the number of discrete Fourier transform points;
to P m (n, k) performing conventional thresholdingThe operation is as follows: if P m If (n, k) is greater than the set threshold, the point X = (n, k) is a discrete point of the modal dispersion curve of A0, i.e. the corresponding angular frequency ω is equal to k ＝2πkf s Arrival time t of A0 mode of/N 1 (ω k )＝n/f s ，f s The accelerometer sampling frequency.
Further, solving the expected frequency dispersion curve of the A0 mode corresponding to each expected ice layer thickness comprises:
desired thickness d of ice layer i The corresponding modal A0 dispersion curve is:
in the formula, c g (ω k ,d i ) In the A0 mode at an angular frequency of omega k Desired ice layer thickness d i The group velocity of time is calculated by the formula:
in the formula, c p (ω k ,d i ) At an angular frequency of ω for the A0 mode k Desired ice layer thickness d i The phase velocity of the time of flight is,
k r the horizontal wave number of the A0 mode.
Further, the correlation coefficient ρ (d) of the expected frequency dispersion curve of the A0 mode corresponding to each expected ice layer thickness is respectively associated with the frequency dispersion curve of the A0 mode i ) The method specifically comprises the following steps:
in the formula, K is the discrete point number of the A0 modal dispersion curve obtained in the step 2,
and
respectively is the mean value and the standard deviation of the modal dispersion curve A0 obtained in the step 2,
and
respectively desired ice thickness d i Mean and standard deviation of the corresponding expected dispersion curves.
The invention has the beneficial effects that: the invention firstly analyzes the wave equation of the A0 mode based on the elastic wave theory, and solves the equation based on a numerical method to obtain acoustic parameters of the mode, such as horizontal wave number, phase velocity, group velocity and the like. Performing high-resolution deconvolution time-frequency analysis on the A0 mode received by the ice layer accelerometer to extract a time-frequency curve of the A0 mode of the ice layer; and finally, constructing a cost function to realize the measurement of the ice thickness. Compared with the prior art, the invention has the following advantages:
1. compared with an in-situ measurement method, the method has the advantages of small working strength, simplicity in operation and convenience in implementation, and effectively guarantees the safety of polar science investigation personnel;
2. compared with the method for measuring the ice thickness underwater, the method has the advantages that an expensive underwater vehicle and a carried acoustic emission sonar are not needed, and the method is more economical;
3. compared with the device for measuring the ice thickness on the ice, the device does not need to integrate acoustic emission equipment, and only needs the accelerometer to be used for collecting natural acoustic signals such as knocking and the like on the ice;
4. the outfield experiment verifies the actual effect of the method for measuring the thickness of the ice layer.
Drawings
FIG. 1 is a flow chart of accelerometer thickness measurement in the present invention;
FIG. 2 is a waveform of an impact signal collected at 140m in the present invention;
FIG. 3 is a deconvolution time-frequency curve in the present invention;
FIG. 4 is a plot of the desired dispersion in the present invention;
FIG. 5 is a correlation coefficient of a dispersion curve according to the present invention;
fig. 6 is a group velocity dispersion curve of the A0 mode.
Detailed Description
The invention is further described with reference to the drawings and examples.
Research shows that three acoustic modes, namely A0, S0 and SH, mainly exist in the ice layer acoustic wave due to the fact that the ice layer macroscopically has a plate-shaped configuration. According to the propagation characteristics of the ice layer sound wave, the energy of the A0 mode is larger than that of the S0 mode and the SH mode. The inherent dispersion characteristic of the A0 mode is more sensitive to ice layer thickness and frequency than the S0 mode and the SH mode. The dispersion characteristic here means that the same mode has different group velocities at different frequencies, that is, the mode is collected by the accelerometer after propagating for a certain distance, and the time when different frequency components of the mode arrive at the receiving point is in sequence. As shown in fig. 6, when the thickness of the ice layer is constant, the group velocity of the A0 mode gradually increases from 0 to a certain maximum value and then gradually decreases to a stable value as the frequency increases. The thickness of the ice layer has a one-to-one correspondence with the dispersion curve of the A0 mode.
Therefore, the A0 mode signal is used as a reference signal for measuring the ice thickness, and the problem of interference of noise on the S0 mode and the SH mode is effectively avoided.
An accelerometer is arranged on the ice surface to collect acoustic signals. Tapping the ice surface at a distance r from the accelerometer can excite the A0 mode in the ice layer. Intercepting the A0 mode waveform, wherein the arrival time of different frequencies is as follows:
in the formula, is t 0 As signal intercept time point, d is ice layer thickness, c g (omega, d) is the group velocity of the A0 mode when the angular frequency is omega and the thickness of the ice layer is d, and the group velocity calculation formula
In which k and c p The horizontal wave number and the phase velocity of the A0 mode are respectively solved through an ice water coupling acoustic propagation model.
The existing extraction dispersion method comprises Hilbert-Huang transform, short-time Fourier transform, wavelet transform and Weiganan distribution. However, the actually acquired signal noise is still low, and the method is verified to be incapable of effectively extracting the frequency dispersion curve of the ice layer A0 mode, so that the practicability of the method is reduced.
The application provides that a deconvolution method aiming at A0 modal dispersion is adopted to obtain a high-resolution time-frequency spectrogram, and a dispersion curve is extracted through thresholding. The deconvolution algorithm can be solved by a Bayesian iterative method, denoted as
In which m represents the number of iterations,
a two-dimensional correlation operation is represented,
representing two-dimensional convolution operation, B is a spectrogram of an accelerometer for acquiring an A0 modal signal, P is a spectrogram optimized based on a deconvolution method, n and k are respectively a time domain sampling point and a frequency domain sampling point of the spectrogram, and particularly S is a specific point scattering function in the method
Wherein T is the number of rectangular window function points, and N is the number of discrete Fourier transform points.
The verification proves that the method can effectively extract the A0 mode in the ice layer, overcome the interference of environmental noise and improve the practicability of the ice sound positioning method.
And performing cross correlation on the actual A0 modal dispersion curve and a theoretical dispersion curve solved based on the expected ice layer thickness to obtain a correlation coefficient, wherein the expected ice thickness with the maximum correlation coefficient is the estimated actual ice layer thickness.
The first embodiment is as follows:
the invention discloses a method for measuring the thickness of an ice layer, which comprises the following steps:
step 1: acquiring an A0 modal impact signal excited by knocking the ice surface at a known distance through an accelerometer;
step 2: extracting an A0 modal dispersion curve by adopting deconvolution time-frequency analysis;
and step 3: setting an expected sequence of ice layer thicknesses d = [ d ] according to thickness measurement resolution requirements 1 ,d 2 ,…,d M ]Wherein d is i Represents the ith desired ice layer thickness, i =1,2.., M;
and 4, step 4: solving an A0 modal expected frequency dispersion curve corresponding to each expected ice layer thickness;
and 5: calculating a correlation coefficient rho (d) of the expected frequency dispersion curve of the A0 mode corresponding to each expected ice layer thickness respectively by the frequency dispersion curve of the A0 mode i )；
And 6: obtaining an ice layer thickness measurement D:
the second embodiment:
on the basis of the above embodiment, extracting the A0 modal dispersion curve by deconvolution time-frequency analysis includes:
performing short-time Fourier transform on the A0 modal impact signal to obtain a conventional time-frequency spectrogram B (n, k), wherein n and k are respectively an nth sampling point in a time domain and a kth sampling point in a frequency domain of the spectrogram;
and (3) performing deconvolution operation on B (n, k), solving by a Bayesian iterative method, and expressing that:
in the formula, P m (n, k) is based onThe spectrum after the m-th iteration optimization of the deconvolution method, m represents the iteration number,
a two-dimensional correlation operation is represented,
representing a two-dimensional convolution operation, P when m =1 m (n, k) = B (n, k), S (n, k) is a point scattering function, and satisfies:
in the formula, T is the number of rectangular window function points of short-time Fourier transform, and N is the number of discrete Fourier transform points;
to P m (n, k) performing a conventional thresholding operation: if P m If (n, k) is greater than the set threshold, the point X = (n, k) is a discrete point of the modal dispersion curve of A0, i.e. the corresponding angular frequency ω is equal to k ＝2πkf s Arrival time t of A0 mode of/N 1 (ω k )＝n/f s ，f s The accelerometer sampling frequency.
Example three:
on the basis of the above embodiment, solving the expected frequency dispersion curve of the A0 mode corresponding to each expected ice layer thickness includes:
desired thickness d of ice layer i The corresponding A0 modal dispersion curve is:
in the formula, c g (ω k ,d i ) In the A0 mode at an angular frequency of omega k Expected ice layer thickness of d i The group velocity of time is calculated by the formula:
in the formula, c p (ω k ,d i ) At an angular frequency of ω for the A0 mode k Expected ice layer thickness of d i The phase velocity of the time of flight is,
k r the horizontal wavenumber of the A0 mode.
Example four:
based on the above embodiment, the correlation coefficient ρ (d) of the expected dispersion curve of the A0 mode corresponding to each expected ice layer thickness is respectively associated with the dispersion curve of the A0 mode i ) The method comprises the following specific steps:
wherein K is the discrete point number of the modal A0 frequency dispersion curve obtained in the step 2,
and
respectively the mean value and the standard deviation of the modal A0 dispersion curve obtained in the step 2,
and
respectively desired ice thickness d i Mean and standard deviation of the corresponding expected dispersion curves.
The examples are given below with specific parameters:
as shown in fig. 1, the present invention comprises the steps of:
step 1: an accelerometer is arranged on the ice surface to collect acoustic signals. Tapping the ice surface at a distance r from the accelerometer excites the A0 mode in the ice layer. As shown in figure 2, the A0 mode waveform segment excited by the impact sound source at 140m is collected by the accelerometer, the A0 mode duration is 20-40ms, and the sampling frequency of the accelerometer isRate f s ＝40kHz；
Step 2: and extracting a modal dispersion curve based on deconvolution time-frequency analysis. The application provides that a deconvolution method aiming at A0 modal dispersion is adopted to obtain a high-resolution time-frequency spectrogram, and a dispersion curve is extracted through thresholding.
Firstly, performing short-time Fourier transform on the A0 mode signal in the step 1 to obtain a conventional time-frequency spectrogram B (n, k), wherein n and k are time domain sampling points and frequency domain sampling points of the spectrogram respectively.
Next, a deconvolution operation is performed on B (n, k). The deconvolution algorithm can be solved by a Bayesian iterative method, represented as
In the formula P m (n, k) is a spectrogram after the mth iteration optimization based on a deconvolution method, m represents the iteration times,
a two-dimensional correlation operation is represented,
representing a two-dimensional convolution operation, when m =1, P m (n, k) = B (n, k). In particular, S is a point scattering function specific to the method
In the formula, T is the number of rectangular window function points, and N is the number of discrete Fourier transform points.
Finally, to P m (n, k) performing a conventional thresholding operation. If P m (n, k) is greater than the threshold, the point X = (n, k) is a discrete point of the modal A0 dispersion, i.e. the corresponding angular frequency ω is ω k ＝2πkf s Arrival time t of A0 mode of/N 1 (ω k )＝n/f s 。
As shown in fig. 3, in a time-frequency spectrum obtained by deconvolving the waveform of the A0 mode, the window function length T is 512 points, the number N of fourier points is 1024 points, the main energy of the A0 mode is concentrated at 200-1600Hz, and as the frequency increases, the relative arrival time of the A0 mode gradually decreases, which means the increase of the group velocity, and when the frequency is above 1000Hz, the relative arrival time thereof gradually increases, the group velocity thereof decreases, and the energy above 1600Hz is smaller, and the arrival time of the A0 mode of 200-1600Hz is mainly used as a parameter for estimating the thickness of the ice layer.
And 3, step 3: and automatically setting a desired sequence of ice layer thicknesses according to the thickness measurement resolution requirement. Here, it is desirable that the ice thickness is set to 0.1m-2.0m with a spacing of 0.1m, i.e., d c ＝[0.1 0.2 0.3...2.0]。
And 4, step 4: and solving an expected frequency dispersion curve. For each desired ice layer thickness, the arrival time of the A0 mode, i.e., the dispersion curve, is
In the formula, c g (ω k ,d c ) In the A0 mode at an angular frequency of omega k The desired thickness of the ice layer is d c Group velocity of time. The group velocity is calculated by the formula
In the formula, c p (ω k ,d c ) In the A0 mode at an angular frequency of omega k The desired thickness of the ice layer is d c The phase velocity of the time of flight is,
k r for the horizontal wave number of the A0 mode, solve for k r The classical expression of the method is:
|H(k r )|＝0
wherein | is a determinant, H is an A0 mode matrix, and the fluid sound pressure fluctuation equation is used
Elastic wave equation and boundary continuity condition control, k 0 ＝ω/c 0 ，c 0 Is the speed of sound in water.
And 5: calculating the correlation between the signal frequency dispersion curve and the expected curve, and defining the frequency dispersion curve t extracted based on the deconvolution method in the step 2 1 (ω k ) And the ice thickness calculated in step 4 is d c Time theory dispersion curve t 2 (ω k ,d c ) Has a correlation coefficient of
Wherein K is the discrete point number of the dispersion curve,
and
are each t 1 (ω k ) The mean value and the standard deviation of (a),
and
respectively, the expected dispersion curve t 2 (ω k ) Mean and standard deviation of (d).
As shown in table 1, correlation coefficients for different desired ice thicknesses.
TABLE 1 correlation coefficient of expected ice thickness
Step 6: from the result of step 5, the estimated ice layer thickness is
As shown in fig. 5, when the desired ice layer thickness is 0.5m, the correlation coefficient is the largest, i.e., the estimated ice layer thickness is D =0.5m, with an error of about 0.03m compared to the actually measured value of 0.47 m.
The measured data result proves that the method can effectively measure the thickness of the ice layer through the accelerometer on the ice.
It is to be understood that the invention is not limited to the examples described above, but that modifications and variations may be effected thereto by those of ordinary skill in the art in light of the foregoing description, and that all such modifications and variations are intended to be within the scope of the invention as defined by the appended claims.
Claims (4)
1. A method for measuring ice thickness based on an A0 modal dispersion curve is characterized by comprising the following steps:
step 1: acquiring an A0 modal impact signal excited by knocking the ice surface at a known distance through an accelerometer;
step 2: extracting an A0 modal dispersion curve by adopting deconvolution time-frequency analysis;
and step 3: setting an expected sequence of ice layer thicknesses d = [ d ] according to thickness measurement resolution requirements 1 ,d 2 ,…,d M ]Wherein d is i Represents the ith desired ice layer thickness, i =1,2.., M;
and 4, step 4: solving an A0 modal expected frequency dispersion curve corresponding to each expected ice layer thickness;
and 5: calculating a correlation coefficient rho (d) of the expected frequency dispersion curve of the A0 mode corresponding to each expected ice layer thickness respectively by the frequency dispersion curve of the A0 mode i )；
Step 6: obtaining an ice layer thickness measurement D:
2. the method for measuring the ice thickness based on the A0 modal dispersion curve according to claim 1, characterized in that: the method for extracting the A0 modal dispersion curve by adopting deconvolution time-frequency analysis comprises the following steps:
performing short-time Fourier transform on the A0 modal impact signal to obtain a conventional time-frequency spectrogram B (n, k), wherein n and k are respectively an nth sampling point in a time domain and a kth sampling point in a frequency domain of the spectrogram;
and (3) performing deconvolution operation on B (n, k), solving by a Bayesian iterative method, and expressing as:
in the formula, P m (n, k) is a spectrogram after the mth iteration optimization based on a deconvolution method, m represents the iteration times,
a two-dimensional correlation operation is represented,
representing a two-dimensional convolution operation, P when m =1 m (n, k) = B (n, k), S (n, k) is a point scattering function, and satisfies:
in the formula, T is the number of rectangular window function points of short-time Fourier transform, and N is the number of discrete Fourier transform points;
to P m (n, k) performing a conventional thresholding operation: if P m If (n, k) is greater than the set threshold, the point X = (n, k) is a discrete point of the modal dispersion curve of A0, i.e. the corresponding angular frequency ω is equal to k ＝2πkf s Arrival time t of A0 mode of/N 1 (ω k )＝n/f s ，f s The accelerometer sampling frequency.
3. The method for measuring the ice thickness based on the A0 modal dispersion curve according to claim 2, characterized in that: the solving of the expected frequency dispersion curve of the A0 mode corresponding to each expected ice layer thickness comprises:
desired thickness d of ice layer i The corresponding modal A0 dispersion curve is:
in the formula, c g (ω k ,d i ) At an angular frequency of ω for the A0 mode k Desired ice layer thickness d i The group velocity of the time is calculated by the following formula:
in the formula, c p (ω k ,d i ) In the A0 mode at an angular frequency of omega k Expected ice layer thickness of d i The phase velocity of the time of flight is,
k r the horizontal wave number of the A0 mode.
4. The method for measuring ice thickness based on the A0 mode dispersion curve according to any one of claims 1 to 3, wherein: the A0 modal dispersion curve is respectively corresponding to the correlation coefficient rho (d) of the A0 modal expected dispersion curve of each expected ice layer thickness i ) The method specifically comprises the following steps:
in the formula, K is the discrete point number of the A0 modal dispersion curve obtained in the step 2,
and
respectively the mean value and the standard of the A0 modal dispersion curve obtained in the step 2The difference is that the number of the first and second,
and
respectively desired ice thickness d i Mean and standard deviation of the corresponding expected dispersion curves.
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