A method for predicting the fluctuation interval of ocean sound field based on parabolic equation theory

Abstract

The present invention discloses a method for predicting the fluctuation interval of ocean sound field based on parabolic equation theory. The present invention comprises the following steps: first, obtaining original environmental information and determining the disturbance interval of ocean environmental parameters; then, combining the disturbance interval of ocean environmental parameters, rasterizing the ocean environmental area with disturbance to obtain a regional grid set; and determining the starting regional grid; then, according to the environmental information of the current regional grid, calculating the interval disturbance propagation matrix corresponding to the current regional grid; combining the sound pressure fluctuation interval at the previous regional grid and the interval disturbance propagation matrix corresponding to the current regional grid, calculating the sound pressure fluctuation interval corresponding to the current regional grid; sequentially traversing each regional grid in the processing regional grid set, obtaining the sound pressure fluctuation interval corresponding to each regional grid, and thus obtaining the ocean sound field fluctuation interval. The method proposed by the present invention based on the parabolic equation sound propagation and interval analysis theory can effectively estimate the ocean sound field fluctuation interval.

Description

Technical Field

[0001] The invention belongs to the technical field of underwater acoustic physics and relates to a method for predicting an ocean sound field, and in particular to a method for predicting an ocean sound field fluctuation interval based on a parabolic equation theory. Background Art

[0002] The speed of sound, density, depth, sea surface waves, seabed reflection coefficient, sediment absorption coefficient and other factors in seawater will affect the underwater sound field. Affected by the uncertain distribution of marine environment and climate conditions in space and time, the seawater medium and its boundary conditions are uncertain and uneven. When the signal propagates through seawater to the receiver, the signal will be delayed, lost, distorted and fluctuate, resulting in the underwater acoustic channel being a variable parameter channel with uncertainty in the time domain, frequency domain and space-frequency domain. In various underwater acoustic science and engineering applications such as detection, positioning, and communication, the prediction of the fluctuating ocean sound field has important practical significance.

[0003] Most of the existing methods for predicting the fluctuation of sound fields in uncertain ocean environments are developed based on a probabilistic framework, such as the Monte Carlo simulation method. This type of probabilistic method usually establishes the evolution process of the probability density function from uncertain environmental parameters to the fluctuating sound field, so the description of random underwater sound propagation is relatively intuitive. However, when the number of uncertain ocean environmental parameters increases, the scale of the sound propagation area of ​​concern increases, and other factors lead to an increase in the scale of the problem to be solved, or when the actual environment presents distance-dependent characteristics such as strong cutting and fast-changing terrain, the Monte Carlo method will face computational efficiency problems in practical applications. Therefore, in practice, such methods are often only used in simple cases or as a reference for other methods. In addition to efficiency, probabilistic methods also have a type of inherent problem: since the evolution of the probability density function is the key core of such methods, in order to establish the statistical distribution of uncertain environmental parameters, the method requires sufficient environmental information, but in actual measurements, it is often difficult to obtain sufficient data to construct the required probability density function.

[0004] In summary, more effective methods still need to be developed to predict the fluctuation range of ocean sound fields in actual scenarios. Summary of the invention

[0005] In order to solve the problems and needs in the background technology, the present invention provides a method for predicting the fluctuation interval of ocean sound field based on parabolic equation theory. Based on the parabolic equation underwater sound propagation theory, the present invention applies the interval analysis method to improve the original underwater sound parabolic equation, which can effectively analyze the ocean sound propagation problem under non-deterministic environmental parameters, thereby effectively estimating the ocean sound field fluctuation interval under the disturbed ocean environment.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] 1. A method for predicting the fluctuation range of ocean sound field based on parabolic equation theory

[0008] Step 1: Obtain original environmental information and determine the disturbance range of marine environmental parameters;

[0009] Step 2: Combined with the disturbance interval of the marine environmental parameters, the marine environmental area with disturbance is rasterized to obtain a regional grid set; and the starting regional grid is determined;

[0010] Step 3: Calculate the interval disturbance propagation matrix corresponding to the current regional grid according to the environmental information of the current regional grid;

[0011] Step 4: Combine the sound pressure fluctuation interval at the previous regional grid and the interval disturbance propagation matrix corresponding to the current regional grid, calculate the sound pressure fluctuation interval corresponding to the current regional grid and update the sound pressure fluctuation interval;

[0012] Step 5: Repeat steps 3 to 4, traverse each regional grid in the processing regional grid set in turn, obtain the sound pressure fluctuation interval corresponding to each regional grid, and thus obtain the ocean sound field fluctuation interval.

[0013] The original environmental information includes a sound velocity field, a terrain and a density field in the form of a disturbance interval.

[0014] The regional grid is a two-dimensional grid or a three-dimensional grid.

[0015] The step three is specifically as follows:

[0016] The interval disturbance propagation matrix in the sound propagation parabolic equation corresponding to the current grid area is calculated according to the environmental information of the current regional grid itself and its format.

[0017] If the environmental information of the current regional grid is in analytical format, the analytical method is used for calculation; if the environmental information of the current regional grid is in numerical format, the numerical differentiation method is used for calculation.

[0018] In step 4, the sound pressure fluctuation interval corresponding to the current regional grid is calculated according to the following formula:

[0019] u c n+1 =exp(ik0△r)p0(B c )A c u c n

[0020] △u n+1,I = exp(ik0△r) (p1(B c ) △B I A c u c n + p0(B c) △A I u c n + p0(B c )A c △u n,I )

[0021] Among them, u c n+1 is the center value vector of the sound pressure at the current regional grid, △u n+1,I is the sound pressure fluctuation range at the current regional grid, u c n is the sound pressure center value vector at the previous regional grid, △u n,I is the sound pressure fluctuation interval at the previous area grid; i is the imaginary unit; k0 is the reference wave number; △r is the distance step; p0(B c ) and p1(B c ) are the zero-order and first-order coefficients of the series expansion of the inverse matrix in interval perturbation analysis; △A I With △ B I They are the right-hand propagation matrix A after numerical discretization of the original sound propagation parabolic equation. c With the left propagation matrix B c The corresponding interval disturbance propagation matrix.

[0022] 2. A device for predicting the fluctuation range of ocean sound field based on parabolic equation theory

[0023] A marine environment parameter disturbance interval generating unit, used to obtain original environmental information and determine the marine environment parameter disturbance interval;

[0024] A rasterization processing unit, used for performing rasterization processing on the marine environment area with disturbance to obtain a regional raster set;

[0025] An interval disturbance propagation matrix generating unit is used to calculate the corresponding interval disturbance propagation matrix according to the environmental information of each regional grid;

[0026] The sound pressure fluctuation interval generating unit is used to calculate the sound pressure fluctuation interval of the current regional grid according to the sound pressure fluctuation interval of the previous regional grid and the interval disturbance propagation matrix of the current regional grid, so as to obtain the ocean sound field fluctuation interval.

[0027] 3. A computer device

[0028] The device includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the method for predicting the fluctuation interval of the ocean sound field based on the parabolic equation theory are implemented.

[0029] 4. A computer-readable storage medium

[0030] The medium stores a computer program, and when the computer program is executed by a processor, the computer program implements the steps of any one of the methods for predicting the fluctuation interval of the ocean sound field based on the parabolic equation theory.

[0031] V. A computer program product

[0032] The product includes a computer program / instruction, which, when executed by a processor, implements the steps of a method for predicting the fluctuation interval of an ocean sound field based on the parabolic equation theory.

[0033] The beneficial effects of the present invention are:

[0034] 1) Compared with the probability-based methods, the present invention uses the interval analysis method, which does not require knowing the specific probability distribution of environmental parameters, but only needs to determine the upper and lower limits of the environmental information interval (i.e., the disturbance interval of the marine environmental parameters), and can effectively predict the ocean undulating sound field in practical application scenarios where uncertain information measurement is insufficient;

[0035] 2) Based on the parabolic equation theory of underwater acoustic propagation, the present invention can efficiently couple the disturbance environment parameters in the step-by-step solution process, and is particularly suitable for predicting the fluctuating sound field in the actual ocean environment that is distance-dependent. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a flow chart of the method proposed by the present invention.

[0037] Figure 2 This is a schematic diagram of the scenario of disturbed ocean environment sound propagation problem in shallow sea conditions.

[0038] Figure 3 It is a comparison diagram of the fluctuation range of the ocean sound propagation loss field at typical depths (10 meters and 20 meters) of shallow sea scenes calculated using the method proposed in the present invention and the Monte Carlo simulation results, wherein (a) is a comparison diagram of the fluctuation range of the ocean sound propagation loss field at a depth of 10 meters and the Monte Carlo simulation results, and (b) is a comparison diagram of the fluctuation range of the ocean sound propagation loss field at a depth of 20 meters and the Monte Carlo simulation results.

[0039] Figure 4 It is a comparison diagram of the fluctuation range of the ocean sound propagation loss field at typical depths (70 meters and 120 meters) of shallow sea scenes calculated using the method proposed in the present invention and the Monte Carlo simulation results, wherein (a) is a comparison diagram of the fluctuation range of the ocean sound propagation loss field at a depth of 70 meters and the Monte Carlo simulation results, and (b) is a comparison diagram of the fluctuation range of the ocean sound propagation loss field at a depth of 120 meters and the Monte Carlo simulation results.

[0040] Figure 5This is a statistical display of the accuracy of the calculation results of various depth positions at various distances in shallow sea scenes using the method proposed in the present invention compared with the Monte Carlo simulation results.

[0041] Figure 6 It is a schematic diagram of the scenario of disturbed ocean environment sound propagation problem in deep sea conditions.

[0042] Figure 7 It is a profile diagram of the sound velocity of the water layer and its disturbance interval in the deep sea scene.

[0043] Figure 8 It is a comparison diagram of the fluctuation range of the ocean sound propagation loss field at typical depths (10 meters and 34 meters) of deep sea scenes calculated using the method proposed in the present invention and the Monte Carlo simulation results, wherein (a) is a comparison diagram of the fluctuation range of the ocean sound propagation loss field at a depth of 10 meters and the Monte Carlo simulation results, and (b) is a comparison diagram of the fluctuation range of the ocean sound propagation loss field at a depth of 34 meters and the Monte Carlo simulation results.

[0044] Fig. 9 It is a comparison diagram of the fluctuation range of the ocean sound propagation loss field at typical depths (500 meters and 1200 meters) of deep-sea scenes calculated using the method proposed in the present invention and the Monte Carlo simulation results, wherein (a) is a comparison diagram of the fluctuation range of the ocean sound propagation loss field at a depth of 500 meters and the Monte Carlo simulation results, and (b) is a comparison diagram of the fluctuation range of the ocean sound propagation loss field at a depth of 1200 meters and the Monte Carlo simulation results.

[0045] Fig.10 The figure is a comparison chart of the fluctuation range of the ocean sound propagation loss field at typical depths (1800 meters and 2480 meters) of deep-sea scenes calculated using the method proposed in the present invention and the Monte Carlo simulation results, wherein (a) is a comparison chart of the fluctuation range of the ocean sound propagation loss field at a depth of 1800 meters and the Monte Carlo simulation results, and (b) is a comparison chart of the fluctuation range of the ocean sound propagation loss field at a depth of 2480 meters and the Monte Carlo simulation results.

[0046] Fig.11 This is a statistical display of the accuracy of the calculation results of the depth positions at various distances in deep-sea scenes using the method proposed in the present invention compared with the Monte Carlo simulation results. DETAILED DESCRIPTION

[0047] In order to make the objectives, technical solutions and advantages of the present invention more clear, the technical solutions of the present invention will be described in more detail below in conjunction with the embodiments of the present invention and the corresponding drawings.

[0048] The present invention proposes a method for predicting the fluctuation interval of ocean sound field based on parabolic equation theory. The method broadens the applicability of the ocean sound field prediction method to practical application scenarios, efficiently couples the disturbance environment parameters in the step-by-step solution process of the parabolic equation, and is suitable for distance-dependent environments in scenarios where uncertain information measurement is insufficient, thereby realizing the prediction of the ocean fluctuation sound field interval in this environment.

[0049] Example 1

[0050] In this embodiment, the bottom sound velocity, density and attenuation coefficient are taken as non-deterministic parameters, and the other environmental parameters are deterministic parameters. Figure 2 As shown, the scenario of this embodiment is the shallow sea Pekeris environment, the water depth is 130m, the horizontal propagation distance is 0~30km, and the water layer sound speed c w =1500m / s, density ρ w =1.0g / cm 3 ; Sound speed at the bottom of the ocean c b ∈[1575,1650]m / s, density ρ b ∈[1.7,1.9]g / cm 3 , attenuation coefficient α∈[0.8,1.0]dB / λ; the sound source is at distance 0 and depth z s =20m, frequency f=100Hz.

[0051] like Figure 1 As shown, the specific process of the method is as follows:

[0052] Step 1: Obtain original environmental information and determine the disturbance interval of ocean environmental parameters; the original environmental information includes the sound velocity field, topography and density field in the form of the disturbance interval.

[0053] Step 2: Combine the disturbance interval of the marine environment parameters, rasterize the marine environment area with disturbance to obtain a regional grid set; and determine the starting regional grid; this embodiment is a two-dimensional scene, Figure 2 The scene diagram also illustrates the selected two-dimensional uniform step Cartesian coordinate system grid. In actual implementation, non-uniform grids can be used as needed and the parabolic equation discretization format can be adjusted accordingly.

[0054] Step 3: Calculate the interval disturbance propagation matrix in the sound propagation parabolic equation corresponding to the current grid area according to the environmental information of the current area grid itself and its format.

[0055] Specifically:

[0056] The discretized form of the original sound propagation parabolic equation is as follows:

[0057] B(a ;r)u n+1 =exp(ik0△r)A(a;r)un

[0058] Among them, the environmental parameter vector a is the vector composed of all environmental parameters, with a total of L components, satisfying a=(c w , ρ w ,c b , ρ b , α, …)=(a1, a2, …,a s , … , a L ), a s is the sth component of vector a, s=1, …, L; u n+1 with u n are the sound pressure vectors corresponding to the current regional grid (i.e., step position) and the previous regional grid, i is an imaginary unit; k0 is the reference wave number; △r is the distance step; A(a;r) and B(a;r) are the right-end propagation matrix and the left-end propagation matrix after the numerical discretization of the parabolic equation method, respectively. Both use the environmental parameter vector a as the independent variable and the propagation distance r as the parameter. The specific form is related to the operator approximation and numerical discretization format selected by the parabolic equation method. In actual implementation, the original sound propagation parabolic equation can select various commonly used operator approximation and numerical discretization methods, such as split step Padé operator approximation and Galerkin discretization, etc. At this time, the above propagation matrix can be expressed as:

[0059] A(a;r)=∏ m j=1 A j (a;r)

[0060] B(a;r)=∏ m j=1 B j (a;r)

[0061] Among them, A j (a;r) and B j (a; r) are the discrete matrices corresponding to the jth numerator rational factors and the jth denominator rational factors in the Padé operator approximation; m is the order of the Padé operator approximation; in the two-dimensional case, B j Taking (a;r) as an example, after Galerkin discretization, its form is a tridiagonal matrix, and the tridiagonal elements are:

[0062]

[0063] Among them, b i,i-1 、b i,i With b i,i+1 They are tridiagonal matrices B j The elements in the i-th row, i-1th column, i-th row, i-th column, and i-th row, i+1th column of (a;r), i represents the i-th grid in the corresponding depth direction, and the same is true for other quantities involving this subscript in the formula; βj,m is the rational coefficient of the denominator of the jth group in the Padé operator approximation; k sq =k 2 -k0 2 is the difference between the square of wave number k and the square of reference wave number k0 and is recorded as the wave number square difference, k sq,i-1 , k sq,i With k sq,i+1 are the squared wavenumber differences of the i-1th grid, the i-th grid, and the i+1th grid, respectively; Δz is the discrete step length of the grid in the depth direction; ρ i-1 , i and ρ i+1 are the densities of the i-1th grid, the i-th grid, and the i+1th grid respectively; η i-1 , η i With η i+1 are the approximate normalized parameters of energy conservation for the i-1th grid, the i-th grid, and the i+1th grid, respectively, satisfying η=(ρ / k) 0.5 .

[0064] According to the total differential formula, the interval disturbance propagation matrix can be expressed by the environmental parameter corresponding to the interval disturbance vector:

[0065]

[0066] Among them, a c is the central value vector formed by taking the central value of each element of the environmental parameter vector a, △ a s I The disturbance interval form corresponding to its sth component; △A I With △ B I They are the right-hand propagation matrix A after numerical discretization of the original sound propagation parabolic equation. c With the left propagation matrix B c The corresponding interval disturbance propagation matrix.

[0067] The scenario of this embodiment is the Pekeris waveguide environment. Environmental parameters such as the water layer sound velocity, density and bottom sound velocity, density and attenuation coefficient are each scalar constants in the layered structure and can be regarded as constant functions in an analytical format. Therefore, in this embodiment, the interval disturbance propagation matrix can be combined with the closed form of the propagation matrix elements of the parabolic equation method for analytical calculation.

[0068] Step 4: Combine the sound pressure fluctuation interval of the previous regional grid and the interval disturbance propagation matrix corresponding to the current regional grid, calculate the sound pressure fluctuation interval corresponding to the current regional grid and update the sound pressure fluctuation interval;

[0069] In step 4, the discrete recursive form of the original parabolic equation is perturbed by intervals, and the perturbed equation is:

[0070] (Bc +△B I ) (u c n+1 +△u n+1,I ) = exp(ik0△r) (A c +△A I ) (u c n +△u n,I )

[0071] In the calculation process of the present invention, it is necessary to select a specific series expansion form for the inverse matrix. In the embodiment, a linear approximation as shown in the following formula is taken:

[0072] (B c +△B I ) -1 =p(△B I ;B c )≈p0(B c )+ p1(B c ) △B I

[0073] Among them, p(△B I ;B c ) represents the general formula of inverse matrix series; p0(B c ) and p1(B c ) are the inverse matrices of the interval perturbation matrix △B I The expanded zero-order and first-order coefficients are expressed in terms of B c is the parameter. According to the selected series expansion form, the discrete recursive form of the interval format parabolic equation is constructed as follows:

[0074] u c n+1 =exp(ik0△r)p0(B c )A c u c n

[0075] △u n+1,I = exp(ik0△r) (p1(B c ) △B I A c u c n + p0(B c ) △A I u c n + p0(B c )A c △u n,I )

[0076] Among them, uc n+1 is the center value vector of the sound pressure at the current regional grid, △u n+1,I is the sound pressure fluctuation range at the current regional grid, u c n is the sound pressure center value vector at the previous regional grid, △u n,I is the sound pressure fluctuation range at the grid in the previous area.

[0077] In step 4, if the current grid is the initial area grid, that is, n=0, then the initial sound pressure center value vector u c 0 The initial sound pressure fluctuation interval △u can be constructed by specifying data or calculated according to the parabolic equation self-initialization method. 0,I =0. The specified data can be obtained from actual forecast data or forecast calculations using other numerical methods; the parabolic equation self-initialization method can be derived based on modal theory. Taking the two-dimensional cylindrical coordinate system as an example, the commonly used reference calculation formula is as follows:

[0078]

[0079] Among them, u c (r0,z) is the center value of the sound pressure at the horizontal propagation distance r0 and depth z; is the Helmholtzian operator of the parabolic equation for sound propagation under the energy conservation approximation; δ(z-z0) is the impulse function centered at z0.

[0080] Step 5: Repeat steps 3 to 4, traverse each regional grid in the processing regional grid set in turn, obtain the sound pressure fluctuation interval corresponding to each regional grid, and thus obtain the ocean sound field fluctuation interval.

[0081] In step 5, the center value and fluctuation range of the ocean sound field sound pressure of all grids in the area of ​​interest are obtained, that is, u at all grids n=0,1,2,… c n and △u n,I In practical science and engineering applications, the energy distribution of the sound field is often of concern to technicians. Sound propagation loss is a commonly used description of the water sound field in terms of energy. According to actual needs, the fluctuation range of the ocean sound field predicted by the present invention can also be converted into the form of the fluctuation range of sound propagation loss. Its calculation formula is expressed by the following formula:

[0082] TL n lower,j ≈-20×log 10 [(|u n c,j |+|△u n j |) / |u ref |]

[0083] TL n upper,j ≈-20×log 10 [(|u n c,j |-|△u n j |) / |u ref |]

[0084] Among them, TL n lower,j with TL n upper,j They represent the lower and upper bounds of the acoustic propagation loss fluctuation range at the jth depth of the nth grid; |u n c,j | represents the modulus of the central value of the sound pressure at the jth depth of the nth grid; |△u n j | represents the modulus of the sound pressure disturbance at the jth depth of the nth grid, that is, the radius of the sound pressure fluctuation interval; |u ref | is the reference sound pressure modulus selected when defining the sound propagation loss. The above formula is an estimation method for the fluctuation range of the sound propagation loss. In the actual application of this embodiment, when |△u n j |<<|u n c,j |, that is, when the modulus of the sound pressure fluctuation is smaller than the modulus of the sound pressure center value, the estimation is more accurate.

[0085] Figure 3 and Figure 4 All of them are comparison diagrams of the fluctuation range of ocean sound propagation loss at typical depths of the shallow sea Pekeris waveguide environmental problem calculated by the method proposed in the present invention and the Monte Carlo simulation results, wherein the red solid line and the gray filled area in the figure respectively represent the central value of the sound propagation loss and the fluctuation range of the sound propagation loss calculated by the method proposed in the present invention, and the blue scattered points represent the corresponding sound propagation loss values ​​of each sampling realization obtained by Monte Carlo simulation of the uncertain ocean environmental parameter interval; the typical depths selected are 10m near the sea surface, 20m deep to the sound source, 70m deep inside the water layer and 120m deep near the seabed, as shown in FIG. Figure 3 (a) and Figure 3 (b) Figure 4 (a) and Figure 4As shown in (b). In general, the estimated results of the ocean sound field fluctuation interval calculated by the method proposed in the present invention are in good agreement with the Monte Carlo simulation results, and most of the Monte Carlo sample point results at each depth can fall within the calculated fluctuation interval. Since the propagation loss is defined by a logarithmic function, due to the characteristics of logarithmic operation, the difference between the lower bound and the average value is greater than the difference between the upper bound and the average value, so the lower bound of the estimated sound propagation loss fluctuation interval in the figure is slightly looser than the upper bound. For each selected depth, at a depth of 10m, approximately 87.6% of the Monte Carlo simulation calculated sound propagation loss sample points fall within the sound propagation loss interval calculated by the method proposed in the present invention, at a depth of 20m, approximately 89.9% of the Monte Carlo simulation calculated sound propagation loss sample points fall within the sound propagation loss interval calculated by the method proposed in the present invention, at a depth of 70m, approximately 95.9% of the Monte Carlo simulation calculated sound propagation loss sample points fall within the sound propagation loss interval calculated by the method proposed in the present invention, and at a depth of 120m, approximately 90.1% of the Monte Carlo simulation calculated sound propagation loss sample points fall within the sound propagation loss interval calculated by the method proposed in the present invention.

[0086] The accuracy statistics of the comparison between the calculation results of each distance depth position and the Monte Carlo simulation results using the method proposed in the present invention are as follows: Figure 5 As shown, the results can be further evaluated to verify the effectiveness of the proposed method. Figure 5 The pseudo-color image shows the percentage of the number of Monte Carlo sample points at each position that fall into the calculated ocean sound field fluctuation interval to the total number of Monte Carlo sample points at that position. According to the color axis in the figure, the statistical chart is dark blue as a whole, indicating that the percentage values ​​in most areas are relatively high. The average percentage obtained from statistics at each position of the water layer is 90.8%, that is, at each grid position, an average of about 90.8% of the Monte Carlo simulation calculated sound propagation loss sample points fall into the sound propagation loss interval calculated by the method proposed in the present invention, indicating that the proposed method can accurately estimate the ocean sound field fluctuation interval. Example

[0087] In this embodiment, the water layer sound velocity is an undetermined parameter, and the other environmental parameters are deterministic parameters. Figure 6 As shown, the scenario of this embodiment is a deep-sea slope terrain environment, the horizontal propagation distance of interest is in the range of 0~100km, the water depth changes linearly from 2500m to 4500m within the horizontal propagation distance of interest, and the water layer density ρ w =1.0g / cm 3 ; Sound speed at the bottom of the ocean c b =1575 m / s, density ρ b =1.7g / cm 3 , attenuation coefficient α = 1.0dB / λ; the sound source is at distance 0 and depth z s =1200m, frequency f=50Hz. Figure 7 As shown, the water layer sound velocity c in this embodiment is w Take the typical statistical values ​​of a certain sea area. The solid red line in the figure represents the center value of the sound speed of the water layer, and the black line segments at each depth represent the sound speed disturbance range at that depth. For the sake of drawing clarity, the sound speed disturbance range only shows part of the depth. This set of sound speed and disturbance range values ​​is obtained based on the analysis and processing of the temperature field and salinity field data of a typical ocean dynamic model. The data statistics of a typical deep sea area for 24 hours on a certain day are taken, and the sound speed center value and disturbance range value are calculated using the Mackenzie empirical formula. Figure 7 As shown in the figure, the sound velocity profiles of this group are isothermal mixed layers near the sea surface in the depth range of about 0 to 34m, thermocline layers in the depth range of about 34 to 1200m, and deep sea isothermal zones below about 1200m, showing a typical deep sea sound velocity profile structure as a whole. In terms of the distribution of sound velocity disturbances at various depths, the size of the disturbance interval increases first and then decreases from the sea surface to the seabed.

[0088] like Figure 1 As shown, the specific process of the method is as follows:

[0089] Step 1: Obtain original environmental information and determine the disturbance interval of ocean environmental parameters; the original environmental information includes the sound velocity field, topography and density field in the form of the disturbance interval.

[0090] Step 2: Combined with the disturbance interval of the marine environmental parameters, the marine environmental area with disturbance is rasterized to obtain a regional grid set; and the starting regional grid is determined;

[0091] This embodiment is a two-dimensional scene. Figure 7 The scene diagram of exemplifies the selected two-dimensional uniform-step Cartesian coordinate system grid. In actual implementation, a non-uniform grid can be used as needed and the parabolic equation discretization format can be adjusted accordingly.

[0092] Step 3: Calculate the interval disturbance propagation matrix in the sound propagation parabolic equation corresponding to the current grid area according to the environmental information of the current area grid itself and its format.

[0093] Specifically:

[0094] The discretized form of the original sound propagation parabolic equation is as follows:

[0095] B(a;r)u n+1 =exp(ik0△r)A(a;r)u n

[0096] Among them, the environmental parameter vector a is the vector composed of all environmental parameters, with a total of L components, satisfying a=(c w , ρ w ,c b , ρb , α, …)=(a1, a2, …,a s , … , a L ), a s is the sth component of vector a, s=1, …, L; u n+1 with u n are the sound pressure vectors corresponding to the current regional grid and the previous regional grid, respectively, i is the imaginary unit; k0 is the reference wave number; △r is the distance step; A(a;r) and B(a;r) are the right-end propagation matrix and the left-end propagation matrix after the numerical discretization of the parabolic equation method, respectively, both of which take the environmental parameter vector a as the independent variable and the propagation distance r as the parameter. The specific form is related to the operator approximation method and the numerical discretization format selected by the parabolic equation method. In actual implementation, the original sound propagation parabolic equation can select various commonly used operator approximation and numerical discretization technical solutions, such as split step Padé operator approximation and Galerkin discretization, etc. At this time, the above propagation matrix can be expressed as:

[0097] A(a;r)=∏ m j=1 A j (a;r)

[0098] B(a;r)=∏ m j=1 B j (a;r)

[0099] Among them, A j ( a ;r) and B j ( a ;r) are the discrete matrices corresponding to the j-th group of numerator rational factors and the discrete matrices corresponding to the j-th group of denominator rational factors in the Padé operator approximation; m is the order of the Padé operator approximation;

[0100] According to the total differential formula, the interval disturbance propagation matrix can be expressed by the environmental parameter corresponding to the interval disturbance vector:

[0101]

[0102] Among them, a c is the central value vector formed by taking the central value of each element of the environmental parameter vector a, △a s I The disturbance interval form corresponding to its sth component; △A I With △ B I They are the right-hand propagation matrix A after numerical discretization of the original sound propagation parabolic equation. c With the left propagation matrix B c The corresponding interval disturbance propagation matrix.

[0103] In the scenario of this embodiment, there is no analytical expression for the water layer sound velocity and its disturbance interval distribution, which is in numerical format. The interval disturbance propagation matrix can be calculated using the numerical differentiation method.

[0104] Step 4: Combine the sound pressure fluctuation interval of the previous regional grid and the interval disturbance propagation matrix corresponding to the current regional grid, calculate the sound pressure fluctuation interval corresponding to the current regional grid and update the sound pressure fluctuation interval;

[0105] In step 4, the discrete recursive form of the original parabolic equation is perturbed by intervals, and the perturbed equation is:

[0106] (B c +△B I ) (u c n+1 +△u n+1,I ) = exp(ik0△r) (A c +△A I ) (u c n +△u n,I )

[0107] In the calculation process of the present invention, it is necessary to select a specific series expansion form for the inverse matrix. In this embodiment, a linear approximation as shown in the following formula is taken:

[0108] (B c +△B I ) -1 =p(△B I ;B c )≈p0(B c )+ p1(B c ) △B I

[0109] Among them, p(△B I ;B c ) represents the general formula of inverse matrix series; p0(B c ) and p1(B c ) are the inverse matrices of the interval perturbation matrix △B I The expanded zero-order and first-order coefficients are expressed in terms of B c is the parameter. According to the selected series expansion form, the discrete recursive form of the interval format parabolic equation is constructed as follows:

[0110] u c n+1 =exp(ik0△r)p0(B c )A c u c n

[0111] △u n+1,I= exp(ik0△r) (p1(B c ) △B I A c u c n + p0(B c ) △A I u c n + p0(B c )A c △u n,I )

[0112] Among them, u c n+1 is the center value vector of the sound pressure at the current regional grid, △u n+1,I is the sound pressure fluctuation interval at the current regional grid, which is in vector form, u c n is the sound pressure center value vector at the previous regional grid, △u n,I is the sound pressure fluctuation range at the grid in the previous area.

[0113] In step 4, if the current grid is the initial area grid, that is, n=0, then the initial sound pressure center value vector u c 0 The initial sound pressure fluctuation interval △u can be constructed by specifying data or calculated according to the parabolic equation self-initialization method. 0,I = 0. The specified data can be obtained from actual forecast data or forecast calculations using other numerical methods;

[0114] Step 5: Repeat steps 3 to 4, traverse each regional grid in the processing regional grid set in turn, obtain the sound pressure fluctuation interval corresponding to each regional grid, and thus obtain the ocean sound field fluctuation interval.

[0115] In step 5, the center value and fluctuation range of the ocean sound field sound pressure of all grids in the area of ​​interest are obtained, that is, u at all grids n=0,1,2,… c n and △u n,I In practical science and engineering applications, the energy distribution of the sound field is often of concern to technicians. Sound propagation loss is a commonly used description of the water sound field in terms of energy. According to actual needs, the fluctuation range of the ocean sound field predicted by the present invention can also be converted into the form of the fluctuation range of sound propagation loss. Its calculation formula is expressed by the following formula:

[0116] TL n lower,j ≈-20×log 10 [(|u n c,j |+|△u nj |) / |u ref |]

[0117] TL n upper,j ≈-20×log 10 [(|u n c,j |-|△u n j |) / |u ref |]

[0118] Among them, TL n lower,j with TL n upper,j They represent the lower and upper bounds of the acoustic propagation loss fluctuation range at the jth depth of the nth grid; |u n c,j | represents the modulus of the central value of the sound pressure at the jth depth of the nth grid; |△u n j | represents the modulus of the sound pressure disturbance at the jth depth of the nth grid, that is, the radius of the sound pressure fluctuation interval; |u ref | is the reference sound pressure modulus selected when defining the sound propagation loss. The above formula is an estimation method for the fluctuation range of the sound propagation loss. In practical applications such as the following embodiments, when |△u n j |<<|u n c,j |, that is, when the modulus of the sound pressure fluctuation is smaller than the modulus of the sound pressure center value, the estimation is more accurate.

[0119] Figure 8 , Fig. 9 and Fig.10 All of them are comparison diagrams of the fluctuation range of ocean sound propagation loss at typical depths of deep-sea slope terrain environmental problems calculated by the method proposed in the present invention and the Monte Carlo simulation results, wherein the red solid line and the gray filled area in the figure respectively represent the central value of the sound propagation loss and the fluctuation range of the sound propagation loss calculated by the method proposed in the present invention, and the blue scattered points represent the corresponding sound propagation loss values ​​of each sampling realization obtained by Monte Carlo simulation of the uncertain ocean environmental parameter interval; the typical depths selected are 10m near the sea surface, 34m at the bottom of the mixed layer, 500m inside the thermocline, 1200m deep-sea sound channel axis depth and sound source depth, 1800m inside the deep-sea isothermal layer and 2480m near the bottom of the slope top. Figure 8 (a) and Figure 8 (b) Fig. 9 (a) and Fig. 9 (b) Fig.10 (a) and Fig.10In general, the ocean acoustic field fluctuation interval estimation result calculated by the method proposed in the present invention is in good agreement with the Monte Carlo simulation result, and most of the Monte Carlo sample point results at each depth can fall within the calculated fluctuation interval. For each selected depth, at a depth of 10m, about 99.1% of the Monte Carlo simulation calculated sound propagation loss sample points fall within the sound propagation loss interval calculated by the method proposed in the present invention, at a depth of 34m, about 98.8% of the Monte Carlo simulation calculated sound propagation loss sample points fall within the sound propagation loss interval calculated by the method proposed in the present invention, at a depth of 500m, about 96.2% of the Monte Carlo simulation calculated sound propagation loss sample points fall within the sound propagation loss interval calculated by the method proposed in the present invention, at a depth of 1200m, about 96.0% of the Monte Carlo simulation calculated sound propagation loss sample points fall within the sound propagation loss interval calculated by the method proposed in the present invention, at a depth of 1800m, about 97.8% of the Monte Carlo simulation calculated sound propagation loss sample points fall within the sound propagation loss interval calculated by the method proposed in the present invention, and at a depth of 2480m, about 98.2% of the Monte Carlo simulation calculated sound propagation loss sample points fall within the sound propagation loss interval calculated by the method proposed in the present invention.

[0120] The accuracy statistics of the comparison between the calculation results of each distance depth position and the Monte Carlo simulation results using the method proposed in the present invention are as follows: Fig.11 As shown, the results can be further evaluated to verify the effectiveness of the proposed method. Fig.11 The pseudo-color image shows the percentage of the number of Monte Carlo sample points at each position that fall into the calculated ocean sound field fluctuation interval to the total number of Monte Carlo sample points at that position. According to the color axis in the figure, the statistical chart is dark blue as a whole, indicating that the percentage values ​​in most areas are relatively high. The average percentage obtained from statistics at each position of the water layer is 97.4%, that is, at each grid position, an average of about 97.4% of the Monte Carlo simulation calculated sound propagation loss sample points fall into the sound propagation loss interval calculated by the method proposed in the present invention, indicating that the proposed method can accurately estimate the ocean sound field fluctuation interval.

[0121] The above two embodiments respectively illustrate the method proposed by the present invention for the problem of sound field fluctuation interval prediction in typical shallow sea and deep sea uncertain marine environments, reflecting the purpose, technical scheme, implementation effect and advantages of the implementation of the present invention.

[0122] The present invention also proposes a device for predicting the fluctuation interval of ocean sound field based on parabolic equation theory, the device comprising:

[0123] A marine environment parameter disturbance interval generating unit, used to obtain original environmental information and determine the marine environment parameter disturbance interval;

[0124] A rasterization processing unit, used for performing rasterization processing on the marine environment region with disturbance within the marine environment parameter disturbance interval to obtain a regional raster set;

[0125] An interval disturbance propagation matrix generating unit is used to calculate the corresponding interval disturbance propagation matrix according to the environmental information of each regional grid;

[0126] The sound pressure fluctuation interval generating unit is used to calculate the sound pressure fluctuation interval of the current regional grid according to the sound pressure fluctuation interval of the previous regional grid and the interval disturbance propagation matrix of the current regional grid, so as to obtain the ocean sound field fluctuation interval.

[0127] The present invention also proposes a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of a method for predicting the fluctuation interval of an ocean sound field based on the parabolic equation theory are implemented.

[0128] The present invention also proposes a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of a method for predicting the fluctuation interval of an ocean sound field based on the parabolic equation theory are implemented.

[0129] The present invention also proposes a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of a method for predicting the fluctuation interval of an ocean sound field based on the parabolic equation theory.

[0130] The present invention is described in detail above. The contents described in the embodiments of this specification are merely examples of the implementation forms of the inventive concept. The protection scope of the present invention should not be considered as limited to the specific forms described in the embodiments. The protection scope of the present invention also extends to equivalent technical means that can be thought of by those skilled in the art based on the inventive concept.

Claims

1. A method for predicting the fluctuation interval of ocean sound field based on parabolic equation theory, characterized in that: The steps include: Step 1: Obtain original environmental information and determine the disturbance range of marine environmental parameters; Step 2: Combined with the disturbance interval of the marine environmental parameters, the marine environmental area with disturbance is rasterized to obtain a regional grid set; and the starting regional grid is determined; Step 3: Calculate the interval disturbance propagation matrix corresponding to the current regional grid according to the environmental information of the current regional grid; Step 4: Calculate the sound pressure fluctuation interval corresponding to the current regional grid by combining the sound pressure fluctuation interval at the previous regional grid and the interval disturbance propagation matrix corresponding to the current regional grid; Step 5: Repeat steps 3 to 4, traverse each regional grid in the processing regional grid set in turn, obtain the sound pressure fluctuation interval corresponding to each regional grid, and thus obtain the ocean sound field fluctuation interval; In step 4, the sound pressure fluctuation interval corresponding to the current regional grid is calculated according to the following formula: u c n+1 =exp(ik0△r)p0(B c )A c u c n △u n+1,I = exp(ik0△r) (p1(B c ) △B I A c u c n + p0(B c ) △A I u c n + p0(B c ) A c △u n,I ) Among them, u c n+1 is the center value vector of the sound pressure at the current regional grid, △u n+1,I is the sound pressure fluctuation range at the current regional grid, u c n is the sound pressure center value vector at the previous regional grid, △u n,I is the sound pressure fluctuation interval at the previous area grid; i is the imaginary unit; k0 is the reference wave number; △r is the distance step; p0(B c ) and p1(B c ) are the zero-order and first-order coefficients of the series expansion of the inverse matrix in interval perturbation analysis; △A I With △ B I They are the right-hand propagation matrix A after numerical discretization of the original sound propagation parabolic equation. c With the left propagation matrix B c The corresponding interval disturbance propagation matrix.

2. The method for predicting the fluctuation interval of ocean sound field based on parabolic equation theory according to claim 1, characterized in that: The original environmental information includes a sound velocity field, a terrain and a density field in the form of a disturbance interval.

3. The method for predicting ocean sound field fluctuation interval based on parabolic equation theory according to claim 1 is characterized in that: The regional grid is a two-dimensional grid or a three-dimensional grid.

4. The method for predicting ocean sound field fluctuation interval based on parabolic equation theory according to claim 1, characterized in that: The step three is specifically as follows: The interval disturbance propagation matrix in the sound propagation parabolic equation corresponding to the current grid area is calculated according to the environmental information of the current regional grid itself and its format.

5. The method for predicting the fluctuation interval of ocean sound field based on parabolic equation theory according to claim 4 is characterized in that: If the environmental information of the current regional grid is in analytical format, the analytical method is used for calculation; if the environmental information of the current regional grid is in numerical format, the numerical differentiation method is used for calculation.

6. A device for predicting the fluctuation interval of ocean sound field based on parabolic equation theory, characterized in that: include: A marine environment parameter disturbance interval generating unit, used to obtain original environmental information and determine the marine environment parameter disturbance interval; A rasterization processing unit is used to rasterize the disturbed marine environment area in combination with the disturbance interval of the marine environment parameter to obtain a regional raster set; An interval disturbance propagation matrix generating unit is used to calculate the corresponding interval disturbance propagation matrix according to the environmental information of each regional grid; A sound pressure fluctuation interval generating unit is used to calculate the sound pressure fluctuation interval of the current regional grid according to the sound pressure fluctuation interval of the previous regional grid and the interval disturbance propagation matrix of the current regional grid, so as to obtain the ocean sound field fluctuation interval; The sound pressure fluctuation range corresponding to the current regional grid is calculated according to the following formula: u c n+1 =exp(ik0△r)p0(B c )A c u c n △u n+1,I = exp(ik0△r) (p1(B c ) △B I A c u c n + p0(B c ) △A I u c n + p0(B c ) A c △u n,I ) Among them, u c n+1 is the center value vector of the sound pressure at the current regional grid, △u n+1,I is the sound pressure fluctuation range at the current regional grid, u c n is the sound pressure center value vector at the previous regional grid, △u n,I is the sound pressure fluctuation range at the grid in the previous area; i is the imaginary unit; k0 is the reference wave number; △r is the distance step; p0(B c ) and p1(B c ) are the zero-order and first-order coefficients of the series expansion of the inverse matrix in interval perturbation analysis; △A I With △ B I They are the right-hand propagation matrix A after numerical discretization of the original sound propagation parabolic equation. c With the left propagation matrix B c The corresponding interval disturbance propagation matrix.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, the steps of a method for predicting the ocean sound field fluctuation interval based on parabolic equation theory as described in any one of claims 1 to 5 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of a method for predicting the fluctuation interval of an ocean sound field based on the parabolic equation theory as described in any one of claims 1 to 5 are implemented.

9. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the steps of a method for predicting the fluctuation interval of an ocean sound field based on the parabolic equation theory as described in any one of claims 1 to 5 are implemented.

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