CN117419794A - Interference structural rule analysis method for sound field of underwater vertical motion sound source - Google Patents

Interference structural rule analysis method for sound field of underwater vertical motion sound source Download PDF

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CN117419794A
CN117419794A CN202311358243.8A CN202311358243A CN117419794A CN 117419794 A CN117419794 A CN 117419794A CN 202311358243 A CN202311358243 A CN 202311358243A CN 117419794 A CN117419794 A CN 117419794A
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邱龙皓
赵春鹏
王晋晋
齐滨
邹男
郝宇
付进
张光普
王逸林
梁国龙
王燕
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Abstract

An interference structural rule analysis method of an underwater vertical motion sound source sound field relates to the field of underwater sound field characteristic analysis. The invention aims to solve the problem that the existing underwater moving object generation analysis method cannot analyze the underwater vertical movement characteristics, so that accurate marine environment information cannot be obtained. The invention comprises the following steps: the Doppler multi-path signal sound field model of the shallow sea underwater vertical motion sound source is constructed based on the ray theory, and then a time-frequency domain spectrogram of a signal received by a receiver is obtained by utilizing the Doppler multi-path signal sound field model: acquiring the continuously changing position of the wave crest in a time-frequency domain spectrogram of a received signal, and taking the continuously changing position as a track of interference fringes among shallow sea multipath signals; based on the tracks of interference fringes among the shallow sea multipath signals, the interference period and the interference fringe width of the interference fringes are obtained, so that the change rule of the interference fringes is obtained. The method is used for analyzing the interference structure of the underwater high-speed vertical motion sound source field.

Description

Interference structural rule analysis method for sound field of underwater vertical motion sound source
Technical Field
The invention relates to the field of underwater sound field characteristic analysis, in particular to an interference structure rule analysis method of an underwater vertical motion sound source sound field.
Background
The underwater motion sound source generates broadband continuous spectrum noise signals due to cavitation of the propeller, the broadband continuous spectrum noise signals are influenced by shallow sea interfaces, interference phenomena are generated by superposition of path signals, and a stable interference structure can be observed by a receiving signal of a receiving end in a time-frequency domain. The interference structure contains the information of sound source movement speed, position, radiation noise, underwater channel and the like, so that the analysis of the interference structure of the underwater sound field of the moving sound source is helpful for the analysis of sound source movement state and marine environment information.
At present, the sound field analysis of the underwater moving target aims at the horizontal moving target, the moving time is long, the channel change is slow, and stable interference fringes are easy to observe. While a vertically moving sound source generally exits a fixed depth in the sea floor or sea water and moves at a higher velocity toward the sea surface. In shallow sea conditions, the whole motion process is shorter in duration and is generally completed in a few seconds, and in the signal duration, the multi-path structure between the sound source and the receiving point is rapidly changed, and the received signal shows high non-stationary characteristic. Therefore, the current method for generating and analyzing the underwater moving object is not suitable for analyzing the underwater vertical moving characteristics, so that accurate marine environment information cannot be obtained.
Disclosure of Invention
The invention aims to solve the problem that the existing underwater moving object generation analysis method cannot analyze underwater vertical movement characteristics, so that accurate marine environment information cannot be obtained, and provides an interference structure rule analysis method of an underwater vertical movement sound source sound field.
The interference structural rule analysis method of the sound field of the underwater vertical motion sound source specifically comprises the following steps:
step one, constructing a Doppler multi-path signal sound field model of a shallow sea vertical motion sound source, and then acquiring a time-frequency domain spectrogram of a signal received by a receiver by using the Doppler multi-path signal sound field model:
step two, obtaining the position of continuous change of wave peaks in the time-frequency domain spectrogram of the received signal obtained in the step one, and taking the position as a track of interference fringes among shallow sea multipath signals;
step three, based on the tracks of interference fringes among the shallow sea multipath signals obtained in the step two, obtaining the interference period and the interference fringe width of the interference fringes, so as to obtain the change rule of the interference fringes;
the interference period of the interference fringes includes: a frequency interference period of the interference fringes and a time interference period of the interference fringes;
the interference fringe width includes: the frequency axis direction width of the interference fringes and the time axis direction width of the interference fringes;
and step four, obtaining marine environment information based on the interference fringe change rule obtained in the step three.
Further, in the first step, a Doppler multi-path signal sound field model of the shallow sea vertical motion sound source is constructed, and the Doppler multi-path signal sound field model is represented by the following formula:
wherein A is m (t) is the amplitude of the mth multipath signal at the moment t, D m (t) is the Doppler coefficient of the mth multipath signal at the moment t, τ m (t) is the propagation delay of the mth multi-path signal at the moment t, v is the vertical movement speed of the sound source, and theta m (t) is the emergence angle of the mth multi-path signal at the moment t, delta (·) is the underwater channel response, c is the underwater sound velocity, and h (t) is the sparse time-varying underwater sound channel.
Further, in the first step, a time-frequency domain spectrogram of a signal received by a receiver is obtained by using a doppler multi-path signal sound field model, which includes the following steps:
first, a signal x (t) received by a receiver is acquired, as follows:
wherein s (t) is an underwater moving sound source broadband radiation noise signal;
then, the signal x (t) received by the receiver is truncated to obtain a truncated signal at the time t, and fourier transform is performed on the truncated signal at the time t to obtain a spectrogram I (t, ω) of the received signal at the time t.
Further, a spectrogram I (t, ω) of the received signal at time t is as follows:
τ mn (t)＝τ n (t)-τ m (t)
wherein,for the spectrum of the mth multi-path signal at the time t, tau mn (t) is the time delay difference between the nth multi-path signal and the mth multi-path signal, j is the conjugate transpose, X (t, omega) is the intermediate variable, A m,t 、D m,t 、τ m,t 、A n,t 、D n,t Is constant, & lt>Is a fourier transform and ω is the angular frequency of the received signal.
Further, the position of continuous change of the peak in the time-frequency domain spectrogram of the received signal obtained in the first step is taken as the track of the interference fringe between the shallow sea multipath signals, specifically:
first, when r 2 ＞＞z s z r And acquiring the arrival time delay of the multi-path signal, wherein the arrival time delay is as follows:
wherein τ 0 For the propagation arrival time delay of the direct sound, τ 1 For sea surface reflected sound propagation arrival time delay, r is the horizontal distance between the sound source and the receiver, z s For sound source depth, z r For receiver depth sd 0 The initial depth of the sound source;
then, the arrival time delay tau is propagated by using the direct sound 0 And sea surface reflected sound propagation arrival time delay tau 1 Obtaining the arrival time delay difference tau of direct sound and sea surface reflected sound 01 ；
Finally, utilizing the arrival time delay difference tau of the direct sound and the sea surface reflected sound 01 And obtaining the track of interference fringes among the shallow sea multipath signals.
Further, the direct sound is the sea surfaceTime delay difference tau of arrival of reflected sound 01 The following formula:
further, the track of the interference fringes among the shallow sea multipath signals is as follows:
wherein k is the interference fringe number, f k And (t) is the trace of interference fringes between shallow sea multipath signals.
Further, the frequency interference period of the interference fringes in the third step is obtained by the following formula:
further, the time interference period of the interference fringes in the third step is obtained by the following formula:
wherein t is k (f) Is an intermediate variable and f is the received signal frequency.
Further, the interference fringe width is obtained by the following formula:
wherein B is f (t) the width of the interference fringe in the frequency axis direction is B t (f) Is the width of the interference fringe in the time axis direction.
The beneficial effects of the invention are as follows:
the invention provides a method for analyzing a track equation, an interference period and a variation rule of an interference fringe width of an underwater vertical motion sound source sound field interference structure. The invention carries out underwater sound field modeling based on the ray model, has simple and visual form and small operand. The invention deduces the track equation of the underwater sound field interference fringes of the underwater vertical motion sound source, obtains the period and the width of the interference fringes of the underwater sound field of the underwater vertical motion sound source, analyzes the change relation of the interference fringes along with the motion state of the sound source and the position of the receiver, and can better analyze the underwater vertical motion characteristics so as to accurately obtain the marine environment information.
Drawings
FIG. 1 is a multi-pass signal interference fringe trace;
FIG. 2 (a) shows interference fringes at a receiving depth of 10 m;
FIG. 2 (b) shows interference fringes at a reception depth of 30 m;
FIG. 3 (a) is an interference fringe at a receiving distance of 500 m;
FIG. 3 (b) is an interference fringe at a receiving distance of 1100 m;
FIG. 4 (a) is an interference fringe at a sound source moving speed of 5 m/s;
FIG. 4 (b) is an interference fringe at a sound source movement speed of 50 m/s;
FIG. 5 (a) receives a lake test data interferometry structure at a horizontal distance of 128 m;
FIG. 5 (b) receives the lake test data interferometry structure at a horizontal distance of 236m.
Detailed Description
The first embodiment is as follows: the specific process of the interference structural rule analysis method of the sound field of the underwater vertical motion sound source in the embodiment is as follows:
firstly, constructing a Doppler multi-path signal sound field model of a shallow sea underwater vertical motion sound source based on a ray theory, and then acquiring a time-frequency domain spectrogram of a signal received by a receiver by using the Doppler multi-path signal sound field model:
step one, constructing a Doppler multi-path signal sound field model of a shallow sea underwater vertical motion sound source based on a ray theory:
sparse time-varying underwater acoustic channels are typically modeled as the sum of a plurality of time-varying impulse responses, namely:
wherein A is m (t) is the amplitude of the mth multipath signal at the moment t, D m (t) is the Doppler coefficient of the mth multipath signal at the moment t, τ m (t) is the propagation delay of the mth multi-path signal at the moment t, v is the vertical movement speed of the sound source, and theta m (t) is the emergence angle of the mth multi-path signal at the moment t, the direction of the sound source is 0 DEG, the direction of the sound source is positive, delta (·) is the underwater channel response, c is the underwater sound velocity, and h (t) is the sparse time-varying underwater sound channel;
wherein shallow sea refers to an area with a water depth of less than 500m.
Step two, acquiring a time-frequency domain spectrogram of a signal received by a receiver by utilizing the Doppler multi-path signal sound field model obtained in the step one to one:
first, a signal received by a receiver is acquired: the broadband radiation noise signal of the underwater motion sound source is s (t). The receiver received signal x (t) is the convolution of the source radiated noise signal s (t) and the channel h (t), and the relation is:
then, the receiver receives the signal according to the length TCut-off, T should be as small as possible in order to guarantee that the signal of intercepting signal is steady in the multiple paths, have higher relativity. Because the time window is shorter in length, the signal amplitude, doppler coefficient and time delay in the time window at the moment t are assumed to be constant, namely A m (t)≈A m,t ，D m (t)≈D m,t ，τ m (t)≈τ m,t . Fourier transforming the intercepted signal at the time t to obtain a spectrogram I (t, ω) of the received signal at the time t:
wherein,for the spectrum of the mth multi-path signal at the time t, ω represents the angular frequency of the received signal, τ mn (t)＝τ n (t)-τ m (t)，τ mn (t) is the time delay difference of any two multi-path signals, wherein the time delay difference is conjugate transpose, m and n are two different multi-path signal labels, j is an imaginary unit, X (t, omega) is an intermediate variable, and A m,t 、D m,t 、τ m,t 、A n,t 、D n,t Is constant, & lt>Is a fourier transform.
Step two, obtaining the track of interference fringes among the shallow sea multipath signals by utilizing the time-frequency domain spectrogram of the received signals obtained in the step one:
when ωτ mn (t) = (2 k-1) pi, k=1, 2,3 …, i.e. the locus of interference fringes between shallow sea multipass signalsIn this case, the peak is represented in the time spectrum I (t, ω) of the received signal, and the position of the continuous change of the peak is definedFor the interference fringe trace, k represents the interference fringe order number, f=ω/2pi, and f represents the frequency of the received signal.
The main components of the interference structure are interference fringes formed between direct sound and sea surface primary reflection sound. Under ideal isoacoustic speed hydrologic conditions, the expression of the propagation arrival time delay of the direct sound and the sea surface reflected sound can be written as:
wherein τ 0 For the propagation arrival time delay of the direct sound, τ 1 For sea surface reflected sound propagation arrival time delay, r is the horizontal distance between the sound source and the receiver, z s For sound source depth, z r For receiver depth sd 0 The initial depth of the sound source;
when r is 2 ＞＞z s z r In this case, the arrival delay of the multi-path signal may be:
the arrival time delay difference tau of the direct sound and the sea surface reflected sound 01 The method comprises the following steps:
the direct sound-sea surface reflected sound interference fringe trace is:
the above formula can also be expressed as:
where f is the received signal frequency;
step three, based on the tracks of interference fringes among the shallow sea multipath signals obtained in the step two, the interference period and the interference fringe width of the interference fringes are obtained, and therefore the change rule of the interference fringes is obtained:
step three, obtaining a frequency interference period of the direct reaching sound-sea surface reflection sound interference fringe by utilizing the tracks of the interference fringes among the shallow sea multipath signals obtained in the step two:
step three, obtaining a time interference period of the direct sound-sea surface reflected sound interference fringe by utilizing the frequency interference period of the direct sound-sea surface reflected sound interference fringe obtained in the step two:
step three, the frequency interference period obtained in the step three and the time interference period obtained in the step three are utilized to obtain the frequency axis direction width and the time axis direction width of the interference acquisition fringes:
defining the width of the power spectrum peak at the moment t along the frequency axis direction as the width B of the interference fringe in the frequency axis direction when the power spectrum peak is reduced by 6dB f (t) the width in the time axis direction of the power spectrum peak at the frequency f at 6dB is the interference fringe time axis direction width B t (f)：
Step three, utilizing the interference period and the interference fringe width of the interference fringe to obtain the change rule of the interference fringe:
(1) The sound field interference structure of the underwater high-speed vertical motion sound source is formed by superposing a plurality of interference fringes, the main components of the sound field interference structure are direct sound-sea surface reflection sound interference fringes, the interference fringe tracks are only related to the time delay difference of the multi-path signals, and the interference period is in inverse relation with the time delay difference.
(2) Frequency interference period Δf (t) of interference fringe and width B in frequency axis direction f (t) with receiver depth z r Is decreased with increasing horizontal distance r and movement time t.
(3) Time interference period Δt (f) of interference fringe and width B in time axis direction t (f) With receiver depth z r And the frequency f decreases with increasing horizontal distance r.
And step four, obtaining marine environment information based on the interference fringe change rule obtained in the step three.
Examples: in order to verify the effect of the invention, the invention is verified by adopting a simulation and lake test data analysis method:
simulation 1 is used for verifying a shallow sea multi-path signal interference fringe track equation in the invention:
the simulation parameters are as follows: the underwater sound velocity is 1500m/s and the like, the horizontal distance of the receiver is 500m, the depth is 20m, and the sound source moves vertically from the underwater depth of 90m to the depth of 10m at a constant speed, and the velocity is 30m/s. Sediment is taken as a submarine sediment layer, the thickness of the sediment layer is 10m, the sound velocity of the sediment layer is 1677m/s, and the density is 1.83g/cm 3 The attenuation coefficient is 0.1 dB/lambda, the sound velocity of the infinite semi-space layer of the seabed is 1900m/s, and the density is 2.0g/cm 3 The attenuation coefficient was 0.5 dB/lambda.
The time-frequency domain interference fringes of the received signal of the receiver are shown in fig. 1, wherein the dark gray dotted line is the theoretical trace of the interference fringes in the invention. Analysis of FIG. 1 shows that the theoretical trajectory coincides with the direct sound-sea surface reflected sound interference fringes, and the calculation of the multi-path signal interference fringe trajectory equation in the invention is verified to be correct.
Simulation 2 is used for verifying the rule of influence of the receiving depth of the receiver on interference fringes in the invention:
the simulation parameters are as follows: the underwater sound velocity is 1500m/s and the like, the horizontal distance of the receiver is 500m, and the depth is 10m and 30m respectively. The sound source moves vertically from the underwater 90m depth to the underwater 10m depth at a constant speed of 30m/s. Sediment is taken as a submarine sediment layer, the thickness of the sediment layer is 10m, the sound velocity of the sediment layer is 1677m/s, and the density is 1.83g/cm 3 The attenuation coefficient is 0.1 dB/lambda, the sound velocity of the infinite semi-space layer of the seabed is 1900m/s, and the density is 2.0g/cm 3 The attenuation coefficient was 0.5 dB/lambda.
The time-frequency domain interference fringes of the reception distance reception signals of different levels are shown in fig. 2 (a) -2 (b). As can be seen from analysis of fig. 2 (a) -2 (b), the horizontal receiving distance of the receiver is increased, and the interference period in the frequency axis direction and the time axis direction of the interference fringes is reduced, so that the influence of the horizontal receiving distance on the variation rule of the interference fringe period in the invention is verified.
Simulation 3 is used to verify the effect rule of the horizontal distance of the receiver on the interference fringes in the invention.
The simulation parameters are as follows: the underwater sound velocity is 1500m/s and the like, the depth of the receiver is 30m, and the horizontal distances are 500m and 1100m respectively. The sound source moves vertically from the underwater 90m depth to the underwater 10m depth at a constant speed of 30m/s. Sediment is taken as a submarine sediment layer, the thickness of the sediment layer is 10m, the sound velocity of the sediment layer is 1677m/s, and the density is 1.83g/cm 3 The attenuation coefficient is 0.1 dB/lambda, the sound velocity of the infinite semi-space layer of the seabed is 1900m/s, and the density is 2.0g/cm 3 The attenuation coefficient was 0.5 dB/lambda.
The time-frequency domain interference fringes of the reception distance reception signals of different levels are shown in fig. 3 (a) -3 (b). As can be seen from analysis of fig. 3 (a) -3 (b), the horizontal receiving distance of the receiver is increased, and the interference period in the frequency axis direction and the time axis direction of the interference fringes is reduced, so that the influence of the receiving depth on the variation rule of the interference fringe period in the invention is verified.
Simulation 4 is used for verifying the influence rule of the sound source movement speed on interference fringes in the invention.
The simulation parameters are as follows: the underwater sound velocity is 1500m/s and the like, the depth of the receiver is 30m, and the horizontal distance is 500m. The sound source moves vertically from the underwater 90m depth to the underwater 10m depth at a constant speed of 5m/s and 50m/s respectively. Sediment is taken as a submarine sediment layer, the thickness of the sediment layer is 10m, the sound velocity of the sediment layer is 1677m/s, and the density is 1.83g/cm 3 The attenuation coefficient is 0.1 dB/lambda, the sound velocity of the infinite semi-space layer of the seabed is 1900m/s, and the density is 2.0g/cm 3 The attenuation coefficient was 0.5 dB/lambda.
The time-frequency domain interference fringes of the received signals at different sound source movement speeds are shown in fig. 4 (a) -4 (b).
As can be seen from analysis of fig. 4 (a) -4 (b), when the sound source speed is low, the interference fringes are clear due to the more number of interference fringe sampling points; when the sound source speed was 50m/s, interference fringes were still observed, but the interference fringes were poor in definition. In both cases, the position, number, period and width of the interference fringe track are unchanged. The Doppler coefficient is verified to have no effect on the trace, period and width of the interference fringes.
The lake test data processing verifies the influence rule of the receiving horizontal distance on the interference fringes in the invention through actual data. Relevant experiments were performed in the thousand island lake at month 4 of 2022. The water depth of the test area is about 67m, the water surface is calm, and the reflection coefficient of the lake bottom is larger because a large number of artificial buildings and submerged roads exist at the lake bottom. The measured sound velocity profile and the experimental situation are shown in fig. 5. And closing main and auxiliary machines of the test ship during the test, so as to reduce the interference of ship noise to the greatest extent. The test uses 2 buoys, the sound pressure hydrophone depth is about 42m, and the horizontal distance between the buoys and the sound source is 128m and 236m respectively. The sound source is hung at the stern, and is lifted up to the depth of 10.8m from the depth of 36m at a constant speed through a motor, and the movement time is 140s. The sound source signal is broadband continuous spectrum noise, the short-time Fourier transform time window is a hamming window, and the length is 1s. The data processing frequency band is 1500 Hz-5000 Hz. Wherein, the white solid line is the theoretical track of direct sound-sea surface reflected sound interference fringes, and the white dotted line is the theoretical track of direct sound-primary sea surface reflected sound interference fringes.
The interference structures of the different reception horizontal distances are shown in fig. 5 (a) -5 (b). As can be seen from an analysis of fig. 5 (a) to 5 (b), as the receiving distance increases, the interference period of both the direct sound-sea surface reflected sound interference fringes and the direct sound-sea bottom reflected sound interference fringes increases, the interference fringe width increases, and the interference fringes become sparse. The lake test data verifies the influence of the receiving horizontal distance on the interference fringe rule in the invention.

Claims (10)

1. An interference structural rule analysis method of an underwater vertical motion sound source sound field is characterized by comprising the following specific processes:
step one, constructing a Doppler multi-path signal sound field model of a shallow sea vertical motion sound source, and then acquiring a time-frequency domain spectrogram of a signal received by a receiver by using the Doppler multi-path signal sound field model:
step two, obtaining the position of continuous change of wave peaks in the time-frequency domain spectrogram of the received signal obtained in the step one, and taking the position as a track of interference fringes among shallow sea multipath signals;
step three, based on the tracks of interference fringes among the shallow sea multipath signals obtained in the step two, obtaining the interference period and the interference fringe width of the interference fringes, so as to obtain the change rule of the interference fringes;
the interference period of the interference fringes includes: a frequency interference period of the interference fringes and a time interference period of the interference fringes;
the interference fringe width includes: the frequency axis direction width of the interference fringes and the time axis direction width of the interference fringes;
and step four, obtaining marine environment information based on the interference fringe change rule obtained in the step three.
2. The method for analyzing the interference structural rule of the sound field of the underwater vertical movement sound source according to claim 1, which is characterized in that: in the first step, a Doppler multi-path signal sound field model of a shallow sea vertical motion sound source is constructed, and the Doppler multi-path signal sound field model is represented by the following formula:
wherein A is m (t) is the amplitude of the mth multipath signal at the moment t, D m (t) is the Doppler coefficient of the mth multipath signal at the moment t, τ m (t) is the propagation delay of the mth multi-path signal at the moment t, v is the vertical movement speed of the sound source, and theta m (t) is the emergence angle of the mth multi-path signal at the moment t, delta (·) is the underwater channel response, c is the underwater sound velocity, and h (t) is the sparse time-varying underwater sound channel.
3. The method for analyzing the interference structural rule of the sound field of the underwater vertical movement sound source according to claim 2, which is characterized in that: the step one of obtaining a time-frequency domain spectrogram of a signal received by a receiver by using a Doppler multi-path signal sound field model comprises the following steps:
first, a signal x (t) received by a receiver is acquired, as follows:
wherein s (t) is an underwater moving sound source broadband radiation noise signal;
then, the signal x (t) received by the receiver is truncated to obtain a truncated signal at the time t, and fourier transform is performed on the truncated signal at the time t to obtain a spectrogram I (t, ω) of the received signal at the time t.
4. The interference structural rule analysis method of the sound field of the underwater vertical movement sound source according to claim 3, wherein the interference structural rule analysis method is characterized by comprising the following steps of: the spectrogram I (t, omega) of the received signal at the time t is as follows:
τ mn (t)＝τ n (t)-τ m (t)
wherein,for the spectrum of the mth multi-path signal at the time t, tau mn (t) is the time delay difference between the nth multi-path signal and the mth multi-path signal, j is the conjugate transpose, X (t, omega) is the intermediate variable, A m,t 、D m,t 、τ m,t 、A n,t 、D n,t Is constant, & lt>Is a fourier transform and ω is the angular frequency of the received signal.
5. The method for analyzing the interference structural rule of the sound field of the underwater vertical movement sound source according to claim 4, which is characterized in that: the position of continuous change of the wave crest in the time-frequency domain spectrogram of the received signal obtained in the first step is taken as the track of interference fringes among the shallow sea multipath signals, and the method specifically comprises the following steps:
first, when r 2 ＞＞z s z r And acquiring the arrival time delay of the multi-path signal, wherein the arrival time delay is as follows:
wherein τ 0 For the propagation arrival time delay of the direct sound, τ 1 For sea surface reflected sound propagation arrival time delay, r is the horizontal distance between the sound source and the receiver, z s For sound source depth, z r For receiver depth sd 0 The initial depth of the sound source;
then, the arrival time delay tau is propagated by using the direct sound 0 And sea surface reflected sound propagation arrival time delay tau 1 Obtaining the arrival time delay difference tau of direct sound and sea surface reflected sound 01 ；
Finally, utilizing the arrival time delay difference tau of the direct sound and the sea surface reflected sound 01 And obtaining the track of interference fringes among the shallow sea multipath signals.
6. The method for analyzing the interference structural rule of the sound field of the underwater vertical movement sound source according to claim 5, which is characterized in that: the arrival time delay difference tau of the direct sound and the sea surface reflected sound 01 The following formula:
7. the method for analyzing the interference structural rule of the sound field of the underwater vertical movement sound source according to claim 6, which is characterized in that: the track of interference fringes among the shallow sea multipath signals is represented by the following formula:
wherein k is the interference fringe number, f k And (t) is the trace of interference fringes between shallow sea multipath signals.
8. The method for analyzing the interference structural rule of the sound field of the underwater vertical movement sound source according to claim 7, which is characterized in that: the frequency interference period of the interference fringes in the third step is obtained by the following formula:
9. the method for analyzing the interference structural rule of the sound field of the underwater vertical movement sound source according to claim 8, which is characterized in that: the time interference period of the interference fringes in the third step is obtained by the following formula:
wherein t is k (f) Is an intermediate variable and f is the received signal frequency.
10. The method for analyzing the interference structural rule of the sound field of the underwater vertical movement sound source according to claim 9, which is characterized in that: the interference fringe width is obtained by the following formula:
wherein B is f (t) the width of the interference fringe in the frequency axis direction is B t (f) Is the width of the interference fringe in the time axis direction.
CN202311358243.8A 2023-10-19 2023-10-19 Interference structural rule analysis method for sound field of underwater vertical motion sound source Pending CN117419794A (en)

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