CN102799770B

CN102799770B - A kind of wave significant wave height inverse model modeling method based on the matching of PSO dispositif de traitement lineaire adapte

Info

Publication number: CN102799770B
Application number: CN201210219893.XA
Authority: CN
Inventors: 刘利强; 戴运桃; 范志超
Original assignee: Harbin Engineering University
Current assignee: Harbin Engineering University
Priority date: 2012-06-29
Filing date: 2012-06-29
Publication date: 2015-08-26
Anticipated expiration: 2032-06-29
Also published as: CN102799770A

Abstract

The invention proposes a PSO self-adaptive piecewise linear fitting-based modeling method for the effective wave height inversion model of ocean waves, which belongs to the technical field of ocean wave parameter inversion, including data removal of wild value point processing, data sparse processing, and initialization particles The parameters in the group, the initialization of particle velocity, the update of particle velocity and the update of particle displacement are steps. The present invention proposes an adaptive piecewise linear particle swarm effective wave height inversion model modeling method, using the particle swarm algorithm to invert the wave height, which can not only complete the functions of the traditional algorithm, but also achieve the accuracy of the traditional algorithm. Perform more accurate wave height inversion, and when the number of segments in the present invention is greater than or equal to two, it has higher modeling accuracy than the traditional modeling method, and the inversion model established by the present invention is better than that established by the traditional method. The inversion model has higher inversion accuracy, and the method of the invention has wide applicability and high flexibility.

Description

A Modeling Method for Significant Wave Height Retrieval Model Based on PSO Adaptive Piecewise Linear Fitting

技术领域 technical field

本发明属于海浪参数反演技术领域，具体涉及的是一种基于PSO自适应分段线性拟合的海浪有效波高反演模型建模方法。The invention belongs to the technical field of sea wave parameter inversion, and in particular relates to a modeling method for sea wave effective wave height inversion model based on PSO adaptive piecewise linear fitting.

背景技术 Background technique

海浪是一种与人类关系最直接、最密切的海洋现象，其波高、波向、波周期等因素对航运、港口、以及海上石油平台的安全都具有非常重要的意义。船用X波段导航雷达回波形成的海杂波图像中包含丰富的海浪信息，可以利用雷达的回波强度反演海浪谱和海浪参数。1985年，Young等人首次提出了根据“海杂波”雷达图像序列提取海浪信息的方法。该方法一经发现，就引起了人们的极大兴趣。在此后10年间，Zimer、Rosenthal和Günther等人也纷纷开展了基于X波段导航雷达的海浪信息反演研究工作。1995年，德国GKSS实验室研制出了基于导航雷达的海浪监测系统WaMoS(Wave Monitoring System)；1996年，挪威Miros公司也研制出了类似的产品WAVEX。除以上主流研究机构外，目前美国、日本、丹麦、中国也在积极从事该方面的研究。Ocean waves are the ocean phenomenon most directly and closely related to human beings. Factors such as wave height, wave direction, and wave cycle are of great significance to the safety of shipping, ports, and offshore oil platforms. Sea clutter images formed by marine X-band navigation radar echoes contain rich ocean wave information, and the ocean wave spectrum and wave parameters can be retrieved by using the echo intensity of the radar. In 1985, Young et al. proposed for the first time the method of extracting ocean wave information from the "sea clutter" radar image sequence. Once the method was discovered, it aroused great interest. In the following 10 years, Zimer, Rosenthal, Günther and others also carried out the research work of ocean wave information inversion based on X-band navigation radar. In 1995, the German GKSS laboratory developed the wave monitoring system WaMoS (Wave Monitoring System) based on navigation radar; in 1996, the Norwegian Miros company also developed a similar product WAVEX. In addition to the above mainstream research institutions, the United States, Japan, Denmark, and China are also actively engaged in research in this area.

有效波高是海浪信息的一种。由于海浪成像机制的非线性，利用X波段雷达图像进行海浪参数反演时，只能获得海浪谱能量的相对值，难以直接获取海浪有效波高。1982年，Alpers和Hasselmann提出了利用合成孔径雷达(SAR)信息估计有效波高的方法，该方法认为有效波高与雷达图像信噪比的平方根存在线性关系，可建立线性模型，通过计算得到雷达图像信噪比的平方根，进而根据线性模型得到有效波高。1994年，Ziemer和Günther将该方法推广到X波段导航雷达图像，计算获取了有效波高。到目前为止，该方法一直被作为基于X波段导航雷达图像有效波高的标准反演方法而使用。其线性模型如公式（1）和公式（2）所示：Significant wave height is a type of wave information. Due to the nonlinearity of the wave imaging mechanism, when X-band radar images are used for wave parameter inversion, only the relative value of the wave spectral energy can be obtained, and it is difficult to directly obtain the effective wave height of the wave. In 1982, Alpers and Hasselmann proposed a method of estimating the effective wave height by using synthetic aperture radar (SAR) information. This method believed that there was a linear relationship between the effective wave height and the square root of the radar image signal-to-noise ratio, and a linear model could be established. Through calculation, the radar image signal The square root of the noise ratio, and then the effective wave height is obtained according to the linear model. In 1994, Ziemer and Günther extended the method to X-band navigation radar images, and calculated the effective wave height. So far, this method has been used as a standard inversion method for effective wave height based on X-band navigation radar images. Its linear model is shown in formula (1) and formula (2):

$Hs Hs = = A A + + B B * * \sqrt{SNR SNR} - - - - - - ((11))$

SNR＝SIG/BGN （2）SNR＝SIG/BGN （2）

其中，Hs是有效波高，A和B是待定系数，SNR是雷达图像的信噪比，SIG是海浪波谱的能量，BGN是背景噪声的能量。Among them, Hs is the effective wave height, A and B are undetermined coefficients, SNR is the signal-to-noise ratio of the radar image, SIG is the energy of the wave spectrum, and BGN is the energy of the background noise.

在实际使用中发现，由于信噪比的计算方法不同，雷达系统的差异，以及海域的环境差异等因素，虽然海浪有效波高是随着雷达图像信噪比的增大而增大，但在整个变化范围内，海浪有效波高与雷达图像信噪比的平方根之间并不是完全线性的。因此，采用线性模型表达雷达图像信噪比的平方根与海浪有效波高之间的关系是不准确的。In actual use, it is found that due to factors such as different calculation methods of signal-to-noise ratio, differences in radar systems, and environmental differences in sea areas, although the effective wave height of sea waves increases with the increase of radar image signal-to-noise ratio, it is in the whole Within the range of variation, the relationship between the effective wave height of ocean waves and the square root of the signal-to-noise ratio of radar images is not completely linear. Therefore, it is inaccurate to use a linear model to express the relationship between the square root of the signal-to-noise ratio of radar images and the significant wave height of ocean waves.

针对这一问题，2009年，中国海洋大学的段华敏和王剑提出了分段线性化反演模型，将有效波高分为低波高和高波高两个区域，每个区域分别采用各自的线性模型表达。这种分段线性化反演模型的基本思想与线性模型的思想是相同的。虽然分段线性化反演模型在有效波高反演精度上较线性模型有所改善，但仍然存在一些问题。例如，在整个有效波高变化范围内在何处进行分段，分段的各线段如何连接等In response to this problem, in 2009, Duan Huamin and Wang Jian of Ocean University of China proposed a piecewise linearization inversion model, which divides the effective wave height into two regions of low wave height and high wave height, and each region adopts its own linear model Express. The basic idea of this piecewise linearized inversion model is the same as that of the linear model. Although the piecewise linearization inversion model has improved the accuracy of significant wave height inversion compared with the linear model, there are still some problems. For example, where to segment within the entire significant wave height variation range, how to connect the segments of each segment, etc.

发明内容 Contents of the invention

针对现有技术中存在的问题，本发明提出一种自适应分段线性粒子群的海浪有效波高反演模型建模方法。本发明公开的方法区别于现有方法的显著特征在于：认为海浪有效波高是随着雷达图像信噪比平方根增加而增加的，但二者之间在不同的波高阶段并非完全承线性关系，所以现有方法采用最小二乘方法对信噪比比平方根和波高分段线性的进行拟合，来表示信噪比比平方根与波高的关系，但分段线性化带来的问题是，分段位置的确定和各线段之间如何进行连接等问题，利用粒子群算法多维度空间搜索功能，可自适应的解决最小二乘无法完成的，分段位置的确定和各段的连接等问题，进而提高使用雷达图像信噪比平方根反演海浪有效波高的精度。Aiming at the problems existing in the prior art, the present invention proposes a modeling method for the effective wave height inversion model of ocean waves based on adaptive piecewise linear particle swarms. The method disclosed in the present invention differs from the existing methods in that it is considered that the effective wave height of the ocean wave increases with the increase of the square root of the signal-to-noise ratio of the radar image, but the relationship between the two is not completely linear at different wave height stages, so The existing method uses the least squares method to fit the square root of the SNR and the wave height piecewise linearly to represent the relationship between the square root of the SNR and the wave height, but the problem brought by the piecewise linearization is that the segment position How to determine the determination of each line segment and how to connect each line segment, using the multi-dimensional space search function of the particle swarm optimization algorithm, can adaptively solve the problems that cannot be completed by least squares, the determination of the segment position and the connection of each segment, etc., and then improve Using the square root of radar image signal-to-noise ratio to retrieve the accuracy of significant wave height of ocean waves.

本发明提出一种基自适应分段线性粒子群的海浪有效波高反演模型建模方法，具体包括以下几个步骤：The present invention proposes a method for modeling the effective wave height inversion model of sea waves based on adaptive piecewise linear particle swarm, which specifically includes the following steps:

步骤一：数据的去野值点处理：Step 1: Data outlier point processing:

原始数据点集为Y，有任意数据点A，若对于数据点A的某一邻域ρ(A,r),r＞0，r表示邻域的半径，存在数据点B，使得B∈ρ(A,r)，则点A属于真值集，Y中所有满足点A这一性质的点组成的集合构成真值集Z；有任意数据点A′，若对于点A′的某一邻域ρ(A′,r),r＞0，对于均有则点A′属于野值集，Y中所有满足点A′这一性质的点组成的集合构成野值集U，根据真值集和野值集进行去野值点处理：The original data point set is Y, with any data point A, If for a certain neighborhood ρ(A,r) of data point A, r>0, r represents the radius of the neighborhood, there is data point B, Make B∈ρ(A,r), then point A belongs to the truth set, and the set of all points satisfying the property of point A in Y constitutes the truth set Z; any data point A′, If for a certain neighborhood ρ(A',r) of point A', r>0, for have Then point A' belongs to the outlier set, and the set of all points satisfying the property of point A' in Y constitutes the outlier set U, and the outlier point processing is performed according to the true value set and the outlier set:

第1步：将原始数据点集Y中的数据点按照数据点的横坐标由小到大进行排序，得到排序后的数据点集为{A^k′}k′＝1,2,3,...,m，其中m为原始数据点集Y中的所有数据点的个数，角标k′表示数据点按照横坐标大小由小到大依次排列，邻域半径为r，令k′＝1，向左判断参数tl初始值满足tl＝1，向右判断参数tr初始值满足tr＝1；Step 1: sort the data points in the original data point set Y according to the abscissa of the data points from small to large, and obtain the sorted data point set as {A ^k ′}k′=1,2,3,. ..,m, where m is the number of all data points in the original data point set Y, subscript k' indicates that the data points are arranged in order from small to large according to the size of the abscissa, and the neighborhood radius is r, let k'= 1. The initial value of the left judgment parameter tl satisfies tl=1, and the right judgment parameter tr initial value satisfies tr=1;

第2步：判断k′-tl＞0是否成立，若不成立进入第4步，若成立判断A^k′-A^k′^-tl＜r是否成立，若不成立进入第4步，若成立判断是否成立，若成立，记录点A^k′属于集合B中，进入第6步，其中集合B表示剔除野值之后的真值集，若不成立进入第3步；Step 2: Judging whether k′-tl>0 is true, if not true, go to step 4, if true, judge whether A ^k ′-A ^k ′ ^-tl <r is true, if not true, go to step 4, if true Whether it is true, if it is true, the record point A ^k ′ belongs to the set B, and enter the sixth step, where the set B represents the true value set after removing outliers, if it is not established, enter the third step;

第3步：令向左判断参数tl加1，即tl＝tl+1，返回到第2步；The 3rd step: make the left judgment parameter tl add 1, promptly tl=tl+1, return to the 2nd step;

第4步：判断k′+tr＜m是否成立，若不成立进入第6步，若成立判断A^k′^+tr-A^k′＜r是否成立，若不成立进入第6步，若成立判断是否成立，若成立，记录点A^k′属于集合B中，进入第6步，若不成立进入第5步；Step 4: Judging whether k′+tr<m is true, if not true, go to step 6, if true, judge whether A ^k ′ ^+tr -A ^k ′<r is true, if not true, go to step 6, if true Whether it is true, if it is true, the record point A ^k ′ belongs to the set B, go to step 6, if it is not true, go to step 5;

第5步：令向右判断参数tr加1，即tr＝tr+1，返回到第4步；The 5th step: make the judgment parameter tr to the right add 1, promptly tr=tr+1, return to the 4th step;

第6步：令角标k′加1，即k′＝k′+1，判断k′≤m是否成立，若不成立进入第7步，若成立令tl＝1，tr＝1，返回到第2步；Step 6: add 1 to subscript k', namely k'=k'+1, judge whether k'≤m is established, if not established, enter step 7, if established set tl=1, tr=1, return to the first step 2 steps;

第7步：集合B中的所有点组成剔除野值点之后的真值集；Step 7: All points in set B form the true value set after removing outlier points;

步骤二：数据的稀疏化处理：Step 2: Data sparse processing:

原始数据点集为Y，存在任意点C，若对于点C的某一邻域ρ(C,r′),r′＞0，使得D∈ρ(A,r′)，则称点C属于密集集，r′表示邻域判断半径，Y中所有满足点C这一性质的点组成的集合构成密集集M；存在任意点C′，若对于点C′的某一邻域ρ(C′,r′),r′＞0，对于均有则称点C′属于稀疏集，Y中所有满足点C′这一性质的点组成的集合构成稀疏集S；野值集、真值集、密集集和稀疏集之间存在交叉关系为：设Z_s＝Z ∩S，当r′≤r时，有U ∩Z_s＝Φ，并且U ∪Z_s＝S，Z_s表示真值集与稀疏集的交集；稀疏化处理的具体步骤为：The original data point set is Y, there is any point C, If for a certain neighborhood of point C ρ(C,r′), r′>0, If D∈ρ(A,r′), then point C is said to belong to a dense set, r′ represents the neighborhood judgment radius, and the set of all points satisfying the property of point C in Y constitutes a dense set M; there is any point C ', If for a certain neighborhood ρ(C',r') of point C', r'>0, for have Then point C′ is said to belong to a sparse set, and the set of all points satisfying the property of point C′ in Y constitutes a sparse set S; there is a cross relationship between the outlier set, the true value set, the dense set and the sparse set as follows: Let Z _s ＝Z ∩S, when r′≤r, we have U ∩ Z _s = Φ, and U ∪ Z _s = S, Z _s represents the intersection of the truth set and the sparse set; the specific steps of sparse processing are:

第1步：将步骤一中得到的集合B中的数据点，按照数据点的横坐标由小到大进行排序，得到排序后的数据点集{C^k″}k″＝1,2,3,...,n，其中n为集合B中所有数据点的个数，角标k″表示数据点按照横坐标大小由小到大依次排列，设稀疏化处理时邻域判断半径为r′，令k″＝1，t＝1，m′＝n，{D^k″}＝{C^k″}k″＝1,2,3,...,m′；t表示向右判断参数，{D^k″}用于表示将去野值后的数据又进行了稀疏化处理的数据点，m′表示每次提出野值后集合{D^k″}中所剩下的数据点的个数；Step 1: sort the data points in set B obtained in step 1 according to the abscissa of the data points from small to large, and obtain the sorted data point set {C ^k ″}k″=1,2,3 ,...,n, where n is the number of all data points in set B, subscript k″ indicates that the data points are arranged in order according to the size of the abscissa from small to large, and the neighborhood judgment radius is r′ during sparse processing , set k″=1, t=1, m′=n, {D ^k ″}={C ^k ″}k″=1,2,3,...,m′; t represents the rightward judgment parameter, {D ^k ″} is used to represent the data points that have been sparsely processed after the outliers are removed, and m′ represents the number of remaining data points in the set {D ^k ″} after each outlier is proposed ;

第2步：判断k″+t＜m′是否成立，若不成立进入第4步，若成立判断D^k"^+t-D^k"＜r′是否成立，若不成立进入第4步，若成立判断是否成立，若成立，剔除点D^k″^+t，令m′＝m′-1，进入第3步，若不成立进入第4步；Step 2: Judging whether k″+t<m′ is true, if not true, go to step 4, if true, judge whether D ^k " ^{+ t} -D ^k "<r′ is true, if not true, go to step 4, if true Whether it is true, if it is true, remove the point D ^k ″ ^+t , let m'=m'-1, enter the third step, if it is not true, enter the fourth step;

第3步：令t＝t+1，返回到第2步；The 3rd step: make t=t+1, return to the 2nd step;

第4步：将集合{D^k″}中剩余的数据点，按照原横坐标大小由小到大排列顺序依次重新记录到{D^k″}k″＝1,2,3,...,m′中，令k″＝k″+1，判断k″≤m′是否成立，若不成立进入第5步，若成立令t＝1，返回到第2步；Step 4: Re-record the remaining data points in the set {D ^k ″} to {D ^k ″}k″=1,2,3,..., In m', let k″=k″+1, judge whether k″≤m′ is established, if not established, enter step 5, if established, set t=1, return to step 2;

第5步：集合{D^k″}k″＝1,2,3,...,m′中的点便是将去野值后的数据又进行了稀疏化处理的数据点；Step 5: The points in the set {D ^k ″}k″=1, 2, 3, ..., m′ are the data points that have been sparsely processed after the outliers are removed;

步骤三：设置粒子的编码方式并初始化粒子群各参数：直线方程由截距式表示，每个粒子由所有确定直线的截距A和斜率B构成，粒子群算法粒子的编码方式为：Step 3: Set the coding method of the particles and initialize the parameters of the particle swarm: the linear equation is expressed by the intercept formula, and each particle is composed of the intercept A and slope B of all determined straight lines. The particle swarm algorithm particle coding method is:

${X x}_{i i}^{k k} = = {{{X x}_{i i,, j j,, 11}^{k k},, {X x}_{i i,, j j,, 22}^{k k}}}$

其中i＝1,2,...,N，N≥2为粒子个数，j＝1,2,...,l，l≥1表示分段数，即参与拟合的直线条数；k表示粒子群的迭代次数；分别表示第k次迭代中第i个粒子第j条直线的截距、斜率，表示第i个粒子的位置；Where i=1,2,...,N, N≥2 is the number of particles, j=1,2,...,l, l≥1 represents the number of segments, that is, the number of straight lines involved in fitting; k represents the number of iterations of the particle swarm; Respectively represent the intercept and slope of the i-th particle j-th line in the k-th iteration, Indicates the position of the i-th particle;

初始化直线的截距和斜率为：Initialize the intercept and slope of the line as:

$\{\begin{matrix} {X x}_{i i,, j j,, 11}^{11} = = {A A}_{max max} - - \frac{((rand rand + + j j - - 11)) \cdot &Center Dot; (({A A}_{max max} - - {A A}_{min min}))}{l l} \\ {X x}_{i i,, j j,, 22}^{11} = = {B B}_{min min} + + \frac{((rand rand + + j j - - 11)) \cdot &Center Dot; (({B B}_{max max - -} {B B}_{min min}))}{l l} \end{matrix} - - - - - - ((33))$

其中rand为0到1之间的随机数；A_max和A_min分别表示截距的最大和最小值，满足min(Hs)≤A_max≤max(Hs)，min(Hs)和max(Hs)分别为波高数据中波高的最大值和最小值，A_min＜A_max；B_max和B_min分别表示斜率的最大值和最小值，满足0≤B_min≤B_max；i＝1,2,...,N，N≥2为粒子个数，j＝1,2,...,l，l≥1表示分段数，和分别表示初始化中第i个粒子第j条直线的截距和斜率；Where rand is a random number between 0 and 1; A _max and A _min represent the maximum and minimum values of the intercept respectively, satisfying min(Hs)≤A _max ≤max(Hs), min(Hs) and max(Hs) are the maximum and minimum values of the wave height in the wave height data, A _min < A _max ; B _max and B _min respectively represent the maximum and minimum values of the slope, satisfying 0≤B _min ≤B _max ; i=1,2,. .., N, N≥2 is the number of particles, j=1,2,...,l, l≥1 represents the number of segments, and Respectively represent the intercept and slope of the i-th particle j-th line in the initialization;

粒子位移的初始化为：The initialization of the particle displacement is:

$\{\begin{matrix} {v v}_{i i,, j j,, 11}^{11} = = rand rand \cdot &Center Dot; {v v}_{max max} \\ {v v}_{i i,, j j,, 22}^{11} = = rand rand \cdot \cdot {v v}_{max max} \end{matrix} - - - - - - ((44))$

其中rand为0到1之间的随机数；v_max＞0为粒子位移的最大值；分别表示初始化中第i个粒子第j条直线的截距位移项和斜率位移项；Where rand is a random number between 0 and 1; v _max > 0 is the maximum value of particle displacement; represent the intercept displacement term and the slope displacement term of the jth straight line of the i-th particle in the initialization, respectively;

粒子群各参数初始化如下：The parameters of the particle swarm are initialized as follows:

设种群数为N；初始化时第i个粒子为i＝1,2,...,N，j＝1,2,...,l；自身学习因子为c₁≥0，全局学习因子为c₂≥0；惯性权重上限和下限分别为ω_max和ω_min，0≤ω_min≤ω_max≤1；分段个数为l，l≥1；最大迭代次数k_max满足k_max≥2；种群数为N；零次项系数最大值和最小值分别为A_max和A_min，A_max≥A_min，一次项系数最大值和最小值分别为B_max和B_min，B_max≥B_min≥0；位移最大步长v_max满足v_max＞0；迭代停止阀值h_max为h_max＝l·E，其中E用于确定随分段个数的增加，循环跳出的阀值随之增大的速度；Let the population number be N; the i-th particle is i=1,2,...,N, j=1,2,...,l; the self-learning factor is c ₁ ≥ 0, the global learning factor is c ₂ ≥ 0; the upper limit and lower limit of the inertia weight are ω _max and ω _min , 0≤ω _min ≤ω _max ≤1; the number of segments is l, l≥1; the maximum number of iterations k _max satisfies k _max ≥2; the number of populations is N; The values are A _max and A _min , A _max ≥ A _min , the maximum and minimum values of the first-order coefficient are B _max and B _min , B _max ≥ B _min ≥ 0; the maximum displacement step v _max satisfies v _max >0; Iteration stop threshold h _max is h _max = 1 · E, wherein E is used to determine the speed at which the threshold value of loop jumping out increases with the increase of the number of segments;

步骤四：粒子速度的初始化方法如下：Step 4: The initialization method of the particle velocity is as follows:

令i＝1，j＝1，根据式（4），初始化第i个粒子位移为 $\{\begin{matrix} v_{i, j, 1}^{1} = rand \cdot v_{\max} \\ v_{i, j, 2}^{1} = rand \cdot v_{\max} \end{matrix}$ 其中rand为0到1之间的随机数；根据式（3）初始化第i个粒子位置为Let i=1, j=1, according to formula (4), initialize the i-th particle displacement as $\{\begin{matrix} v_{i, j, 1}^{1} = rand \cdot v_{\max} \\ v_{i, j, 2}^{1} = rand \cdot v_{\max} \end{matrix}$ where rand is a random number between 0 and 1; according to formula (3), the position of the i-th particle is initialized as

$\{\begin{matrix} {X x}_{i i,, j j,, 11}^{11} = = {A A}_{max max} - - \frac{((rand rand + + j j - - 11)) \cdot \cdot (({A A}_{max max} - - {A A}_{min min}))}{l l} \\ {X x}_{i i,, j j,, 22}^{11} = = {B B}_{min min} + + \frac{((rand rand + + j j - - 11)) \cdot \cdot (({B B}_{max max - -} {B B}_{min min}))}{l l} \end{matrix}$

其中rand为0到1之间的随机数；A_max和A_min分别表示截距的最大和最小值，满足min(Hs)≤A_max≤max(Hs)，min(Hs)和max(Hs)分别中波高的最大值和最小值，A_min＜A_max；B_max和B_min分别表示斜率的最大值和最小值，满足0≤B_min≤B_max；i＝1,2,...,N，N≥2为粒子个数，即群体大小；j＝1,2,...,l，l≥1表示分段数，即参与拟合的直线条数；和分别表示第1次迭代（即初始化）中第i个粒子第j条直线的截距和斜率；Where rand is a random number between 0 and 1; A _max and A _min represent the maximum and minimum values of the intercept respectively, satisfying min(Hs)≤A _max ≤max(Hs), min(Hs) and max(Hs) The maximum and minimum values of the wave height, A _min < A _max ; B _max and B _min respectively represent the maximum and minimum values of the slope, satisfying 0≤B _min ≤B _max ; i=1,2,..., N, N≥2 is the number of particles, that is, the group size; j=1,2,...,l, l≥1 represents the number of segments, that is, the number of straight lines involved in fitting; and Respectively represent the intercept and slope of the i-th particle j-th straight line in the first iteration (that is, initialization);

步骤五：令粒子数加1，即i＝i+1，判断i≤N是否成立，若成立返回步骤四，否则进入步骤六；Step 5: Add 1 to the number of particles, that is, i=i+1, judge whether i≤N is true, if true, return to step 4, otherwise enter step 6;

步骤六：令分段数加1，即j＝j+1，判断j≤l是否成立，若成立返回步骤四，否则进入步骤七；Step 6: Add 1 to the number of segments, i.e. j=j+1, judge whether j≤l is established, if established, return to step 4, otherwise enter step 7;

步骤七：粒子群速度位置更新公式：Step 7: Particle swarm velocity position update formula:

$\{\begin{matrix} {v v}_{i i}^{k k + + 11} = = ω ω \cdot \cdot {v v}_{i i}^{k k} + + {c c}_{11} {r r}_{11}^{k k} \cdot \cdot (({P P}_{i i}^{b b} - - {X x}_{i i}^{k k})) + + {c c}_{22} {r r}_{22}^{k k} \cdot \cdot (({P P}^{g g} - - {X x}_{i i}^{k k})) \\ {X x}_{i i}^{k k + + 11} = = {X x}_{i i}^{k k} + + {v v}_{i i}^{k k + + 11} \end{matrix} - - - - - - ((55))$

其中表示第i个粒子的位移；表示第i个粒子的位置，i＝1,2,...,N，N≥2为粒子个数，即群体大小，j＝1,2,...,l，l≥1表示分段数，即参与拟合的直线条数，k表示粒子群的迭代次数；为惯性权重，0≤ω_min≤ω_max≤1为惯性权重的最大最小值，ω_max和ω_min分别为惯性权重上限和下限，k_max表示最大迭代次数；u≥0为单调控制量；c₁≥0为自身学习因子；c₂≥0为全局学习因子；为[0,1]区间的随机数；为粒子自身寻到的最优值；P^g为种群寻到的最优值；粒子群方法适应度函数如下：in Indicates the displacement of the i-th particle; Indicates the position of the i-th particle, i=1,2,...,N, N≥2 is the number of particles, that is, the group size, j=1,2,...,l, l≥1 represents the segment The number is the number of straight lines participating in the fitting, and k represents the number of iterations of the particle swarm; is the inertia weight, 0 ≤ ω _min ≤ ω _max ≤ 1 is the maximum and minimum value of the inertia weight, ω _max and ω _min are the upper limit and lower limit of the inertia weight respectively, k _max represents the maximum number of iterations; u ≥ 0 is the monotonic control amount; c ₁ ≥ 0 is the self-learning factor; c ₂ ≥ 0 is the global learning factor; is a random number in the interval [0,1]; P g is the optimal value found for the particle itself; P ^g is the optimal value found for the population; the fitness function of the particle swarm optimization method as follows:

$F f (({X x}_{i i}^{k k})) = = {Σ Σ}_{t t = = 11}^{{m m}^{' '}} {(({X x}_{i i,, {j j}^{' '},, 11}^{k k} + + {X x}_{i i,, {j j}^{' '},, 22}^{k k} \cdot &Center Dot; {D D.}_{x x}^{t t} - - {D D.}_{y the y}^{t t}))}^{22} + + M m \cdot &Center Dot; m m - - - - - - ((66))$

其中t＝1,2,...,m′，分别为数据点对应的信噪比平方根和波高，D^t表示由信噪比平方根和波高值组成的向量，m′为数据去野并稀疏化后的个数；分别为直线的截距和斜率，j′＝1,2,...,l，设相邻直线间的交点依次为O＝{O^j″}，分别表示交点O^j″的横纵坐标，j″＝1,2,...,l-1，判断若则令j′＝1，若(j＝1,2,...，l-2，则令j′＝j″+1，若则令j′＝l；M＞0为惩罚因子，m为满足限制条件的次数；in t=1,2,...,m', are the SNR square root and wave height corresponding to the data points, respectively, D ^t represents the vector composed of the SNR square root and wave height values, and m′ is the number of data after dewilding and thinning; are the intercept and slope of the straight line respectively, j′=1,2,...,l, and the intersection points between adjacent straight lines are O={O ^j ″} in turn, Represent the horizontal and vertical coordinates of the intersection point O ^j ″ respectively, j″=1, 2,..., l-1, judge if Then let j'=1, if (j=1,2,..., l-2, then let j'=j "+1, if Then let j'=l;M>0 is the penalty factor, and m is the number of times of satisfying the restriction;

根据适应度函数公式（6）计算各粒子的适应度值：Calculate the fitness value of each particle according to the fitness function formula (6):

令粒子群的迭代次数k＝1，为粒子自身寻到的最优值，为第i个粒子的位置；（i＝1,2,...,N），根据公式（6）计算适应度函数值 Let the number of iterations of particle swarm k=1, The optimal value found for the particle itself, is the position of the i-th particle; (i=1,2,...,N), calculate the fitness function value according to the formula (6)

$F f (({X x}_{i i}^{k k})) = = {Σ Σ}_{t t = = 11}^{{m m}^{' '}} {(({X x}_{i i,, {j j}^{' '},, 11}^{k k} + + {X x}_{i i,, {j j}^{' '},, 22}^{k k} \cdot &Center Dot; {D D.}_{x x}^{t t} - - {D D.}_{y the y}^{t t}))}^{22} + + M m \cdot &Center Dot; m m$

步骤八：应用粒子群速度更新公式，根据式（5）中的位移更新公式，计算粒子位移为Step 8: Apply the particle swarm velocity update formula, and calculate the particle displacement according to the displacement update formula in formula (5) for

${v v}_{i i}^{' ' k k + + 11} = = ω ω \cdot &Center Dot; {v v}_{i i}^{k k} + + {c c}_{11} {r r}_{11}^{k k} \cdot &Center Dot; (({P P}_{i i}^{b b} - - {X x}_{i i}^{k k})) + + {c c}_{22} {r r}_{22}^{k k} \cdot \cdot (({P P}^{g g} - - {X x}_{i i}^{k k}))$

其中表示第i个粒子的位移；表示第i个粒子的位置，i＝1,2,...,N，N≥2为粒子个数，即群体大小，j＝1,2,...,l，l≥1表示分段数，即参与拟合的直线条数，k表示粒子群的迭代次数；为惯性权重，0≤ω_min≤ω_max≤1为惯性权重的最大最小值，k_max表示最大迭代次数；u≥0为单调控制量；c₁≥0为自身学习因子；c₂≥0为全局学习因子；为[0,1]区间的随机数；为粒子自身寻到的最优值；P^g为种群寻到的最优值；in Indicates the displacement of the i-th particle; Indicates the position of the i-th particle, i=1,2,...,N, N≥2 is the number of particles, that is, the group size, j=1,2,...,l, l≥1 represents the segment The number is the number of straight lines participating in the fitting, and k represents the number of iterations of the particle swarm; is the inertia weight, 0≤ω _min ≤ω _max ≤1 is the maximum and minimum value of the inertia weight, k _max represents the maximum number of iterations; u≥0 is the monotonic control quantity; c ₁ ≥0 is the self-learning factor; c ₂ ≥0 is the global learning factor; is a random number in the interval [0,1]; is the optimal value found by the particle itself; P ^g is the optimal value found by the population;

步骤九：判断是否成立，若成立令否则令其中为根据位移更新公式（5）计算的位移，v_max为位移长度最大值；i＝1,2,...,N；j＝1,2,...,l；s分别取值1或2，s＝1、s＝2分别表示直线的截距、斜率；粒子表示实际的位移；Step Nine: Judgment Whether established, if established order Otherwise order in is the displacement calculated according to the displacement update formula (5), v _max is the maximum displacement length; i=1,2,...,N; j=1,2,...,l; s takes the value 1 or 2. s=1 and s=2 represent the intercept and slope of the straight line respectively; The particles represent the actual displacement;

步骤十：应用粒子群位置更新公式，根据式（5）中的位置更新公式，计算粒子位置为Step 10: Apply the particle swarm position update formula, and calculate the particle position according to the position update formula in formula (5) for

${X x}_{i i}^{' ' k k + + 11} = = {X x}_{i i}^{k k} + + {v v}_{i i}^{k k + + 11}$

其中为位置更新公式（5）所计算的新位置，表示上一次迭代粒子的位置、粒子的位移；in is the new position calculated by the position update formula (5), Indicates the position of the particle in the last iteration, particle displacement;

步骤十一：判断i＝1,2,...,N，j＝1,2,...,l是否成立，若成立令 $X_{i, j, 2}^{k + 1} = \frac{X_{i, j, 2}^{k + 1}}{| | X_{i, j, 2}^{k + 1} | |} \cdot B_{\max},$ $X_{i, j, 1}^{k + 1} = X_{i, j, 1}^{' k + 1},$ 否则令 $X_{i, j, s}^{k + 1} = X_{i, j, s}^{' k + 1},$ s＝1,2；表示粒子实际更新后的位置；B_max表示斜率的最大值；Step Eleven: Judgment i=1,2,...,N, whether j=1,2,...,l is established, if it is established, order $x_{i, j, 2}^{k + 1} = \frac{x_{i, j, 2}^{k + 1}}{| | x_{i, j, 2}^{k + 1} | |} &Center Dot; B_{\max},$ $x_{i, j, 1}^{k + 1} = x_{i, j, 1}^{' k + 1},$ Otherwise order $x_{i, j, the s}^{k + 1} = x_{i, j, the s}^{' k + 1},$ s=1,2; Indicates the actual updated position of the particle; B _max indicates the maximum value of the slope;

步骤十二：计算适应度函数值 $F (X_{i}^{k + 1}) = Σ_{t = 1}^{m^{'}} {(X_{i, j^{'}, 1}^{k + 1} + X_{i, j^{'}, 2}^{k + 1} \cdot D_{x}^{t} - D_{y}^{t})}^{2} + M \cdot m,$ 若则令否则进入步骤十三；表示粒子的适应度函数值，表示粒子所经过的最好位置的适应度函数值；Step 12: Calculate the fitness function value $f (x_{i}^{k + 1}) = Σ_{t = 1}^{m^{'}} {(x_{i, j^{'}, 1}^{k + 1} + x_{i, j^{'}, 2}^{k + 1} &Center Dot; {D.}_{x}^{t} - {D.}_{the y}^{t})}^{2} + m &Center Dot; m,$ like order Otherwise, go to step 13; represent particles The fitness function value of represent particles The fitness function value of the best position passed;

步骤十三：设为中适应度值最小的位置，若则令否则进入步骤十四；Step Thirteen: Set for The position with the smallest fitness value in the middle, if order Otherwise, go to step fourteen;

步骤十四：判断最优位置P^g，在连续h_max次迭代中是否发生变化，若没有发生变化则进入步骤十五，否则令k＝k+1，判断k≤k_max是否成立，若成立转向步骤八，否则进入步骤十五；Step 14: Determine whether the optimal position P ^g has changed in consecutive h _max iterations. If no change occurs, go to step 15. Otherwise, let k=k+1, and judge whether k≤k _max is established. If it is established Turn to step eight, otherwise go to step fifteen;

步骤十五：得的P^g即为找到的各分段直线的最优截距和斜率数值。Step 15: The obtained P ^g is the optimal intercept and slope value of each segmented straight line found.

本发明的优点在于：The advantages of the present invention are:

1、本发明提出的一种自适应分段线性粒子群的海浪有效波高反演模型建模方法，利用粒子群算法对波高进行反演，不但可以完成传统算法的功能，达到传统算法的精度，还可以进行更精确的波高反演。1. A method for modeling the effective wave height inversion model of ocean waves proposed by the present invention uses the particle swarm algorithm to invert the wave height, which can not only complete the function of the traditional algorithm, but also achieve the accuracy of the traditional algorithm. A more accurate wave height inversion is also possible.

2、本发明提出的一种自适应分段线性粒子群的海浪有效波高反演模型建模方法，本发明方法的适用性广，灵活性高。2. The present invention proposes an adaptive piecewise linear particle swarm inversion model modeling method for effective wave height of ocean waves. The method of the present invention has wide applicability and high flexibility.

3、本发明提出的一种自适应分段线性粒子群的海浪有效波高反演模型建模方法，本发明的方法较已有分段波高反演算法，无需人为确定分段拟合位置，所以具有较高的自适应性，理论上可以自适应的找到最佳分段位置。3. The present invention proposes an adaptive piecewise linear particle swarm effective wave height inversion model modeling method. Compared with the existing piecewise wave height inversion algorithm, the method of the present invention does not need to manually determine the piecewise fitting position, so It has high adaptability, theoretically it can adaptively find the best segmentation position.

4、本发明提出的一种自适应分段线性粒子群的海浪有效波高反演模型建模方法，分段个数大于等于两段时，与传统建模方法相比具有更高的建模精度，利用本发明建立的反演模型比传统方法建立的反演模型具有更高的反演精度。4. The modeling method of an adaptive segmented linear particle swarm effective wave height inversion model proposed by the present invention has higher modeling accuracy than traditional modeling methods when the number of segments is greater than or equal to two segments , the inversion model established by the invention has higher inversion accuracy than the inversion model established by the traditional method.

附图说明 Description of drawings

图1：本发明提出的一种自适应分段线性粒子群的海浪有效波高反演模型建模方法的建模方法流程图；Fig. 1: the modeling method flowchart of the ocean wave effective wave height inversion model modeling method of a kind of self-adaptive piecewise linear particle swarm that the present invention proposes;

图2：原始数据的信噪比平方根和波高；Figure 2: SNR square root and wave height of raw data;

图3：各数据点与其他数据点中距离最小的数据点的距离曲线；Figure 3: The distance curve between each data point and the data point with the smallest distance among other data points;

图4：去野值后的数据点；Figure 4: Data points after outlier removal;

图5：去野值并稀疏化后的数据点；Figure 5: Data points after outlier removal and thinning;

图6：采用本发明提出的一种自适应分段线性粒子群的海浪有效波高反演模型建模方法，对去野值并稀疏化后的数据点分一段进行拟合所得的拟合效果图；Figure 6: Using an adaptive piecewise linear particle swarm inversion model modeling method for ocean wave significant wave height proposed by the present invention, the fitting effect diagram obtained by fitting the data points after removing outliers and thinning them into sections ;

图7：采用本发明提出的一种自适应分段线性粒子群的海浪有效波高反演模型建模方法，对去野值并稀疏化后的数据点分一段进行拟合，并对去野值后的数据进行反演，得到的反演效果图；Figure 7: Using an adaptive piecewise linear particle swarm inversion model modeling method for ocean wave significant wave height proposed by the present invention, the data points after removing outliers and thinning are divided into sections to fit, and the outliers are removed The final data is inverted, and the inversion effect diagram is obtained;

图8：采用本发明提出的一种自适应分段线性粒子群的海浪有效波高反演模型建模方法，对去野值并稀疏化后的数据点分一段进行拟合，并对去野值后的数据进行反演，得到的反演波高与实际波高的相关度曲线；Fig. 8: Using an adaptive piecewise linear particle swarm inversion model modeling method of ocean wave significant wave height proposed by the present invention, the data points after removing outliers and thinning are divided into sections to fit, and the outliers are removed After the data is inverted, the correlation curve between the inverted wave height and the actual wave height is obtained;

图9：采用本发明提出的一种自适应分段线性粒子群的海浪有效波高反演模型建模方法，对去野值并稀疏化后的数据点分两段进行拟合所得的拟合效果图；Figure 9: Using an adaptive piecewise linear particle swarm inversion model modeling method for ocean wave significant wave height proposed by the present invention, the fitting effect obtained by fitting the data points after removing outliers and thinning them into two segments picture;

图10：采用本发明提出的一种自适应分段线性粒子群的海浪有效波高反演模型建模方法，对去野值并稀疏化后的数据点分两段进行拟合，并对去野值后的数据进行反演，得到的反演效果图；Figure 10: Using an adaptive piecewise linear particle swarm inversion model modeling method for ocean wave significant wave height proposed by the present invention, the data points after removing outliers and sparseness are fitted in two sections, and the outliers are removed Invert the data after the value, and get the inversion effect diagram;

图11：采用本发明提出的一种自适应分段线性粒子群的海浪有效波高反演模型建模方法，对去野值并稀疏化后的数据点分两段进行拟合，并对去野值后的数据进行反演，得到的反演波高与实际波高的相关度曲线；Figure 11: Using an adaptive piecewise linear particle swarm inversion model modeling method for ocean wave significant wave height proposed by the present invention, the data points after removing outliers and thinning are divided into two sections to fit, and the outliers are removed The data after the value is inverted, and the correlation curve between the inverted wave height and the actual wave height is obtained;

图12：采用本发明提出的一种自适应分段线性粒子群的海浪有效波高反演模型建模方法，对去野值并稀疏化后的数据点分三段进行拟合所得的拟合效果图；Figure 12: Using an adaptive piecewise linear particle swarm inversion model modeling method for ocean wave significant wave height proposed by the present invention, the fitting effect obtained by fitting the data points after removing outliers and thinning them into three segments picture;

图13：采用本发明提出的一种自适应分段线性粒子群的海浪有效波高反演模型建模方法，对去野值并稀疏化后的数据点分三段进行拟合，并对去野值后的数据进行反演，得到的反演效果图；Figure 13: Using an adaptive piecewise linear particle swarm inversion model modeling method for ocean wave significant wave height proposed by the present invention, the data points after removing outliers and thinning are divided into three segments to fit, and the outliers are removed Invert the data after the value, and get the inversion effect diagram;

图14：采用本发明提出的一种自适应分段线性粒子群的海浪有效波高反演模型建模方法，对去野值并稀疏化后的数据点分三段进行拟合，并对去野值后的数据进行反演，得到的反演波高与实际波高的相关度曲线；Figure 14: Using an adaptive piecewise linear particle swarm inversion model modeling method for ocean wave significant wave height proposed by the present invention, the data points after removing outliers and thinning are divided into three segments to fit, and the outliers are removed The data after the value is inverted, and the correlation curve between the inverted wave height and the actual wave height is obtained;

图15：采用传统波高反演算法，对去野值并稀疏化后的数据点进行拟合所得的拟合效果图；Figure 15: Using the traditional wave height inversion algorithm, the fitting effect diagram obtained by fitting the data points after removing outliers and thinning them;

图16：采用传统波高反演算法，对去野值并稀疏化后的数据点进行拟合，并对去野值后的数据进行反演，得到的反演效果图；Figure 16: Using the traditional wave height inversion algorithm, fit the data points after the outliers are removed and thinned out, and invert the data after the outliers are removed, and the obtained inversion effect diagram;

图17：采用传统波高反演算法，对去野值并稀疏化后的数据点进行拟合，并对去野值后的数据进行反演，得到的反演波高与实际波高的相关度曲线。Figure 17: The traditional wave height inversion algorithm is used to fit the data points after the wild value is removed and thinned out, and the data after the wild value is removed is inverted, and the correlation curve between the inverted wave height and the actual wave height is obtained.

具体实施方式 Detailed ways

下面将结合附图对本发明进行详细说明：The present invention will be described in detail below in conjunction with accompanying drawing:

本发明提出一种自适应分段线性粒子群的海浪有效波高反演模型建模方法，如图1所示，具体包括以下几个步骤：The present invention proposes an adaptive segmented linear particle swarm effective wave height inversion model modeling method, as shown in Figure 1, which specifically includes the following steps:

步骤一：数据的去野值点处理：野值点是与大多数据点走势差别较大的一类数据点，它的形成与测量误差有直接关系，本发明中野值点的产生主要是由于波高与信噪比的测量都有可能出现误差所致。数据点的横坐标为信噪比平方根，纵坐标为有效波高，所有的数据点中的野值点组成的集合为野值集，数据点中除野值点以外的点组成的集合为真值集，去野值点的目的就是尽量找出野值集中的所有野值点，并把它们从数据点中剔除掉。对真值集进行研究发现，在真值集中任意一点的某一较小邻域内，都至少存在一个或多个真值点，相反研究野值集后发现，尽管野值集中的任意一野值点也存在某一邻域，使真值集或野值集中的点属于这一邻域，但野值集中的点相对于真值集中的点的邻域范围要大很多，根据这一特点，可以设一种方法，适当的选择邻域范围，判断某点的这一邻域内是否还有其他原数据点（包括野值点和真值点），若有，则说明该点属于真值集，保留该点，否则说明该点属于野值集，剔除该点。综上所述可以严格定义野值集和真值集如下：Step 1: processing of outliers of data: outliers are a type of data points that are quite different from most data points in trend, and its formation has a direct relationship with measurement error. The generation of outliers in the present invention is mainly due to wave height There may be errors in the measurement of the signal-to-noise ratio. The abscissa of the data point is the square root of the signal-to-noise ratio, and the ordinate is the effective wave height. The set of outlier points in all data points is the outlier set, and the set of points other than the outlier points in the data points is the true value. The purpose of removing outlier points is to find out all the outlier points in the outlier set and remove them from the data points. Research on the true value set found that there are at least one or more true value points in a small neighborhood of any point in the true value set. On the contrary, after studying the outlier set, it was found that although any outlier in the outlier set Points also have a certain neighborhood, so that the points in the true value set or the outlier set belong to this neighborhood, but the points in the outlier set have a much larger neighborhood range than the points in the true value set. According to this feature, A method can be set up to properly select the neighborhood range to determine whether there are other original data points (including wild value points and true value points) in the neighborhood of a certain point. If so, it means that the point belongs to the true value set , keep this point, otherwise it means that this point belongs to the outlier set, and remove this point. In summary, the outlier set and the truth set can be strictly defined as follows:

真值集：设原始数据点集为Y，设有任意数据点A，若对于数据点A的某一邻域ρ(A,r),r＞0，r表示邻域的半径，存在数据点B，使得B∈ρ(A,r)，则称点A属于真值集，Y中所有满足点A这一性质的点组成的集合称为真值集，设真值集为Z。Truth set: Let the original data point set be Y, set any data point A, If for a certain neighborhood ρ(A,r) of data point A, r>0, r represents the radius of the neighborhood, there is data point B, If B∈ρ(A,r), then point A is said to belong to the truth set, and the set of all points in Y satisfying the property of point A is called the truth set, and the truth set is Z.

野值集：设原始数据点集为Y，设有任意数据点A′，若对于点A′的某一邻域ρ(A′,r),r＞0，r表示邻域的半径，对于均有则称点A′属于野值集，Y中所有满足点A′这一性质的点组成的集合称为野值集，设野值集为U。Outlier value set: Let the original data point set be Y, set any data point A′, If for a neighborhood ρ(A′,r) of point A′, r>0, r represents the radius of the neighborhood, for have Then the point A' is said to belong to the outlier set, and the set of all points in Y satisfying the property of point A' is called the outlier set, and the outlier set is U.

真值集和野值集定义中的邻域半径r≥0相等，Z∩U＝Φ，并且Z∪U＝Y，真值集和野值集定义中的邻域半径始终相等。The neighborhood radii r≥0 in the definition of the truth set and the outlier set are equal, Z∩U=Φ, and Z∪U=Y, the neighborhood radii in the definition of the truth set and the outlier set are always equal.

野值剔除包括以下几步：Outlier removal includes the following steps:

第7步：集合B中的所有点组成剔除野值点之后的真值集。Step 7: All the points in set B form the true value set after removing the outlier points.

步骤二：数据的稀疏化处理：由于原始数据量一般比较大，对其所有的数据进行拟合，会消耗大量的运算时间，并且在数据采集过程中，会出现由于某些范围内的数据点比较容易观测到，而得到大量的这一范围的数据点，而某些范围的数据点比较难观测到，从而只得到较少的这一范围内的数据点，如本发明中，低波高和高波高不容易在真实的海洋环境下观测到，而中间高度的波高却比较容易出现，这样就会使采集到的数据点多处在中间波高的区域内，而低波高和高波高的区域内的数值较少，在对这样的数据进行拟合时，会导致中间波高对拟合曲线的走势影响比较大，而低波高和高波高的数据对拟合曲线的影响比较小，而实际中无论是低波高、高波高还是中间波高，对曲线拟合所起到的作用应该是等价的，并不是能因为数据采集中产生的数据疏密不同，而影响拟合结果，直接对原始数据进行数据拟合，并不能反映出海浪的真实性质，基于上述两点原因，出对原始数据进行去野值点处理外，还要对其进行稀疏化处理。Step 2: Data sparse processing: Since the amount of original data is generally relatively large, fitting all of its data will consume a lot of computing time, and in the process of data collection, there will be some data points in a certain range It is relatively easy to observe, and a large number of data points in this range are obtained, while data points in some ranges are relatively difficult to observe, so only a few data points in this range are obtained, as in the present invention, low wave height and High wave heights are not easy to observe in the real ocean environment, while wave heights at intermediate heights are more likely to appear, so that the collected data points are mostly in the area of intermediate wave heights, while the areas of low wave heights and high wave heights are more likely to appear. When fitting such data, the middle wave height will have a greater impact on the trend of the fitted curve, while the data of low and high wave heights will have a relatively small impact on the fitted curve. In practice, no matter Whether it is a low wave height, a high wave height or an intermediate wave height, the effect on curve fitting should be equivalent. It is not because the data density generated in the data collection is different, which will affect the fitting result, and the original data can be directly Data fitting cannot reflect the true nature of ocean waves. Based on the above two reasons, in addition to removing wild value points from the original data, it is also necessary to perform sparse processing.

对原始数据中过于密集的部分进行稀疏处理，而保留原始数据中数据点比较稀疏的部分，从而做到在公平的环境下对不同区域的数据进行拟合，这样做除做到了公平拟合外，还减少了数据点的个数，从而降低了拟合过程中的运算量，节省了运算时间。Thinning the overly dense part of the original data, while retaining the sparse part of the original data, so as to fit the data of different regions in a fair environment, in addition to achieving fair fitting , also reduces the number of data points, thereby reducing the amount of computation in the fitting process and saving computation time.

通过对稀疏化问题的研究发现，稀疏化处理与去野值点过程正好是一矛盾的过程，稀疏化处理是为了保留数据点中稀疏的部分，从过密集的数据中，剔除掉一部分点，因为数据点稀疏的部分理论上，是那些不易观测的到的数据部分，实际中野值点也是一类不太经常出现的数据点，他们的密度也很低，所以在稀疏化处理的过程中除保留了真实的数据点外，同时还留下了野值点；去野值点是为了保留数据点较密集部分的点，而剔除数据较稀疏的部分的点，因为理论上认为有用点，是一类比较集中、密集的数据点，而野值点是一类比较分散，稀疏的一类数据点，实际中数据的稀疏有可能是因为某些数据比较难获得而产生的，这样如果野值点剔除的不当，有可能会把稀疏的那一部分有用值的点也剔除掉了；可以看到，稀疏化处理与去野值点是一对矛盾的过程，适当的把握稀疏化处理与去野值点的程度，才能够做到既去掉了数据中的野值点，保留了数据中较少部分的有用值，同时稀疏了数据中过于密集的部分。Through the research on the sparsification problem, it is found that the sparsification process and the outlier point removal process are exactly a contradictory process. The sparsity process is to retain the sparse part of the data points and remove some points from the over-dense data. Because in theory, the part with sparse data points is the part of the data that is not easy to observe, the actual outlier value point is also a kind of data point that does not appear frequently, and their density is also very low, so in the process of sparse processing, except In addition to retaining the real data points, outlier points are also left at the same time; removing outlier points is to retain the points in the denser part of the data points, and remove the points in the sparser part of the data, because theoretically it is considered useful points, is A class of relatively concentrated and dense data points, while outlier points are a kind of scattered and sparse data points. In practice, the sparseness of data may be caused by the difficulty of obtaining some data. In this way, if the outlier Improper point elimination may remove the sparse points with useful values; it can be seen that sparse processing and wild point removal are a pair of contradictory processes, and proper grasp of sparse processing and wild point removal The extent of the value points can remove the outlier points in the data, retain the useful values of a small part of the data, and at the same time sparse the too dense part of the data.

正是由于稀疏化处理与去野值点是一矛盾的过程，所以将某些去野值点的方法的思想逆向进行考虑，便可以达到稀疏化的目的。为便于说明首先定义密集集和稀疏集为：It is precisely because the sparsification process and the removal of outliers are a contradictory process, so the purpose of sparsification can be achieved by reversely considering the ideas of some methods of removing outliers. For the sake of illustration, first define the dense set and sparse set as:

密集集：设原始数据点集为Y，设存在任意点C，若对于点C的某一邻域ρ(C,r′),r′＞0，使得D∈ρ(A,r′)，则称点C属于密集集，r′表示邻域判断半径，Y中所有满足点C这一性质的点组成的集合称为密集集，设密集集为M。Dense set: Let the original data point set be Y, let there be any point C, If for a certain neighborhood of point C ρ(C,r′), r′>0, If D ∈ ρ(A,r′), then point C is said to belong to a dense set, r′ represents the neighborhood judgment radius, and the set of all points satisfying the property of point C in Y is called a dense set. Let the dense set be M.

稀疏集：设原始数据点集为Y，设存在任意点C′，若对于点C′的某一邻域ρ(C′,r′),r′＞0，对于均有则称点C′属于稀疏集，Y中所有满足点C′这一性质的点组成的集合称为稀疏集，设稀疏集为S。Sparse set: Let the original data point set be Y, let there be any point C′, If for a certain neighborhood ρ(C',r') of point C', r'>0, for have Then the point C' is said to belong to a sparse set, and the set of all points in Y satisfying the property of point C' is called a sparse set, and the sparse set is S.

可以看到当密集集和稀疏集定义中的邻域半径r′≥0且相等时，M∩S＝Φ，并且M∪S＝Y，密集集和稀疏集定义中的半径r′始终相等。It can be seen that when the neighborhood radius r'≥0 and equal in the definition of dense set and sparse set, M∩S=Φ, and M∪S=Y, the radius r' in the definition of dense set and sparse set is always equal.

根据稀疏集合野值集的定义，当r′＞r时，有即稀疏集中的点，都是野值点，这显然是不合理的，所以应取r′≤r，此时即稀疏集中包含野值集，这是符合实际的，但问题在于，稀疏集中除野值外还有真值点，需要将稀疏集中的野值点和真值点区分开才能将野值点剔除掉。野值集、真值集、密集集和稀疏集之间存在交叉关系为：According to the definition of sparse set outlier set, when r′>r, there is That is, the points in the sparse set are all outlier points, which is obviously unreasonable, so r′≤r should be taken, at this time That is, the sparse set contains the outlier set, which is in line with the reality, but the problem is that there are true value points in the sparse set besides the outlier, and it is necessary to distinguish the outlier points from the true value points in the sparse set to remove the outlier points Lose. There is a cross relationship between the wild value set, the true value set, the dense set and the sparse set as follows:

设Z_s＝Z∩S，当r′≤r时，有U∩Z_s＝Φ，并且U∪Z_s＝S。其中，Z_s表示真值集与稀疏集的交集。因此当r′≤r时，由于U∪Z_S＝S，所以稀疏集仅由真值集中稀疏点集Z_S和野值集组成，并且U∩Z_s＝Φ，所以当r′≤r时，并适当的选择r′，r的大小，便可以将实际中稀疏集中的野值和真值区分开，从而将稀疏集中的野值点剔除掉，并保留真值点。Let Z _s =Z∩S, when r′≤r, we have U∩Z _s =Φ, and U∪Z _s =S. Among them, Z _s represents the intersection of the truth set and the sparse set. Therefore, when r′≤r, since U∪Z _S =S, the sparse set is only composed of the sparse point set Z _S in the true value set and the wild value set, and U∩Z _s =Φ, so when r′≤r, And by properly selecting the size of r′ and r, the outliers in the sparse set can be distinguished from the true values in practice, so that the outliers in the sparse set can be eliminated and the true points can be retained.

稀疏化方法：既然可以将稀疏集和密集集用定义加以区分，在进行稀疏化处理是，只需要将密集集中的点，按照应定的法则进行稀疏化，便能达到稀疏密集数据，保留稀疏数据的目的，稀疏化处理的具体步骤为：Thinning method: Since sparse sets and dense sets can be distinguished by definition, when performing sparse processing, only the densely concentrated points need to be thinned according to the prescribed rules to achieve sparse dense data and retain sparse data. The purpose of the data, the specific steps of sparse processing are:

设固定邻域判断半径为r′，若集合Y中某一点A，根据定义判断有A∈S，即点A属于稀疏集，便保留点A，否则A∈M，点A属于密集集，于是点A的邻域ρ(A,r′)中，会包含集合Y中一个或多个数据点，显然这些数据点的邻域半径为r′的邻域中至少会包含点A，所以这些点也属于密集集，所以此时只要将邻域ρ(A,r′)中的数据点去掉一部分，保留一部分便能到达，稀疏密集点的目的，本发明中保留点A，剔除掉邻域ρ(A,r′)中所有除点A外的点，这样做的好处是，不会重复计算，并可根据设置邻域判断半径为r′的大小，确定剔除点的多少，容易看到，邻域判断半径为r′越大，剔除密集点的数量越多，反之剔除密集点的数量则越少。Let the judgment radius of the fixed neighborhood be r′, if a point A in the set Y is judged to have A∈S according to the definition, that is, the point A belongs to the sparse set, then the point A is kept, otherwise A∈M, the point A belongs to the dense set, then The neighborhood ρ(A,r′) of point A will contain one or more data points in the set Y. Obviously, the neighborhood of these data points with a neighborhood radius of r′ will contain at least point A, so these points It also belongs to the dense set, so at this time, as long as a part of the data points in the neighborhood ρ(A,r′) is removed, and a part is kept, it can be reached. The purpose of sparse dense points is to keep point A in the present invention and remove the neighborhood ρ All points in (A,r′) except point A, the advantage of doing this is that it will not be repeatedly calculated, and the size of the radius r′ can be judged according to the set neighborhood, and the number of eliminated points can be determined, which is easy to see. The larger the neighborhood judgment radius is r', the more dense points will be eliminated, and vice versa.

对数据进行稀疏化，再进拟合前需要对数据过于密集的区域进行数据稀疏化出，Sparse the data, and before fitting, it is necessary to sparse the data in the area where the data is too dense.

第1步：将步骤一中得到的集合B中的数据点，按照数据点的横坐标由小到大进行排序，得到排序后的数据点集{C^k″}k″＝1,2,3,...,n，其中n为集合B中所有数据点的个数，角标k″表示数据点按照横坐标大小由小到大依次排列，设稀疏化处理时邻域判断半径为r′，令k″＝1，t＝1，m′＝n，{D^k"}＝{C^k"}k″＝1,2,3,...,m′；t表示向右判断参数，由于稀疏化不需要向左进行判断，所以仅用t来表示，{D^k″}用于表示将去野值后的数据又进行了稀疏化处理的数据点，m′为变量，用于表示每次提出野值后，集合{D^k"}中所剩下的数据点的个数，集合{D^k"}和集合{C^k″}最终表示的含义不同，m′是个变量，而n为常量，在第2步可以看到，当剔除一个点时便令m′＝m′-1。Step 1: sort the data points in set B obtained in step 1 according to the abscissa of the data points from small to large, and obtain the sorted data point set {C ^k ″}k″=1,2,3 ,...,n, where n is the number of all data points in set B, subscript k″ indicates that the data points are arranged in order according to the size of the abscissa from small to large, and the neighborhood judgment radius is r′ during sparse processing , set k″=1, t=1, m’=n, {D ^k "}={C ^k "}k"=1,2,3,...,m'; t represents the rightward judgment parameter, Since the sparseness does not need to be judged to the left, it is only represented by t, {D ^k ″} is used to represent the data points that have undergone sparse processing of the data after the wild value is removed, and m′ is a variable used to represent After each outlier is proposed, the number of remaining data points in the set {D ^k "}, the final meaning of the set {D ^k "} and the set {C ^k ″} is different, m′ is a variable, and n As a constant, it can be seen in the second step that m'=m'-1 is set when a point is eliminated.

第2步：判断k″+t＜m′是否成立，若不成立进入第4步，若成立判断D^k″^+t-D^k"＜r′是否成立，若不成立进入第4步，若成立判断是否成立，若成立，剔除点D^k"^+t，令m′＝m′-1，进入第3步，若不成立进入第4步；Step 2: Judging whether k″+t<m′ is true, if not true, go to step 4, if true, judge whether D ^k ″ ^+t -D ^k "<r′ is true, if not true, go to step 4, if true, judge Whether it is true, if it is true, remove the point D ^k " ^{+ t} , let m'=m'-1, enter the third step, if it is not true, enter the fourth step;

第4步：将集合{D^k"}中剩余的数据点，按照原横坐标大小由小到大排列顺序依次重新记录到{D^k″}k″＝1,2,3,...,m′中，令k″＝k″+1，判断k″≤m′是否成立，若不成立进入第5步，若成立令t＝1，返回到第2步；Step 4: Re-record the remaining data points in the set {D ^k "} to {D ^k ″}k″=1,2,3,..., In m', let k″=k″+1, judge whether k″≤m′ is established, if not established, enter step 5, if established, set t=1, return to step 2;

第5步：集合{D^k″}k″＝1,2,3,...,m′中的点便是将去野值后的数据又进行了稀疏化处理的数据点。Step 5: The points in the set {D ^k ″}k″=1, 2, 3, .

步骤三：设置粒子的编码方式并初始化粒子群各参数：直线方程由截距式表示，如y＝A+B·x，则每一条直线可由A，B确定，则每个粒子由所有确定直线的截距A和斜率B构成，粒子群算法粒子的编码方式为：Step 3: Set the encoding method of the particles and initialize the parameters of the particle swarm: the straight line equation is expressed by the intercept formula, such as y=A+B x, each straight line can be determined by A, B, and each particle is determined by all the straight lines The intercept A and slope B are composed of the particle swarm algorithm particle encoding method is:

其中i＝1,2,...,N，N≥2为粒子个数，即群体大小；j＝1,2,...,l，l≥1表示分段数，即参与拟合的直线条数；k表示粒子群的迭代次数；分别表示第k次迭代中第i个粒子第j条直线的截距、斜率。表示第i个粒子的位置。Among them, i=1,2,...,N, N≥2 is the number of particles, that is, the size of the group; j=1,2,...,l, l≥1 represents the number of segments, that is, the number of particles participating in the fitting The number of straight lines; k represents the number of iterations of the particle swarm; Respectively represent the intercept and slope of the j-th straight line of the i-th particle in the k-th iteration. Indicates the position of the i-th particle.

粒子位置的初始化：由于波高随着信噪比的平方根的增加承递增趋势，所以当参与拟合的直线大于等于两条时，处在低波高的直线的斜率，应小于处在高波段的直线的斜率，所以直线的斜率应随信噪比平方根的递增，在一定范围内递增变化，由于本发明表示直线的方式为截距式，所以直线方程中的截距应随斜率的递增，在一定范围内递减变化，根据上述分析，为减少不必要的运算，提升运算效率，初始化直线的截距和斜率为：Initialization of particle position: Since the wave height increases with the increase of the square root of the signal-to-noise ratio, when there are two or more straight lines participating in the fitting, the slope of the straight line at the low wave height should be smaller than the straight line at the high band The slope of the straight line, so the slope of the straight line should increase with the increase of the square root of the signal-to-noise ratio within a certain range. Since the method of expressing the straight line in the present invention is the intercept formula, the intercept in the straight line equation should increase with the increase of the slope within a certain range. Decreasing changes within the range, according to the above analysis, in order to reduce unnecessary calculations and improve calculation efficiency, the intercept and slope of the initialized line are:

$\{\begin{matrix} {X x}_{i i,, j j,, 11}^{11} = = {A A}_{max max} - - \frac{((rand rand + + j j - - 11)) \cdot \cdot (({A A}_{max max} - - {A A}_{min min}))}{l l} \\ {X x}_{i i,, j j,, 22}^{11} = = {B B}_{min min} + + \frac{((rand rand + + j j - - 11)) \cdot &Center Dot; (({B B}_{max max - -} {B B}_{min min}))}{l l} \end{matrix} - - - - - - ((33))$

其中rand为0到1之间的随机数；A_max和A_min分别表示截距的最大和最小值，满足min(Hs)≤A_max≤max(Hs)，min(Hs)和max(Hs)分别为波高数据中波高的最大值和最小值，A_min＜A_max；B_max和B_min分别表示斜率的最大值和最小值，满足0≤B_min≤B_max；i＝1,2,...,N，N≥2为粒子个数，即群体大小；j＝1,2,...,l，l≥1表示分段数，即参与拟合的直线条数；和分别表示第1次迭代（即初始化）中第i个粒子第j条直线的截距和斜率。Where rand is a random number between 0 and 1; A _max and A _min represent the maximum and minimum values of the intercept respectively, satisfying min(Hs)≤A _max ≤max(Hs), min(Hs) and max(Hs) are the maximum and minimum values of the wave height in the wave height data, A _min < A _max ; B _max and B _min respectively represent the maximum and minimum values of the slope, satisfying 0≤B _min ≤B _max ; i=1,2,. .., N, N≥2 is the number of particles, that is, the group size; j=1,2,...,l, l≥1 represents the number of segments, that is, the number of straight lines involved in fitting; and Respectively represent the intercept and slope of the i-th particle j-th line in the first iteration (that is, initialization).

粒子位移的初始化：粒子的移动速度应限定在一定的范围内，所以粒子速度初始化为：Initialization of particle displacement: The moving speed of particles should be limited within a certain range, so the particle speed is initialized as:

$\{\begin{matrix} {v v}_{i i,, j j,, 11}^{11} = = rand rand \cdot &Center Dot; {v v}_{max max} \\ {v v}_{i i,, j j,, 22}^{11} = = rand rand \cdot &Center Dot; {v v}_{max max} \end{matrix} - - - - - - ((44))$

其中rand为0到1之间的随机数；v_max＞0为粒子位移的最大值；分别表示第1次迭代（即初始化）中第i个粒子第j条直线的截距位移项和斜率位移项。Where rand is a random number between 0 and 1; v _max > 0 is the maximum value of particle displacement; Respectively represent the intercept displacement term and the slope displacement term of the i-th particle j-th straight line in the first iteration (that is, initialization).

设种群数为N；第一次迭代（即初始化）第i个粒子为i＝1,2,...,N，j＝1,2,...,l；自身学习因子为c₁≥0，全局学习因子为c₂≥0；惯性权重上限和下限分别为ω_max和ω_min，0≤ω_min≤ω_max≤1；分段个数为l，l≥1；最大迭代次数k_max满足k_max≥2；种群数为N；零次项系数（截距）最大值和最小值分别为A_max和A_min，且A_max≥A_min，一次项系数（斜率）最大值和最小值分别为B_max和B_min，B_max≥B_min≥0；位移最大步长v_max满足v_max＞0；迭代停止阀值h_max为h_max＝l·E，其中E≥1为正整数，用于确定随分段个数的增加，循环跳出的阀值随之增大的速度。Let the population number be N; the i-th particle of the first iteration (that is, initialization) is i=1,2,...,N, j=1,2,...,l; the self-learning factor is c ₁ ≥ 0, the global learning factor is c ₂ ≥ 0; the upper limit and lower limit of the inertia weight are ω _max and ω _min , 0≤ω _min ≤ω _max ≤1; the number of segments is l, l≥1; the maximum number of iterations k _max satisfies k _max ≥2; the number of populations is N; the zero-order term coefficient (intercept) The maximum and minimum values are A _max and A _min respectively, and A _max ≥ A _min , the maximum and minimum values of the first-order coefficient (slope) are B _max and B _min respectively, and B _max ≥ B _min ≥ 0; the maximum displacement step The length v _max satisfies that v _max >0; the iteration stop threshold h _max is h _max = l · E, where E≥1 is a positive integer, which is used to determine that as the number of segments increases, the threshold for loop jumping increases accordingly speed.

$\{\begin{matrix} {X x}_{i i,, j j,, 11}^{11} = = {A A}_{max max} - - \frac{((rand rand + + j j - - 11)) \cdot &Center Dot; (({A A}_{max max} - - {A A}_{min min}))}{l l} \\ {X x}_{i i,, j j,, 22}^{11} = = {B B}_{min min} + + \frac{((rand rand + + j j - - 11)) \cdot &Center Dot; (({B B}_{max max - -} {B B}_{min min}))}{l l} \end{matrix}$

其中rand为0到1之间的随机数；A_max和A_min分别表示截距的最大和最小值，满足min(Hs)≤A_max≤max(Hs)，min(Hs)和max(Hs)分别中波高的最大值和最小值，A_min＜A_max；B_max和B_min分别表示斜率的最大值和最小值，满足0≤B_min≤B_max；i＝1,2,...,N，N≥2为粒子个数，即群体大小；j＝1,2,...,l，l≥1表示分段数，即参与拟合的直线条数；和分别表示第1次迭代（即初始化）中第i个粒子第j条直线的截距和斜率。Where rand is a random number between 0 and 1; A _max and A _min represent the maximum and minimum values of the intercept respectively, satisfying min(Hs)≤A _max ≤max(Hs), min(Hs) and max(Hs) The maximum and minimum values of the wave height, A _min < A _max ; B _max and B _min respectively represent the maximum and minimum values of the slope, satisfying 0≤B _min ≤B _max ; i=1,2,..., N, N≥2 is the number of particles, that is, the group size; j=1,2,...,l, l≥1 represents the number of segments, that is, the number of straight lines involved in fitting; and Respectively represent the intercept and slope of the i-th particle j-th line in the first iteration (that is, initialization).

$\{\begin{matrix} {v v}_{i i}^{k k + + 11} = = ω ω \cdot &Center Dot; {v v}_{i i}^{k k} + + {c c}_{11} {r r}_{11}^{k k} \cdot &Center Dot; (({P P}_{i i}^{b b} - - {X x}_{i i}^{k k})) + + {c c}_{22} {r r}_{22}^{k k} \cdot &Center Dot; (({P P}^{g g} - - {X x}_{i i}^{k k})) \\ {X x}_{i i}^{k k + + 11} = = {X x}_{i i}^{k k} + + {v v}_{i i}^{k k + + 11} \end{matrix} - - - - - - ((55))$

其中表示第i个粒子的位移；表示第i个粒子的位置，i＝1,2,...,N，N≥2为粒子个数，即群体大小，j＝1,2,...,l，l≥1表示分段数，即参与拟合的直线条数，k表示粒子群的迭代次数；为惯性权重，0≤ω_min≤ω_max≤1为惯性权重的最大最小值，ω_max和ω_min分别为惯性权重上限和下限，k_max表示最大迭代次数；u≥0为单调控制量；c₁≥0为自身学习因子；c₂≥0为全局学习因子；为[0,1]区间的随机数；为粒子自身寻到的最优值；P^g为种群寻到的最优值；in Indicates the displacement of the i-th particle; Indicates the position of the i-th particle, i=1,2,...,N, N≥2 is the number of particles, that is, the group size, j=1,2,...,l, l≥1 represents the segment The number is the number of straight lines participating in the fitting, and k represents the number of iterations of the particle swarm; is the inertia weight, 0 ≤ ω _min ≤ ω _max ≤ 1 is the maximum and minimum value of the inertia weight, ω _max and ω _min are the upper limit and lower limit of the inertia weight respectively, k _max represents the maximum number of iterations; u ≥ 0 is the monotonic control amount; c ₁ ≥ 0 is the self-learning factor; c ₂ ≥ 0 is the global learning factor; is a random number in the interval [0,1]; is the optimal value found by the particle itself; P ^g is the optimal value found by the population;

粒子群方法适应度函数的设计：为达到与拟合曲线函数值与波高真值误差最小的目的，设计适应度函数如下：The design of the fitness function of the particle swarm method: in order to achieve the purpose of minimizing the error between the function value of the fitting curve and the true value of the wave height, the fitness function is designed as follows:

其中t＝1,2,...,m′，分别为数据点对应的信噪比平方根和波高，D^t表示由信噪比平方根和波高值组成的向量。m′为数据去野并稀疏化后的个数；分别为直线的截距和斜率，j′＝1,2,...，l，j′取值方法如下，设相邻直线间的交点依次为O＝{O^j″}，分别表示交点O^j″的横纵坐标，j″＝1,2,...,l-1，判断若则令j′＝1，若(j＝1,2,...,l-2)，则令j′＝j″+1，若则令j′＝l；M＞0为惩罚因子，m为满足限制条件的次数，设初始化时m＝0，在各次迭代过程中m的取值限制条件满足：in t=1,2,...,m', are the square root of the signal-to-noise ratio and the wave height corresponding to the data points, respectively, and D ^t represents a vector composed of the square root of the signal-to-noise ratio and the wave height. m' is the number of data after dewilding and thinning; Respectively be the intercept and the slope of the straight line, j'=1,2,..., l, the value method of j' is as follows, the intersection point between the adjacent straight lines is set as O={O ^j ″} successively, Represent the horizontal and vertical coordinates of the intersection point O ^j ″ respectively, j″=1, 2,..., l-1, judge if Then let j'=1, if (j=1,2,...,l-2), then let j′=j″+1, if Then let j′=l; M>0 is the penalty factor, m is the number of times to meet the restriction conditions, let m=0 at the time of initialization, and the value restriction conditions of m in each iteration process are satisfied:

（1）相邻直线，是否平行，若某次迭代中有m₁个相邻直线平行，则令m＝m+m₁；(1) Adjacent straight lines, whether they are parallel, if m ₁ adjacent straight lines are parallel in a certain iteration, set m=m+m ₁ ;

（2）计算相邻直线的交点，判断相邻的交点中，排在前面的（即O^j″的角标j″值较小的）交点的横坐标是否大于排在后面的（即O^j″的角标j″值较大的）交点的横坐标，若某次迭代中有m₂次排在前面的交点的横坐标大于排在后面的交点的横坐标，则令m＝m+m₂；(2) Calculate the intersection points of adjacent straight lines, and judge whether the abscissa of the intersection points ranked in the front (that is, the value of the subscript j" of O ^j ″ is smaller) is greater than that of the adjacent intersection points (that is, O ^j ″ The abscissa of the intersection point with the larger value of the subscript j of "", if there are m ₂ times in a certain iteration, the abscissa of the intersection point in the front is greater than the abscissa of the intersection point in the back, then let m=m+m ₂ ;

（3）判断交点是否处在数据点所在的横坐标范围内，若某次迭代中有m₃个交点不在数据点所在的横坐标范围内，则令m＝m+m₃；(3) Judging whether the intersection point is within the range of the abscissa where the data point is located, if there are m ₃ intersection points in a certain iteration that are not within the range of the abscissa where the data point is located, then set m=m+m ₃ ;

（4）判断相邻直线中前一条直线（设j表示前一条直线j＝1,2,...,l-1，则j+1就表示后一条直线）的斜率是否大于后一条直线的斜率，若某次迭代中有m₄各相邻直线的前一条直线的斜率大于后一条直线的斜率，则令m＝m+m₄。(4) Judging whether the slope of the previous straight line among the adjacent straight lines (let j means the previous straight line j=1, 2,..., l-1, then j+1 means the next straight line) is greater than that of the latter straight line Slope, if there are m ₄ adjacent straight lines in a certain iteration, the slope of the previous straight line is greater than the slope of the next straight line, then set m=m+m ₄ .

$F f (({X x}_{i i}^{k k})) = = {Σ Σ}_{t t = = 11}^{{m m}^{' '}} {(({X x}_{i i,, {j j}^{' '},, 11}^{k k} + + {X x}_{i i,, {j j}^{' '},, 22}^{k k} \cdot &Center Dot; {D D.}_{x x}^{t t} - - {D D.}_{y the y}^{t t}))}^{22} + + M m \cdot \cdot m m$

${v v}_{i i}^{' ' k k + + 11} = = ω ω \cdot &Center Dot; {v v}_{i i}^{k k} + + {c c}_{11} {r r}_{11}^{k k} \cdot \cdot (({P P}_{i i}^{b b} - - {X x}_{i i}^{k k})) + + {c c}_{22} {r r}_{22}^{k k} \cdot &Center Dot; (({P P}^{g g} - - {X x}_{i i}^{k k}))$

步骤九：判断是否成立，若成立令否则令其中为根据位移更新公式（5）计算的位移，v_max为位移长度最大值。i＝1,2,...,N；j＝1,2,...,l；s分别取值1或2，s＝1、s＝2分别表示直线的截距、斜率；粒子表示实际的位移；Step Nine: Judgment Whether established, if established order Otherwise order in is the displacement calculated according to the displacement update formula (5), and v _max is the maximum value of the displacement length. i=1,2,...,N; j=1,2,...,l; s takes the value of 1 or 2 respectively, and s=1 and s=2 represent the intercept and slope of the straight line respectively; The particles represent the actual displacement;

步骤十一：判断i＝1,2,...,N，j＝1,2,...,l是否成立，若成立令 $X_{i, j, 2}^{k + 1} = \frac{X_{i, j, 2}^{k + 1}}{| | X_{i, j, 2}^{k + 1} | |} \cdot B_{\max},$ $X_{i, j, 1}^{k + 1} = X_{i, j, 1}^{' k + 1},$ 否则令 $X_{i, j, s}^{k + 1} = X_{i, j, s}^{' k + 1},$ s＝1,2；表示粒子实际更新后的位置；B_max表示斜率的最大值。Step Eleven: Judgment i=1,2,...,N, whether j=1,2,...,l is established, if it is established, order $x_{i, j, 2}^{k + 1} = \frac{x_{i, j, 2}^{k + 1}}{| | x_{i, j, 2}^{k + 1} | |} &Center Dot; B_{\max},$ $x_{i, j, 1}^{k + 1} = x_{i, j, 1}^{' k + 1},$ Otherwise order $x_{i, j, the s}^{k + 1} = x_{i, j, the s}^{' k + 1},$ s=1,2; Indicates the actual updated position of the particle; B _max indicates the maximum value of the slope.

步骤十五：得的P^g即为找到的各分段直线的最优截距和斜率数值。由于P^g是一个2*l的向量，l为分段的条数，每条直线有两个参数截距和斜率，所以可以同时表示所有直线。Step 15: The obtained P ^g is the optimal intercept and slope value of each segmented straight line found. Since P ^g is a vector of 2*l, l is the number of segments, and each straight line has two parameters intercept and slope, so all straight lines can be represented at the same time.

利用2009年10月在福建平潭进行科研实验获取的雷达图像信噪比平方根与对应的海浪有效波高真值数据（简称现场实测数据），数据总数为1386对信噪比平方根和波高，如图2所示，在选取去野阀值r之前，首先计算各数据点与其他数据点中距离最小的数据点距离曲线，如图3所示，可以看到在距离大小为0.1225时，数据的最小距离有一个分层现象，说明最小距离大于0.1225的数据点与其他数据点严重脱离，为野值点，应被剔除，所以选取去野阀值r＝0.1225，在r＝0.1225时去野效果如图4所示；为使数据点不致过于稀疏，取稀疏数据阀值r′＝0.0526，如图3所示，在r′＝0.0526时，稀疏数据效果如图5所示；粒子群其他参数如表1所示Using the square root of the signal-to-noise ratio of the radar image and the corresponding real-value data of the effective wave height (referred to as on-site measured data) obtained from scientific research experiments in Pingtan, Fujian in October 2009, the total number of data is 1386 pairs of the square root of the signal-to-noise ratio and wave height, as shown in the figure As shown in 2, before selecting the de-wilding threshold r, first calculate the distance curve of the data point with the smallest distance between each data point and other data points, as shown in Figure 3, it can be seen that when the distance is 0.1225, the minimum distance of the data point There is a layering phenomenon in the distance, indicating that the data points with the minimum distance greater than 0.1225 are seriously separated from other data points, which are outliers and should be eliminated. Therefore, the de-wilding threshold r=0.1225 is selected. When r=0.1225, the de-wilding effect is as follows As shown in Figure 4; in order to prevent the data points from being too sparse, take the sparse data threshold r'=0.0526, as shown in Figure 3, when r'=0.0526, the effect of sparse data is shown in Figure 5; other parameters of the particle swarm are as follows Table 1

表1参数列表Table 1 parameter list

采用本发明提出的一种自适应分段线性粒子群的海浪有效波高反演模型建模方法，对去野值并稀疏化后的数据进行拟合，当分段数为一段时，得到结果如表2所示Adopt a kind of self-adaptive piecewise linear particle swarm inversion model modeling method of sea wave significant wave height proposed by the present invention, carry out fitting to the data after removing outliers and thinning, when the number of sections is one section, the results obtained are shown in Table 2 shown

表2拟合结果Table 2 Fitting results

表2中A₁为拟合得到的第一条直线的最优截距；B₁为拟合得到的第一条直线的最优斜率；相关系数和标准方差为根据去野值后的数据的信噪比进行反演得到的波高与实际波高的相关系数和标准方差，拟合效果如图6所示，反演效果如图7所示，相关性如图8所示；In Table 2, A1 is the optimal intercept of the _first straight line obtained by fitting; B1 is the optimal slope of the _first straight line obtained by fitting; The correlation coefficient and standard deviation between the wave height obtained by SNR inversion and the actual wave height, the fitting effect is shown in Figure 6, the inversion effect is shown in Figure 7, and the correlation is shown in Figure 8;

当分两段进行拟合时得到结果如表3所示When fitting in two stages, the results are shown in Table 3

表3拟合结果Table 3 Fitting results

表3中A₁、A₂分别为拟合得到的第一条、第二条直线的最优截距；B₁、B₂分别为拟合得到的第一条、第二条直线的最优斜率；相关系数和标准方差为根据去野值后的数据的信噪比进行反演得到的波高与实际波高的相关系数和标准方差，拟合效果如图9所示，反演效果如图10所示，相关性如图11所示；In Table 3, A ₁ and A ₂ are the optimal intercepts of the first and second straight lines obtained by fitting, respectively; B ₁ and B ₂ are the optimal intercepts of the first and second straight lines obtained by fitting, respectively. The slope; the correlation coefficient and standard deviation are the correlation coefficient and standard deviation between the wave height and the actual wave height obtained by inversion according to the signal-to-noise ratio of the data after the outlier removal, the fitting effect is shown in Figure 9, and the inversion effect is shown in Figure 10 As shown, the correlation is shown in Figure 11;

当分三段进行拟合时得到结果如表4所示When fitting in three sections, the results are shown in Table 4

表4拟合结果Table 4 Fitting results

表4中A₁、A₂、A₃分别为拟合得到的第一条、第二条和第三条直线的最优截距；B₁、B₂、B₃分别为拟合得到的第一条、第二条和第三条直线的最优斜率；相关系数和标准方差为根据去野值后的数据的信噪比进行反演得到的波高与实际波高的相关系数和标准方差，拟合效果如图12所示，反演效果如图13所示，相关性如图14所示；In Table 4, A ₁ , A ₂ , and A ₃ are the optimal intercepts of the first, second, and third straight lines obtained by fitting, respectively; B ₁ , B ₂ , and B ₃ are the optimal intercepts of the first straight line The optimal slopes of the first, second and third straight lines; the correlation coefficient and standard deviation are the correlation coefficient and standard deviation between the wave height and the actual wave height obtained by inversion according to the signal-to-noise ratio of the data after the outlier removal, and the approximate The combination effect is shown in Figure 12, the inversion effect is shown in Figure 13, and the correlation is shown in Figure 14;

采用传统最小二乘算法对去野并稀疏化后的数据进行拟合，得到拟合结果如表5所示The traditional least squares algorithm is used to fit the data after dewilding and sparseness, and the fitting results are shown in Table 5

表5拟合结果Table 5 Fitting results

表5中A为最小二乘拟合得到的截距，B为最小二乘拟合得到的斜率，相关系数和标准方差为根据去野值后的数据的信噪比进行反演得到的波高与实际波高的相关系数和标准方差。拟合效果如图15所示，反演效果如图16所示，相关性如图17所示；In Table 5, A is the intercept obtained by least squares fitting, B is the slope obtained by least squares fitting, and the correlation coefficient and standard deviation are the wave height and Correlation coefficient and standard deviation of actual wave heights. The fitting effect is shown in Figure 15, the inversion effect is shown in Figure 16, and the correlation is shown in Figure 17;

比较本专利设计的算法分一段进行拟合，与传统最小二乘拟合的反演结果，有本专利设计算法得到的相关系数，和标准方差与最小二乘反演得到的相关系数，和标准方差是相等的，可见本专利设计的算法可以完成传统算法所做的分一段进行拟合的任务，并可达到传统算法的反演精度，比较本专利设计的算法分两段进行拟合，与传统最小二乘拟合的反演结果，可以看到相关度较传统算法提高3.36%，反演误差降低了19.99%，表明分两段拟合要比传统算法和分一段拟合具有更高的反演精度。比较分三段与分两段的反演效果，可见分三段的相关系数比分两段反演得到的相关系数仅提高0.03%，反演误差仅降低了0.06%，表明分三段已经不能对反演精度有太高的提高，但计算量要比分两段的计算量大的多，所以在一定的精度要求范围内，对数据分两段进行拟合就能达到较理想的反演精度。Comparing the algorithm designed by this patent for fitting in one segment, and the inversion results of the traditional least squares fitting, there are the correlation coefficients obtained by the algorithm designed by this patent, and the correlation coefficients obtained by the standard deviation and least squares inversion, and the standard The variances are equal. It can be seen that the algorithm designed by this patent can complete the task of fitting in one segment as done by the traditional algorithm, and can achieve the inversion accuracy of the traditional algorithm. Compared with the algorithm designed by this patent, it can be fitted in two segments. In the inversion results of the traditional least squares fitting, it can be seen that the correlation is increased by 3.36% compared with the traditional algorithm, and the inversion error is reduced by 19.99%, indicating that the two-stage fitting has a higher accuracy than the traditional algorithm and one-stage fitting. Inversion accuracy. Comparing the inversion effects of three-stage and two-stage inversion, it can be seen that the correlation coefficient of three-stage inversion is only 0.03% higher than the correlation coefficient obtained by two-stage inversion, and the inversion error is only reduced by 0.06%. The inversion accuracy has been greatly improved, but the amount of calculation is much larger than that of the two sections. Therefore, within a certain range of accuracy requirements, fitting the data in two sections can achieve a more ideal inversion accuracy.

Claims

1. A method for modeling the effective wave height inversion model of ocean waves of self-adaptive piecewise linear particle swarm, is characterized in that: comprise the following steps:

Step 1: Data outlier point processing:

The original data point set is Y, with any data point A, If for a certain neighborhood ρ(A,r) of data point A, r>0, r represents the radius of the neighborhood, there is data point B, Make B∈ρ(A,r), then point A belongs to the truth set, and the set of all points satisfying the property of point A in Y constitutes the truth set Z; any data point A′, If for a certain neighborhood ρ(A',r) of point A', r>0, for have Then point A' belongs to the outlier set, and the set of all points satisfying the property of point A' in Y constitutes the outlier set U, and the outlier point processing is performed according to the true value set and the outlier set:

Step 1: sort the data points in the original data point set Y according to the abscissa of the data points from small to large, and obtain the sorted data point set as {A ^k′ }k′=1,2,3,. ..,m, where m is the number of all data points in the original data point set Y, subscript k' indicates that the data points are arranged in order from small to large according to the size of the abscissa, and the neighborhood radius is r, let k'= 1. The initial value of the left judgment parameter tl satisfies tl=1, and the right judgment parameter tr initial value satisfies tr=1;

Step 2: Judging whether k′-tl>0 is true, if not true, go to step 4, if true, judge whether A ^k′ -A k′ ^-tl <r is true, if not true, go to step 4, if true Whether it is true, if it is true, the record point A ^k′ belongs to the set B, and enter the sixth step, where the set B represents the true value set after removing the wild value, if it is not established, enter the third step;

Indicates that the length between two points "A ^k' " and "A k' ^-tl " is less than the value of the neighborhood radius;

The 3rd step: make the left judgment parameter tl add 1, promptly tl=tl+1, return to the 2nd step;

Step 4: Judging whether k′+tr<m is true, if not true, go to step 6, if true, judge whether A ^k′+tr -A ^k′ <r is true, if not true, go to step 6, if true Whether it is true, if true, record point A ^k' belongs to set B, enter step 6, if not true, enter step 5;

Indicates that the length between two points "A ^k' " and "A ^k'+tl " is less than the value of the neighborhood radius;

The 5th step: make the judgment parameter tr to the right add 1, promptly tr=tr+1, return to the 4th step;

Step 6: add 1 to subscript k', namely k'=k'+1, judge whether k'≤m is established, if not established, enter step 7, if established set tl=1, tr=1, return to the first step 2 steps;

Step 7: All points in set B form the true value set after removing outlier points;

Step 2: Data sparse processing:

The original data point set is Y, there is any point C, If for a certain neighborhood of point C ρ(C,r′), r′>0, If D∈ρ(A,r′), then point C is said to belong to a dense set, r′ represents the neighborhood judgment radius, and the set of all points satisfying the property of point C in Y constitutes a dense set M; there is any point C ', If for a certain neighborhood ρ(C',r') of point C', r'>0, for have Then point C′ is said to belong to a sparse set, and the set of all points satisfying the property of point C′ in Y constitutes a sparse set S; there is a cross relationship between the outlier set, the true value set, the dense set and the sparse set as follows: Let Z _s = Z∩S, when r′≤r, there is U∩Z _s ＝Φ, and U∪Z _S ＝S, Z _s represents the intersection of the truth set and the sparse set; the specific steps of the sparse processing are:

Step 1: sort the data points in set B obtained in step 1 according to the abscissa of the data points from small to large, and obtain the sorted data point set {C ^k″ }k″=1,2,3 ,...,n, where n is the number of all data points in set B, subscript k″ indicates that the data points are arranged in order according to the size of the abscissa from small to large, and the neighborhood judgment radius is r′ during sparse processing , let k″=1, t=1, m′=n, {D ^k″ }={C ^k″ }k″=1,2,3,...,m′; t represents the rightward judgment parameter, {D ^k″ } is used to represent the data points that have been sparsely processed after the outliers are removed, and m′ represents the number of remaining data points in the set {D ^k″ } after each outlier is proposed ;

Step 2: Judging whether k″+t<m′ is true, if not true, go to step 4, if true, judge whether D ^k″+t -D ^k″ <r′ is true, if not true, go to step 4, if true, judge Whether it is true, if it is true, remove the point D ^k″+t , let m'=m'-1, enter the third step, if it is not true, enter the fourth step;

Indicates that the length between two points "D ^k' " and "D ^k'+tl " is less than the value of the neighborhood radius;

The 3rd step: make t=t+1, return to the 2nd step;

Step 4: Re-record the remaining data points in the set {D ^k″ } to {D ^k″ }k″=1,2,3,..., In m', let k″=k″+1, judge whether k″≤m′ is established, if not established, enter step 5, if established, set t=1, return to step 2;

Step 5: The points in the set {D ^k″ }k″=1,2,3,...,m′ are the data points that have been sparsely processed after the outliers are removed;

Step 3: Set the coding method of the particles and initialize the parameters of the particle swarm: the linear equation is expressed by the intercept formula, and each particle is composed of the intercept A and slope B of all determined straight lines. The particle swarm algorithm particle coding method is:

{X x}_{i i}^{k k} = = {{{X x}_{i i,, j j,, 11}^{k k},, {X x}_{i i,, j j,, 22}^{k k}}}

Where i=1,2,...,N, N≥2 is the number of particles, j=1,2,...,l, l≥1 represents the number of segments, that is, the number of straight lines involved in fitting; k represents the number of iterations of the particle swarm; Respectively represent the intercept and slope of the i-th particle j-th line in the k-th iteration, Indicates the position of the i-th particle;

Initialize the intercept and slope of the line as:

\{\begin{matrix} {X x}_{i i,, j j,, 11}^{11} = = {A A}_{max max} - - \frac{((rand rand + + j j - - 11)) \cdot \cdot (({A A}_{max max} - - {A A}_{min min}))}{l l} \\ {X x}_{i i,, j j,, 22}^{11} = = {B B}_{min min} + + \frac{((rand rand + + j j - - 11)) \cdot \cdot (({B B}_{max max} - - {B B}_{min min}))}{l l} \end{matrix} - - - - - - ((33))

Where rand is a random number between 0 and 1; A _max and A _min represent the maximum and minimum values of the intercept respectively, satisfying

min(Hs)≤A _max ≤max(Hs), min(Hs) and max(Hs) are the maximum and minimum values of the wave height in the wave height data, A _min <A _max ; B _max and B _min represent the slope The maximum and minimum values satisfy 0≤B _min ≤B _max ; i=1,2,...,N, N≥2 is the number of particles, j=1,2,...,l, l≥1 Indicates the number of segments, and Respectively represent the intercept and slope of the i-th particle j-th line in the initialization;

The initialization of the particle displacement is:

\{\begin{matrix} {v v}_{i i,, j j,, 11}^{11} = = rand rand \cdot \cdot {v v}_{max max} \\ {v v}_{i i,, j j,, 22}^{11} = = rand rand \cdot &Center Dot; {v v}_{max max} \end{matrix} - - - - - - ((44))

Where rand is a random number between 0 and 1; v _max > 0 is the maximum value of particle displacement; represent the intercept displacement term and the slope displacement term of the jth straight line of the i-th particle in the initialization, respectively;

The parameters of the particle swarm are initialized as follows:

Let the population number be N; the i-th particle is i=1,2,...,N, j=1,2,...,l; the self-learning factor is c ₁ ≥ 0, the global learning factor is c ₂ ≥ 0; the upper limit and lower limit of the inertia weight are ω _max and ω _min , 0≤ω _min ≤ω _max ≤1; the number of segments is l, l≥1; the maximum number of iterations k _max satisfies k _max ≥2; the number of populations is N; The values are A _max and A _min , A _max ≥ A _min , the maximum and minimum values of the first-order coefficient are B _max and B _min , B _max ≥ B _min ≥ 0; the maximum displacement step v _max satisfies v _max >0; Iteration stop threshold h _max is h _max = 1 · E, wherein E is used to determine the speed at which the threshold value of loop jumping out increases with the increase of the number of segments;

Step 4: The initialization method of the particle velocity is as follows:

Let i=1, j=1, according to formula (4), initialize the i-th particle displacement as

\{\begin{matrix} v_{i, j, 1}^{1} = rand \cdot v_{\max} \\ v_{i, j, 2}^{1} = rand &Center Dot; v_{\max} \end{matrix}

where rand is a random number between 0 and 1; according to formula (3), the i-th particle position is initialized as

\{\begin{matrix} {X x}_{i i,, j j,, 11}^{11} = = {A A}_{max max} - - \frac{((rand rand + + j j - - 11)) \cdot &Center Dot; (({A A}_{max max} - - {A A}_{min min}))}{l l} \\ {X x}_{i i,, j j,, 22}^{11} = = {B B}_{min min} + + \frac{((rand rand + + j j - - 11)) \cdot &Center Dot; (({B B}_{max max} - - {B B}_{min min}))}{l l} \end{matrix}

Where rand is a random number between 0 and 1; A _max and A _min represent the maximum and minimum values of the intercept respectively, satisfying min(Hs)≤A _max ≤max(Hs), min(Hs) and max(Hs) The maximum and minimum values of the wave height, A _min < A _max ; B _max and B _min respectively represent the maximum and minimum values of the slope, satisfying 0≤B _min ≤B _max ; i=1,2,..., N, N≥2 is the number of particles, that is, the group size; j=1,2,...,l, l≥1 represents the number of segments, that is, the number of straight lines involved in fitting; and Respectively represent the intercept and slope of the j-th straight line of the i-th particle in the first iteration (that is, initialization);

Step 5: Add 1 to the number of particles, that is, i=i+1, judge whether i≤N is true, if true, return to step 4, otherwise enter step 6;

Step 6: Add 1 to the number of segments, i.e. j=j+1, judge whether j≤l is established, if established, return to step 4, otherwise enter step 7;

Step 7: Particle swarm velocity position update formula:

\{\begin{matrix} {v v}_{i i}^{k k + + 11} = = ω ω \cdot &Center Dot; {v v}_{i i}^{k k} + + {c c}_{11} {r r}_{11}^{k k} \cdot &Center Dot; (({P P}_{i i}^{b b} - - {X x}_{i i}^{k k})) + + {c c}_{22} {r r}_{22}^{k k} \cdot &Center Dot; (({P P}^{g g} - - {X x}_{i i}^{k k})) \\ {X x}_{i i}^{k k + + 11} = = {X x}_{i i}^{k k} + + {V V}_{i i}^{k k + + 11} \end{matrix} - - - - - - ((55))

in Indicates the displacement of the i-th particle; Indicates the position of the i-th particle, i=1,2,...,N, N≥2 is the number of particles, that is, the group size, j=1,2,...,l, l≥1 represents the segment The number is the number of straight lines participating in the fitting, and k represents the number of iterations of the particle swarm; is the inertia weight, 0 ≤ ω _min ≤ ω _max ≤ 1 is the maximum and minimum value of the inertia weight, ω _max and ω _min are the upper limit and lower limit of the inertia weight respectively, k _max represents the maximum number of iterations; u ≥ 0 is the monotonic control amount; c ₁ ≥ 0 is the self-learning factor; c ₂ ≥ 0 is the global learning factor; is a random number in the interval [0,1]; is the optimal value found by the particle itself; P ^g is the optimal value found by the population;

Particle Swarm Method Fitness Function as follows:

F f (({X x}_{i i}^{k k})) = = {Σ Σ}_{t t = = 11}^{{m m}^{' '}} {(({X x}_{i i,, {j j}^{' '},, 11}^{k k} + + {X x}_{i i,, {j j}^{' '},, 22}^{k k} \cdot &Center Dot; {D D.}_{x x}^{t t} - - {D D.}_{y the y}^{t t}))}^{22} + + M m \cdot &Center Dot; m m - - - - - - ((66))

in t=1,2,...,m', are the SNR square root and wave height corresponding to the data points, respectively, D ^t represents the vector composed of the SNR square root and wave height values, and m′ is the number of data after dewilding and thinning; are the intercept and slope of the straight line respectively, j′=1,2,...,l, and the intersection points between adjacent straight lines are O={O ^j″ } in turn, Represent the horizontal and vertical coordinates of the intersection point O ^j″ respectively, j″=1,2,...,l-1, judge if Then let j'=1, if

(j=1,2,....,l-2), then let j′=j″+1, if Then let j'=l;M>0 is the penalty factor,

m is the number of times to meet the constraints;

Calculate the fitness value of each particle according to the fitness function formula (6):

Let the number of iterations of particle swarm k=1, The optimal value found for the particle itself, is the position of the i-th particle; (i=1,2,...,N), calculate the fitness function value according to the formula (6)

F f (({X x}_{i i}^{k k})) = = {Σ Σ}_{t t = = 11}^{{m m}^{' '}} {(({X x}_{i i,, {j j}^{' '},, 11}^{k k} + + {X x}_{i i,, {j j}^{' '},, 22}^{k k} \cdot \cdot {D D.}_{x x}^{t t} - - {D D.}_{y the y}^{t t}))}^{22} + + M m \cdot &Center Dot; m m

Step 8: Apply the particle swarm velocity update formula, and calculate the particle displacement according to the displacement update formula in formula (5) for

{v v}_{i i}^{' ' k k + + 11} = = ω ω \cdot \cdot {v v}_{i i}^{k k} + + {c c}_{11} {r r}_{11}^{k k} \cdot \cdot (({P P}_{i i}^{b b} - - {X x}_{i i}^{k k})) + + {c c}_{22} {r r}_{22}^{k k} \cdot \cdot (({P P}^{g g} - - {X x}_{i i}^{k k}))

in Indicates the displacement of the i-th particle; Indicates the position of the i-th particle, i=1,2,...,N, N≥2 is the number of particles, that is, the group size, j=1,2,...,l, l≥1 represents the segment The number is the number of straight lines participating in the fitting, and k represents the number of iterations of the particle swarm; is the inertia weight, 0≤ω _min ≤ω _max ≤1 is the maximum and minimum value of the inertia weight, k _max represents the maximum number of iterations; u≥0 is the monotonic control quantity; c ₁ ≥0 is the self-learning factor; c ₂ ≥0 is the global learning factor; is a random number in the interval [0,1]; is the optimal value found by the particle itself; P ^g is the optimal value found by the population;

Step Nine: Judgment Whether established, if established order Otherwise order in

is the displacement calculated according to the displacement update formula (5), v _max is the maximum displacement length; i=1,2,...,N; j=1,2,...,l; s takes the value 1 or 2. s=1 and s=2 represent the intercept and slope of the straight line respectively; The particles represent the actual displacement; express The length of is greater than v _max ;

Step 10: Apply the particle swarm position update formula, and calculate the particle position according to the position update formula in formula (5) for

{X x}_{i i}^{' ' k k + + 11} = = {X x}_{i i}^{k k} + + {v v}_{i i}^{k k + + 11}

in is the new position calculated by the position update formula (5), Indicates the position of the particle in the last iteration, particle displacement;

Step Eleven: Judgment i=1,2,...,N, whether j=1,2,...,l is established, if it is established, order

x_{i, j, 2}^{k + 1} = \frac{x_{i, j, 2}^{k + 1}}{| | x_{i, j, 2}^{k + 1} | |} &Center Dot; B_{\max}, x_{i, j, 1}^{k + 1} = x_{i, j, 1}^{' k + 1},

Otherwise order

x_{i, j, the s}^{k + 1} = x_{i, j, the s}^{' k + 1},

s=1,2; Indicates the actual updated position of the particle; B _max indicates the maximum value of the slope; express The length of is greater than B _max ;

Step 12: Calculate the fitness function value

f (x_{i}^{k + 1}) = Σ_{t = 1}^{m^{'}} {(x_{i, j^{'}, 1}^{k + 1} + x_{i, j^{'}, 2}^{k + 1} &Center Dot; {D.}_{x}^{t} - {D.}_{the y}^{t})}^{2} + m \cdot m,

like order Otherwise, go to step 13; represent particles The fitness function value of represent particles The fitness function value of the best position passed;

Step Thirteen: Set The position with the smallest fitness value in the middle, if order Otherwise, go to step fourteen;

Step 14: Determine whether the optimal position P ^g has changed in the continuous h _max iterations, if not, go to step 15, otherwise let k=k+1, judge whether k≤k _max is true, if true Turn to step eight, otherwise go to step fifteen;

Step 15: The obtained P ^g is the optimal intercept and slope value of each segmented straight line found.

2. the ocean wave effective wave height inversion model modeling method of a kind of self-adaptive piecewise linear particle swarm according to claim 1, is characterized in that: the number of times m that satisfies restriction condition gets m=0 when initializing in step 7, The value of m in each iteration process satisfies:

(1) Adjacent straight lines, whether they are parallel, if there are m ₁ adjacent straight lines parallel in a certain iteration, then let m=m+m ₁ ;

(2) Calculate the intersection of adjacent straight lines, and judge whether the abscissa of the intersection with the smaller value of the subscript j" of O ^j" is greater than the abscissa of the intersection with the larger value of the subscript j" of O ^j" among the adjacent intersections Coordinates, if there are m ₂ times in a certain iteration, the abscissa of the intersection point arranged in front is greater than the abscissa of the intersection point arranged in the back, then let m=m+m ₂ ;

(3) judge whether the point of intersection is in the abscissa range where the data point is located, if there are m ₃ intersection points not in the abscissa range where the data point is in a certain iteration, then make m=m+m ₃ ;

(4) Judging whether the slope of the previous straight line in the adjacent straight lines is greater than the slope of the latter straight line, if there are m ₄ adjacent straight lines in a certain iteration, the slope of the previous straight line is greater than the slope of the latter straight line, then let m= m+m ₄ , where j represents the previous straight line j=1,2,...,l-1, then j+1 represents the next straight line.