Curling wave sea surface modeling method, device and equipment based on modified Lie transformation

Abstract

The invention provides a curly wave sea surface modeling method, device and equipment based on modified Lie transformation, and relates to the technical field of computer modeling. The method comprises the steps that when a curly wave sea surface model is constructed, sea spectrum information of a to-be-modeled target sea surface can be firstly acquired; based on the sea spectrum information, constructing a linear sea surface height model of a frequency domain dimension corresponding to the target sea surface; transforming the linear sea surface height model of the frequency domain dimension to obtain a linear sea surface height model of the time domain dimension; under a linear sea surface height model of a time domain dimension, correcting Lie transformation based on a wind condition of a target sea surface; and then based on the corrected Lie transformation, carrying out superposition on the linear sea surface height model of the frequency domain dimension so as to construct a curled wave sea surface model of the target sea surface. In this way, the Lie transformation is corrected in combination with the wind condition of the sea surface, so that the corrected Lie transformation can better simulate the curl wave under the high sea condition, and the modeling effect of the constructed curl wave sea surface model is effectively improved.

Description

Technical Field

[0001] The present application relates to the technical field of computer modeling, and in particular to a method, device and equipment for modeling choppy sea surface based on modified Lie transform. Background Art

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

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

[0004] However, the above-mentioned Lie transformation cannot simulate the curled waves under high sea conditions, resulting in poor modeling effect of the constructed curled sea surface model. Summary of the invention

[0005] The present application provides a method, device and equipment for modeling a cluttered sea surface based on a modified Lie transform, so as to solve the defect in the prior art that the Lie transform cannot simulate clutter under high sea conditions, resulting in poor modeling effect of the constructed cluttered sea surface model, thereby improving the modeling effect of the constructed cluttered sea surface model.

[0006] The present application provides a method for modeling a choppy sea surface based on a modified Lie transform, comprising: Obtaining sea spectrum information of the target sea surface to be modeled; Based on the sea spectrum information, construct a linear sea surface height model in the frequency domain dimension corresponding to the target sea surface; 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, the Lie transform is corrected based on the wind condition of the target sea surface to obtain a corrected 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.

[0007] 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, and the Lie transform is corrected 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, including: Under the linear sea surface height model in the time domain dimension, performing Hilbert transform on the Lie transform to obtain a transform result; 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.

[0008] According to a choppy sea surface modeling method based on modified Lie transform provided by the present application, the Lie transform is subjected to Hilbert transform under the linear sea surface 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.

[0009] According to a choppy sea surface modeling method based on 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 in the second-order approximate derivative process, and obtaining a second-order approximate derivative result includes: 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; 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 the x dimension, represents the wind direction in the y dimension, and Represents a function term.

[0010] 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, including: 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 modified 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.

[0011] 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 obtain a modified nonlinear sea surface height model in the frequency domain dimension, including: 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 corrected nonlinear sea surface height model in the 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.

[0012] According to a method for modeling a choppy sea surface based on a 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: 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.

[0013] A choppy sea surface modeling device based on modified Lie transform provided by the present application includes: An acquisition unit, used for acquiring sea 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 transformation unit, used for 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; 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; 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.

[0014] 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, wherein when the processor executes the computer program, the method for modeling a choppy sea surface based on a modified Lie transform as described above is implemented.

[0015] 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.

[0016] The present application also provides a computer program product, comprising a computer program, wherein 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.

[0017] The choppy sea surface modeling method, device and equipment based on the modified Lie transform provided by the present application can first obtain the sea spectrum information of the target sea surface to be modeled when constructing the choppy sea surface model; and based on the sea spectrum information, construct a linear sea surface height model of the frequency domain dimension corresponding to the target sea surface; transform the linear sea surface height model of the frequency domain dimension 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, 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 of the frequency domain dimension to construct the choppy sea surface model of the target sea surface. In this way, the Lie transform is modified in combination with the wind conditions of the sea surface, so that the modified Lie transform can better simulate the choppy sea under high sea conditions, thereby effectively improving the modeling effect of the constructed choppy sea surface model. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] 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 paying any creative work.

[0019] 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.

[0020] Figure 2 A schematic diagram of Elfouhaily sea spectrum information at a wind speed of 10 m / s provided in an embodiment of the present application.

[0021] Figure 3 A schematic diagram of a process for correcting Lie transformation based on wind conditions at a target sea surface is provided in an embodiment of the present application.

[0022] Figure 4 A schematic diagram of a process for constructing a choppy sea surface model of a target sea surface provided in an embodiment of the present application.

[0023] Figure 5 A comparative schematic diagram provided for an embodiment of the present application.

[0024] Figure 6 A 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 the present application at different wind speeds provided in an embodiment of the present application.

[0025] Figure 7 A schematic diagram of comparing restored sea spectrum information with original sea spectrum information used to construct a choppy sea surface model provided in an embodiment of the present application.

[0026] Figure 8 A schematic diagram of comparing restored sea spectrum information with original sea spectrum information used to construct a choppy sea surface model provided in an embodiment of the present application.

[0027] Fig. 9 A schematic diagram of sea surface radar simulation echo conditions under sea conditions 1, 5 and 7 provided in an embodiment of the present application.

[0028] Fig.10 A schematic structural diagram of a choppy sea surface modeling device based on a modified Lie transform provided in an embodiment of the present application.

[0029] Fig.11 A schematic diagram of the physical structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0030] In order to make the purpose, technical solutions and advantages of this application clearer, the technical solutions in this application will be clearly and completely described below in conjunction with the drawings in this application. Obviously, the described embodiments are part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0031] In the embodiments of the present application, "at least one" means one or more, and "more" means two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone, where A and B can be singular or plural. In the text description of the present application, the character " / " generally indicates that the associated objects before and after are in an "or" relationship.

[0032] The technical solution provided by the embodiment of the present application can be adapted to some special scenarios, such as high sea condition scenarios. Taking high sea condition scenarios as an example, in the prior art, when modeling the choppy sea surface, a linear sea surface height model is usually first constructed based on the sea spectrum information of the sea surface, and the linear sea surface height model is superimposed based on the Lie transformation developed by Creamer, thereby obtaining a nonlinear choppy sea surface modeling.

[0033] 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.

[0034] However, the above-mentioned Lie transformation cannot simulate the curled waves under high sea conditions, resulting in poor modeling effect of the constructed curled sea surface model.

[0035] In order to solve the defect in the prior art that the Lie transform cannot simulate the clutter under high sea conditions, resulting in poor modeling effect of the constructed clutter sea surface model, thereby improving the modeling effect of the constructed clutter sea surface model, an embodiment of the present application provides a clutter sea surface modeling method based on a modified Lie transform. When modeling the clutter sea surface model, the influence of the wind conditions on the sea surface on the clutter 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 a clutter 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 clutter under high sea conditions, thereby effectively improving the modeling effect of the constructed clutter sea surface model.

[0036] It can be understood that the executor of the present method can be an electronic device such as a cirrus sea surface modeling platform, a computer or a server. Of course, it can also be a cirrus sea surface modeling device based on the modified Lie transform set in the electronic device. The cirrus sea surface modeling device based on the modified Lie transform can be implemented by software, hardware or a combination of the two, and can be specifically set according to actual needs.

[0037] The following specific embodiments will be used to describe in detail the method for modeling the choppy sea surface based on the modified Lie transform provided by the present application. It is understandable that the following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0038] 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 modified Lie transform may include: S101, obtaining sea spectrum information of a target sea surface to be modeled.

[0039] 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., which may be specifically set according to actual needs.

[0040] 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 2 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 figure in the middle is the Elfouhaily variance spectrum, and the right figure is the Elfouhaily curvature spectrum.

[0041] 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 reciprocal 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.

[0042] The horizontal axis of the Elfouhaily curvature spectrum represents the wave number, in rad / m (radians per meter). The wave number is the reciprocal 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, in , which is used to describe the detailed distribution of wave energy as a function of wave number.

[0043] Combination Figure 2From the Elfouhaily two-dimensional ocean spectrum information shown, it can be found that the Elfouhaily two-dimensional ocean spectrum information has a double peak value, and 370rad / m is the second spectrum peak of the curvature spectrum, which is consistent with the double peak value of the real sea area. Therefore, in the embodiment of the present application, the Elfouhaily two-dimensional ocean spectrum information can be used as the ocean spectrum information of the target sea surface.

[0044] 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.

[0045] Formula 1 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 spectrum information, represents the angle 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, represents the length of the target sea surface constructed, Indicates the width of the constructed target sea surface.

[0046] After the sea spectrum information of the target sea surface to be modeled is obtained, the following S102 may be executed.

[0047] S102: constructing a linear sea surface height model in the frequency domain corresponding to the target sea surface based on the sea spectrum information.

[0048] 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 may be referred to.

[0049] Formula 2 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 an imaginary number, represents the angular frequency and * represents the complex conjugate.

[0050] After a linear sea surface height model in the frequency domain dimension corresponding to the target sea surface is constructed based on the sea spectrum information, the following S103 may be executed.

[0051] S103, 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.

[0052] 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.

[0053] Formula 3 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.

[0054] S104. 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.

[0055] For example, in the embodiment of the present application, wind conditions may include wind speed and wind direction, which may be set according to actual needs.

[0056] In the embodiment of the present application, the influence of the wind condition on the cluttered sea surface modeling is fully considered. Therefore, when modeling the cluttered sea surface model, the Lie transformation can be first corrected based on the wind condition on the sea surface to obtain a corrected Lie transformation; then, based on the corrected Lie transformation, the linear sea surface height model is superimposed to construct the cluttered sea surface model of the sea surface, that is, the following S105 is executed. In this way, the Lie transformation is corrected in combination with the wind condition on the sea surface, so that the corrected Lie transformation can better simulate the clutter under high sea conditions, thereby effectively improving the modeling effect of the constructed cluttered sea surface model.

[0057] 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.

[0058] It can be seen that in the embodiment of the present application, when constructing a choppy sea surface model, the sea spectrum information of the target sea surface to be modeled can be obtained first; and based on the sea 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 the choppy waves under high sea conditions, thereby effectively improving the modeling effect of the constructed choppy sea surface model.

[0059] Based on the above Figure 1 In the embodiment shown in the above S104, the specific implementation of correcting 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.

[0060] Figure 3 A schematic diagram of a process for correcting Lie transformation based on the wind conditions of the target sea surface provided in an embodiment of the present application, the method may include: S301. Under a linear sea surface height model in the time domain dimension, perform Hilbert transform on the Lie transform to obtain a transformation result.

[0061] 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: Under the linear sea surface height model in the time domain, 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.

[0062] After the Hilbert transform is performed on the Lie transform and the transform result is obtained, the following S302 can be executed.

[0063] S302, performing a second-order approximate derivation on the transformation result, superimposing the wind speed and wind direction in the second-order approximate derivation process to obtain a second-order approximate derivation result, and the second-order approximate derivation result is used to characterize the modified Lie transform.

[0064] For example, in the embodiment of the present application, performing a second-order approximate derivation on the transformation result, superimposing the wind speed and wind direction in the second-order approximate derivation process, and obtaining a second-order approximate derivation result may include: based on The transformation result is subjected to a second-order approximate derivation, and the wind speed and wind direction are superimposed during the second-order approximate derivation process.

[0065] 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 the x dimension, represents the wind direction in the y dimension, and Represents a function term.

[0066] 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 cirrus 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 cirrus sea of ​​the target sea surface, thereby effectively improving the modeling effect of the constructed cirrus sea surface model.

[0067] 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 specific implementation, please refer to the following Figure 4 The embodiment shown.

[0068] 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, the method may include: 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.

[0069] For example, in an embodiment of the present application, 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, which may include: 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 corrected nonlinear sea surface height model in the 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.

[0070] In this way, based on the modified Lie transform, the linear sea surface height model in the frequency domain dimension is superimposed, which can better simulate the rolling waves under high sea conditions, and then the modified nonlinear sea surface height model in the frequency domain dimension is converted 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 rolling wave effect changes with the changes in the sea condition parameters.

[0071] 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, wherein the nonlinear sea surface height model in the time domain dimension is a choppy sea surface model.

[0072] For example, in an embodiment of the present application, 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 may include: based on The nonlinear sea surface height model in the modified frequency domain dimension is transformed into the spatial domain.

[0073] 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.

[0074] 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 modified nonlinear sea surface height model in the frequency domain dimension is converted into the spatial domain, which can quickly generate breaking waves in a large area of ​​sea area, and the curling wave effect changes with the sea condition parameters. Therefore, the modeling effect of the constructed curling wave sea surface model can be effectively improved.

[0075] 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 on the sea surface. For example, see Figure 5 As shown, Figure 5 A comparative schematic diagram provided for the embodiment of the present application, combined with Figure 5It can be seen that for the choppy sea surface, on the one hand, the differences between the sea surface height models of slices in each dimension 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.

[0076] For example, see the following Figure 6 As shown, Figure 6 A schematic diagram of the 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 under different wind speeds provided in the embodiment of the present application, assuming that the length and width of the simulated sea surface are both 100m, the number of sampling points in both dimensions is 1000, and the wind direction is , Figure 6 The left picture shows that the sea surface is relatively flat at a wind speed of 5m / s, and it is difficult to form breaking waves at this wind speed. Figure 6 In the right figure, under a wind speed of 10m / s, the sea surface fluctuates greatly, wave breaking is obvious, and the direction of wave formation is consistent with the wind direction, which can better simulate the waves under high sea conditions, thereby effectively improving the modeling effect of the constructed wave sea surface model.

[0077] In addition to the above verification, verification can also be performed from the perspectives of energy conservation and mean square slope.

[0078] Among them, the energy conservation verification is mainly to inversely restore the corresponding sea spectrum information through the sea surface of the constructed choppy sea surface model. The inversely restored sea spectrum information can be shown in the following formula 3.

[0079] Formula 3 in, Represents the Fourier transform of sea surface height, and N represents the number of sampling points in each dimension of the sea surface.

[0080] The recovered sea spectrum information is compared and verified with the original sea spectrum information used to construct the choppy sea surface model. For example, see Figure 7 As shown, Figure 7 A schematic diagram of comparing the restored sea spectrum information with the original sea spectrum information used to construct the choppy sea surface model provided in an embodiment of the present application shows that the restored sea spectrum information and the original sea spectrum information used to construct the choppy sea surface model basically conserve energy.

[0081] When verifying from the perspective of the mean square slope of the sea surface, the standard Lie transformation sea surface model and the wave sea surface model constructed in this application can be compared. For example, see Figure 8 As shown, Figure 8A schematic diagram of comparing the restored sea spectrum information with the original sea spectrum information used to construct the crinkled sea surface model provided in the embodiment of the present application shows 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 crinkled sea surface model constructed in the present application satisfies the relationship between the Cox-Munk and wind speed, and can truly restore the slope of the sea surface under high sea conditions.

[0082] After constructing a cluttered sea surface model using the modified Lie transform-based cluttered sea surface model provided by the embodiment 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, 5, and 7 can be seen in Fig. 9 As shown, Fig. 9 A schematic diagram of sea surface radar simulation 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 simulation 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 shows a stronger texture component, which is consistent with the observation results in the real world. Therefore, it can be better used for radar signal echo simulation.

[0083] In combination with the above description, it can be seen that the choppy sea surface modeling method based on the modified Lie transform according to the embodiment of the present application can simulate the choppy sea surface under high sea conditions and the sea surface that is more robust to changes in wind speed and wind direction, and has low computational complexity, and can simulate choppy seas in a large range of sea areas. 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.

[0084] The cluttered sea surface modeling device based on the modified Lie transform provided in the present application is described below. 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.

[0085] Fig.10 A schematic diagram of a structure of a wave sea surface modeling device based on a modified Lie transform provided in an embodiment of the present application, for example, see Fig.10 As shown, the wave sea surface modeling device 100 based on modified Lie transform may include: An acquisition unit 1001 is used to acquire sea spectrum information of a target sea surface to be modeled; A construction unit 1002 is used to construct a linear sea surface height model in the frequency domain dimension corresponding to the target sea surface based on the sea spectrum information; A transformation unit 1003 is used to 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; A correction unit 1004 is used 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; The processing unit 1005 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.

[0086] For example, in an embodiment of the present application, the wind condition includes wind speed and wind direction, and the correction unit 1004 is used 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, including: Under the linear sea surface height model in the time domain dimension, performing Hilbert transform on the Lie transform to obtain a transform result; 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.

[0087] For example, in the embodiment of the present application, the correction unit 1004 is used to perform Hilbert transform on the Lie transform under the linear sea surface 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.

[0088] For example, in the embodiment of the present application, the correction unit 1004 is used to perform a second-order approximate derivation on the transformation result, and superimpose the wind speed and the wind direction in the second-order approximate derivation process to obtain a second-order approximate derivation result, including: 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; 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 the x dimension, represents the wind direction in the y dimension, and Represents a function term.

[0089] For example, in the embodiment of the present application, the processing unit 1005 is used to superimpose the linear sea surface height model in the frequency domain dimension based on the modified Lie transform to construct the choppy sea surface model of the target sea surface, including: 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 modified 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.

[0090] For example, in an embodiment of the present application, the processing unit 1005 is used to superimpose the linear sea surface height model in the frequency domain dimension based on the modified Lie transform to obtain a modified nonlinear sea surface height model in the frequency domain dimension, including: 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 corrected nonlinear sea surface height model in the 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.

[0091] For example, in the embodiment of the present application, the processing unit 1005 is used to perform 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, including: 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.

[0092] The cluttered sea surface modeling device 100 based on the modified Lie transform provided in the 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, and 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, which will not be repeated here.

[0093] Fig.11 A schematic diagram of the physical structure of an electronic device provided in an embodiment of the present application, such as Fig.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 through the communication bus 1140. The processor 1110 may call the logic instructions in the memory 1130 to execute the choppy sea surface modeling method based on the modified Lie transform, the method comprising: obtaining the sea spectrum information of the target sea surface to be modeled; constructing a linear sea surface height model of the frequency domain dimension corresponding to the target sea surface based on the sea spectrum information; transforming the linear sea surface height model of the frequency domain dimension 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, modifying the Lie transform based on the wind condition of the target sea surface to obtain a modified Lie transform; and superimposing the linear sea surface height model of the frequency domain dimension based on the modified Lie transform to construct the choppy sea surface model of the target sea surface.

[0094] In addition, the logic 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 it is sold or used as an independent product. Based on this understanding, the technical solution of the present application can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium, including several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to perform 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, etc. Various media that can store program codes.

[0095] On the other hand, the present application also provides a computer program product, which includes a computer program, and the computer program 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-mentioned methods, and the method includes: obtaining the sea 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 dimension corresponding to the target sea surface; 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.

[0096] 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; based on the sea spectrum information, constructing a linear sea surface height model in the frequency domain dimension corresponding to the target sea surface; 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.

[0097] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0098] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0099] 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 it. 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 sea spectrum information of the target sea surface to be modeled; Based on the sea spectrum information, construct a linear sea surface height model in the frequency domain dimension corresponding to the target sea surface; 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, the Lie transform is corrected based on the wind condition of the target sea surface to obtain a corrected 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 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: Under the linear sea surface height model in the time domain dimension, performing Hilbert transform on the Lie transform to obtain a transform result; 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.

3. The method for modeling choppy sea surface based on modified Lie transform according to claim 2, characterized in that: The Hilbert transform is performed on the Lie transform under the linear sea surface 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.

4. The method for modeling choppy sea surface based on modified Lie transform according to claim 2, characterized in that: The 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 to obtain a second-order approximate derivation result, includes: 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; 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 the x dimension, represents the wind direction in the y dimension, and Represents a function term.

5. The method for modeling choppy sea surface based on modified Lie transform according to any one of claims 1 to 4, 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 choppy 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 modified 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.

6. The method for modeling choppy sea surface based on modified Lie transform according to claim 5, 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 obtain a modified nonlinear sea surface 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 corrected nonlinear sea surface height model in the 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.

7. The method for modeling choppy sea surface based on modified Lie transform according to claim 5, 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.

8. A choppy sea surface modeling device based on modified Lie transform, characterized in that: include: An acquisition unit, used for acquiring sea 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 transformation unit, used for 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; 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; 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.

9. 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 choppy sea surface modeling method based on modified Lie transform as described in any one of claims 1 to 7 is implemented.

10. 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 as claimed in any one of claims 1 to 7 is implemented.

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