Method, device and equipment for modeling of swell sea surface based on modified lie transformation

Abstract

The application provides a swell sea surface modeling method, device and equipment based on a modified Lie transformation, and relates to the technical field of computer modeling. The method comprises the following steps: when a swell sea surface model is constructed, the spectrum information of a target sea surface to be modeled is acquired; a linear sea surface height model of a frequency domain dimension corresponding to the target sea surface is constructed based on the spectrum information; the linear sea surface height model of the frequency domain dimension is transformed to obtain a linear sea surface height model of a time domain dimension; the Lie transformation is modified based on the wind condition of the target sea surface under the linear sea surface height model of the time domain dimension; and the linear sea surface height model of the frequency domain dimension is superimposed based on the modified Lie transformation to construct a swell sea surface model of the target sea surface. In this way, the Lie transformation is modified in combination with the wind condition of the sea surface, so that the modified Lie transformation can better simulate the swell under high sea conditions, thereby effectively improving the modeling effect of the constructed swell sea surface model.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer modeling, and particularly relates to a swell sea surface modeling method, device and equipment based on a modified Lie transformation. BACKGROUND

[0002] Radar sea clutter data is used for sea clutter analysis. However, in some special scenarios, such as in high sea state scenarios, considering the difficulty of collecting radar sea clutter data, the swell sea surface modeling is used as the basis for radar electromagnetic echo simulation to better analyze the sea clutter.

[0003] At present, when the swell sea surface modeling is performed, a linear sea surface height model is usually constructed based on sea spectrum information of the sea surface, and the Lie transformation developed by Creamer is used to superimpose the linear sea surface height model to obtain a nonlinear swell sea surface modeling.

[0004] However, the Lie transformation cannot simulate the swell in high sea states, resulting in poor modeling effect of the constructed swell sea surface model. SUMMARY

[0005] The present application provides a swell sea surface modeling method, device and equipment based on a modified Lie transformation to solve the problem that the Lie transformation cannot simulate the swell in high sea states, resulting in poor modeling effect of the constructed swell sea surface model, thereby improving the modeling effect of the constructed swell sea surface model.

[0006] The present application provides a swell sea surface modeling method based on a modified Lie transformation, comprising:

[0007] Obtaining sea spectrum information of a target sea surface to be modeled;

[0008] Based on the sea spectrum information, a linear sea surface height model of a frequency domain dimension corresponding to the target sea surface is constructed;

[0009] The linear sea surface height model of the frequency domain dimension is transformed to obtain a linear sea surface height model of a time domain dimension;

[0010] Based on the wind conditions of the target sea surface, the Lie transformation is modified under the linear sea surface height model of the time domain dimension to obtain a modified Lie transformation;

[0011] Based on the modified Lie transformation, the linear sea surface height model of the frequency domain dimension is superimposed to construct a swell sea surface model of the target sea surface.

[0012] According to a choppy sea surface modeling method based on a modified Lie transform provided by the present application, the wind condition includes wind speed and wind direction. Under the linear sea surface height model in the time domain dimension, the Lie transform is corrected based on the wind condition of the target sea surface to obtain a corrected Lie transform, including:

[0013] Under the linear sea surface height model in the time domain dimension, performing Hilbert transform on the Lie transform to obtain a transformation result;

[0014] A second-order approximate derivative is performed on the transformation result, and the wind speed and the wind direction are superimposed during the second-order approximate derivative process to obtain a second-order approximate derivative result, and the second-order approximate derivative result is used to characterize the modified Lie transform.

[0015] According to a choppy sea surface modeling method based on a modified Lie transform provided by the present application, the Lie transform is subjected to a Hilbert transform under the linear sea surface height model in the time domain dimension to obtain a transformation result, including:

[0016] Under the linear sea surface height model in the time domain dimension, based on Perform Hilbert transform on Lie transform;

[0017] in, represents the transformation result, k represents the wave number, t represents the time, N represents the number of sampling points, exp() represents the Fourier transform, represents an imaginary number, Represents the linear sea surface height model in the time domain dimension, Represents the time domain space of the target sea surface.

[0018] According to a choppy sea surface modeling method based on a modified Lie transform provided by the present application, performing a second-order approximate derivative on the transformation result, superimposing the wind speed and the wind direction during the second-order approximate derivative process, and obtaining a second-order approximate derivative result, includes:

[0019] based on performing a second-order approximate derivation on the transformation result, and superimposing the wind speed and the wind direction during the second-order approximate derivation;

[0020] in, represents the second-order approximate derivative result, k represents the wave number, t represents the time, Indicates 10m high wind speed, represents the x-dimensional wave number of the target sea surface, represents the y-dimensional wave number of the target sea surface, represents the wind direction in x dimension, represents the wind direction in the y dimension, and Represents a function term.

[0021] According to a method for modeling a choppy sea surface based on a modified Lie transform provided by the present application, the linear sea surface height model in the frequency domain dimension is superimposed based on the modified Lie transform to construct a choppy sea surface model of the target sea surface, comprising:

[0022] Based on the modified Lie transform, the linear sea surface height model in the frequency domain dimension is superimposed to obtain a modified nonlinear sea surface height model in the frequency domain dimension;

[0023] The corrected nonlinear sea surface height model in the frequency domain dimension is converted into a space domain to obtain a nonlinear sea surface height model in the time domain dimension, and the nonlinear sea surface height model in the time domain dimension is the choppy sea surface model.

[0024] According to a choppy sea surface modeling method based on a modified Lie transform provided by the present application, the linear sea surface height model in the frequency domain dimension is superimposed based on the modified Lie transform to obtain a modified nonlinear sea surface height model in the frequency domain dimension, including:

[0025] based on Superimposing the linear sea surface height model in the frequency domain dimension to obtain a corrected nonlinear sea surface height model in the frequency domain dimension;

[0026] in, represents the nonlinear sea surface height model in the modified frequency domain, k represents the wave number, t represents the time, represents the linear sea surface height model in the frequency domain dimension, represents a second-order approximate derivative result, and the second-order approximate derivative result is used to characterize the modified Lie transform.

[0027] According to a choppy sea surface modeling method based on modified Lie transform provided by the present application, the modified nonlinear sea surface height model in the frequency domain dimension is converted into a spatial domain to obtain a nonlinear sea surface height model in the time domain dimension, including:

[0028] based on Performing spatial domain conversion on the corrected nonlinear sea surface height model in the frequency domain dimension;

[0029] in, Represents the nonlinear sea surface height model in the time domain dimension k represents the wave number, t represents the time, Represents the nonlinear sea surface height model in the corrected frequency domain dimension, exp() represents the inverse Fourier transform, which is used for spatial domain conversion. Represents an imaginary number.

[0030] The present application provides a device for modeling a choppy sea surface based on a modified Lie transform, comprising:

[0031] An acquisition unit, used for acquiring ocean spectrum information of a target sea surface to be modeled;

[0032] A construction unit, configured to construct a linear sea surface height model in a frequency domain dimension corresponding to the target sea surface based on the sea spectrum information;

[0033] a transform unit, configured to transform the linear sea level height model in the frequency domain dimension to obtain a linear sea level height model in the time domain dimension;

[0034] a correction unit, configured to correct the Lie transform based on the wind condition of the target sea surface under the linear sea surface height model in the time domain dimension to obtain a corrected Lie transform;

[0035] A processing unit is used to superimpose the linear sea surface height model in the frequency domain dimension based on the modified Lie transform to construct a choppy sea surface model of the target sea surface.

[0036] The present application also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method for modeling a choppy sea surface based on the modified Lie transform as described above is implemented.

[0037] The present application also provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for modeling a choppy sea surface based on a modified Lie transform as described above is implemented.

[0038] The present application also provides a computer program product, comprising a computer program, which, when executed by a processor, implements any of the above-described methods for modeling choppy sea surfaces based on modified Lie transform.

[0039] The present application provides a method, device, and apparatus for modeling a choppy sea surface based on a modified Lie transform. When constructing a choppy sea surface model, the method, device, and apparatus can first obtain the ocean spectrum information of the target sea surface to be modeled; and based on the ocean spectrum information, construct a linear sea surface height model in the frequency domain dimension corresponding to the target sea surface; transform the linear sea surface height model in the frequency domain dimension to obtain a linear sea surface height model in the time domain dimension; under the linear sea surface height model in the time domain dimension, modify the Lie transform based on the wind conditions of the target sea surface; and then, based on the modified Lie transform, superimpose the linear sea surface height model in the frequency domain dimension to construct a choppy sea surface model of the target sea surface. In this way, by modifying the Lie transform in combination with the wind conditions of the sea surface, the modified Lie transform can better simulate choppy waves under high sea conditions, thereby effectively improving the modeling effect of the constructed choppy sea surface model. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the present application or the prior art, a brief introduction will be given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0041] Figure 1 A schematic flow chart of a method for modeling choppy sea surface based on modified Lie transform provided in an embodiment of the present application.

[0042] Figure 2 This is a schematic diagram of Elfouhaily sea spectrum information at a wind speed of 10 m / s provided in an embodiment of the present application.

[0043] Figure 3 A schematic diagram of a process for correcting the Lie transform based on the wind conditions of the target sea surface provided in an embodiment of the present application.

[0044] Figure 4 A schematic diagram of a process for constructing a wave surface model of a target sea surface provided in an embodiment of the present application.

[0045] Figure 5 A comparative schematic diagram provided for an embodiment of the present application.

[0046] Figure 6 Schematic diagram of sea surface morphology of a linear sea surface model, a standard Lie transformation sea surface model and a choppy sea surface model constructed in this application at different wind speeds provided in an embodiment of the present application.

[0047] Figure 7 A schematic diagram of comparing restored ocean spectrum information with original ocean spectrum information used to construct a choppy sea surface model provided in an embodiment of the present application.

[0048] Figure 8 A schematic diagram of comparing restored ocean spectrum information with original ocean spectrum information used to construct a choppy sea surface model provided in an embodiment of the present application.

[0049] Figure 9 A schematic diagram of sea surface radar simulated echo conditions under sea conditions 1, 5 and 7 provided in an embodiment of the present application.

[0050] Figure 10 A schematic structural diagram of a wave sea surface modeling device based on a modified Lie transform provided in an embodiment of the present application.

[0051] Figure 11 A schematic diagram of the physical structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0052] To make the objectives, technical solutions, and advantages of this application more clear, the technical solutions in this application will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0053] In the embodiments of this application, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can mean: A exists alone, A and B exist simultaneously, or B exists alone. A and B can be singular or plural. In the text description of this application, the character " / " generally indicates that the associated objects are in an "or" relationship.

[0054] The technical solutions provided by the embodiments of this application can be adapted to certain special scenarios, such as those in high sea conditions. Taking high sea conditions as an example, in the prior art, when modeling a choppy sea surface, a linear sea surface height model is typically constructed based on the sea spectrum information of the sea surface. This linear sea surface height model is then superimposed using the Lie transform developed by Creamer to obtain a nonlinear choppy sea surface model.

[0055] Among them, the ocean spectrum information is the Fourier transform of the wave height fluctuation correlation function, and the ocean spectrum information itself contains rich distribution information of the harmonic components of the waves.

[0056] However, the above-mentioned Lie transformation cannot simulate the curled waves under high sea conditions, resulting in poor modeling effect of the constructed curled wave sea surface model.

[0057] In order to solve the defect in the prior art that the Lie transform cannot simulate the waves under high sea conditions, resulting in poor modeling effect of the constructed wave sea surface model, thereby improving the modeling effect of the constructed wave sea surface model, an embodiment of the present application provides a wave sea surface modeling method based on a modified Lie transform. When modeling the wave sea surface model, the influence of the wind conditions on the wave sea surface modeling is fully considered. Therefore, the Lie transform is first corrected based on the wind conditions on the sea surface to obtain a corrected Lie transform; then, based on the corrected Lie transform, the linear sea surface height model is superimposed to construct the wave sea surface model of the sea surface. In this way, the Lie transform is corrected in combination with the wind conditions on the sea surface, so that the corrected Lie transform can better simulate the waves under high sea conditions, thereby effectively improving the modeling effect of the constructed wave sea surface model.

[0058] It can be understood that the execution subject of this method can be an electronic device such as a cluttered sea surface modeling platform, a computer or a server. Of course, it can also be a cluttered sea surface modeling device based on the modified Lie transform set in the electronic device. The cluttered sea surface modeling device based on the modified Lie transform can be implemented through software, hardware or a combination of the two, and can be specifically set according to actual needs.

[0059] The following specific embodiments will be used to describe in detail the wave sea surface modeling method based on the modified Lie transform provided by this application. It is understood that the following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments.

[0060] Figure 1 A flow chart of a method for modeling a choppy sea surface based on a modified Lie transform provided in an embodiment of the present application. For example, see Figure 1 As shown, the choppy sea surface modeling method based on the modified Lie transform may include:

[0061] S101: Acquire ocean spectrum information of a target sea surface to be modeled.

[0062] For example, the ocean spectrum information may be Elfouhaily two-dimensional ocean spectrum information, or other ocean spectrum information, such as PM ocean spectrum information or JONSWAP ocean spectrum information, etc., and may be specifically set according to actual needs.

[0063] Taking the Elfouhaily two-dimensional ocean spectrum information as an example, the Elfouhaily two-dimensional ocean spectrum information may include the Elfouhaily variance spectrum and the Elfouhaily curvature spectrum. For example, see Figure 2 As shown, Figure 2This is a schematic diagram of Elfouhaily sea spectrum information at a wind speed of 10 m / s provided in an embodiment of the present application, wherein: Figure 2 The left image in the middle is the Elfouhaily variance spectrum, and the right image is the Elfouhaily curvature spectrum.

[0064] The horizontal axis of the Elfouhaily variance spectrum represents the wave number, with the unit of rad / m (radians per meter). The wave number is the inverse of the wavelength and is used to describe the spatial frequency of the wave. The vertical axis of the Elfouhaily variance spectrum represents the variance spectrum, with the unit of , which is used to describe the distribution of wave energy at different wave numbers.

[0065] The horizontal axis of the Elfouhaily curvature spectrum represents the wave number, which is measured in rad / m (radians per meter). The wave number is the inverse of the wavelength and is used to describe the spatial frequency of the wave. The vertical axis of the Elfouhaily curvature spectrum represents the curvature spectrum, which is measured in rad / m (radians per meter). , which is used to describe the detailed distribution of wave energy as a function of wave number.

[0066] Combine Figure 2 The Elfouhaily 2D ocean spectrum information shown has a double peak value, with 370 rad / m being the second peak of the curvature spectrum, which coincides with the double peak value of the real sea area. Therefore, in this embodiment of the present application, the Elfouhaily 2D ocean spectrum information can be used as the ocean spectrum information of the target sea surface.

[0067] For example, in the embodiment of the present application, the representation of the Elfouhaily two-dimensional ocean spectrum can be shown in the following formula 1.

[0068] Formula 1

[0069] in, represents the Elfouhaily two-dimensional ocean spectrum information, that is, the ocean spectrum information of the target sea surface, k represents the wave number, represents the Elfouhaily omnidirectional one-dimensional ocean spectrum information, represents the angular distribution function, represents the wave number direction angle, , represents the wave number in the x dimension, represents the wave number in the y dimension, , , n represents the number of sampling points in the x-dimension of the target sea surface, m represents the number of sampling points in the y-dimension of the target sea surface, Indicates the length of the target sea surface constructed, Indicates the width of the constructed target sea surface.

[0070] After the ocean spectrum information of the target sea surface to be modeled is obtained, the following S102 may be executed.

[0071] S102: Construct a linear sea surface height model in the frequency domain corresponding to the target sea surface based on the sea spectrum information.

[0072] For example, in an embodiment of the present application, when constructing a linear sea surface height model in the frequency domain dimension corresponding to the target sea surface based on the sea spectrum information, the following formula 2 can be referred to.

[0073] Formula 2

[0074] in, represents the linear sea surface height model in the frequency domain, t represents time, represents a complex Gaussian random sequence with a mean of 0 and a variance of 1. represents the Elfouhaily two-dimensional ocean spectrum information, that is, the ocean spectrum information of the target sea surface, exp() represents Fourier transform, j represents imaginary number, represents the angular frequency, and * represents the complex conjugate.

[0075] After constructing a linear sea surface height model in the frequency domain corresponding to the target sea surface based on the sea spectrum information, the following S103 may be executed.

[0076] S103 : transforming the linear sea level height model in the frequency domain dimension to obtain a linear sea level height model in the time domain dimension.

[0077] For example, when the linear sea surface height model in the frequency domain dimension is transformed to obtain the linear sea surface height model in the time domain dimension, the following formula 3 can be referred to.

[0078] Formula 3

[0079] in, Represents the linear sea surface height model in the time domain dimension, represents the linear sea surface height model in the frequency domain dimension, Represents an imaginary number.

[0080] S104. Under the linear sea level height model in the time domain dimension, the Lie transform is corrected based on the wind condition of the target sea surface to obtain a corrected Lie transform.

[0081] For example, in the embodiment of the present application, wind conditions may include wind speed and wind direction, which can be set according to actual needs.

[0082] In the embodiment of the present application, the influence of the wind conditions on the choppy sea surface modeling is fully taken into consideration. Therefore, when modeling the choppy sea surface model, the Lie transform can be first corrected based on the wind conditions on the sea surface to obtain a corrected Lie transform; then, based on the corrected Lie transform, the linear sea surface height model is superimposed to construct the choppy sea surface model of the sea surface, that is, the following S105 is executed. In this way, the Lie transform is corrected in combination with the wind conditions on the sea surface, so that the corrected Lie transform can better simulate choppy waves under high sea conditions, thereby effectively improving the modeling effect of the constructed choppy sea surface model.

[0083] S105. Based on the modified Lie transform, the linear sea surface height model in the frequency domain dimension is superimposed to construct a choppy sea surface model of the target sea surface.

[0084] It can be seen that in the embodiment of the present application, when constructing a choppy sea surface model, the ocean spectrum information of the target sea surface to be modeled can be first obtained; and based on the ocean spectrum information, a linear sea surface height model of the frequency domain dimension corresponding to the target sea surface is constructed; the linear sea surface height model of the frequency domain dimension is transformed to obtain a linear sea surface height model of the time domain dimension; under the linear sea surface height model of the time domain dimension, the Lie transform is corrected based on the wind conditions of the target sea surface to obtain a corrected Lie transform; and then, based on the corrected Lie transform, the linear sea surface height model of the frequency domain dimension is superimposed to construct a choppy sea surface model of the target sea surface. In this way, the Lie transform is corrected in combination with the wind conditions of the sea surface, so that the corrected Lie transform can better simulate choppy waves under high sea conditions, thereby effectively improving the modeling effect of the constructed choppy sea surface model.

[0085] Based on the above Figure 1 In the embodiment shown, in the above S104, the specific implementation of modifying the Lie transform based on the wind conditions of the target sea surface under the linear sea surface height model in the time domain dimension can be seen in the following Figure 3 The embodiment shown.

[0086] Figure 3 A schematic diagram of a process for correcting a Lie transform based on wind conditions at a target sea surface is provided in an embodiment of the present application. The method may include:

[0087] S301. Under a linear sea level height model in the time domain dimension, perform Hilbert transform on the Lie transform to obtain a transformation result.

[0088] For example, in an embodiment of the present application, under a linear sea level height model in the time domain dimension, a Hilbert transform is performed on the Lie transform to obtain a transformation result, which may include:

[0089] Under the linear sea surface height model in the time domain, based on Perform Hilbert transform on Lie transform;

[0090] in, Indicates the transformation result, k indicates the wave number, t indicates the time, N indicates the number of sampling points, exp() indicates the Fourier transform, represents an imaginary number, Represents the linear sea surface height model in the time domain dimension, Represents the time domain space of the target sea surface.

[0091] After performing Hilbert transform on the Lie transform and obtaining the transform result, the following S302 can be executed.

[0092] S302: Perform a second-order approximate derivative on the transformation result, superimpose the wind speed and wind direction during the second-order approximate derivative process to obtain a second-order approximate derivative result, and use the second-order approximate derivative result to represent the modified Lie transform.

[0093] For example, in an embodiment of the present application, performing a second-order approximate derivative on the transformation result, superimposing the wind speed and wind direction during the second-order approximate derivative process, and obtaining a second-order approximate derivative result may include:

[0094] based on Perform a second-order approximate derivative on the transformation result, and superimpose the wind speed and wind direction during the second-order approximate derivative process.

[0095] in, represents the second-order approximate derivative result, k represents the wave number, t represents the time, Indicates 10m high wind speed, represents the x-dimensional wave number of the target sea surface, Represents the y-dimensional wave number of the target sea surface, represents the wind direction in x dimension, represents the wind direction in the y dimension, and Represents a function term.

[0096] In combination with the above description, the wind speed and wind direction factors are superimposed in the process of performing the second-order approximate derivation of the transformation results to correct the Lie transform, so that the corrected Lie transform can better simulate the choppy waves under high sea conditions; then, based on the corrected Lie transform, the linear sea surface height model in the frequency domain dimension is superimposed to construct the choppy sea of ​​the target sea surface, thereby effectively improving the modeling effect of the constructed choppy sea surface model.

[0097] Based on the above Figure 1 In the embodiment shown, in the above S105, based on the modified Lie transform, the linear sea surface height model in the frequency domain dimension is superimposed to construct the wave sea surface model of the target sea surface. For a specific implementation, please refer to the following Figure 4The embodiment shown.

[0098] Figure 4 A schematic diagram of a process for constructing a wave surface model of a target sea surface provided in an embodiment of the present application may include:

[0099] S401 : Based on the modified Lie transform, the linear sea surface height model in the frequency domain dimension is superimposed to obtain a modified nonlinear sea surface height model in the frequency domain dimension.

[0100] For example, in an embodiment of the present application, based on the modified Lie transform, the linear sea level model in the frequency domain dimension is superimposed to obtain a modified nonlinear sea level model in the frequency domain dimension, which may include:

[0101] based on Superimposing the linear sea surface height model in the frequency domain dimension to obtain a corrected nonlinear sea surface height model in the frequency domain dimension;

[0102] in, represents the nonlinear sea surface height model in the modified frequency domain, k represents the wave number, t represents the time, represents the linear sea surface height model in the frequency domain dimension, Represents the second-order approximate derivative result, which is used to characterize the modified Lie transform.

[0103] In this way, based on the modified Lie transform, the linear sea surface height model in the frequency domain dimension is superimposed to better simulate the curling waves under high sea conditions. Then, the modified nonlinear sea surface height model in the frequency domain dimension is transformed into the spatial domain, that is, the following S402 is executed, which can quickly generate breaking waves in a large area of ​​the sea, and the curling wave effect changes with the changes in the sea state parameters.

[0104] S402 , performing spatial domain conversion on the corrected nonlinear sea surface height model in the frequency domain dimension to obtain a nonlinear sea surface height model in the time domain dimension, where the nonlinear sea surface height model in the time domain dimension is a choppy sea surface model.

[0105] For example, in an embodiment of the present application, performing spatial domain conversion on the corrected nonlinear sea level height model in the frequency domain dimension to obtain a nonlinear sea level height model in the time domain dimension may include:

[0106] based on The nonlinear sea surface height model in the modified frequency domain dimension is transformed into the spatial domain.

[0107] in, Represents the nonlinear sea surface height model in the time domain dimension k represents the wave number, t represents the time, Represents the nonlinear sea surface height model in the corrected frequency domain dimension, exp() represents the inverse Fourier transform, which is used for spatial domain conversion. Represents an imaginary number.

[0108] Combined with the above description, based on the modified Lie transform, the linear sea surface height model in the frequency domain dimension is superimposed, which can better simulate the curling waves under high sea conditions. Then the nonlinear sea surface height model in the modified frequency domain dimension is converted into the spatial domain, which can quickly generate breaking waves in a large area of ​​the sea, and the curling wave effect changes with the changes in sea state parameters. Therefore, the modeling effect of the constructed curling wave sea surface model can be effectively improved.

[0109] In order to verify the choppy sea surface modeling method based on the modified Lie transform provided in the embodiment of the present application, the linear sea surface model, the standard Lie transform sea surface model and the choppy sea surface model constructed in the present application can be compared with each other with the wind speed of 10 m / s. For example, see Figure 5 As shown, Figure 5 A comparative schematic diagram provided in the embodiment of the present application, combined with Figure 5 It can be seen that for the choppy sea surface, on the one hand, the differences between the sea surface height models of slices in different dimensions are small, but the slope, sharpness and curling degree change greatly with the change of wind speed, which can show the effect of choppy waves in three-dimensional space.

[0110] For example, see the following Figure 6 As shown, Figure 6 Schematic diagram of the sea surface morphology of a linear sea surface model, a standard Lie transform sea surface model and a wave sea surface model constructed in this application under different wind speeds provided in the embodiment of this application. It is assumed that the length and width of the simulated sea surface are both 100m, the number of sampling points in both dimensions are 1000, and the wind direction is , Figure 6 The left picture shows a wind speed of 5m / s, where the sea surface is relatively flat and it is difficult for breaking waves to form at this wind speed. Figure 6 In the right figure, under a wind speed of 10m / s, the sea surface fluctuates greatly, breaking waves are formed obviously, and the direction of curling waves is consistent with the wind direction. This can better simulate curling waves under high sea conditions, thereby effectively improving the modeling effect of the constructed curling wave sea surface model.

[0111] In addition to the above verification, verification can also be performed from the perspectives of energy conservation and mean square slope.

[0112] The energy conservation verification is mainly carried out by inversely recovering the corresponding ocean spectrum information from the constructed choppy sea surface model. The inversely recovered ocean spectrum information can be shown in the following formula 3.

[0113] Formula 3

[0114] in, Represents the Fourier transform of sea surface height, and N represents the number of sampling points in each dimension of the sea surface.

[0115] The recovered ocean spectrum information is compared with the original ocean spectrum information used to construct the wave sea surface model. For example, see Figure 7 As shown, Figure 7 A schematic diagram of comparing the restored ocean spectrum information with the original ocean spectrum information used to construct the choppy sea surface model provided in an embodiment of the present application shows that the restored ocean spectrum information and the original ocean spectrum information used to construct the choppy sea surface model basically conserve energy.

[0116] When verifying from the perspective of the mean square slope of the sea surface, the standard Lie transform sea surface model and the wave sea surface model constructed in this application can be compared. For example, see Figure 8 As shown, Figure 8 A schematic diagram of an embodiment of the present application is provided for comparing the restored ocean spectrum information with the original ocean spectrum information used to construct a choppy sea surface model. It is not difficult to see that after a wind speed of 10 m / s, the minimum average difference in the mean square slope of the sea surface is 0.0145, and the maximum average difference is 0.0255. The error with the standard Lie transform sea surface model is more than 20%, and the restoration effect is poor under high sea conditions. The mean square slope of the sea surface of the choppy sea surface model constructed in the present application satisfies the relationship with wind speed proposed by Cox-Munk, and can accurately restore the slope of the sea surface even under high sea conditions.

[0117] After constructing a cluttered sea surface model using the modified Lie transform method provided in the embodiments of the present application, radar signal echo simulation can be performed based on the constructed cluttered sea surface model to reflect the influence of the sea surface environment. For example, assuming that the sea level is set to 500 meters, the pulse repetition rate of the X-band radar is 2000Hz, and the scattering coefficient model adopts the TSC model, the sea surface radar simulation echo conditions under different sea conditions 1, sea conditions 5, and sea conditions 7 can be seen in Figure 1. Figure 9 As shown, Figure 9 A schematic diagram of the sea surface radar simulated echo conditions under sea conditions 1, 5 and 7 is provided for an embodiment of the present application. It is not difficult to see from the sea surface radar simulated echo conditions of sea conditions 1, 5 and 7 that as the sea conditions increase, the sea surface becomes rougher and the radar echo signal exhibits a stronger texture component, which is consistent with the observation results in the real world. Therefore, it can be well used for radar signal echo simulation.

[0118] Combined with the above description, it can be seen that the embodiment of the present application is improved to a choppy sea surface modeling method based on the modified Lie transform, which can simulate a choppy sea surface under high sea conditions and a sea surface that is more robust to changes in wind speed and wind direction, and has low computational complexity. It can simulate choppy seas in a large area of ​​sea. Through sea surface energy verification and slope verification experiments, the sea surface slope of the choppy sea surface model is consistent with the Cox-Munk model under high sea conditions, which is better than the traditional sharp wave sea surface and can provide realistic statistical data for subsequent electromagnetic simulation sea clutter.

[0119] The following describes the cluttered sea surface modeling device based on the modified Lie transform provided in the present application. The cluttered sea surface modeling device based on the modified Lie transform described below and the cluttered sea surface modeling method based on the modified Lie transform described above can be referenced to each other.

[0120] Figure 10 This is a structural diagram of a wave sea surface modeling device based on modified Lie transform provided in an embodiment of the present application. For example, see Figure 10 As shown, the wave sea surface modeling device 100 based on the modified Lie transform may include:

[0121] An acquisition unit 1001 is used to acquire ocean spectrum information of a target sea surface to be modeled;

[0122] A construction unit 1002 is configured to construct a linear sea surface height model in the frequency domain corresponding to the target sea surface based on the sea spectrum information;

[0123] A transformation unit 1003 is configured to transform the linear sea level height model in the frequency domain dimension to obtain a linear sea level height model in the time domain dimension;

[0124] a correction unit 1004 configured to correct the Lie transform based on the wind condition of the target sea surface under the linear sea surface height model in the time domain dimension to obtain a corrected Lie transform;

[0125] The processing unit 1005 is configured to superimpose the linear sea surface height model in the frequency domain dimension based on the modified Lie transform to construct a choppy sea surface model of the target sea surface.

[0126] For example, in an embodiment of the present application, the wind condition includes wind speed and wind direction. The correction unit 1004 is configured to correct the Lie transform based on the wind condition of the target sea surface under the linear sea level model in the time domain dimension to obtain a corrected Lie transform, including:

[0127] Under the linear sea surface height model in the time domain dimension, performing Hilbert transform on the Lie transform to obtain a transformation result;

[0128] A second-order approximate derivative is performed on the transformation result, and the wind speed and the wind direction are superimposed during the second-order approximate derivative process to obtain a second-order approximate derivative result, and the second-order approximate derivative result is used to characterize the modified Lie transform.

[0129] For example, in the embodiment of the present application, the correction unit 1004 is configured to perform a Hilbert transform on the Lie transform under the linear sea level height model in the time domain dimension to obtain a transformation result, including:

[0130] Under the linear sea surface height model in the time domain dimension, based on Perform Hilbert transform on Lie transform;

[0131] in, represents the transformation result, k represents the wave number, t represents the time, N represents the number of sampling points, exp() represents the Fourier transform, represents an imaginary number, Represents the linear sea surface height model in the time domain dimension, Represents the time domain space of the target sea surface.

[0132] For example, in an embodiment of the present application, the correction unit 1004 is configured to perform a second-order approximate derivative on the transformation result, and superimpose the wind speed and the wind direction during the second-order approximate derivative to obtain a second-order approximate derivative result, including:

[0133] based on performing a second-order approximate derivation on the transformation result, and superimposing the wind speed and the wind direction during the second-order approximate derivation;

[0134] in, represents the second-order approximate derivative result, k represents the wave number, t represents the time, Indicates 10m high wind speed, represents the x-dimensional wave number of the target sea surface, represents the y-dimensional wave number of the target sea surface, represents the wind direction in x dimension, represents the wind direction in the y dimension, and Represents a function term.

[0135] For example, in an embodiment of the present application, the processing unit 1005 is configured to superimpose the linear sea surface height model in the frequency domain dimension based on the modified Lie transform to construct a choppy sea surface model of the target sea surface, including:

[0136] Based on the modified Lie transform, the linear sea surface height model in the frequency domain dimension is superimposed to obtain a modified nonlinear sea surface height model in the frequency domain dimension;

[0137] The corrected nonlinear sea surface height model in the frequency domain dimension is converted into a space domain to obtain a nonlinear sea surface height model in the time domain dimension, and the nonlinear sea surface height model in the time domain dimension is the choppy sea surface model.

[0138] For example, in an embodiment of the present application, the processing unit 1005 is configured to superimpose the linear sea level height model in the frequency domain dimension based on the modified Lie transform to obtain a modified nonlinear sea level height model in the frequency domain dimension, including:

[0139] based on Superimposing the linear sea surface height model in the frequency domain dimension to obtain a corrected nonlinear sea surface height model in the frequency domain dimension;

[0140] in, represents the nonlinear sea surface height model in the modified frequency domain, k represents the wave number, t represents the time, represents the linear sea surface height model in the frequency domain dimension, represents a second-order approximate derivative result, and the second-order approximate derivative result is used to characterize the modified Lie transform.

[0141] For example, in an embodiment of the present application, the processing unit 1005 is configured to perform spatial domain conversion on the corrected nonlinear sea level height model in the frequency domain dimension to obtain a nonlinear sea level height model in the time domain dimension, including:

[0142] based on Performing spatial domain conversion on the corrected nonlinear sea surface height model in the frequency domain dimension;

[0143] in, Represents the nonlinear sea surface height model in the time domain dimension k represents the wave number, t represents the time, Represents the nonlinear sea surface height model in the corrected frequency domain dimension, exp() represents the inverse Fourier transform, which is used for spatial domain conversion. Represents an imaginary number.

[0144] The cluttered sea surface modeling device 100 based on the modified Lie transform provided in an embodiment of the present application can execute the technical solution of the cluttered sea surface modeling method based on the modified Lie transform in any of the above-mentioned embodiments. Its implementation principle and beneficial effects are similar to the implementation principle and beneficial effects of the cluttered sea surface modeling method based on the modified Lie transform. Please refer to the implementation principle and beneficial effects of the cluttered sea surface modeling method based on the modified Lie transform, and no further details will be given here.

[0145] Figure 11 A schematic diagram of the physical structure of an electronic device provided in an embodiment of the present application is shown in FIG. Figure 11 As shown, the electronic device may include: a processor 1110, a communication interface 1120, a memory 1130, and a communication bus 1140, wherein the processor 1110, the communication interface 1120, and the memory 1130 communicate with each other via the communication bus 1140. The processor 1110 may call logic instructions in the memory 1130 to execute a method for modeling a choppy sea surface based on a modified Lie transform, the method comprising: obtaining ocean spectrum information of a target sea surface to be modeled; constructing a linear sea surface height model in a frequency domain corresponding to the target sea surface based on the ocean spectrum information; transforming the linear sea surface height model in the frequency domain to obtain a linear sea surface height model in the time domain; modifying the Lie transform based on the wind conditions of the target sea surface in the time domain linear sea surface height model to obtain a modified Lie transform; and superimposing the linear sea surface height models in the frequency domain based on the modified Lie transform to construct a choppy sea surface model of the target sea surface.

[0146] In addition, the logical instructions in the above-mentioned memory 1130 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present application, or the part that contributes to the existing technology, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, and other media that can store program code.

[0147] On the other hand, the present application also provides a computer program product, which includes a computer program, which can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the choppy sea surface modeling method based on the modified Lie transform provided by the above methods, the method including: obtaining sea spectrum information of the target sea surface to be modeled; constructing a linear sea surface height model in the frequency domain dimension corresponding to the target sea surface based on the sea spectrum information; transforming the linear sea surface height model in the frequency domain dimension to obtain a linear sea surface height model in the time domain dimension; under the linear sea surface height model in the time domain dimension, correcting the Lie transform based on the wind conditions of the target sea surface to obtain a modified Lie transform; based on the modified Lie transform, superimposing the linear sea surface height model in the frequency domain dimension to construct a choppy sea surface model of the target sea surface.

[0148] On the other hand, the present application also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to execute the choppy sea surface modeling method based on the modified Lie transform provided by the above-mentioned methods, the method comprising: obtaining sea spectrum information of the target sea surface to be modeled; constructing a linear sea surface height model in the frequency domain dimension corresponding to the target sea surface based on the sea spectrum information; transforming the linear sea surface height model in the frequency domain dimension to obtain a linear sea surface height model in the time domain dimension; under the linear sea surface height model in the time domain dimension, correcting the Lie transform based on the wind conditions of the target sea surface to obtain a corrected Lie transform; and superimposing the linear sea surface height model in the frequency domain dimension based on the corrected Lie transform to construct a choppy sea surface model of the target sea surface.

[0149] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0150] Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented using software plus a necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the essence of the above technical solution, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, or an optical disk, and includes a number of instructions for causing a computer device (such as a personal computer, server, or network device) to execute the methods described in each embodiment or certain portions of the embodiments.

[0151] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application 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 make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for modeling choppy sea surface based on modified Lie transform, characterized in that: include: Obtaining ocean spectrum information of the target sea surface to be modeled; Based on the sea spectrum information, constructing a linear sea surface height model in the frequency domain corresponding to the target sea surface; Transforming the linear sea level height model in the frequency domain dimension to obtain a linear sea level height model in the time domain dimension; Under the linear sea surface height model in the time domain dimension, performing Hilbert transform on the Lie transform to obtain a transformation result; based on performing a second-order approximate derivation on the transformation result, and superimposing the wind speed of the target sea surface and the wind direction of the target sea surface during the second-order approximate derivation process to obtain a second-order approximate derivation result; in, represents the second-order approximate derivative result, k represents the wave number, t Indicates time, Indicates 10m high wind speed, represents the x-dimensional wave number of the target sea surface, represents the y-dimensional wave number of the target sea surface, represents the wind direction in x dimension, represents the wind direction in the y dimension, and represents a function term; the second-order approximate derivative result is used to characterize the modified Lie transform; Based on the modified Lie transform, the linear sea surface height model in the frequency domain dimension is superimposed to construct a choppy sea surface model of the target sea surface.

2. The method for modeling choppy sea surface based on modified Lie transform according to claim 1, characterized in that: The Hilbert transform is performed on the Lie transform under the linear sea level height model in the time domain dimension to obtain a transformation result, including: Under the linear sea surface height model in the time domain dimension, based on Perform Hilbert transform on Lie transform; in, represents the transformation result, k represents the wave number, t represents the time, N represents the number of sampling points, exp() represents the Fourier transform, represents an imaginary number, Represents the linear sea surface height model in the time domain dimension, Represents the time domain space of the target sea surface.

3. The method for modeling choppy sea surface based on modified Lie transform according to any one of claims 1 or 2, characterized in that: The method of superimposing the linear sea surface height model in the frequency domain dimension based on the modified Lie transform to construct a wave sea surface model of the target sea surface includes: Based on the modified Lie transform, the linear sea surface height model in the frequency domain dimension is superimposed to obtain a modified nonlinear sea surface height model in the frequency domain dimension; The corrected nonlinear sea surface height model in the frequency domain dimension is converted into a space domain to obtain a nonlinear sea surface height model in the time domain dimension, and the nonlinear sea surface height model in the time domain dimension is the choppy sea surface model.

4. The method for modeling choppy sea surface based on modified Lie transform according to claim 3, characterized in that: The method of superimposing the linear sea level height model in the frequency domain dimension based on the modified Lie transform to obtain a modified nonlinear sea level height model in the frequency domain dimension includes: based on Superimposing the linear sea surface height model in the frequency domain dimension to obtain a corrected nonlinear sea surface height model in the frequency domain dimension; in, represents the nonlinear sea surface height model in the modified frequency domain, k represents the wave number, t represents the time, represents the linear sea surface height model in the frequency domain dimension, represents a second-order approximate derivative result, and the second-order approximate derivative result is used to characterize the modified Lie transform.

5. The method for modeling choppy sea surface based on modified Lie transform according to claim 3, characterized in that: The step of performing spatial domain conversion on the corrected nonlinear sea surface height model in the frequency domain dimension to obtain the nonlinear sea surface height model in the time domain dimension includes: based on Performing spatial domain conversion on the corrected nonlinear sea surface height model in the frequency domain dimension; in, Represents the nonlinear sea surface height model in the time domain dimension k represents the wave number, t represents the time, Represents the nonlinear sea surface height model in the corrected frequency domain dimension, exp() represents the inverse Fourier transform, which is used for spatial domain conversion. Represents an imaginary number.

6. A wave sea surface modeling device based on modified Lie transform, characterized in that: include: An acquisition unit, used for acquiring ocean spectrum information of a target sea surface to be modeled; A construction unit, configured to construct a linear sea surface height model in a frequency domain dimension corresponding to the target sea surface based on the sea spectrum information; a transform unit, configured to transform the linear sea level height model in the frequency domain dimension to obtain a linear sea level height model in the time domain dimension; A correction unit is used to perform Hilbert transform on Lie transform under the linear sea level height model of the time domain dimension to obtain a transformation result; based on Performing a second-order approximate derivation on the transformation result, superimposing the wind speed and the wind direction of the target sea surface during the second-order approximate derivation process to obtain a second-order approximate derivation result; wherein, represents the second-order approximate derivative result, k represents the wave number, t Indicates time, Indicates 10m high wind speed, represents the x-dimensional wave number of the target sea surface, represents the y-dimensional wave number of the target sea surface, represents the wind direction in x dimension, represents the wind direction in the y dimension, and represents a function term; the second-order approximate derivative result is used to characterize the modified Lie transform; A processing unit is used to superimpose the linear sea surface height model in the frequency domain dimension based on the modified Lie transform to construct a choppy sea surface model of the target sea surface.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the method for modeling choppy sea surface based on modified Lie transform according to any one of claims 1 to 5 is implemented.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for modeling choppy sea surface based on modified Lie transform according to any one of claims 1 to 5 is implemented.

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