A method and device for nonlinear wave field reconstruction and prediction based on lidar

Abstract

This invention provides a method and apparatus for nonlinear wave field reconstruction and prediction based on lidar. The method involves scanning the wave field with lidar to obtain the coordinates of sampling points, setting a cost function, and solving the cost function with the sampling point coordinates to obtain the wave surface expression. This improves the efficiency of wave surface reconstruction while ensuring reconstruction accuracy. Based on the wave surface expression, a predictable region is obtained. An objective equation is set to iteratively solve the wave surface expression to obtain the corresponding discrete values ​​of velocity potential, avoiding the Jacobian matrix generated during Newton iteration, thus improving the efficiency of velocity potential solution. Finally, based on the wave surface expression and the corresponding discrete values ​​of velocity potential, the wave surface condition at subsequent time points is predicted, and the prediction results within the predictable region are taken as the valid prediction results.

Description

Technical Field

[0001] This invention relates to the field of wave field deterministic technology, and in particular to a method and apparatus for nonlinear wave field reconstruction and prediction based on lidar. Background Technology

[0002] Wave field prediction research comprises two indispensable parts: wave information acquisition and wave prediction methods. For shipborne applications, deterministic wave field methods utilize data acquisition techniques such as lidar and X-band radar. Wave field prediction employs linear and nonlinear wave models. In existing technologies, wave surface reconstruction often requires extensive data collection and calculation of feature points, resulting in low reconstruction efficiency. Furthermore, when predicting wave surfaces at subsequent time points, it is necessary to pre-solve the velocity potential at earlier time points. Conventional velocity potential solutions involve iteratively solving large nonlinear equation systems, typically using Newton's iteration method to solve the Jacobian matrix. However, solving the Jacobian matrix is ​​prone to non-invertibility issues, making the velocity potential solution impossible and further complicating wave surface prediction efficiency.

[0003] Therefore, overcoming the shortcomings of the existing technology is an urgent problem to be solved in this technical field. Summary of the Invention

[0004] The technical problem to be solved by this invention is how to overcome the low efficiency of wavefront reconstruction and the problem that the Newton iteration method cannot avoid solving the Jacobian matrix when solving the velocity potential.

[0005] The present invention adopts the following technical solution:

[0006] Firstly, a nonlinear wave field reconstruction and prediction method based on lidar includes:

[0007] The wave field is scanned by lidar to obtain the coordinates of the sampling points of the wave field;

[0008] Set a cost function, and solve the cost function based on the coordinates of the sampling points to obtain the reconstructed wavefront expression;

[0009] The objective equation is solved iteratively based on the wavefront expression to obtain discrete values ​​of the velocity potential in the wavefront expression.

[0010] Set a prediction time point and obtain the predictable region at the prediction time point based on the wavefront expression;

[0011] Based on the wave surface expression and the discrete value of the velocity potential of the wave surface expression, the wave height and velocity potential at the prediction time point are predicted, and the prediction results within the predictable region are taken as valid prediction results.

[0012] Preferably, the step of obtaining the sampling point coordinates of the wave field by scanning the wave field with a lidar specifically includes:

[0013] Obtain the distance r of the sampling point of the lidar reaching the wave field, and the horizontal angle of the lidar's emitted rays. and vertical angle Based on distance r and horizontal angle and vertical angle The polar coordinates of the sampling points of the wave field are obtained, and the polar coordinates of the sampling points of the wave field are converted into the sampling point coordinates in a preset coordinate system.

[0014] Wherein, the x and y coordinates of the sampling point in the preset coordinate system represent the wavefront position, and the z coordinate of the sampling point in the preset coordinate system represents the wave height of the sampling point.

[0015] Preferably, the step of setting the cost function, which involves solving the cost function based on the sampling point coordinates to obtain the reconstructed wavefront expression, specifically includes:

[0016] A cost function is defined by the sampling point coordinates and a preset wavefront expression. The cost function is the sum of squares of the errors between the sampling point wave height and the preset wavefront expression.

[0017] By taking the partial derivative of the coefficients in the preset wavefront expression with the cost function, a set of nonlinear equations is obtained, and the wavefront expression is obtained by solving the set of nonlinear equations.

[0018] Preferably, the cost function is as follows:

[0019] ;

[0020] in, Let η be the cost function, k be the number of samplings, j be the number of sampling points per sampling, and η be the cost function. jk For the preset wavefront expression, At spatial location r j (j=1, 2, ..., J) and time t k Wave height at sampling points (k=1, 2, ..., K).

[0021] Preferably, the step of iteratively solving the objective equation based on the wavefront expression to obtain discrete values ​​of the velocity potential of the wavefront expression specifically includes:

[0022] The wavefront expression and velocity potential are nonlinearly linked by an objective equation. By iteratively solving the objective equation, the discrete velocity potential values ​​at the reconstructed time points corresponding to the wavefront expression are obtained. The objective equation is:

[0023] ;

[0024] in, For the wavefront expression, This is the partial derivative of the wavefront expression with respect to time. for t is time. Let W be the velocity potential. Partial derivative with respect to the wave height at the sampling point.

[0025] Preferably, the iterative solution of the objective equation specifically includes:

[0026] Setting residuals The formula is used to solve the Krylov subspace, and the approximate value after iteration is obtained based on the Krylov subspace. The approximate value after iteration Substitute the residual The formula, when the residual When the value is less than the preset value, the approximate value after iteration The exact solution is the discrete velocity potential value at the reconstructed time point corresponding to the wavefront expression; where the residual... The formula is:

[0027] ;

[0028] Where x is the initial value, To obtain the approximate value after k iterations based on the Krylov subspace, To approximate the value The value of the objective equation, To approximate the value Jacobi matrix, This is a correction value.

[0029] Preferably, the maximum group velocity and reconstruction time interval corresponding to the wavefront expression are obtained, and the maximum group velocity and time interval are substituted into the region boundary formula to obtain the region boundary corresponding to the wavefront expression. The region boundary formula is as follows:

[0030] ;

[0031] in, The minimum boundary of the region. The maximum boundary of the region. This refers to the sampling point range of the lidar. For the maximum group velocity, This is the interval length of the reconstruction time interval corresponding to the wavefront expression.

[0032] Preferably, the step of setting the prediction time point and obtaining the predictable region at the prediction time point based on the wavefront expression specifically includes:

[0033] Obtain the minimum group velocity corresponding to the wavefront expression, and based on the minimum group velocity, the maximum group velocity, and the region boundary corresponding to the wavefront expression, obtain the predictable region relationship at the prediction time point.

[0034] The predictable region relationship is as follows:

[0035] ;

[0036] in, Let x be the minimum group velocity, x be the location point to be predicted, and t be the prediction time point. This represents the reconstruction time corresponding to the wavefront expression.

[0037] Preferably, the step of predicting the wave height and velocity potential at the prediction time point based on the wave surface expression and the discrete value of the velocity potential of the wave surface expression, and taking the prediction result within the predictable region as the valid prediction result, specifically includes:

[0038] The discrete values ​​of the velocity potential in the wavefront expression are obtained by solving the objective equation. The discrete values ​​of the velocity potential, the discrete values ​​of the wave height, and the prediction time point are then substituted into the pseudospectral Fourier Legendre model to predict the discrete values ​​of the velocity potential and the wave height at the prediction time point. The prediction results within the predictable region are then obtained as valid prediction results based on the predictable region relation.

[0039] In a second aspect, a lidar-based nonlinear wave field reconstruction and prediction device includes at least one processor and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the processor to perform the lidar-based nonlinear wave field reconstruction and prediction method.

[0040] This invention provides a method and apparatus for nonlinear wave field reconstruction and prediction based on lidar. The method involves scanning the wave field with lidar to obtain the coordinates of sampling points, setting a cost function, and solving the cost function with the sampling point coordinates to obtain the wave surface expression. This improves the efficiency of wave surface reconstruction while ensuring reconstruction accuracy. Based on the wave surface expression, a predictable region is obtained. An objective equation is set to iteratively solve the wave surface expression to obtain the corresponding discrete values ​​of the velocity potential, avoiding the Jacobian matrix generated during the Newton-Raphson iteration method, thus improving the efficiency of velocity potential solution. Finally, based on the wave surface expression and the corresponding discrete values ​​of the velocity potential, the wave surface condition at subsequent time points is predicted, and the prediction results within the predictable region are taken as the valid prediction results. Attached Figure Description

[0041] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments of the present invention will be briefly described below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0042] Figure 1 This is a flowchart of a nonlinear wave field reconstruction and prediction method based on lidar provided in an embodiment of the present invention;

[0043] Figure 2 This is a schematic diagram of lidar sampling for a nonlinear wave field reconstruction and prediction method based on lidar provided in an embodiment of the present invention;

[0044] Figure 3 This is a schematic diagram of sampling points for a nonlinear wave field reconstruction and prediction method based on lidar provided in an embodiment of the present invention;

[0045] Figure 4 This is a time-varying diagram of the predictable region of a nonlinear wave field reconstruction and prediction method based on lidar provided in an embodiment of the present invention.

[0046] Figure 5 This is a flowchart of the method for iteratively solving the target equation in a nonlinear wave field reconstruction and prediction method based on lidar provided in an embodiment of the present invention;

[0047] Figure 6 This is a schematic diagram of a nonlinear wave field reconstruction and prediction device based on lidar provided in an embodiment of the present invention. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0049] In the description of this invention, the terms "inner", "outer", "longitudinal", "lateral", "upper", "lower", "top", "bottom", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and do not require that this invention must be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0050] Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0051] Example 1:

[0052] Embodiment 1 of this invention provides a method for reconstructing and predicting nonlinear wave fields based on lidar, such as... Figure 1 As shown, the method flow includes:

[0053] In step 101, the wave field is scanned by lidar to obtain the coordinates of the sampling points of the wave field.

[0054] The lidar is a scanning and detection device that emits laser light. In this embodiment, in addition to lidar, X-band radar can also be used for scanning. The wave field is the area that needs to be reconstructed and predicted. The application scenario of this embodiment is to scan the wave surface of the wave field using lidar to obtain the coordinates of various positions on the wave surface, which are the sampling point coordinates. Figure 2 As shown in the figure, the dashed line represents the laser beam. In this embodiment, the scanning area is the region between the uppermost and lowermost laser beams of the lidar. From a vertical view directly above the ocean field, all the laser beams are on the same straight line. Figure 3 As shown, the scanning area of ​​the lidar is a fan-shaped ring. The uppermost boundary of the fan-shaped ring is obtained by scanning with the uppermost laser beam of the lidar, and the lowermost boundary of the fan-shaped ring is obtained by scanning with the lowermost laser beam of the lidar. The area between the uppermost and lowermost boundaries of the fan-shaped ring is the scanning area. The sampling points of the wave field are obtained by scanning the wave field with the lidar and converting it into coordinate points, thereby obtaining the coordinates of each position in the wave field scanning area. The wave height at each position is determined based on the z-axis height. It should be noted that the wave height is the horizontal height of the wave surface.

[0055] In step 102, a cost function is set, and the cost function is solved based on the coordinates of the sampling points to obtain the reconstructed wavefront expression.

[0056] Based on the coordinates of the sampling points obtained from scanning the scanning area, the area is reconstructed. The wavefront expression can represent the wavefront situation of the scanning area. It should be noted that since the reconstruction of the wavefront is actually the acquisition of the wave height at a specified location, and since there is a corresponding time for scanning the area, and the wavefront changes every moment, the wavefront expression can only represent the wavefront situation within the scanning time interval. In the following text, this time interval is the reconstruction time. Therefore, the wavefront expression in this embodiment is suitable for calculating the wave height within the reconstruction time interval. That is, by inputting the location coordinates and time point into the wavefront expression, and the time point being within the reconstruction time interval, the wave height at the location coordinates of the input time point can be obtained.

[0057] It is worth mentioning that this embodiment uses the least squares method to reconstruct the wave field and obtain the wave surface expression. By setting a cost function, which is the sum of the squares of the errors between the actual wave height and the wave height obtained from the preset wave surface expression, when the cost function is minimized, it means that the preset wave surface expression can obtain the wave height relatively accurately. At this time, the preset wave surface expression is the required wave surface expression. The above method is simple to calculate. Under the premise of maintaining the wave surface reconstruction accuracy, it adopts the least squares method, which is relatively simple in principle, and the GMRES (Generalized Minimum Residual Method) iterative algorithm, which maintains the reconstruction accuracy and improves the reconstruction efficiency.

[0058] In step 103, the objective equation is solved iteratively based on the wave surface expression to obtain discrete values ​​of the velocity potential of the wave surface expression.

[0059] The discrete values ​​of the velocity potential are used as input for wavefront prediction at subsequent time points. These discrete values ​​represent all velocity potentials at the reconstructed time points corresponding to the wavefront expression. The reconstructed time point is a specific moment within the reconstruction time interval. A target equation is used to link the wave height, the partial derivative of the wave height with respect to time, and the velocity potential. The objective function is iteratively solved to obtain the discrete values ​​of the velocity potential at the preset time points, where the wave height is represented by the wavefront expression. In the conventional process of solving the velocity potential using the Newton-Raphson iteration method, it is necessary to iteratively solve a large set of nonlinear equations. This usually requires solving the Jacobian matrix, which is prone to irreversibility, making it impossible to solve the velocity potential. The above method avoids the generation of the Jacobian matrix in the process of solving the velocity potential, thus enabling faster solution of the velocity potential based on the wavefront expression.

[0060] In step 104, a prediction time point is set, and the predictable region at the prediction time point is obtained according to the wavefront expression.

[0061] The predicted time point is a subsequent time point of the reconstructed time interval, which is set by those skilled in the art. The purpose of finding the predictable region in this step is that, since the wave surface changes every moment, the relatively accurate prediction region will change with time. When the wave surface of the subsequent time is predicted according to the wave surface expression of the previous time, the wave height of all sampling points at the predicted time point will be obtained. However, some sampling points may exist outside the predictable region. Therefore, the prediction results of these sampling points are not accurate enough and need to be excluded. Thus, it is necessary to obtain the predictable region.

[0062] In step 105, the wave height and velocity potential at the prediction time point are predicted based on the wave surface expression and the discrete value of the velocity potential of the wave surface expression, and the prediction result within the predictable region is taken as the valid prediction result.

[0063] In this embodiment, during prediction, the wave height and velocity potential at the reconstruction time point need to be obtained through the wave surface expression. By inputting the discrete values ​​of the wave height and velocity potential at the reconstruction time point into the pseudospectral Fourier Legendre wave model, the wave surface at the prediction time point can be accurately predicted nonlinearly. Similarly, the predicted wave height and velocity potential are used to predict the wave surface at the next time point, gradually completing the nonlinear wave surface prediction at multiple locations. Compared with existing high-order spectral methods, the pseudospectral Fourier Legendre wave model can be applied to steep wave surfaces and has a wider range of applicable scenarios.

[0064] In existing technologies, wavefront reconstruction often requires large-scale acquisition and calculation of feature points, resulting in low reconstruction efficiency. Furthermore, when predicting wavefronts at subsequent time points, it is necessary to pre-solve the velocity potential of the wavefront at earlier time points. However, the conventional process of solving the velocity potential requires iteratively solving a large set of nonlinear equations, which usually requires solving the Jacobian matrix. Solving the Jacobian matrix is ​​prone to irreversibility, making it impossible to solve the velocity potential and thus reducing the efficiency of wavefront prediction.

[0065] In this embodiment, the wave field is scanned by a lidar to obtain the coordinates of the sampling points. A cost function is set, and the coordinates of the sampling points are substituted into the cost function to obtain the wave surface expression. This improves the efficiency of wave surface reconstruction while ensuring reconstruction accuracy. Then, the predictable region is obtained based on the wave surface expression. By setting an objective equation, the discrete values ​​of the corresponding velocity potential are obtained by iteratively solving the wave surface expression. This avoids the Jacobian matrix generated in the conventional method of solving the velocity potential using Newton's iteration method, thereby improving the efficiency of velocity potential solution. Finally, the wave surface situation at subsequent time points is predicted based on the wave surface expression and the corresponding discrete values ​​of velocity potential. The prediction results within the predictable region are taken as the valid prediction results.

[0066] When scanning a wave field using a lidar system, the scanning results need to be converted to a right-handed Cartesian coordinate system for subsequent calculations. Therefore, this embodiment involves the following design:

[0067] The step of scanning the wave field with a lidar to obtain the coordinates of the sampling points of the wave field specifically includes:

[0068] Obtain the distance r of the sampling point of the lidar reaching the wave field, and the horizontal angle of the lidar's emitted rays. and vertical angle Based on distance r and horizontal angle and vertical angle The polar coordinates of the sampling points of the wave field are obtained, and the polar coordinates of the sampling points of the wave field are converted into the sampling point coordinates in a preset coordinate system; wherein, the x and y coordinates of the sampling point coordinates in the preset coordinate system are the wave surface position, and the z coordinate of the sampling point coordinates in the preset coordinate system is the wave height of the sampling point.

[0069] In this embodiment, the scanning process is as follows: within a time interval, the wavefront is scanned multiple times according to the frequency, and each scan is performed on the wavefront condition of all sampling points within a specified area.

[0070] The preset coordinates are right-handed Cartesian coordinates. The distance between the laser radar and the sampling point in the wave field is the distance between the laser emission point and the sampling point. Since the laser radars are all set at a horizontal position higher than the wave field, when the laser radar emits laser light onto the wave surface, the light emission path must be at a certain angle to both the horizontal and vertical planes. Based on the distance *r* between the laser radar and the sampling point in the wave field, and the horizontal angle... and vertical angle This yields the corresponding polar coordinates. Since subsequent calculations require coordinates in the right-hand Cartesian coordinate system, it is necessary to convert the corresponding angle and distance information in the polar coordinates to x, y, and z coordinates in the right-hand Cartesian coordinate system. The conversion formula is shown below:

[0071] .

[0072] Based on the coordinates of the sampling points obtained from the lidar scan, the wavefront expression is solved. Existing technologies often involve relatively complex and cumbersome solutions. This embodiment uses the least squares method, setting a cost function to solve the wavefront expression, as follows:

[0073] The setting of the cost function, which involves solving the cost function based on the coordinates of the sampling points to obtain the reconstructed wavefront expression, specifically includes:

[0074] A cost function is defined using the sampling point coordinates and a preset wavefront expression. The cost function is the sum of squares of the errors between the wave height of the sampling point and the preset wavefront expression. The cost function is minimized to obtain the reconstructed wavefront expression. The partial derivatives of the cost function with respect to the coefficients in the preset wavefront expression are used to obtain a system of nonlinear equations. Solving the system of nonlinear equations yields the wavefront expression.

[0075] The cost function is as follows:

[0076] ;

[0077] in, Let η be the cost function, k be the number of samplings, j be the number of sampling points per sampling, and η be the cost function. jk For the preset wavefront expression, At spatial location r j (j=1, 2, ..., J) and time t k Wave height at sampling points (k=1, 2, ..., K).

[0078] It should be noted that the wavefront expression obtained in this embodiment is used to calculate the wave height based on the position coordinates of the sampling points. Substituting the position coordinates of the sampling points into the wavefront expression yields the wave height. The preset wavefront expression is a wavefront expression with unknown parameters. Therefore, substituting the preset wavefront expression into the sampling point coordinates yields the corresponding wave height obtained under this preset wavefront expression. Comparing this wave height with the actual wave height, the smaller the error, the closer the preset wavefront expression is to the actual wavefront expression. Therefore, minimizing the corresponding cost function can typically be achieved by making... =0, thus for η jk Solve to obtain the unknown parameters in the preset wavefront expression.

[0079] The obtained expression for the predefined wavefront is as follows:

[0080] ;

[0081] ;

[0082] ;

[0083] in, For the preset wavefront expression, the , , and That is, the unknown parameters in the preset wavefront expression. and t is the wavenumber; r is the coordinate of the sampling point, and t is the sampling time; and The wave angular frequency; The phase of the wave component. Let i be the phase, and N be the number of wave components; where i = 1, 2, ... N, n=1, 2, , N, and i≠n.

[0084] The solution process for the cost formula is as follows:

[0085] ;

[0086] and The unknown parameters in the preset wavefront expression are m=1, 2, ... 、N.

[0087] The matrix obtained by assigning values ​​to the spatiotemporal coordinates and wavefront parameters of the sampling points; The vector is obtained by assigning spatiotemporal coordinates and wavefront parameters to the sampling points, where m is the row of the matrix and n is the column of the matrix.

[0088] Transform the 2N system of equations into a matrix form AX=B, and change the unknowns in solving the system of equations into the solution vector X.

[0089] The spatiotemporal coordinates of the sampling points and the wavefront parameters are substituted into... and ,as follows:

[0090] ;

[0091] ;

[0092] ;

[0093] ;

[0094] ;

[0095] Where r is a two-dimensional coordinate (x, y), and the wavenumber k includes Nk and Nθ (0~2). The maximum and minimum wavenumber values ​​can be determined by selecting a finite wavenumber bandwidth with relevant cutoff limits. = , This represents the maximum value of the distance between measurement points; = , The minimum distance between measurement points is l; l represents the number of lidar sampling points (l takes values ​​1, 2, ..., L, L=j k); This represents the actual wave height. Sampling time.

[0096] In this embodiment, during the process of solving AX=B, Gaussian elimination is used for smaller orders, while the more efficient iterative method GMRES is used for larger orders. The preset wavefront expression is obtained by superimposing N wave components, and each wave component contains an a. n b n Therefore, we obtain N pairs of a. n b n Solving for N pairs (a) yields N pairs (a) n b n The obtained amplitude-related coefficient, a), will be used to calculate the amplitude-related coefficient. n b n Substituting the expression from the wave model yields the wave surface expression.

[0097] It should be noted that the wavefront expression can represent a single time point or multiple time points. When the wavefront expression can represent a single time point, it can only obtain the wave height at that time point. When the wavefront expression can represent multiple time points, it can be applied to the wave height calculation of any one of the multiple time points.

[0098] Since it is necessary to obtain the discrete values ​​of the velocity potential in the wavefront expression when predicting the wavefront at subsequent time points, the following design is adopted in this embodiment:

[0099] The step of iteratively solving the objective equation based on the wavefront expression to obtain discrete values ​​of the velocity potential of the wavefront expression specifically includes:

[0100] The wavefront expression and velocity potential are nonlinearly linked by an objective equation. By iteratively solving the objective equation, the discrete velocity potential values ​​at the reconstructed time points corresponding to the wavefront expression are obtained. The objective equation is:

[0101] ;

[0102] in:

[0103] ;

[0104] ;

[0105] in, For the wavefront expression, This is the partial derivative of the wavefront expression with respect to time. for , The reconstruction time point corresponding to the wavefront expression. Let W be the velocity potential. Partial derivative with respect to the wave height at the sampling point; M is determined by those skilled in the art, m=1, 2, M, W are Partial derivative with respect to wave height z, I = 0, 1, 2 、Mm.

[0106] This equation uses a nonlinear approach , and Connected; due to It is a function that changes over time, so it can be obtained directly. The Newton-Krylov method, which avoids generating the Jacobian matrix, is used to obtain discrete values ​​of the velocity potential.

[0107] like Figure 5 As shown, the method for solving the velocity potential is as follows:

[0108] In step 201, the formula for the residual r0 is set.

[0109] Among them, according to Newton's iteration, we get:

[0110] ;

[0111] Based on the above formula, we can obtain:

[0112] ;

[0113] in, To obtain the approximate value after k iterations based on the Krylov subspace, To approximate the value The value of the objective equation, To approximate the value Jacobi matrix, This is the initial correction value.

[0114] In step 202, an initial x is set, which is obtained by solving a linear wave model.

[0115] In step 203, the initial x or the iterated x is substituted into the formula for the residual r0 to obtain the residual r0.

[0116] In step 204, it is determined whether r0 is less than a preset value. If r0 is less than the preset value, step 206 is executed. If r0 is not less than the preset value, step 205 is executed.

[0117] Then x is not an exact solution to F(x)=0. We add Δxj to the original x to get a new x.

[0118] In step 205, when r0 is not less than a preset value, an iterative correction value is obtained based on the Krylov subspace and the weighted distribution of elements within the Krylov subspace. Based on this iterative correction value, an approximate value x is obtained after the iteration. k Proceed to step 203.

[0119] Wherein, the iterative correction value is The approximate value after the previous iteration is ,but .

[0120] The Composed of Krylov subspace, the The following formula represents:

[0121] .

[0122] in, This is the initial correction value. This represents the weighted distribution of elements within the Krylov subspace.

[0123] Solving based on least squares method By minimizing the vector 2 norm || +F(x)||2 is calculated; for large systems of equations, GMRES can be used to solve them; , i = 1, 2, 3, ..., j.

[0124] in, .

[0125] for We need to calculate first. Then use its result as a new Calculate it again You can get And so on for the others.

[0126] In step 206, when r0 is less than a preset value, As the exact solution, the discrete values ​​of the velocity potential at the reconstructed time point are obtained based on the exact solution.

[0127] Since the wavefront changes constantly, the relatively accurate prediction area changes over time. When predicting the wavefront for subsequent times based on the wavefront expression of previous times, the wave height of all sampled points at the prediction time point is obtained. However, some sampled points may exist outside the predictable area, so the prediction results for these sampled points are not accurate enough and need to be excluded. Therefore, it is necessary to obtain the predictable area, which is obtained by the change of the region boundary of the wavefront expression over time. Therefore, it is necessary to obtain the region boundary of the wavefront expression first. Hence, this embodiment also involves the following preferred design:

[0128] By taking the maximum group velocity and reconstruction time interval corresponding to the wavefront expression, and substituting the maximum group velocity and time interval into the region boundary formula, the region boundary corresponding to the wavefront expression is obtained. The region boundary formula is as follows:

[0129] ;

[0130] in, The minimum boundary of the region. The maximum boundary of the region. This refers to the sampling point range of the lidar. For the maximum group velocity, This is the interval length of the reconstruction time interval corresponding to the wavefront expression.

[0131] The maximum and minimum group velocities are obtained from the frequencies in the wavefront expression, as shown in the following formula:

[0132] ;

[0133] in, For group velocity, The frequency in the wavefront expression, the The maximum group velocity is calculated using the minimum frequency. The minimum group velocity is calculated using the maximum frequency. This is the interval length of the time interval corresponding to the wavefront expression.

[0134] After obtaining the region boundary corresponding to the wavefront expression, the predictable region is then obtained based on the region boundary corresponding to the wavefront expression. Therefore, this embodiment also involves the following design:

[0135] Obtain the minimum group velocity corresponding to the wavefront expression, and based on the minimum group velocity, the maximum group velocity, and the region boundary corresponding to the wavefront expression, obtain the predictable region relationship at the prediction time point.

[0136] The predictable region relationship is as follows:

[0137] ;

[0138] in, Let x be the minimum group velocity, x be the location point to be predicted, and t be the prediction time point. This represents the reconstruction time point corresponding to the wavefront expression.

[0139] Because the position of the same wavefront changes over time, the predictable region also changes over time. Furthermore, since the wavefront expression's predictive value for a given time point weakens over time, the size of the predictable region decreases over time. Converting the wave field's sampling point coordinates into vectors allows us to reflect changes in the size of the predictable region through vector variations. Figure 4 The diagram shown illustrates the relationship between the size of the predictable region and time. Figure 4 As can be seen from this, when time t is 0, the reconstructed region range is... arrive When time t is At that time, the predictable area range is arrive When t is At that time, the size of the predictable area range is 0.

[0140] It should be noted that the boundary of the region is all the sampling points actually sampled by the lidar. Due to the lidar scanning, these sampling points are unevenly distributed. Therefore, after the wavefront expression is reconstructed, the uniformly distributed spatial points are reset according to the wavefront expression. In this embodiment, the set of spatial points is called the solution domain.

[0141] The method for determining whether a spatial point is within a predictable region is as follows: Substitute the coordinates of the spatial point and the predicted time point into the predictable region relation. When the predictable region relation is satisfied, it means that the spatial point is within the predictable region.

[0142] Once the predictable region relationship is obtained, the prediction time point can be made based on the wave surface expression and the corresponding velocity potential. Therefore, this embodiment also involves the following design:

[0143] The step of predicting the wave height and velocity potential at the predicted time point based on the wave surface expression and the discrete values ​​of the velocity potential in the wave surface expression, and taking the prediction results within the predictable region as the valid prediction results, specifically includes:

[0144] The discrete values ​​of the velocity potential in the wavefront expression are obtained by solving the objective equation. The discrete values ​​of the velocity potential in the wavefront expression, the discrete values ​​of the wave height in the wavefront expression, and the prediction time point are substituted into the pseudospectral Fourier Legendre model to predict the discrete values ​​of the velocity potential at the prediction time point and the discrete values ​​of the wave height corresponding to the wavefront expression at the prediction time point. The prediction results within the predictable region are obtained as valid prediction results according to the predictable region relationship.

[0145] In this embodiment, the results predicted based on the discrete values ​​of the velocity potential and wave height of the wave surface expression are the velocity potential and wave height of all spatial points within the solution domain of the wave surface expression at the prediction time point. However, not all spatial points in the solution domain are within the aforementioned predictable region, so the prediction results are not all valid. All spatial points in the solution domain are substituted into the predictable region relation. Spatial points that satisfy the predictable region relation are within the predictable region. The prediction results of the spatial points within the predictable region are obtained, which are the final valid prediction results for the prediction time point.

[0146] It is worth mentioning that the pseudospectral Fourier Legendre model adopts the fourth-order Runge-Kutta numerical algorithm and the GMRES iterative algorithm, thereby ensuring the accuracy of the predicted velocity potential.

[0147] Example 2:

[0148] like Figure 6 The diagram shown is a schematic representation of a lidar-based nonlinear wave field reconstruction and prediction device according to an embodiment of the present invention. This lidar-based nonlinear wave field reconstruction and prediction device includes one or more processors 61 and a memory 62. Figure 6 Take a processor 61 as an example.

[0149] Processor 61 and memory 62 can be connected via a bus or other means. Figure 6 Taking the example of a connection between China and Israel via a bus.

[0150] The memory 62, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs and non-volatile computer-executable programs, such as the lidar-based nonlinear wave field reconstruction and prediction method in the above embodiment. The processor 61 executes the lidar-based nonlinear wave field reconstruction and prediction method by running the non-volatile software programs and instructions stored in the memory 62.

[0151] Memory 62 may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other non-volatile solid-state storage device. In some embodiments, memory 62 may optionally include memory remotely located relative to processor 61, which can be connected to processor 61 via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0152] The program instructions / modules are stored in the memory 62. When executed by one or more processors 61, they perform the nonlinear wave field reconstruction and prediction method based on lidar in the above embodiments, for example, the method described above. Figures 1 to 5 The steps shown.

[0153] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for nonlinear wave field reconstruction and prediction based on lidar, characterized in that, include: The wave field is scanned by lidar to obtain the coordinates of the sampling points of the wave field; Set a cost function, and solve the cost function based on the coordinates of the sampling points to obtain the reconstructed wavefront expression; The objective equation is solved iteratively based on the wavefront expression to obtain discrete values ​​of the velocity potential in the wavefront expression. Set a prediction time point and obtain the predictable region at the prediction time point based on the wavefront expression; Based on the wave surface expression and the discrete value of the velocity potential of the wave surface expression, the wave height and velocity potential at the prediction time point are predicted, and the prediction results within the predictable region are taken as valid prediction results.

2. The LIDAR-based non-linear wave field reconstruction and prediction method according to claim 1, characterized in that, The step of scanning the wave field with a lidar to obtain the coordinates of the sampling points of the wave field specifically includes: Obtain the distance r of the sampling point of the lidar reaching the wave field, and the horizontal angle of the lidar's emitted rays. and vertical angle Based on distance r and horizontal angle and vertical angle The polar coordinates of the sampling points of the wave field are obtained, and the polar coordinates of the sampling points of the wave field are converted into the sampling point coordinates in a preset coordinate system. Wherein, the x and y coordinates of the sampling point in the preset coordinate system represent the wavefront position, and the z coordinate of the sampling point in the preset coordinate system represents the wave height of the sampling point.

3. The method for reconstructing and predicting nonlinear wave fields based on lidar according to claim 2, characterized in that, The setting of the cost function, which involves solving the cost function based on the coordinates of the sampling points to obtain the reconstructed wavefront expression, specifically includes: A cost function is defined by the sampling point coordinates and a preset wavefront expression. The cost function is the sum of squares of the errors between the wave height of the sampling point and the preset wavefront expression. By taking the partial derivative of the coefficients in the preset wavefront expression with the cost function, a set of nonlinear equations is obtained, and the wavefront expression is obtained by solving the set of nonlinear equations.

4. The nonlinear wave field reconstruction and prediction method based on lidar according to claim 3, characterized in that, The cost function is as follows: ； in, Let η be the cost function, k be the number of samplings, j be the number of sampling points per sampling, and η be the cost function. jk For the preset wavefront expression, At spatial location r j and time t k The wave height of the sampling point is given by j = 1, 2, ..., J, and k = 1, 2, ..., K.

5. The method for reconstructing and predicting nonlinear wave fields based on lidar according to claim 1, characterized in that, The step of iteratively solving the objective equation based on the wavefront expression to obtain discrete values ​​of the velocity potential of the wavefront expression specifically includes: The wavefront expression and velocity potential are nonlinearly linked by an objective equation. By iteratively solving the objective equation, the discrete velocity potential values ​​at the reconstructed time points corresponding to the wavefront expression are obtained. The objective equation is: ； in, For the wavefront expression, This is the partial derivative of the wavefront expression with respect to time. for Where x is the x-coordinate of the sampling point in the preset coordinate system, y is the y-coordinate of the sampling point in the preset coordinate system, and t is time. Let W be the velocity potential. Partial derivative with respect to the wave height at the sampling point.

6. The method for reconstructing and predicting nonlinear wave fields based on lidar according to claim 5, characterized in that, The iterative solution of the objective equation specifically includes: Setting residuals The formula is used to solve the Krylov subspace, and the approximate value after iteration is obtained based on the Krylov subspace. The approximate value after iteration Substitute the residual The formula, when the residual When the value is less than the preset value, the approximate value after iteration The exact solution is the discrete velocity potential value at the reconstructed time point corresponding to the wavefront expression; where the residual... The formula is: ； Where x is the initial value, To obtain the approximate value after k iterations based on the Krylov subspace, To approximate the value The value of the objective equation, To approximate the value Jacobi matrix, This is a correction value.

7. The method for reconstructing and predicting nonlinear wave fields based on lidar according to claim 1, characterized in that, Obtain the maximum group velocity and reconstruction time interval corresponding to the wavefront expression, and substitute the maximum group velocity and time interval into the region boundary formula to obtain the region boundary corresponding to the wavefront expression. The region boundary formula is as follows: ； in, The minimum boundary of the region. The maximum boundary of the region. This refers to the sampling point range of the lidar. For the maximum group velocity, This is the interval length of the reconstruction time interval corresponding to the wavefront expression.

8. The method for reconstructing and predicting nonlinear wave fields based on lidar according to claim 7, characterized in that, The setting of the prediction time point and obtaining the predictable region at the prediction time point based on the wavefront expression specifically includes: Obtain the minimum group velocity corresponding to the wavefront expression, and based on the minimum group velocity, the maximum group velocity, and the region boundary corresponding to the wavefront expression, obtain the predictable region relationship at the prediction time point. The predictable region relationship is as follows: ； in, Let x be the minimum group velocity, x be the position point to be predicted, and t be the prediction time point. This represents the reconstruction time corresponding to the wavefront expression.

9. The method for reconstructing and predicting nonlinear wave fields based on lidar according to claim 8, characterized in that, The step of predicting the wave height and velocity potential at the predicted time point based on the wave surface expression and the discrete values ​​of the velocity potential in the wave surface expression, and taking the prediction results within the predictable region as the valid prediction results, specifically includes: The discrete values ​​of the velocity potential in the wavefront expression are obtained by solving the objective equation. The discrete values ​​of the velocity potential, the discrete values ​​of the wave height, and the prediction time point are then substituted into the pseudospectral Fourier Legendre model to predict the discrete values ​​of the velocity potential and the wave height at the prediction time point. The prediction results within the predictable region are then obtained as valid prediction results based on the predictable region relation.

10. A nonlinear wave field reconstruction and prediction device based on lidar, characterized in that, The method includes at least one processor and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the processor for performing the nonlinear wave field reconstruction and prediction method based on lidar as described in any one of claims 1-9.

Images