Seabed sediment parameter inversion method based on multilayer sensor

Abstract

The invention discloses a seabed sediment parameter inversion method based on a multi-layer perceptron. The method comprises the following steps: calculating a sediment sound attenuation coefficient and a sound velocity; calculating seabed roughness scattering and volume scattering, establishing a back scattering forward modeling model, and calculating back scattering intensity; the acoustic parameters and the physical parameters of the sediment are inverted according to the backscattering intensity, and the physical parameters of the sediment are obtained; establishing a multi-layer perceptron neural network inversion model; and using the established multi-layer perceptron neural network inversion model to invert sedimentary layer parameters of the experimental area. According to the method, the problems of disturbance of traditional measurement and difficulty in large-range measurement are solved by constructing the sediment propagation model, and the sediment propagation theoretical model is used for simulation to obtain a large amount of sediment acoustic propagation theoretical data; the multi-layer sensor is applied to a sediment parameter inversion model, and a complex network structure and a plurality of neurons of the multi-layer sensor are utilized to simulate a complex function, so that the problem of strong nonlinearity is solved, and the inversion efficiency and quality are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of marine information processing, and in particular relates to a method for inverting seabed sediment parameters based on a multi-layer perceptron. Background Art

[0002] Sound waves can be transmitted over long distances in the ocean. Ocean acoustic field calculations can be applied to marine scientific research, information transmission, and marine engineering construction. The seabed is an important boundary of the ocean acoustic field and has an important influence on the propagation of the ocean acoustic field. Therefore, understanding the parameters of the seabed sediment layer is crucial to studying the propagation of the ocean acoustic field. The traditional way to obtain sediment parameters is to conduct in-situ measurements and sediment sampling. With the development of sonar technology, people have discovered that ocean reverberation carries a large amount of seabed information, and the indirect measurement of sediment parameters using sediment acoustic scattering has gradually developed. The traditional sediment parameter measurement method has the following disadvantages:

[0003] (1) Sampling and measurement disturbance: Sampling and measurement of seabed sediment geoacoustic parameters generally use sampling equipment to obtain seabed sediment samples of a certain length, which are then transferred to the laboratory for measurement. However, since most sediments have a porous structure, it is difficult to avoid disturbances to the internal structure of the sediment during the sampling, transportation and testing process, which may affect the measurement results.

[0004] (2) Large consumption of manpower and material resources: Sampling and measurement require on-site testing in the target sea area. Although most sampling equipment is easy to operate, the sampling process consumes a lot of manpower and material resources.

[0005] (3) Difficult to measure over a large area: The seabed environment changes greatly. Whether it is sampling measurement or in-situ measurement, it can only analyze sediment parameters in a small area of ​​the seabed and cannot obtain a larger sound field.

[0006] (4) Insufficient generalization ability: The traditional sediment parameter inversion algorithm has weak generalization ability and is difficult to perform inversion for complex seabed and multi-layer seabed conditions. Summary of the invention

[0007] In order to make up for the deficiencies of the prior art, the present invention aims to provide a seabed sediment parameter inversion method based on a multi-layer perceptron to solve the problems existing in the traditional sediment parameter measurement method.

[0008] The method for inverting seabed sediment parameters based on a multi-layer perceptron comprises the following steps:

[0009] S1. Establish an approximate fluid density model to calculate the sediment acoustic attenuation coefficient and sound velocity;

[0010] S2. Calculate the seabed roughness scattering and volume scattering through small slope approximation and fluid perturbation approximation to establish a backscattering forward model and obtain the backscattering intensity;

[0011] S3. Invert the geoacoustic parameters and physical parameters of the sediment according to the backscattering intensity, and obtain ten sediment physical parameters to be inverted, namely: average particle size φ, fractional porosity β, particle to pore water mass density ratio ρ r , pore water bulk elastic modulus ratio K r , roughness spectrum index γ2, roughness spectrum intensity ω2, volume spectrum index γ3, volume spectrum intensity ω3, correlation length L c , compression rate fluctuation ratio μ, and obtain backscattering intensity data;

[0012] S4. Establish a multi-layer perceptron neural network inversion model based on the backscattering forward model;

[0013] S5. Use the acquired backscattering data as the input layer and use the established multi-layer perceptron neural network inversion model to invert the sedimentary layer parameters of the experimental area.

[0014] Furthermore, in step S1, the approximate fluid theory is obtained by simplifying the parameters of the Biot theory to obtain the equivalent fluid modulus K eff :

[0015]

[0016] Among them, K g , K f and K w are the bulk modulus of sediment, the bulk modulus of solid skeleton and the bulk modulus of pore water respectively, β is the porosity, and the modulus is solved by Biot theory wave equation to obtain the equivalent density ρ eff The expression is:

[0017]

[0018] The expression of longitudinal wave velocity c1 is:

[0019]

[0020] Then the longitudinal wave complex wave number k1 is:

[0021]

[0022] Actual parameters is the energy loss parameter, and the sound attenuation coefficient α can be calculated using the energy loss parameter.

[0023]

[0024] The unit of sound attenuation coefficient is dB / m, where v p is the ratio of sediment sound velocity to seawater sound velocity, c w is the speed of sound in seawater.

[0025] Furthermore, in step S2, according to the Jackson backscattering model, the backscattering intensity in dB / m is calculated as follows:

[0026] S b (θ)=10lgσ

[0027] The backscattering is divided into two parts: roughness scattering caused by the undulation of the seabed surface and volume scattering, that is, the roughness scattering cross section σ r and the volume scattering cross section σ v , so the backscattering formula can be written as:

[0028] S b (θ)=10lg(σ r +σ v )

[0029] The scattering cross section expression of small roughness perturbation approximation is:

[0030]

[0031] The expression of the scattering cross section in the Kirchhoff approximation is:

[0032]

[0033] The scattering cross section of the small slope approximation is:

[0034]

[0035] in,

[0036]

[0037] ω is the angular frequency, c is the speed of sound in seawater, ω = 2πf;

[0038] A ww =1 / 2[1+V ww (θ i )][1+V ww (θ s )]G

[0039]

[0040] in, v p is the sound velocity ratio, δ p is the energy attenuation coefficient;

[0041]

[0042] a p is the complex velocity ratio, which is calculated as

[0043] Among them, I k The solution is:

[0044]

[0045] In addition, V ww It can be solved by the following formula

[0046]

[0047] Among them, θ p is the transmission grazing angle, and Snell’s law can be used to obtain:

[0048]

[0049] Furthermore, in step S3, since the volume scattering is related to the acoustic wave incident depth, the equivalent interface double-base volume scattering cross section is calculated as follows:

[0050]

[0051] Among them, σ can be obtained by perturbation approximation fluid model v is the sediment volume scattering cross section:

[0052]

[0053] This formula implies that the correlation coefficient between density and compression rate is -1, and Δk p is the modulus of the Bragg wave vector, called the Bragg wave number, so for backscattering we can get:

[0054] Δk p =2k w [cos 2 θ i +{Re[P(θ i )]} 2 ] 1 / 2

[0055] A spectrum form commonly used in scattering models is as follows:

[0056]

[0057] Here, κ is defined as:

[0058]

[0059] In the above formula, γ3 and ω3 are the volume spectrum index and volume spectrum intensity, respectively, which are used to characterize the heterogeneity of sediments; μ is used to characterize the compression rate fluctuation ratio of seafloor sediment density disturbance, L c is the correlation length, r2 is the roughness spectrum index, and ω2 is the roughness spectrum intensity.

[0060] Furthermore, the inversion parameters include porosity β, average particle size φ, particle to pore water mass density ratio ρ r And the bulk elastic modulus ratio of particles to pore water K r , as follows:

[0061] Pore ​​water properties: The parameters related to pore water properties in Biot theory include pore water mass density ρ w , pore water bulk elastic modulus K w and the dynamic viscosity of pore water η. It is usually assumed that the properties of pore water are the same as those of overlying seawater, and the parameters of seawater are easy to measure;

[0062] Permeability: The relationship between permeability κ and porosity β and average particle diameter d is given by the following formula:

[0063]

[0064] Among them, the coefficient K is 5 for spherical particles, the unit of the average particle diameter is m, and the relationship with the average particle size φ is:

[0065] φ=-log2(1000d)

[0066] This formula is suitable for loose, well-sorted sediments with spherical particles, so the results are higher than the actual measured values. As correction factor;

[0067] Pore ​​size parameters: The relationship between the pore size parameter a, porosity β and average particle diameter d of uniform spherical particles is obtained based on the hydraulic radius:

[0068]

[0069] Relationship between pore size parameters and permeability:

[0070]

[0071] Curvature: The curvature α is a structural constant of the sediment, and the relationship with φ is used here:

[0072]

[0073] Sediment particle characteristics: The parameters related to sediment particle characteristics in Biot theory include particle mass density ρg and particle bulk elastic modulus K g , the parameter to be inverted is selected as the mass density ratio of particles to pore water ρ r and the ratio of bulk elastic modulus of particles to pore water K r .

[0074] Furthermore, the multilayer perceptron neural network in step S4 is specifically as follows:

[0075] The number of input features is n, the number of output features is m, multiple hidden layers, and the number of neurons in the hidden layer is not fixed. The input parameters are the backscattering intensity data related to the grazing angle, the data range is 1°-90°, the step size is 1, n=90, the output data is the sedimentary layer parameters, there are 10 direct inversion parameters, m=10, and the data are divided into training set and test set in a ratio of 9:1;

[0076] In the case of a single hidden layer:

[0077] y i =f(w·x+b)

[0078] Among them, w is the weight, b is the bias, and f is the activation function. Introducing the activation function can introduce nonlinearity. The activation function uses the Relu function, as shown in the following formula:

[0079] f(x)=max(0,x)

[0080] The case of multiple hidden layers is similar to that of a single hidden layer, except that w and b are different. Five hidden layers are used here, and the number of neurons in the hidden layers is 70, 50, 30, 25, and 20, respectively. The weights and biases are adjusted through network training parameters. The input value is forward propagated through the network, through the hidden layer to the output layer, and the inversion result of the neural network is obtained. The model result is evaluated by the root mean square error (RMSE)

[0081]

[0082] Among them, j is the number of samples, y i is the actual value, The inversion value is calculated through the test set. The root mean square error of the inversion result is back-propagated back to the network to adjust the weights and biases. The training method uses Bayesian regularization. Bayesian regularization introduces constraints on the network weights by introducing prior distributions, and learns the distribution parameters during the training process.

[0083] Furthermore, in step S5, the ten physical property parameters are grouped into one group, several groups are randomly selected as the parameters to be inverted, and the backscattering intensity corresponding to each group is calculated to obtain the corresponding data set, which is divided into a training set and a validation set according to a ratio of 9:1, and the calculated backscattering intensity data is used as the input value x of the multilayer perceptron neural network. i , the parameter to be inverted is taken as the output, and the parameter to be inverted in the data set is y i , the inverse parameters in the multilayer perceptron neural network are The speed of seawater sound is set to 1500 m / s, the learning rate is set to 0.01, the maximum number of training rounds is set to 1000, and the training stop criterion is the root mean square error of 10 -1 , ensuring that the model achieves the expected accuracy while avoiding over-training and completing the training within a reasonable computing time.

[0084] Compared with the prior art, the present invention has the following advantages:

[0085] (1) This application solves the disturbance of traditional measurements and the difficulty of large-scale measurement by constructing a sediment propagation model. It uses the sediment propagation theoretical model for simulation to obtain a large amount of sediment sound propagation theoretical data for training the parameter inversion model.

[0086] (2) This application applies a multilayer perceptron neural network to the sediment parameter inversion model, using its complex network structure and multiple neurons to simulate complex functions, solve strong nonlinear problems, and improve inversion efficiency and quality; and adopts a Bayesian regularization strategy during training. By introducing constraints on network weights based on prior distributions, the learning of distribution parameters during the training process improves the generalization ability of the model and the problem of being unable to adapt to new samples, which can effectively prevent overfitting. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 is a flow chart of the method of the present invention;

[0088] Figure 2 It is a schematic diagram of the volume scattering principle of the present invention;

[0089] Figure 3 It is the roughness backscattering intensity simulation calculation curve of the present invention;

[0090] Figure 4 It is a simulation curve diagram of volume scattering backscattering intensity of the present invention;

[0091] Figure 5 This is a diagram of the multilayer perceptron network structure of the present invention;

[0092] Figure 6 This is a curve diagram of the training error decrease of the present invention;

[0093] Figure 7 The comparison diagram of the actual value and the predicted value of the inversion of the present invention, (a)-(j) are β, φ, ρ respectively r , K r ,γ2,ω2,γ3,ω3,L c , μ;

[0094] Figure 8 This is a backscattering curve diagram of the network prediction results of the present invention. DETAILED DESCRIPTION

[0095] In order to enable those skilled in the art to more clearly understand the technical solution of the present application, the seabed sediment parameter inversion method based on the multi-layer perceptron of the present invention is further described below with reference to the accompanying drawings.

[0096] like Figure 1 As shown in the figure, the specific steps of the seabed sediment parameter inversion method based on multi-layer perceptron are as follows:

[0097] (a) Establish an approximate fluid density model to calculate the sediment acoustic attenuation coefficient and sound velocity.

[0098] Since the actual seabed is a porous medium, the particle vibrations of the fluid phase and the solid phase in the medium are different in response to the excitation of sound waves. Therefore, we use the poroelastic model to establish a correlation model between the physical properties of sediments and geoacoustic parameters.

[0099] Since the approximate fluid theory is a simplification of the parameters of the Biot theory, Williams believes that the sediment framework modulus is much smaller than the bulk modulus of particles and seawater, so it has little effect on the sound velocity and attenuation. The sediment framework modulus can be regarded as 0, and the medium independent modulus becomes one, and the equivalent fluid modulus K is obtained. eff :

[0100]

[0101] Among them, K g , K f and K w are the bulk modulus of sediment, the bulk modulus of solid skeleton and the bulk modulus of pore water respectively. β is the porosity. The modulus is solved by Biot's theoretical wave equation to obtain the equivalent density ρ eff The expression is

[0102]

[0103] The expression of longitudinal wave velocity c1 is:

[0104]

[0105] Then the longitudinal wave complex wave number k1 is

[0106]

[0107] Actual parameters is the energy loss parameter, and the sound attenuation coefficient α can be calculated using the energy loss parameter.

[0108]

[0109] The unit of sound attenuation coefficient is dB / m, where v p is the ratio of sediment sound velocity to seawater sound velocity, c w is the speed of sound in seawater.

[0110] Next, we need to perform numerical simulation based on the approximate fluid density theory derived from the Biot theory to calculate the sound velocity and attenuation of the seabed sediment. The experiment uses the parameters given in the Sediment Acoustic Experiment-1999, and the parameter input values ​​are shown in the table below:

[0111] Table 1 List of BIOT parameter values

[0112]

[0113]

[0114] (ii) The backscattering forward model is established by calculating the seabed roughness scattering and volume scattering through the small slope approximation and the fluid perturbation approximation to obtain the backscattering intensity.

[0115] In order to simulate the seabed backscattering, it is necessary to use the geoacoustic parameters obtained by the approximate fluid density model as intermediate variables to calculate the backscattering intensity. For the dual-base scattering model, Figure 5 As shown in the figure, a sound source is set up underwater, and an angle coordinate system is used. A hydrophone is set up in the x direction as the receiving point. The horizontal direction is used as the reference, and the angle is called the grazing angle. For the scattering intensity measurement of the combined transmitter and receiver, it is very common to place the hydrophone at the sound source position to measure the scattering information. Therefore, for backscattering, it can be considered that θ i =θ s .

[0116] According to the Jackson backscattering model, the backscattering intensity in dB / m is calculated as follows:

[0117] S b (θ)=10lgσ (7)

[0118] Usually, backscattering is divided into two parts: roughness scattering caused by the undulation of the seabed surface and volume scattering. That is, the backscattering formula can be written as:

[0119] Sb (θ)=10lg(σ r +σ v ) (8)

[0120] That is, the calculation of backscattering needs to consider the roughness scattering cross section σ r and the volume scattering cross section σ v , then solving the scattering cross section will become the focus of calculating the backscattering intensity.

[0121] For roughness scattering, only the range of roughness scale equivalent to the wavelength of sound waves will affect sound scattering. The terrain range that affects the intensity of high-frequency sound scattering can be called micro-topography. The relevant parameters of roughness power spectrum density are used to characterize backscattering. A large number of measurements show that when the seabed roughness is isotropic and spatially stable, the power spectrum intensity in the wave number domain conforms to the "power law" fitting form:

[0122]

[0123] W(K) is the roughness spectrum, K represents the two-dimensional wavelength vector. The parameter ω2 is called the "spectral intensity"; the parameter γ2 is called the "spectral index" (here the subscript 2 indicates two-dimensional). The interface fluctuation function z is:

[0124]

[0125] Assuming ergodicity in the measurement area, B(R) is used to represent the covariance function of the elevation digital information. According to the Wiener-Khinchin theorem, W(K) can be solved by the Fourier transform of B(R):

[0126]

[0127] The above is the definition and solution of roughness. The following is the deduction of the solution method of roughness scattering. The widely used models include small roughness perturbation approximation and Kirchhoff approximation, each of which has its own scope of application. Kirchhoff approximation is more suitable for specular scattering direction; while for small roughness perturbation approximation, its scope of application is distributed in the wide-angle scattering range relative to the specular direction.

[0128] It can be obtained that the scattering cross section expression of the small roughness perturbation approximation is:

[0129]

[0130] The expression of the scattering cross section in the Kirchhoff approximation is:

[0131]

[0132] The scattering cross section of the small slope approximation is:

[0133]

[0134] in,

[0135]

[0136] ω is the angular frequency, c is the speed of sound in seawater, ω=2πf.

[0137] A ww =1 / 2[1+V ww (θ i )][1+V ww (θ s )]G (16)

[0138]

[0139] in, v p is the sound velocity ratio, δ p is the energy attenuation coefficient.

[0140]

[0141] a p is the complex velocity ratio, which is calculated as

[0142] Among them, I k It can be solved by (20)

[0143]

[0144] In addition, V ww It can be solved by formula (23)

[0145]

[0146] where θ p is the transmission grazing angle, which can be obtained by Snell's law

[0147]

[0148] σ r It can be solved by interpolating the empirical formula of the small roughness perturbation approximation model Kirchhoff approximation model, or by the small slope approximation method.

[0149] As for volume scattering, it is caused by the internal heterogeneity of the seabed sediments. There are many causes of heterogeneity, such as stratification caused by physical processes such as erosion and sedimentation, spatially continuous heterogeneity caused by benthic biological activities, and the influence of random components such as bubbles and debris. Based on the basic assumption that sediment volume scattering is very weak, Stockhausen established a sediment volume scattering model based on fluid theory, which can be represented by a linear scattering interface with a penetrating volume, and the scattering of the roughness of the seabed-salt water interface can be ignored. The schematic diagram of the volume scattering principle is shown in the figure below. Figure 2 shown.

[0150] (III) The acoustic parameters and physical parameters of the sediments were inverted according to the backscattering intensity, and ten sediment physical parameters to be inverted were obtained, namely: average particle size φ, fractional porosity β, particle to pore water mass density ratio ρ r , pore water bulk elastic modulus ratio K r , roughness spectrum index γ2, roughness spectrum intensity ω2, volume spectrum index γ3, volume spectrum intensity ω3, correlation length L c , compression rate fluctuation ratio μ, and obtain backscattering intensity data.

[0151] The scattering is limited to a wavelength range at the seawater-sediment interface. High-frequency sound wave volume scattering can be processed by interface processes, but volume scattering is difficult to distinguish from interface roughness scattering, so volume scattering also depends on the distance of the sound wave and the sound irradiation area. Since volume scattering is related to the sound wave incident depth, the equivalent interface bistatic volume scattering cross section is calculated as shown in formula (26):

[0152]

[0153] Among them, σ can be obtained by perturbation approximation fluid model v is the sediment volume scattering cross section

[0154]

[0155] This formula implies that the correlation coefficient between density and compression rate is -1, and Δk p is the modulus of the Bragg wave vector, called the Bragg wave number, so for backscattering we can get

[0156] Δk p =2k w [cos 2 θ i +{Re[P(θ i )]} 2 ] 1 / 2 (28)

[0157] From the perspective of volume scattering modeling, sediment heterogeneity is usually divided into two parts: deterministic and stochastic. The deterministic part of a given sediment property is the average value of the property in the studied area, while the stochastic part is the fluctuation relative to this average value. In order for these definitions to be valid, the selected area must be large enough to ensure that the property space is stable and the average is taken along the horizontal direction, so that the deterministic part depends only on the vertical coordinate Z. Therefore, the deterministic part of the property is described by a profile or gradient, and the stochastic part is usually described by statistical characteristics such as variance, covariance or power spectrum. A spectral form commonly used in scattering models is as follows:

[0158]

[0159] Here, κ is defined as

[0160]

[0161] In the above formula, γ3 and ω3 are the volume spectrum intensity and spectrum index, respectively, which are used to characterize the heterogeneity of sediments; μ is used to characterize the compressibility ratio of seabed sediment density disturbance.

[0162] According to the above calculation, when the sound wave frequency is 30kHz, c = 1500, δ p =0.0162, v p =1.178, L c =0.032, a ρ =1.845, ω2=0.000141, γ2=3.25, ω3=0.00644, γ3=3.75, μ=0.934, and the roughness scattering simulation of small slope approximation and small roughness perturbation approximation is obtained as follows Figure 3 As shown in Figure 2, the volume scattering results are shown in Figure 2. Figure 4 shown.

[0163] The backscattering model is established based on the approximate fluid density model. EDFM is an ideal approximation of Biot's theory. Since it ignores the effect of shear force, it does not need to consider the two factors of frame shear modulus and frame bulk modulus during calculation, reducing Biot's 13 parameters to 9. However, considering that the backscattering intensity still needs to consider the influence of parameters such as roughness and spectral index, it is still difficult to ensure the inversion accuracy by inverting many parameters at the same time. Therefore, it is necessary to reduce the number of inversion parameters through some physical relationships. Finally, the inversion parameters selected are porosity, average particle size, particle to pore water mass density ratio, and particle to pore water bulk elastic modulus ratio. Specifically, the following parameters are included:

[0164] ① Pore water characteristics: The parameters related to pore water characteristics in Biot theory include: pore water mass density ρ w, pore water bulk elastic modulus K w And the dynamic viscosity of pore water η, it is usually approximately assumed that the properties of pore water are the same as those of the overlying seawater, and the parameters of seawater are easy to measure.

[0165] ② Permeability: Hovem and Ingram gave the relationship between permeability κ and porosity β and average particle diameter d based on the following Kozeny-Carman equation:

[0166]

[0167] Among them, the coefficient K is 5 for spherical particles, the unit of the average particle diameter is m, and the relationship with the average particle size φ is:

[0168] φ=-log2(1000d) (33)

[0169] This formula is suitable for loose, well-sorted sediments with spherical particles, so the results are higher than the actual measured values. as a correction factor.

[0170] ③ Pore size parameters: Hovem and Ingram obtained the relationship between the pore size parameter a, porosity β and average particle diameter d of uniform spherical particles based on the hydraulic radius:

[0171]

[0172] Relationship between pore size parameters and permeability:

[0173]

[0174] ④Curvature: The curvature α is a structural constant of the sediment, and the relationship with φ is used here:

[0175]

[0176] ⑤ Sediment particle characteristics: The parameters related to sediment particle characteristics in Biot theory include: particle mass density ρ g and particle bulk elastic modulus K g Since there is no reference relationship between porosity and average particle size, it is used as the inversion parameter here. In order to narrow the search space and improve the accuracy of the inversion result, the inversion parameter is selected as the particle to pore water mass density ratio ρ r and the ratio of bulk elastic modulus of particles to pore water K r .

[0177] In summary, the parameters to be inverted are reduced to 10 physical parameters and 2 indirect geoacoustic parameters, sediment attenuation coefficient and sound velocity, as inversion targets through the correlation between sediment parameters. Although the number of inversion parameters has been reduced to a certain extent through some physical relationships, there are still 10 parameters that need to be directly inverted by the inversion algorithm, which is a major difficulty in the inversion of seabed sediments. When dealing with the inversion problem of physical models with complex nonlinear mapping, neural networks show significant applicability. This paper introduces a multilayer perceptron (MLP) neural network to solve the sediment parameter inversion problem with its powerful modeling ability. Multilayer perceptron (MLP) is a feedforward neural network whose structure includes an input layer, several hidden layers and an output layer. Each layer consists of multiple neurons, which are connected to the neuron nodes of the adjacent layer through a fully connected structure. This fully connected structure enables the MLP network to gradually learn and fit complex function mapping relationships by continuously adjusting the weights and biases in the network during the training process, thereby effectively dealing with nonlinear problems.

[0178] Sediment parameter inversion usually involves complex nonlinear relationships. Traditional linear models are difficult to capture these complex features. The MLP network can better capture the deep features in the data through its multi-layer structure. Its training process can gradually optimize the model parameters through the back-propagation algorithm, so that the network can adaptively adjust its inversion ability, thereby improving the accuracy and reliability of the inversion, providing an effective premise for the high-precision inversion of sediment parameters.

[0179] The geoacoustic parameters of sediments are calculated using a multilayer perceptron network through physical property parameters. The geoacoustic parameters are used as intermediate variables to calculate the backscattering intensity simulation data as the model training data set. The model parameters are adjusted through error back propagation to achieve accurate inversion effect.

[0180] (iv) Establish a multi-layer perceptron neural network inversion model based on the backscattering forward model.

[0181] like Figure 5 As shown in the figure, the multilayer perceptron neural network (MLP) includes an input layer, a hidden layer, and an output layer. The main function of the input layer is to receive backscattered data and pass it to the hidden layer of the network. The hidden layer contains multiple neuron nodes, which process the input data layer by layer through nonlinear activation functions to extract complex features in the data. The output layer is responsible for generating the final prediction results, which can output the inversion parameter values ​​and convert the information processed by the hidden layer into the required output form.

[0182] The number of input features is n, the number of output features is m, and there are usually multiple hidden layers. The number of neurons in the hidden layer is not fixed. The input parameters in this paper are the backscattering intensity data related to the grazing angle, the data range is 1°-90°, the step size is 1, n=90, and the output data is the sedimentary layer parameters, as shown in Table 2. There are 10 direct inversion parameters, m=10, and the data is divided into training set and test set in a ratio of 9:1.

[0183] In the case of a single hidden layer

[0184] y i =f(w·x+b) (37)

[0185] Among them, w is the weight, b is the bias, and f is the activation function. Introducing the activation function can introduce nonlinearity. The activation function uses the Relu function, as shown in the following formula:

[0186] f(x)=max(0,x) (38)

[0187] The case of multiple hidden layers is similar to that of a single hidden layer, with only w and b being different. Five hidden layers are used here, with the number of neurons in the hidden layers being 70, 50, 30, 25, and 20, respectively. The input value is forward propagated through the network, through the hidden layer to the output layer, and the error is back-propagated. The weights and biases are adjusted using the gradient descent algorithm. The adjustment method is as follows:

[0188] w kv (t+1)=w kv +Δw kv (39)

[0189] w vl (t+1)=w vl +Δw vl (40)

[0190] Among them, the partial derivative of the input backscatter value and the weight parameter between the hidden layer is Δw jv , and the partial derivative between the hidden layer and the physical parameters is Δw vi , the calculation process uses the learning rate h to calculate, and in the process again, the iteration step t will be based on E RMSE Until the network stop error condition E is met RMSE <10 -1 , the inversion result of the neural network is obtained, and the model result is evaluated by the root mean square error (RMSE). The root mean square error is solved as shown in formula (41):

[0191]

[0192] Among them, j is the number of samples, y i is the actual value, The inversion value is calculated through the test set. The root mean square error of the inversion result is back-propagated back to the network to adjust the weight and bias. The training method uses Bayesian regularization. Bayesian regularization introduces constraints on the network weights through the introduction of prior distribution. The distribution parameters are learned during the training process to solve the problem of weak generalization ability and inability to adapt to new samples, which can effectively prevent overfitting.

[0193] (V) Using the acquired backscattering data as the input layer, the established multi-layer perceptron neural network inversion model is used to invert the sedimentary layer parameters of the experimental area.

[0194] In order to verify the feasibility of the inversion method, the seabed geoacoustic parameters are accurately inverted, the physical relationship between the Biot model parameters is used to simplify the inversion model, and the backscattering process is simulated and calculated through the roughness approximation and the small slope approximation. The inversion parameters and their value ranges are selected as shown in Table 2.

[0195] Table 2 Parameters to be inverted and their value ranges

[0196] parameter Value range Average particle size φ 1-4 Fractional porosity β 0.2-0.8 <![CDATA[Ratio of particle to pore water mass density ρ r > 2.0-3.0 <![CDATA[Pore water bulk modulus ratio K r 。]]> 5-30 <![CDATA[Roughness spectrum index γ2]]> 2.2-3.8 <![CDATA[Roughness spectrum intensity ω2]]> 0.00001-0.005 <![CDATA[Volume spectrum index γ 3 > 1-8 <![CDATA[Volume spectrum intensity ω3]]> 0.001-0.01 <![CDATA[Relevant length L c > 0.001-0.05 Compression ratio μ 0.1-2

[0197] The backscattering intensity data is calculated using the above parameter value range, and a total of 5000 sets of simulation data are generated, that is, 5000 sets of 10 parameters to be inverted and the corresponding data of the backscattering intensity are obtained. The backscattering intensity data is used as the network input, that is, x i , and the parameter to be inverted is the output. The parameter to be inverted in the data set is y i , the parameters of the network inversion are The speed of sound in seawater is set to 1500m / s. The data set is divided into training set and test set in a ratio of 8:2. During the model training process, the learning rate is set to 0.01, which can ensure the stability and convergence of the training process. This value has been verified in many experiments to be a suitable choice for effectively learning data features while controlling oscillation phenomena. In order to ensure that the network is fully trained, the maximum training round is set to 1000 rounds, and the training stop criterion is set to the root mean square error of 10 -1 , ensuring that the model achieves the expected accuracy while avoiding over-training and completing the training within a reasonable computing time.

[0198] like Figure 6 The figure shows the curve of the training error decline. It can be seen that the root mean square error of the network drops rapidly in the early stage of training, indicating that the multilayer perceptron (MLP) network is effectively learning the features in the data. The weights and thresholds in the network are adjusted quickly at this stage. When the training reaches about 600 rounds, the error value tends to stabilize, and the decline thereafter is very small, indicating that the learning effect of the network is close to saturation. Finally, the training of the model stops at nearly 10 -1This meets the set training accuracy requirements and shows the acceptability of the training results in practical applications.

[0199] Further analysis shows that the errors of the training set and the test set remain consistent during the training process, with no significant difference, which indicates that the model has good generalization ability. The comparison curve between the actual value and the inverted value in the test set is plotted as follows Figure 7 The comparison between the inversion values ​​and the actual values ​​shows that β, γ2, and ω2 can be accurately inverted, and φ, ρ r A more accurate estimate can be achieved, K r ,γ3,ω3,L c There are still certain errors in the inversion process of μ and μ. In the high-frequency case, due to the weak penetration of high-frequency sound waves, the contribution of roughness scattering in the backscattering intensity increases significantly. Relatively speaking, it is difficult for sound waves to penetrate deep into the bottom, making the contribution of volume scattering relatively small. Therefore, it is particularly important to accurately invert the parameters related to the roughness of the seabed surface (such as roughness scattering), which are closely related to the propagation process of sound waves on the seabed. Therefore, γ2 and ω2 related to the roughness of the seabed surface can obtain the relevant physical laws of the accurate inversion of the composite sound wave propagation process. Since high-frequency sound waves are difficult to effectively detect the internal structure of the bottom, the accurate inversion of volume scattering related parameters (such as volume scattering intensity) may be limited, thereby introducing certain errors. Therefore, it is inevitable that parameters γ3 and ω3 will produce errors, so the only way is to adjust the network hyperparameters and increase the network complexity to minimize the error. The accuracy of the model inversion can also be verified by the root mean square error of each parameter separately, and the root mean square error is shown in Table 3. In addition, the accuracy of the model inversion can be further verified by analyzing the root mean square error (RMSE) of each parameter separately. The detailed data of these root mean square errors are shown in Table 3. Specifically, Table x shows the root mean square error values ​​of each parameter, which provide a basis for evaluating the model's ability to invert the accuracy of different physical quantities under high frequency conditions. Through the analysis of these error values, the accuracy of the model in processing different parameters can be identified and the model performance can be further optimized.

[0200] Table 3 Parameter root mean square error

[0201]

[0202] According to the analysis of the root mean square error (MSE) of each parameter and its range of values, it can be found that although the root mean square error of some parameters is relatively large, the range of values ​​of these parameters is also quite different from that of other parameters. In addition, considering the sensitivity of each physical property parameter to the backscattering intensity, the changes of porosity β, roughness spectrum index γ2, and spectrum intensity ω2 will lead to large changes in the backscattering intensity. They are sensitive parameters and their MSE values ​​are relatively small, but Kr The change of has only a slight change on the backscattering intensity, and its value range is large. The bulk elastic modulus of pore water is larger than K r The root mean square error is 7.0817, which is still within the acceptable error range.

[0203] Specifically, although the root mean square error of this parameter is high, it is still tolerable overall because its value range is significantly higher than that of other parameters. Relatively speaking, the root mean square errors of the other nine parameters are all less than 1, indicating that the inversion results of these parameters have high accuracy and reliability. These results effectively prove that the network performs well in the inversion task and can achieve relatively accurate model parameter prediction, thereby verifying the effectiveness of neural networks in sediment parameter inversion.

[0204] In order to further verify the accuracy and feasibility of the inversion results using the multilayer perceptron, the backscattering curve calculated by the original parameter simulation and the network inversion parameter values ​​were imported into the forward model to calculate the backscattering intensity for comparison. The comparison results are shown in Figure 2. Figure 8 As shown in the figure, the inversion results meet the prediction requirements in terms of both overall trend and numerical fitting degree, and the error does not exceed 1dB, which further verifies the accuracy of the inversion results of the multilayer perceptron network.

[0205] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for inverting seabed sediment parameters based on a multi-layer perceptron, characterized in that: The method comprises the following steps: S1. Establish an approximate fluid density model to calculate the sediment acoustic attenuation coefficient and sound velocity; S2. Calculate the seabed roughness scattering and volume scattering through small slope approximation and fluid perturbation approximation to establish a backscattering forward model and obtain the backscattering intensity; S3. Invert the geoacoustic parameters and physical parameters of the sediment according to the backscattering intensity, and obtain ten sediment physical parameters to be inverted, namely: average particle size φ, fractional porosity β, particle to pore water mass density ratio ρ r , pore water bulk elastic modulus ratio K r , roughness spectrum index γ2, roughness spectrum intensity ω2, volume spectrum index γ3, volume spectrum intensity ω3, correlation length L c , compression rate fluctuation ratio μ, based on which the backscattering intensity data is obtained; S4. Establish a multi-layer perceptron neural network inversion model based on the backscattering forward model; S5. Use the acquired backscattering data as the input layer and use the established multi-layer perceptron neural network inversion model to invert the sedimentary layer parameters of the experimental area.

2. The method for inverting seabed sediment parameters based on a multi-layer perceptron according to claim 1, characterized in that: In step S1, the approximate fluid theory is obtained by simplifying the parameters of the Biot theory to obtain the equivalent fluid modulus K eff : Among them, K g , K f and K w are the bulk modulus of sediment, the bulk modulus of solid skeleton and the bulk modulus of pore water respectively, β is the porosity, and the modulus is solved by Biot theory wave equation to obtain the equivalent density ρ eff The expression is: The expression of longitudinal wave velocity c1 is: Then the longitudinal wave complex wave number k1 is: Actual parameters is the energy loss parameter, and the sound attenuation coefficient α can be calculated using the energy loss parameter. The unit of sound attenuation coefficient is dB / m, where v p is the ratio of sediment sound velocity to seawater sound velocity, c w is the speed of sound in seawater.

3. The method for inverting seabed sediment parameters based on a multi-layer perceptron according to claim 2, characterized in that: In step S2, according to the Jackson backscattering model, the backscattering intensity in dB / m is calculated as follows: S b (θ)=10lgσ The backscattering is divided into two parts: roughness scattering caused by the undulation of the seabed surface and volume scattering, that is, the roughness scattering cross section σ r and the volume scattering cross section σ v , so the backscattering formula can be written as: S b (θ)=10lg(σ r +σ v ) The scattering cross section expression of small roughness perturbation approximation is: The expression of the scattering cross section in the Kirchhoff approximation is: The scattering cross section of the small slope approximation is: in, ω is the angular frequency, c is the speed of sound in seawater, ω = 2πf; A ww =1 / 2[1+V ww (i i )][1+V ww (i s )]G in, v p is the sound velocity ratio, δ p is the energy attenuation coefficient; a p is the complex velocity ratio, which is calculated as Among them, I k The solution is: In addition, V ww It can be solved by the following formula Among them, θ p is the transmission grazing angle, and Snell’s law can be used to obtain:

4. The method for inverting seabed sediment parameters based on a multi-layer perceptron according to claim 3, characterized in that: In step S3, since volume scattering is related to the acoustic wave incident depth, the equivalent interface double-base volume scattering cross section is calculated as follows: Among them, σ can be obtained by perturbation approximation fluid model v is the sediment volume scattering cross section: This formula implies that the correlation coefficient between density and compression rate is -1, and Δk p is the modulus of the Bragg wave vector, called the Bragg wave number, so for backscattering we can get: Δk p =2k w [cos 2 i i +{Re[P(θ i )]} 2 ] 1 / 2 A spectrum form commonly used in scattering models is as follows: Here, κ is defined as: In the above formula, γ3 and ω3 are the volume spectrum index and volume spectrum intensity, respectively, which are used to characterize the heterogeneity of sediments; μ is used to characterize the compression rate fluctuation ratio of seafloor sediment density disturbance, L c is the correlation length, r2 is the roughness spectrum index, and ω2 is the roughness spectrum intensity.

5. The method for inverting seabed sediment parameters based on a multi-layer perceptron according to claim 4, characterized in that: The inversion parameters include porosity β, average particle size φ, particle to pore water mass density ratio ρ r and the bulk elastic modulus ratio of particles to pore water K r , as follows: Pore ​​water properties: The parameters related to pore water properties in Biot theory include pore water mass density ρ w , pore water bulk elastic modulus K w and the dynamic viscosity of pore water η. It is usually assumed that the properties of pore water are the same as those of overlying seawater, and the parameters of seawater are easy to measure; Permeability: The relationship between permeability κ and porosity β and average particle diameter d is given by the following formula: Among them, the coefficient K is 5 for spherical particles, the unit of the average particle diameter is m, and the relationship with the average particle size φ is: φ=-log2(1000d) This formula is suitable for loose, well-sorted sediments with spherical particles, so the results are higher than the actual measured values. As correction factor; Pore ​​size parameters: The relationship between the pore size parameter a, porosity β and average particle diameter d of uniform spherical particles is obtained based on the hydraulic radius: Relationship between pore size parameters and permeability: Curvature: The curvature α is a structural constant of the sediment, and the relationship with φ is used here: Sediment particle characteristics: The parameters related to sediment particle characteristics in Biot theory include particle mass density ρ g and particle bulk elastic modulus K g , the parameter to be inverted is selected as the mass density ratio of particles to pore water ρ r and the ratio of bulk elastic modulus of particles to pore water K r .

6. The method for inverting seabed sediment parameters based on a multi-layer perceptron according to claim 5, characterized in that: The multilayer perceptron neural network in step S4 is specifically as follows: The number of input features is n, the number of output features is m, multiple hidden layers, and the number of neurons in the hidden layer is not fixed. The input parameters are the backscattering intensity data related to the grazing angle, the data range is 1°-90°, the step size is 1, n=90, the output data is the sedimentary layer parameters, there are 10 direct inversion parameters, m=10, and the data are divided into training set and test set in a ratio of 9:1; In the case of a single hidden layer: y i =f(w·x+b) Among them, w is the weight, b is the bias, and f is the activation function. Introducing the activation function can introduce nonlinearity. The activation function uses the Relu function, as shown in the following formula: f(x)=max(0,x) The case of multiple hidden layers is similar to that of a single hidden layer, except that w and b are different. Five hidden layers are used here, and the number of neurons in the hidden layers are 70, 50, 30, 25, and 20 respectively. The weights and biases are adjusted through network training parameters. The input value is forward propagated through the network, through the hidden layer to the output layer, and the inversion result of the neural network is obtained. The model result is evaluated by the root mean square error (RMSE): Among them, j is the number of samples, y i is the actual value, The inversion value is calculated through the test set. The root mean square error of the inversion result is back-propagated back to the network to adjust the weights and biases. The training method uses Bayesian regularization. Bayesian regularization introduces constraints on the network weights by introducing prior distributions, and learns the distribution parameters during the training process.

7. The method for inverting seabed sediment parameters based on a multi-layer perceptron according to claim 5, characterized in that: In step S5, the ten physical property parameters are grouped into one group, several groups are randomly selected as the parameters to be inverted, and the backscattering intensity corresponding to each group is calculated to obtain the corresponding data set, which is divided into a training set and a validation set according to a ratio of 9:

1. The calculated backscattering intensity data is used as the input value x of the multilayer perceptron neural network. i , the parameter to be inverted is taken as the output, and the parameter to be inverted in the data set is y i , the inverse parameters in the multilayer perceptron neural network are The speed of seawater sound is set to 1500 m / s, the learning rate is set to 0.01, the maximum number of training rounds is set to 1000, and the training stop criterion is the root mean square error of 10 -1 , ensuring that the model achieves the expected accuracy while avoiding over-training and completing the training within a reasonable computing time.

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