Method for enhancing fluctuation characteristic difference of line spectrums of water surface and underwater sound sources

Abstract

The invention discloses a method for enhancing fluctuation characteristic differences of line spectrums of water surface and underwater sound sources. The method comprises the following steps: (1) initializing processing parameters; (2) reading a radiation noise sampling sequence received by the hydrophone, dividing the sampling sequence into a plurality of sub-sampling sequences, and calculating a bispectrum diagonal slice of each sub-sampling sequence; and (3) accumulating the bispectrum diagonal slice energy of each sub-sampling sequence at all frequency points in the line spectrum frequency cluster, and constructing line spectrum frequency cluster energy and sequence. And (4) dividing the line spectrum frequency cluster energy and the sequence into a plurality of segments, calculating a discrete coefficient of each segment, and sequentially forming a fluctuation index sequence based on the discrete coefficients. And (5) constructing intervals for measuring the fluctuation characteristic difference of the water surface and underwater sound source line spectrums under different fluctuation indexes, comparing the interval width corresponding to each fluctuation index, and indicating that the larger the interval width is, the more obvious the enhancement effect of the fluctuation index on the difference is.

Description

Technical Field

[0001] This invention relates to a method for enhancing the differences in the spectral fluctuation characteristics of sound sources on the water surface and underwater, belonging to the field of underwater acoustic target radiated noise signal feature extraction and recognition technology. Background Technology

[0002] Ship radiated noise mainly includes mechanical noise, propeller noise, and hydrodynamic noise. By extracting line spectrum features through power spectrum analysis, or extracting information such as propeller shaft frequency and blade count through modulation spectrum analysis, characteristic parameters related to ship structure and operating status can be obtained from the radiated noise. Among these, the low-frequency line spectrum of radiated noise has become one of the core features for target identification by passive sonar due to its good stability and long propagation distance.

[0003] The depth of a ship target is a key factor in determining its target attributes. Based on its navigation depth, ship targets can be classified into surface targets and underwater targets. In recent years, researchers have proposed a line spectrum source depth identification method based on the fluctuation characteristics of radiated noise line spectra. This method utilizes the depth modulation effect of the marine environment on radiated noise line spectrum sources and analyzes the fluctuation characteristics of the line spectrum to determine the depth attributes of the target sound source.

[0004] However, with the development of vibration reduction and noise reduction technologies in recent years, the line spectrum intensity of ship radiated noise has been significantly reduced, and the mid-to-high frequency line spectrum has been effectively suppressed, making the extraction of the low-frequency line spectrum increasingly difficult. Furthermore, due to the strong low-frequency interference in the marine environment, the extracted radiated noise line spectrum contains a large number of interference components, severely weakening the robustness of traditional depth identification methods based on power spectrum fluctuations, leading to a significant decrease in the accuracy of target attribute discrimination. Therefore, how to effectively enhance the distinguishability of surface and underwater sound source characteristics in low signal-to-noise ratio environments and achieve accurate and robust sound source depth attribute identification has become a key issue that urgently needs to be addressed to improve the detection performance of passive sonar systems.

[0005] Higher-order spectral analysis, as a nonlinear signal processing technique, can suppress Gaussian noise while preserving the amplitude and phase information of the signal, giving it a unique advantage in the field of ship radiated noise feature extraction. With the development of parallel computing technology, feature analysis methods based on higher-order spectra have gradually become a research hotspot in the field of passive sonar target recognition in recent years. However, further research is still needed on how to utilize higher-order spectra to further explore the differences in the spectral fluctuation characteristics of surface and underwater sound sources, in order to achieve effective identification of the depth of radiated noise line spectrum sources in low signal-to-noise ratio environments. Summary of the Invention

[0006] Technical Problem: The purpose of this invention is to address the insufficient distinguishability of surface and underwater sound sources based on power spectrum fluctuation index under low signal-to-noise ratio conditions, and to provide a method for enhancing the difference in line spectrum fluctuation characteristics between surface and underwater sound sources. This method performs bispectral analysis on the radiated noise sampling sequence received by a hydrophone, calculates the energy sum of bispectral diagonal slices within the line spectrum frequency clusters of each sub-sampling sequence, and then constructs a line spectrum frequency cluster energy sum sequence. The line spectrum frequency cluster energy sum sequence is segmented, and the discrete coefficients corresponding to each segment are calculated to form a discrete coefficient sequence. Based on the discrete coefficient sequence, an interval is constructed to measure the difference in line spectrum fluctuation characteristics between surface and underwater sound sources. By increasing the width of the difference interval between sound sources with different attributes, more discriminative feature support is provided for the accurate classification of surface and underwater targets.

[0007] Technical solution: A method for enhancing the difference in line spectrum fluctuation characteristics between surface and underwater sound sources according to the present invention includes the following steps:

[0008] Step 1: Initialize processing parameters, including the line spectrum frequency points of the radiated noise sampling sequence. k 0. Sampling rate f s Sampling time T Number of sampling points N、 Number of points in the integral window of the Discrete Fourier Transform W Step points S Frequency resolution Δ and number of sub-sampling sequences M ;

[0009] Step 2: Read the radiated noise sampling sequence received by the hydrophone and divide the sampling sequence into... M For each subsampled sequence, calculate the Discrete Fourier Transform of that subsampled sequence. X m ( k )(in, X m ( k ) indicates the first m Discrete Fourier transform of each subsampled sequence), take X m ( k At frequency 2 k After the complex conjugation at the point, we get (in, Indicates the first m The discrete Fourier transform of each subsampled sequence at frequency 2 k (the conjugate at the location), X m ( k The square of ) and Multiplication yields a bispectral diagonal slice of each subsample sequence. Bm ( k , k )(in, B m ( k , k ) indicates the first m Values ​​of bispectral diagonal slices of each subsampled sequence k (for frequency index)

[0010] Step 3, divide the subsampled sequence into... k The bispectral diagonal slice energies at all frequency points within the 0-centered line spectrum frequency cluster are summed to obtain the line spectrum frequency cluster energy. E m ( k 0) (wherein, E m ( k 0) indicates the first m The values ​​of the line spectral frequency cluster energies corresponding to each sub-sampling sequence, and the values ​​of the energy of each sub-sampling sequence. E m ( k 0) values ​​form the energy and sequence of line spectrum frequency clusters;

[0011] Step 4, divide the line spectrum frequency cluster energy and sequence into Q Each segment (of which, Q The value is determined based on the line spectrum frequency cluster energy and the total length of the sequence. M Sub-segment length L and sub-segment overlap length K Sure, Calculate the mean and standard deviation of each segment, and use the ratio of the mean to the standard deviation as the coefficient of variation for each segment. The coefficients of variation of each segment are used to form a fluctuation index sequence based on the coefficients of variation.

[0012] Step 5: Take the maximum and minimum values ​​of different fluctuation index sequences as the upper and lower bounds of the fluctuation index interval, calculate the difference between the upper and lower bounds as the interval width, and compare the interval widths corresponding to each fluctuation index. The larger the interval width, the more significant the enhancement effect of the fluctuation index on the difference in the fluctuation characteristics of the water surface and underwater sound source line spectrum.

[0013] in,

[0014] Step 1 specifically includes the following steps:

[0015] Step 1.1: Determine the line spectrum frequency points of the radiated noise sampling sequence. k 0, sampling rate f s Sampling time T and number of sampling points N ;

[0016] Step 1.2: Set the integration window length and number of points for the discrete Fourier transform of the sampled sequence. W and step points S Calculate the frequency resolution Δ = f s / W Calculate the number of subsampled sequences. .

[0017] Step 2 specifically includes the following steps:

[0018] Step 2.1: Read in the radiated noise sampling sequence received by the hydrophone. x ( n ), n = 0, 1,…, N - 1;

[0019] Step 2.2, sample the radiated noise sequence x ( n According to the length of the integral window (points) W and step points S Divided into M There are n subsampling sequences, denoted as _n_i ... x m ( i ), i = 0, 1,…, W – 1, m =1, 2,…, M Calculate each subsample sequence x m ( i (Integral window length points) W The discrete Fourier transform within the range yields the following results: M A discrete Fourier transform sequence X m ( j ), j =0, 1,…, W - 1;

[0020] Step 2.3, calculate each subsample sequence x m ( i bispectral diagonal slices B m ( k , k ):

[0021]

[0022] in, k For frequency index,X m ( k ) is the first m Discrete Fourier transform of subsampled sequences For the first m The discrete Fourier transform of each subsampled sequence at frequency 2 k Complex conjugate at the location, B m ( k , k ) is the first m The values ​​of bispectral diagonal slices of each subsampled sequence.

[0023] Step 3 specifically includes the following steps:

[0024] Step 3.1, calculate the online spectral frequency clusters for each sub-sample sequence [ k 0-2Δ, k 0+2Δ] (where Δ is the frequency resolution, Δ = f s / W Within ) B m ( k , k The square of the modulus of the sampled data is used to sum the bispectral diagonal slice energy at each frequency point within the online spectral frequency cluster, resulting in the subsampled sequence. x m ( i The corresponding line spectrum frequency cluster energy and E m ( k 0):

[0025]

[0026] Step 3.2, all subsampled sequences x m ( i The corresponding line spectrum frequency cluster energy and E m ( k 0) Energy and sequence constituting the frequency clusters of the line spectrum E ( m ),Right now:

[0027] Step 4 specifically includes the following steps:

[0028] Step 4.1, convert the line spectrum frequency cluster energy and sequence E ( m ) divided into Q A length of L The subsequences have an overlap length of 0. K , record theq The subsequences are E q ( m q ), m q The value is 1+( L - K ()( q- 1)≤ m q ≤ L+ ( L - K ()( q- 1), q =1,2,…, Q

[0029] Step 4.2, calculate each subsequence E q ( m q mean m ( q ):

[0030]

[0031] Step 4.3, calculate each subsequence E q ( m q Standard deviation s ( q ):

[0032]

[0033] Step 4.4, calculate each subsequence E q ( m q The coefficients of dispersion C v ( q ):

[0034]

[0035] Step 5 specifically includes the following steps:

[0036] Step 5.1, based on the proposal in the reference (Wagstaff RA The AWSUM filter: a 20-dB gainfluctuation-based processor[J]. IEEE Journal of Oceanic Engineering, 1997, 22(1): 110–118.). d Fluctuation statistics A 1,4 Fluctuation statistics and the present invention C v The calculation methods for fluctuation statistics are as follows: d Fluctuation index series d ( q ), A 1,4 Fluctuation index series A 1,4 ( q )as well as C v Fluctuation index series C v ( q );

[0037] Step 5.2: Construct difference intervals for the three types of fluctuation index sequences mentioned above: extract the minimum value in the fluctuation index sequence corresponding to the surface sound source as the upper bound of the difference interval; extract the maximum value in the fluctuation index sequence corresponding to the underwater sound source as the lower bound of the difference interval; the upper bound and the lower bound together constitute an interval for measuring the difference in the fluctuation characteristics of the line spectrum of surface and underwater sound sources, and the width of the difference interval is defined as the difference between the upper bound and the lower bound.

[0038] Step 5.3: Compare the width of the difference intervals formed by the three fluctuation indices. The wider the interval, the more significant the effect of the corresponding fluctuation index in enhancing the difference in the fluctuation characteristics of the line spectrum of the water surface and underwater sound sources.

[0039] Beneficial Effects: Compared with existing technologies, the method disclosed in this invention has the following advantages: Compared with power spectrum analysis methods, bispectral analysis is more sensitive to line spectrum fluctuations caused by changes in sound source depth and can more effectively suppress background noise. This invention utilizes the discrete coefficients of bispectral diagonal slice energy to replace the traditional power spectrum fluctuation index statistics, which can significantly broaden the difference range of surface and underwater sound source line spectra, thus improving the robustness and reliability of subsequent sound source depth attribute identification algorithms in low signal-to-noise ratio environments. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention.

[0041] Figure 2 The sound source in Example 1 S a and S b Line spectra based on power spectrum d Fluctuation index sequence.

[0042] Figure 3The sound source in Example 1 S a and S b Line spectra based on power spectrum A 1,4 Fluctuation index sequence.

[0043] Figure 4 The sound source in Example 1 S a and S b Line spectra based on bispectral diagonal slice energy spectrum C v Fluctuation index sequence. Detailed Implementation

[0044] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments:

[0045] This invention constructs a discrete coefficient sequence of the frequency cluster energy sum of a bispectral diagonal slice of radiated noise line spectrum. C v ( q This enhances the difference in the undulation characteristics of the sound spectrum between the water surface and underwater sound sources.

[0046] Example 1:

[0047] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.

[0048] A method for enhancing the differences in line spectrum undulation characteristics between surface and underwater sound sources, such as Figure 1 As shown, it includes the following steps:

[0049] Step 1 is as follows:

[0050] Step 1.1: Select the same sound velocity profile as the SwellEx-96 experiment for simulation, and use the Kraken model to simulate and generate a shallow sea channel. Sound source S a The source emits a 10Hz line spectrum signal at a depth of 5m; S b The sound source radiates a 30Hz line spectrum signal at a depth of 50m. The Monte Carlo method is used to simulate the depth fluctuation of the sound source in a real marine environment. S a Harmony Source S b The depths all exhibit random fluctuations following a Gaussian distribution. The marine environmental noise is set to Gaussian colored noise, and the sampling rate of the radiated noise data is [missing information]. f s =3.2kHz, sampling time T= 272s, number of sampling points N=870400.

[0051] Step 1.2: Set the integration time for the discrete Fourier transform of the sampled sequence to 1 second, the step time to 1 second, and the corresponding number of integration window points. W= 3200, step points S= 3200, calculate the resolution Δ = f s / W =1Hz, calculate the number of subsampling sequences. .

[0052] Step 2 is as follows:

[0053] Step 2.1: Read in the radiated noise sampling sequence received by the hydrophone. x ( n ), n = 0, 1,…, N - 1;

[0054] Step 2.2, sample the radiated noise sequence x ( n According to the length of the integral window (points) W and step points S Divided into M There are n subsampling sequences, denoted as _n_i ... x m ( i ), i = 0, 1,…, W – 1, m =1, 2,…, M Calculate each subsample sequence x m ( i (Integral window length points) W The discrete Fourier transform within the range yields the following results: M A discrete Fourier transform sequence X m ( j ), j =0, 1,…, W - 1;

[0055] Step 2.3, calculate each subsample sequence x m ( i bispectral diagonal slices B m ( k , k ):

[0056]

[0057] in, k For frequency index, X m ( k ) is the first m Discrete Fourier transform of subsampled sequences For the first m The discrete Fourier transform of each subsampled sequence at frequency 2 k Complex conjugate at the location, B m ( k , k ) is the first m The values ​​of bispectral diagonal slices of each subsampled sequence.

[0058] Step 3 specifically involves:

[0059] Step 3.1, calculate the online spectral frequency clusters for each sub-sample sequence [ k 0-2Δ, k 0+2Δ] (where Δ is the frequency resolution, Δ = f s / W Within ) B m ( k , k The square of the modulus of the sampled data is used to sum the bispectral diagonal slice energy at each frequency point within the online spectral frequency cluster, resulting in the subsampled sequence. x m ( i The corresponding line spectrum frequency cluster energy and E m ( k 0):

[0060]

[0061] Step 3.2, all subsampled sequences x m ( i The corresponding line spectrum frequency cluster energy and E m ( k 0) Energy and sequence constituting the frequency clusters of the line spectrum E ( m ),Right now:

[0062]

[0063] Step 4 specifically involves:

[0064] Step 4.1, convert the line spectrum frequency cluster energy and sequence E ( m ) divided into Q A length ofL The subsequences have an overlap length of 0. K (in, Q =222, L =50, K =49), let the first q The subsequences are E q ( m q ), m q The value is 1+( L - K ()( q- 1)≤ m q ≤ L+ ( L - K ()( q- 1), q =1,2,…, Q

[0065] Step 4.2, calculate each subsequence E q ( m q mean m ( q ):

[0066]

[0067] Step 4.3, calculate each subsequence E q ( m q Standard deviation s ( q ):

[0068]

[0069] Step 4.4, calculate each subsequence E q ( m q The coefficients of dispersion C v ( q ):

[0070]

[0071] Step 5 specifically involves:

[0072] Step 5.1, based on the proposal in the reference (Wagstaff RA The AWSUM filter: a 20-dB gainfluctuation-based processor[J]. IEEE Journal of Oceanic Engineering, 1997, 22(1): 110–118.). d Fluctuation statistics A 1,4 Fluctuation statistics and the present invention C v The calculation methods for fluctuation statistics are as follows: d Fluctuation index series d ( q ), A 1,4 Fluctuation index series A 1,4 ( q )as well as C v Fluctuation index series C v ( q Sound source S a Harmony Source S b Three types of line spectrum fluctuation index sequences d ( q ), A 1,4 ( q )and C v ( q ) respectively as Figure 2 , Figure 3 and Figure 4 As shown;

[0073] Step 5.2: Construct difference intervals for the three types of fluctuation index sequences mentioned above: extract the minimum value in the fluctuation index sequence corresponding to the surface sound source as the upper bound of the difference interval; extract the maximum value in the fluctuation index sequence corresponding to the underwater sound source as the lower bound of the difference interval; the upper bound and the lower bound together constitute an interval for measuring the difference in the fluctuation characteristics of the line spectrum of surface and underwater sound sources, and the width of the difference interval is defined as the difference between the upper bound and the lower bound. d , A 1,4 and C v The difference intervals corresponding to the three line spectrum fluctuation indices are shown in Table 1.

[0074] Table 1. Range of differences in surface and underwater line spectrum undulation characteristics corresponding to the three line spectrum undulation indices.

[0075]

[0076] Step 5.3: Compare the widths of the difference intervals formed by the three fluctuation indices. As can be seen from Table 1, the present invention proposes... C v The spectral variability index corresponds to the widest range of differences, compared to... A 1,4 index, C v The index widens the difference range of the sound source line spectrum between the surface and underwater by about 32 times, indicating that the method in this invention is most effective in enhancing the difference in the fluctuation characteristics of the sound source line spectrum between the surface and underwater.

[0077] This invention proposes a method to enhance the difference in line spectrum fluctuation characteristics between surface and underwater sound sources. It involves introducing bispectral analysis to process radiated noise sampling sequences, constructing a discrete coefficient sequence based on bispectral energy, and then using this sequence to establish a difference discrimination interval. Experimental results show that, compared to power spectrum analysis, the bispectral analysis employed in this invention is more sensitive to line spectrum fluctuations caused by changes in sound source depth, more effectively suppresses background noise, and significantly broadens the difference interval in line spectrum fluctuation characteristics between surface and underwater sound sources.

[0078] The above embodiments demonstrate that, compared to traditional statistical measures d and A 1,4 The method described in this invention enables a greater differentiation in the spectral fluctuation characteristics of surface and underwater sound sources. The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any modifications or equivalent variations made based on the technical essence of this invention shall still fall within the scope of protection claimed by this invention.

Claims

1. A method for enhancing the difference in line spectrum fluctuation characteristics of surface and underwater acoustic sources, characterized by Comprising the following steps: Step 1, initialize processing parameters, including line spectrum frequency points of radiation noise sampling sequence k 0, sampling rate f s , sampling time T , sampling point number N、 integration window length point number of discrete Fourier transform W , step point number S , frequency resolution Δ and sub-sampling sequence number M ; Step 2, read in the sequence of samples of radiated noise received by the hydrophone, divide the sequence of samples into M sub-sequences of samples, calculate the discrete Fourier transform of each sub-sequence of samples X m ( k ), wherein X m k denotes the discrete Fourier transform of the m th sub-sampled sequence, taken X m k k wherein denotes the discrete Fourier transform of the m th sub-sampled sequence, taken k X m k B m k k , wherein B m k k denotes the bispectrum diagonal slice of the m th sub-sampled sequence taken at k is the frequency index;​​​​​​​​​​​​ Step 3, accumulate the bispectrum diagonal slice energy of all frequency points in the line spectrum frequency cluster centered at k 0 to obtain the line spectrum frequency cluster energy sum E m ( k 0), wherein, E m ( k 0) represents the value of the line spectrum frequency cluster energy sum corresponding to the m th sub-sampling sequence, which is composed of the E m ( k 0) value of the line spectrum frequency cluster energy sum corresponding to each sub-sampling sequence; Step 4: Divide the line spectrum frequency cluster energy and sequence into Q There are several segments, among which... Q The value is determined based on the line spectrum frequency cluster energy and the total length of the sequence. M Sub-segment length L and sub-segment overlap length K Sure, Calculate the mean and standard deviation of each segment, and use the ratio of the mean to the standard deviation as the coefficient of variation for each segment. The coefficients of variation of each segment are used to form a fluctuation index sequence based on the coefficients of variation. Step 5, respectively, the maximum and minimum of different relief index sequence, as the upper and lower bound of the relief index interval, the difference between the upper and lower bound as the interval width, compare the interval width corresponding to each relief index, the greater the interval width, the more significant the effect of the relief index on the difference of the water surface and underwater sound source line spectrum fluctuation characteristics.

2. A method for enhancing the difference in line spectrum fluctuation characteristics of surface and underwater acoustic sources according to claim 1, characterized in that, Step 1 specifically comprises the following steps: Step 1.1, determining line spectrum frequency of radiation noise sampling sequence k 0, sampling rate f s , sampling time T and sampling point number N ; Step 1.2 Set the number of points of the integration window for the DFT of the sampling sequence W and the step number S Calculate the frequency resolution Δ = 1 / T f s / W Calculate the number of sub-sampling sequences .

3. A method for enhancing the difference in line spectrum fluctuation characteristics of surface and underwater acoustic sources according to claim 2, characterized in that, Step 2 specifically comprises the following steps: Step 2.1, reading in a sequence of samples of radiated noise received by a hydrophone x ( n ), n = 0, 1,…, N - 1; Step 2.2, the radiation noise sampling sequence x ( n ) is divided into W sub-sampling sequences according to the integral window length point number S and the step point number M , and each sub-sampling sequence is recorded as x m ( i ), i= 0, 1, …, W - 1, m = 1, 2, …, M , each sub-sampling sequence x m ( i ) is calculated in the discrete Fourier transform of the integral window length point number W , to obtain M discrete Fourier transform sequences X m ( j ), j = 0, 1, …, W - 1; Step 2.

3. Calculate each subsampled sequence x m ( i , the bispectrum diagonal slice B m ( k , k ): ; wherein k is a frequency index, X m ( k ) is a discrete Fourier transform of the m th sub-sampled sequence, is a complex conjugate of a discrete Fourier transform of the m th sub-sampled sequence at frequency 2 k B m ( k , k ) is a bispectrum diagonal slice value of the m th sub-sampled sequence.​ 4. A method for enhancing the difference in line spectrum fluctuation characteristics of surface and underwater acoustic sources according to claim 3, characterized in that, Step 3 specifically comprises the following steps: Step 3.1, compute the modulus squared of each subsampled sequence at the online spectral frequency cluster k 0-2Δ, k 0+2Δ] range B m ( k , k ) where Δ is the frequency resolution, Δ = 1 / N f s / W , sum the bispectrum diagonal slice energy at each frequency bin within the online spectral frequency cluster to obtain the subsampled sequence x m ( i ) corresponding online spectral frequency cluster energy sum E m ( k 0): ; Step 3.2, all sub-sampling sequences x m ( i ) Corresponding line spectral frequency cluster energy sum E m ( k 0) Constituting line spectral frequency cluster energy sum sequence E ( m ), i.e. .

5. A method for enhancing the difference in line spectrum fluctuation characteristics of surface and underwater acoustic sources according to claim 1, characterized in that, Step 4 specifically comprises the following steps: Step 4.1, split the line spectrum frequency cluster energy and sequence E ( m ) into Q sub-sequences with length L , and the overlap length between two adjacent sub-sequences is K , and the q th sub-sequence is denoted as E q ( m q ), m q = 1 + ( L - K ) q- 1) ≤ m q ≤ L+ ( L - K ) q- 1), q = 1, 2, …, Q Step 4.2, calculating the mean value of each sub-sequence E q ( m q ) of the mean value μ ( q ) : ； Step 4.3, calculating the standard deviation of each sub-sequence E q ( m q ) of the standard deviation σ ( q ): ； Step 4.4, calculating the discrete coefficient of each sub-sequence E q ( m q ) of the discrete coefficient C v ( q ): 。 6. A method for enhancing the difference in line spectrum fluctuation characteristics of surface and underwater acoustic sources according to claim 5, characterized in that, Step 5 specifically comprises the following steps: Step 5.1, according to δ , A 1,4 And the invention proposed C v The calculation methods for fluctuation statistics are as follows: δ Fluctuation index series δ ( q ), A 1,4 Fluctuation index series A 1,4 ( q )as well as C v Fluctuation index series C v ( q ); Step 5.2, respectively, for the above three kinds of relief index sequence to build difference interval: extract the minimum value in the relief index sequence corresponding to the water surface sound source as the upper bound of the difference interval; extract the maximum value in the relief index sequence corresponding to the underwater sound source as the lower bound of the difference interval; the upper bound and the lower bound together constitute an interval for measuring the difference of the water surface and underwater sound source line spectrum fluctuation characteristics, the width of the difference interval is defined as the difference between the upper bound and the lower bound; Step 5.3, compare the width of the difference interval formed by the three kinds of relief index, the greater the interval width, the more significant the effect of the corresponding relief index in enhancing the difference of the water surface and underwater sound source line spectrum fluctuation characteristics.

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