A method for sampling ship data

Abstract

The present invention relates to the technical field of data processing, and discloses a ship data sampling method, which includes obtaining a ship data parent sample for predicting ship stability. The ship data parent sample includes several parent sample feature components. Independent data augmentation is performed on each parent sample feature component to obtain a sub-sample of the ship data parent sample and update the ship data parent sample. After repeating the execution for a preset number of iterations, a final sample is obtained. By independently updating each parent sample feature component of the ship data parent sample, compared with the overall sample update, the present invention can not only increase sample diversity, but also effectively address the problem of decreased sampling accuracy caused by large differences in the sampling ranges of different components of ship data. The obtained final sample effectively amplifies the reliable ship data volume for ship stability prediction, thereby improving the accuracy of ship stability prediction.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and particularly relates to a method for sampling ship data. Background Art

[0002] During the ship production design process, a large amount of ship-related characteristic data is often required to train a model to predict the stability of the ship, including the ship length, ship width, draft, initial trim, initial metacentric height, waterline length, roll period, height of the center of gravity, block coefficient, bilge keel area, flooding angle, wind pressure moment, measured projected area, height of the centroid of the measured projected area, and displacement, etc.

[0003] However, in the actual ship production design, due to the small number of channels for obtaining ship type characteristic data and the great difficulty in obtaining it, it is necessary to supplement and collect according to the existing ship characteristic data.

[0004] The existing supplementary collection methods often adopt the evolutionary sampling algorithm (ES algorithm), but the current evolutionary sampling algorithm is difficult to meet the sampling accuracy requirements brought about by complex multi-dimensional probability density functions and variable range differences. Specifically as follows:

[0005] (1) As the complexity of the probability density function increases, it not only involves multi-dimensional variables but also often includes characteristics such as non-linearity and multi-modal, which makes the sampling process extremely difficult. At the same time, with the continuous improvement of the requirements for the quality of samples in the ship sampling field, especially in applications such as machine learning and statistical inference, the requirements for the representativeness and diversity of samples are becoming more and more strict, and the sampling accuracy of the existing evolutionary sampling algorithm has been difficult to meet the requirements;

[0006] (2) There are large differences in the sampling ranges of different variables of ship data. For example, for a specific ship type, it may only be necessary to sample the molded depth within a small range, while for the draft, it is necessary to collect data within a larger range. However, the existing evolutionary sampling algorithm uniformly uses the same transition density function for all components to supplement and collect samples, and it is difficult to handle the situation where the variable distribution ranges are unequal, so it will also lead to a decrease in sampling accuracy.

[0007] The above defects of this algorithm make the effective ship type characteristic data that can be obtained in practice still very limited, which further leads to inaccurate prediction of ship stability.

[0008] In summary, how to provide a ship data sampling method that can efficiently expand the number of effective samples for predicting ship stability has become a technical problem that needs to be solved urgently by those skilled in the art. Summary of the Invention

[0009] The present invention provides a method for sampling ship data, which solves the problems in the related art such as the difficulty in obtaining a large amount of effective ship type characteristic data and the low accuracy of ship stability prediction.

[0010] As a first aspect of the present invention, there is provided a method for sampling ship data, including:

[0011] Obtain a ship data parent sample for predicting ship stability, where the ship data parent sample includes a number of parent sample feature components, and each parent sample feature component corresponds to a ship stability feature;

[0012] Perform data augmentation processing on each parent sample feature component to obtain at least one candidate sample feature component corresponding to each parent sample feature component;

[0013] Obtain at least one candidate sample of the ship data parent sample according to at least one candidate sample feature component corresponding to each parent sample feature component;

[0014] Perform rejection sampling operation on each candidate sample to obtain at least one candidate result sample of the ship data parent sample. The number of candidate result samples of the ship data parent sample, the number of candidate samples of the ship data parent sample, and the number of candidate sample feature components corresponding to each parent sample feature component are all equal;

[0015] If the number of candidate result samples is 1, determine the candidate result sample as a sub-sample of the ship data parent sample;

[0016] If the number of candidate result samples is at least 2, determine one of the at least two candidate result samples as a sub-sample of the ship data parent sample according to the dispersion degree of each candidate result sample;

[0017] Update the ship data parent sample according to the sub-sample, and repeat the above steps until the preset number of iterations is satisfied to obtain the final sample.

[0018] Further, performing data augmentation processing on each parent sample feature component to obtain at least one candidate sample feature component corresponding to each parent sample feature component includes:

[0019] Generate at least two candidate feature components corresponding to each parent sample feature component according to at least two different proposal distributions;

[0020] Obtain at least one candidate sample feature component corresponding to each parent sample feature component according to at least one weight function and at least two candidate feature components corresponding to each parent sample feature component;

[0021] Wherein, the number of candidate sample feature components corresponding to each parent sample feature component is equal to the number of weight functions.

[0022] Further, obtaining at least one candidate sample feature component corresponding to each parent sample feature component according to at least one weight function and at least two candidate feature components corresponding to each parent sample feature component includes:

[0023] Selecting in turn from at least two candidate feature components corresponding to each parent sample feature component according to at least two different weight functions, obtaining at least two temporary feature components corresponding to each parent sample feature component, wherein the number of temporary feature components corresponding to each parent sample feature component is equal to the number of weight functions;

[0024] A rejection sampling operation is performed on each temporary feature component to obtain at least two candidate sample feature components corresponding to each parent sample feature component.

[0025] Further, selecting in turn from at least two candidate feature components corresponding to each parent sample feature component according to at least two different weight functions to obtain at least two temporary feature components corresponding to each parent sample feature component includes:

[0026] At least two different weight functions are obtained according to the adjustment result of the weight parameter of the weight function, wherein the weight parameter represents the bias of the control weight function;

[0027] Calculate the weight value of each candidate feature component corresponding to each parent sample feature component under each weight function;

[0028] For each parent sample feature component, the corresponding candidate feature components calculated by the same weight function are selected as a group, and a temporary feature component of the parent sample feature component is selected from the corresponding candidate feature components by random selection according to the proportion of each group of weight values;

[0029] After traversing each candidate feature component corresponding to each parent sample feature component, at least two temporary feature components corresponding to each parent sample feature component are obtained.

[0030] Furthermore, the at least two different weight functions include: a weight function with a weight parameter of 0 and a weight function with a weight parameter of 2.5.

[0031] Further, a rejection sampling operation is performed on each temporary feature component to obtain at least two candidate sample feature components corresponding to each parent sample feature component, including:

[0032] Calculate the acceptance rate of each temporary feature component separately;

[0033] Generate random numbers in sequence. If the generated random numbers are less than the acceptance rate of the corresponding temporary feature component, then accept the temporary feature component as a candidate sample feature component of the corresponding parent sample feature component.

[0034] If the generated random number is greater than or equal to the acceptance rate of the corresponding temporary feature component, reject accepting the temporary feature component as the candidate sample feature component corresponding to the parent sample feature component, and determine the parent sample feature component as the candidate sample feature component;

[0035] After traversing each temporary feature component corresponding to each parent sample feature component, at least two candidate sample feature components corresponding to each parent sample feature component are obtained.

[0036] Further, at least one candidate sample of the ship data parent sample is obtained according to at least one candidate sample feature component corresponding to each parent sample feature component, including:

[0037] The candidate samples of the ship data parent sample are formed by the candidate sample feature components selected based on the same weight function for each parent sample feature component;

[0038] After traversing each candidate sample feature component corresponding to each parent sample feature component, at least two candidate samples of the ship data parent sample are obtained.

[0039] Further, rejection sampling operations are performed on each candidate sample to obtain at least one candidate result sample of the ship data parent sample, including:

[0040] Calculate the acceptance rate of each candidate sample respectively;

[0041] Generate random numbers in sequence. If the generated random number is less than the acceptance rate of the corresponding candidate sample, accept the candidate sample as the candidate result sample of the ship data parent sample;

[0042] If the generated random number is greater than or equal to the acceptance rate of the corresponding candidate sample, reject accepting the candidate sample as the candidate result sample of the ship data parent sample, and determine the ship data parent sample as the candidate result sample;

[0043] After traversing each candidate sample of the ship data parent sample, at least one candidate result sample of the ship data parent sample is obtained.

[0044] Further, calculate the acceptance rate of each candidate sample respectively, including:

[0045] Calculate the target bandwidth matrix of the multivariate kernel density estimation function according to the AMISE minimization bandwidth calculation method and the Kendall correlation coefficient;

[0046] Calculate the acceptance rate of each candidate sample according to the target bandwidth matrix.

[0047] Further, if the number of candidate result samples is at least 2, determine one of the at least two candidate result samples as the sub-sample of the ship data parent sample according to the dispersion degree of each candidate result sample, including:

[0048] If the number of candidate result samples is at least 2, calculate the standard deviation value of each group of candidate result samples respectively;

[0049] Determine that the candidate result sample with the smallest standard deviation value is the sub-sample of the ship data parent sample.

[0050] By independently updating each parent sample feature component of the ship data parent sample, compared with updating the entire sample as a whole, the present invention can not only increase the diversity of the sample, but also effectively address the problem of decreased sampling accuracy caused by large differences in the sampling ranges of different components of the ship data. The final sample obtained effectively amplifies the reliable ship data volume for ship stability prediction, thereby improving the accuracy of ship stability prediction. Description of the Drawings

[0051] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. Together with the following specific implementation manners, they are used to explain the present invention, but do not constitute a limitation to the present invention.

[0052] Figure 1 It is a brief flowchart of the ship data sampling method provided by the present invention.

[0053] Figure 2 It is a brief flowchart of the data amplification processing provided by the present invention.

[0054] Figure 3 It is a brief flowchart of generating candidate sample feature components provided by the present invention.

[0055] Figure 4 It is a brief flowchart of generating temporary feature components provided by the present invention.

[0056] Figure 5 It is a detailed flowchart of generating candidate sample feature components provided by the present invention.

[0057] Figure 6 It is a brief flowchart of generating candidate samples provided by the present invention.

[0058] Figure 7 It is a brief flowchart of generating candidate result samples provided by the present invention.

[0059] Figure 8 It is a brief flowchart of calculating the acceptance rate provided by the present invention.

[0060] Figure 9 It is a brief flowchart of obtaining sub-samples provided by the present invention.

[0061] Figure 10 Test function π in Table 2 provided by the present invention 1Convergence curve graph of the standard deviation

[0062] Figure 11 For the test function π in Table 2 provided by the present invention 1 Convergence curve graph of the normalization factor

[0063] Figure 12 For the test function π in Table 2 provided by the present invention 2 Convergence curve graph of the standard deviation

[0064] Figure 13 For the test function π in Table 2 provided by the present invention 2 Convergence curve graph of the normalization factor

[0065] Figure 14 For the test function π in Table 2 provided by the present invention 4 Convergence curve graph of the standard deviation

[0066] Figure 15 For the test function π in Table 2 provided by the present invention 4 Convergence curve graph of the normalization factor

[0067] Figure 16 For the test function π in Table 2 provided by the present invention 6 Convergence curve graph of the standard deviation

[0068] Figure 17 For the test function π in Table 2 provided by the present invention 6 Convergence curve graph of the normalization factor

[0069] Figure 18 For the test function π in Table 2 provided by the present invention 8 Convergence curve graph of the standard deviation

[0070] Figure 19 For the test function π in Table 2 provided by the present invention 8 Convergence curve graph of the normalization factor

[0071] Figure 20 For the test function π in Table 2 provided by the present invention 10 Convergence curve graph of the standard deviation

[0072] Figure 21 For the test function π in Table 2 provided by the present invention 10 Convergence curve graph of the normalization factor

[0073] Figure 22 For the test function π in Table 2 provided by the present invention 11 Convergence curve graph of the standard deviation

[0074] Figure 23 The convergence curve graph of the normalization factor of the test function π in Table 2 provided by the present invention 11 .

[0075] Figure 24 The convergence curve graph of the normalization factor of the test function π in Table 2 provided by the present invention 12 .

[0076] Figure 25 The convergence curve graph of the normalization factor of the test function π in Table 2 provided by the present invention 12 .

[0077] Figure 26 The convergence curve graph of the normalization factor of the test function π in Table 2 provided by the present invention 13 .

[0078] Figure 27 The convergence curve graph of the normalization factor of the test function π in Table 2 provided by the present invention 13 . Detailed implementation manners

[0079] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments may be combined with each other. The present invention will be described in detail below with reference to the drawings and in conjunction with the embodiments.

[0080] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0081] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above drawings are used to distinguish similar objects, and do not necessarily need to be used to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so as to implement the embodiments of the present invention described herein. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device including a series of steps or units does not necessarily need to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0082] The embodiment of the present invention provides a ship data sampling method, as Figure 1 shown, including:

[0083] S100. Obtain a parent sample set of ship data for predicting ship stability. The parent sample set of ship data includes several parent sample feature components, and each parent sample feature component corresponds to a ship stability feature;

[0084] In the actual implementation of the embodiments of the present invention, a ship data sample set is obtained. The ship data sample set includes several parent samples of ship data for predicting ship stability. The parent sample set of ship data includes several parent sample feature components, and each parent sample feature component corresponds to a ship stability feature, such as ship length, ship width, draft, initial trim, initial metacentric height, waterline length, rolling period, height of the center of gravity, block coefficient, bilge keel area, flooding angle, wind pressure moment, measured projected area, height of the centroid of the measured projected area, and displacement, etc.

[0085] Specifically, the number of parent samples of ship data is preset as N, that is, the number of parent samples of ship data is N, and the iteration times Iter of the parent samples of ship data are preset. The parent samples of ship data are initialized, and the initialized parent sample set of ship data is specifically expressed as It means that the i-th ship data parent sample in the parent sample set of ship data that has experienced the t-th iteration has D parent sample feature components, where i = 1, 2,..., N, It means the k-th parent sample feature component in this ship data parent sample that has experienced the t-th iteration, k = 1, 2,..., D. The following steps 200-700 are executed for each ship data parent sample in the parent sample set of ship data.

[0086] S200. Perform data augmentation processing on each parent sample feature component to obtain at least one candidate sample feature component corresponding to each parent sample feature component;

[0087] Specifically, in the embodiments of the present invention, the parent sample feature components of the parent samples of ship data can be processed by an evolutionary algorithm, such as random sampling, Latin hypercube sampling, Gibbs sampling, etc. for each parent sample feature component to perform data augmentation processing to obtain at least one candidate sample feature component S≥1.

[0088] S300. Obtain at least one candidate sample of the parent sample set of ship data according to at least one candidate sample feature component corresponding to each parent sample feature component;

[0089] Specifically, according to each parent sample feature component corresponding to at least one candidate sample feature component obtain at least one candidate sample of the parent sample set of ship data

[0090] S400. Perform rejection sampling on each candidate sample to obtain at least one candidate result sample of the parent sample of ship data. The number of candidate result samples of the parent sample of ship data, the number of candidate samples of the parent sample of ship data, and the number of candidate sample features corresponding to each parent sample feature component are all equal.

[0091] Specifically, in this embodiment, by calculating the acceptance rate of the candidate sample of the parent sample of ship data, each candidate sample of the parent sample of ship data is compared and selected one by one with the parent sample of ship data . The selected one is the candidate result sample of the parent sample of ship data, so as to obtain the candidate result sample of the parent sample of ship data s = 1, 2, ……, S. The number of candidate result samples of the parent sample of ship data, the number of candidate samples of the parent sample of ship data, and the number of candidate sample features corresponding to each parent sample feature component of the parent sample of ship data are all equal. of the parent sample of ship data

[0092] S500. If the number of candidate result samples is 1, determine the candidate result sample as the sub-sample of the parent sample of ship data.

[0093] Specifically, when the parent sample of ship data has one and only one candidate result sample , determine this candidate result sample as the sub-sample of the parent sample of ship data

[0094] S600. If the number of candidate result samples is at least 2, determine one of the at least two candidate result samples as the sub-sample of the parent sample of ship data according to the dispersion degree of each candidate result sample.

[0095] When the parent sample of ship data has more than two candidate result samples , further selection needs to be carried out among several candidate result samples . Specifically, in the embodiment of the present invention, the one with the smallest dispersion degree is selected from multiple candidate result samples as the sub-sample of the parent sample of ship data

[0096] ​S700. Update the parent sample of the ship data according to the sub-sample, and repeat the above steps until the preset number of iterations is satisfied to obtain the final sample;

[0097] Specifically, in the embodiment of the present invention, the parent sample of the ship data is updated according to the sub-sample as Iteratively execute the above steps 200-700 on the parent sample of the ship data until the preset number of iterations Iter is satisfied to obtain the final sample. After traversing each parent sample of the ship data parent sample set, the final sample set is obtained.

[0098] In summary, in the embodiment of the present invention, by independently updating each parent sample feature component of the ship data parent sample, compared with updating the whole sample as a whole, it can not only increase the diversity of the sample, but also effectively address the problem of the decrease in sampling accuracy caused by the large difference in the sampling ranges of different components of the ship data. The obtained final sample effectively amplifies the reliable ship data volume for ship stability prediction, thereby improving the accuracy of ship stability prediction.

[0099] Furthermore, as Figure 2 shown, perform data amplification processing on each parent sample feature component to obtain at least one candidate sample feature component corresponding to each parent sample feature component, including:

[0100] S210. Generate at least two candidate feature components corresponding to each parent sample feature component according to at least two different proposal distributions;

[0101] The proposal distribution (Proposal Distribution), also known as the suggestion distribution, is an importance sampling method for obtaining the weighted sub-sample of the posterior probability distribution. Different proposal distributions can affect the search range of the evolutionary sampling.

[0102] In the embodiment of the present invention, the number of proposal distributions is set to M, M≥2. For the parent sample of the ship data of the parent sample feature component generate M candidate feature components z , z 1 , z 2 , …, z M .

[0103] Specifically, due to the characteristics of the Lévy distribution having an infinite second moment and an adjustable control parameter, in the embodiment of the present invention, the Lévy distribution is used to obtain M different proposal distributions by adjusting the control parameter of the Lévy distribution. The control parameter α of the Lévy distribution can control the search range of the proposal distribution, making the probability distribution present different shapes, especially in the tail region. The smaller the parameter α, the longer the tail, 0 < α < 2.

[0104] Next, using each parent sample feature component as the center of the proposal distribution, M proposal distributions are used as the transition probability function to generate candidate feature components for the parent sample feature components.

[0105] Specifically, according to the M proposal distributions as the transition probability function to generate a set of candidate feature components for each parent sample feature component of the corresponding ship data parent sample including M candidate feature components z 1 , z 2 , …, z M , where j represents the j-th proposal distribution, j = 1, 2, …, M.

[0106] In the present invention, multiple different proposal distributions are used to generate multiple candidate feature components for each parent sample feature component of the ship data parent sample. After obtaining M candidate feature components for each parent sample feature component, each parent sample feature component is independently updated, and through subsequent evolution processes, relatively excellent ones are selected from them as candidate sample feature components to form candidate samples. This can not only increase sample diversity and more widely explore the parameter space, but also effectively address the problem of decreased sampling accuracy caused by large differences in the sampling ranges of different components.

[0107] Specifically, since the analytical formula of the candidate feature component that satisfies this integral is unknown for ordinary control parameter α, but in some special cases, the analytical formula of the candidate feature component can be obtained. In particular, for α = 1, this integral can be reduced to a Cauchy distribution. When α → 2, that is, when α approaches 2 infinitely, the distribution is no longer a Lévy distribution but becomes a Gaussian distribution. The candidate feature components generated by the proposal distributions obtained in these two cases often result in a stable evolution process. Therefore, in the specific implementation of the present invention embodiment, the control parameter α = 1 is adjusted to obtain a proposal distribution, that is, a Cauchy distribution, and the control parameter α → 2 is adjusted to obtain another proposal distribution, that is, a Gaussian distribution.

[0108] S220. Obtain at least one candidate sample feature component corresponding to each parent sample feature component according to at least one weight function and at least two candidate feature components corresponding to each parent sample feature component;

[0109] Among them, the number of candidate sample feature components corresponding to each parent sample feature component is equal to the number of weight functions.

[0110] Specifically, in the embodiment of the present invention, the number of weight functions is set to S, S ≥ 1, that is, S different weight functions ω 1 , ω 2 , ……, ω s are set. For the parent sample of ship data of the parent sample feature component Sequentially through the weight function ω 1 , ω 2 , ……, ω s (s = 1, 2, …, S) perform selection and evolution processing on the candidate feature components z corresponding to the parent sample feature components 1 , z 2 , …, z M to obtain at least one candidate sample feature component corresponding to each parent sample feature component

[0111] Further, as Figure 3 shown, according to at least one weight function and at least two candidate feature components corresponding to each parent sample feature component, obtain at least one candidate sample feature component corresponding to each parent sample feature component, including:

[0112] S221. Sequentially select from at least two candidate feature components corresponding to each parent sample feature component according to at least two different weight functions to obtain at least two temporary feature components corresponding to each parent sample feature component, where the number of temporary feature components corresponding to each parent sample feature component is equal to the number of weight functions;

[0113] In specific implementation, for the parent sample of ship data of the parent sample feature components sequentially through the weight function ω 1 , ω 2 , ……, ω s (s = 1, 2, …, S) perform selection in the candidate feature components z corresponding to the parent sample feature components 1 , z 2 , …, Z M and assign the selected candidate feature component to the temporary feature component The proposed distribution corresponding to the selected candidate feature component is denoted as j * , traverse each parent sample feature component of this ship data parent sample to obtain S temporary feature components of each parent sample feature component

[0114]

[0115] S222. Perform rejection sampling operations on each temporary feature component respectively to obtain at least two candidate sample feature components corresponding to each parent sample feature component.

[0115] Specifically, the embodiment of the present invention needs to perform rejection sampling operations on each parent sample feature component The corresponding temporary feature components are screened to obtain each parent sample feature component and at least two candidate sample feature components corresponding thereto It should be understood that the number of candidate sample feature components corresponding to each parent sample feature component is determined by the number of temporary feature components, that is, the number of weight functions

[0116] Since each parent sample feature component of the ship data parent sample is independently updated, and on this basis, in order to take into account the efficiency of evolutionary sampling, the embodiments of the present invention introduce at least two weight functions, that is, the number S of weight functions is ≥2, and candidate samples are obtained from the candidate sample feature components obtained by the same weight function. The optimal sub-samples are selected using the standard deviation values of the candidate samples generated under different weight functions, that is, the weight functions are adaptively selected by the evolutionary process, and the search strategy is dynamically adjusted according to the actual situation of the search process, balancing the global search and local search in the evolutionary process, further improving the efficiency of evolutionary sampling, expanding the adaptation range of the sampling method, and taking into account the sampling efficiency while optimizing the sampling accuracy

[0117] Further, as Figure 4 shown, at least two temporary feature components corresponding to each parent sample feature component are obtained by sequentially selecting from at least two candidate feature components corresponding to each parent sample feature component according to at least two different weight functions, including:

[0118] S221a. Obtain at least two different weight functions according to the adjustment result of the weight parameters of the weight function, where the weight parameters represent the emphasis of controlling the weight function

[0119] The weight parameter β of the weight function can balance the distance of the candidate feature component changing from the current state and the probability under the target proposal distribution. Setting a suitable weight function with the weight parameter β can improve the efficiency of the sampling chain, help the evolutionary sampling algorithm move more effectively in the search space, and find better solutions

[0120] Specifically, the expression of the weight function is as shown in the following formula (1):

[0121]

[0122] Wherein, represents except that the kth parent sample feature component is replaced, and the others remain unchanged, that is

[0123] For λ j,k(x, y) is a non - negative symmetric function. It determines the value of the weight function, and there are various choices, such as: {T j,k (x, y)T j,k (y, x)} -β and 1.

[0124] In the embodiment of the present invention, making λ j,k (x, y) considers both the transition probability and the moving distance at the same time, and the specific expression is shown in formula (2):

[0125] λ j,k (x, y) = T j,k (x, y) -1 ||y - x|| β (2),

[0126] Among them, β represents the weight parameter that controls the bias of the weight function, which can balance the distance of the candidate feature component changing from the current state and the probability under the target proposal distribution, thereby affecting the evolution process and needs to be specifically set according to the actual problem.

[0127] S221b. Calculate the weight values of each candidate feature component corresponding to each parent sample feature component under each weight function respectively;

[0128] In the embodiment of the present invention, calculate the weight values of the M candidate feature components corresponding to each parent sample feature component under S different weight functions in sequence, such as:

[0129] Among them, represents the k - th parent sample feature component of the parent sample of the ship data corresponding to the M - th candidate feature component z under the S - th weight function ω M The weight value. s under the S - th weight function ω

[0130] S221c. For each parent sample feature component, select the corresponding candidate feature components calculated by the same weight function as a group, and select a temporary feature component of this parent sample feature component from the corresponding candidate feature components by a random selection method according to the ratio of each group of weight values;

[0131] Specifically, for each parent sample feature component, select the weight values of the corresponding M candidate feature components calculated by the same weight function as a group, such as: is a group, and select a temporary feature component of this parent sample feature component from the corresponding candidate feature components by a random selection method according to the ratio of each group of weight values The proposed distribution corresponding to the selected temporary feature component is denoted as j * .

[0132] S221d. After traversing each candidate feature component corresponding to each parent sample feature component, at least two temporary feature components corresponding to each parent sample feature component are obtained.

[0133] Since the embodiments of the present invention adopt S different weight functions, for each parent sample feature component it is necessary to make S selections among the corresponding M candidate feature components to obtain S temporary feature components of each parent sample feature component .

[0134] Further, at least two different weight functions include: a weight function with a weight parameter of 0 and a weight function with a weight parameter of 2.5.

[0135] When the weight parameter β is set to 2.5, the evolution process tends to explore in a wide search space, considering both the target probability in the current state and maintaining sufficient exploration to discover potentially better solutions. This setting helps the evolution process jump out of the local optimal solution and search for potentially better solutions globally. When the weight parameter β is set to 0, the evolution process focuses more on the candidate feature components with higher target probability in the current state, causing the evolution process to enter the local search stage, thereby increasing the probability of accepting high-quality solutions and accelerating the convergence speed of the algorithm.

[0136] Therefore, in the subsequent evolution process of the embodiments of the present invention, the standard deviation values of the candidate samples generated under different weight functions are used to select sub-samples, that is, the weight function is adaptively selected by the evolution process, which can dynamically adjust the search strategy according to the actual situation of the search process, and meet the requirements that the algorithm maintains global exploration and can also perform local search when gradually converging to the optimal solution in the subsequent process, improving the adaptability and efficiency of the evolution method.

[0137] Further, as Figure 5 shown, rejection sampling operations are respectively performed on each temporary feature component to obtain at least two candidate sample feature components corresponding to each parent sample feature component, including:

[0138] S222a. Calculate the acceptance rate of each temporary feature component respectively;

[0139] Specifically, taking two proposed distributions and two weight functions as examples in the embodiments of the present invention, the specific calculation formula of the acceptance rate of each temporary feature component is as shown in formula (3):

[0140]

[0141] Wherein, Denote the k-th parent sample feature component of the parent sample of ship data The corresponding first candidate feature component z Under the first weight function ω 1 The weight value 1 Denote the k-th parent sample feature component of the parent sample of ship data The corresponding second candidate feature component z Under the second weight function ω 2 The weight value 2 Denote the temporary feature component Under the corresponding proposal distribution j * The weight value Denote the temporary feature component The weight value under another proposal distribution

[0142] S222b. Generate random numbers in sequence. If the generated random number is less than the acceptance rate of the corresponding temporary feature component, accept the temporary feature component as the candidate sample feature component of the corresponding parent sample feature component;

[0143] Specifically, generate a random number on [0, 1] in sequence. If the generated random number is less than the acceptance rate A of the corresponding temporary feature component, accept the temporary feature component As the candidate sample feature component of the corresponding parent sample feature component That is

[0144] S222c. If the generated random number is greater than or equal to the acceptance rate of the corresponding temporary feature component, reject accepting the temporary feature component as the candidate sample feature component of the corresponding parent sample feature component, and determine the parent sample feature component as the candidate sample feature component;

[0145] If the generated random number is greater than or equal to the acceptance rate A of the corresponding temporary feature component, reject accepting the temporary feature component As the candidate sample feature component of the corresponding parent sample feature component Determine the parent sample feature component As the candidate sample feature component That is

[0146] S222d. After traversing each temporary feature component corresponding to each parent sample feature component, obtain at least two candidate sample feature components corresponding to each parent sample feature component. ​​​​​​

[0147] Based on the above steps, traverse each parent sample feature component Each temporary characteristic component of After that, the characteristic components of each parent sample are obtained The S candidate sample feature components

[0148] Furthermore, if Figure 6 As shown, obtaining at least one candidate sample of the parent sample of the ship data according to at least one candidate sample feature component corresponding to each parent sample feature component includes:

[0149] S310, forming candidate samples of the parent sample of the ship data according to the candidate sample feature components selected based on the same weight function of each parent sample feature component;

[0150] Since each parent sample feature component The S candidate sample feature components They are obtained through S weight functions respectively, and each parent sample feature component Corresponding candidate sample feature components selected based on the same weight function Form the parent sample of the ship data candidate samples.

[0151] S320, after traversing each candidate sample feature component corresponding to each parent sample feature component, obtain at least two candidate samples of the ship data parent sample.

[0152] After traversing each candidate sample feature component corresponding to each parent sample feature component, the parent sample of ship data is obtained S candidate samples

[0153] Furthermore, if Figure 7 As shown, a rejection sampling operation is performed on each candidate sample to obtain at least one candidate result sample of the parent sample of ship data, including:

[0154] S410, respectively calculating the acceptance rate of each candidate sample;

[0155] Specifically, the calculation formula of the acceptance rate of candidate samples is as follows:

[0156]

[0157] Among them, Q represents the target proposal distribution and p represents the multivariate kernel density estimation function.

[0158] S420, generating random numbers in sequence, and if the generated random numbers are less than the acceptance rate of the corresponding candidate samples, accepting the candidate samples as the candidate result samples of the parent samples of the ship data;

[0159] Specifically, a random number is generated on [0, 1] in sequence. If the generated random number is less than the acceptance rate of the corresponding candidate sample of the acceptance rate then accept the candidate sample as the parent sample of the ship data of the candidate result sample That is, let

[0160] S430. If the generated random number is greater than or equal to the acceptance rate of the corresponding candidate sample, then reject the candidate sample as the candidate result sample of the parent sample of the ship data, and determine that the parent sample of the ship data is the candidate result sample;

[0161] Specifically, if the generated random number is greater than or equal to the acceptance rate of the corresponding candidate sample then reject the candidate sample as the parent sample of the ship data of the candidate result sample Determine the parent sample of the ship data itself as the candidate result sample, that is, let

[0162] S440. After traversing each candidate sample of the parent sample of the ship data, at least one candidate result sample of the parent sample of the ship data is obtained.

[0163] Based on the above steps, traverse the parent sample of the ship data each candidate sample Y t+1 After that, obtain the parent sample of the ship data S candidate result samples

[0164] Furthermore, as Figure 8 shown, calculate the acceptance rate of each candidate sample respectively, including:

[0165] S001. Calculate the target bandwidth matrix of the multivariate kernel density estimation function according to the AMISE minimization bandwidth calculation method and the Kendall correlation coefficient;

[0166] Specifically, the expression of the multivariate kernel density estimation function used to calculate the acceptance rate of the candidate sample is as shown in the following formula (5):

[0167]

[0168] Among them, H represents a d×d symmetric positive definite bandwidth matrix, |·| represents calculating the determinant, and it should be understood that here That is, p in the above formula (4), K[·] represents the Gaussian kernel function, and the specific expression of the Gaussian kernel function is as shown in formula (6):

[0169]

[0170] Among them, π represents the pi, d represents the dimension, and T represents the matrix transpose.

[0171] To optimize the calculation process, the embodiment of the present invention calculates the target bandwidth matrix of the multivariate kernel density estimation function through the AMISE minimization bandwidth calculation method to update the above symmetric positive definite bandwidth matrix H.

[0172] Specifically, based on the optimal diagonal bandwidth empirical method of the AMISE minimization bandwidth calculation method, the expression of the AMISE of the multivariate kernel density estimation can be deduced according to the derivation formula of the AMISE of the univariate kernel density estimation as shown in formula (7):

[0173]

[0174] Among them, det represents the determinant, d represents the dimension, tr{·} represents the trace of the matrix, and f(Y) represents the calculation of the candidate sample of the multivariate kernel density estimation function, and f"(Y) represents the second derivative of f(Y), that is, the Hessian Matrix. Assuming that f(Y) follows a multivariate normal distribution, the target bandwidth matrix that minimizes the AMISE can be deduced therefrom, as shown in formula (8):

[0175]

[0176] Among them, σ i represents the standard deviation of the i-th dimension of the sample. This method provides a simple and effective method to select an appropriate bandwidth matrix, especially suitable for datasets with normal distribution characteristics.

[0177] The specific representation form of this target bandwidth matrix is as shown in the following formulas (9) and (10):

[0178]

[0179] Among them, ρ is the Kendall correlation coefficient. The Kendall correlation coefficient has the advantages of being more stable and reliable in evaluating the correlation between variables and being more sensitive to non-linear relationships. Further, considering that in specific candidate samples, there may be correlations between the characteristic components of each candidate sample, and this correlation may affect the accuracy of the kernel density estimation function. Therefore, in the embodiments of the present invention, the correlation of variables is reflected in the target bandwidth matrix. At the same time, considering the different effects of strong correlation and weak correlation on kernel density estimation, the elements on the non-diagonal are set to the square value of the correlation coefficient between variables, amplifying the influence between strongly correlated variables and reducing the influence of weakly correlated values. In addition, by retaining the sign of the correlation coefficient, it is reflected whether the variables are positively correlated or negatively correlated, so as to more accurately adjust the kernel density estimation to reflect the true distribution of the data.

[0180] Since there is a known function when calculating the acceptance rate of the temporary characteristic component in the embodiments of the present invention, there is no need to use the multivariate kernel density estimation function. If there is no known function, the multivariate kernel density estimation function can also be used to calculate the acceptance rate of the temporary characteristic component as shown in the following formula (11):

[0181]

[0182] where s = 1, 2,..., S. It should be understood that refers to the temporary characteristic component under the same weight function. H represents a d×d symmetric positive definite bandwidth matrix, |·| represents calculating the determinant. K[·] represents the Gaussian kernel function. The specific representation form of the target bandwidth matrix H and the form of the correlation coefficient are the same as above and will not be elaborated here.

[0183] S002. Calculate the acceptance rate of each candidate sample or the acceptance rate of each temporary characteristic component according to the target bandwidth matrix.

[0184] In the embodiments of the present invention, the target bandwidth matrix of the multivariate kernel density estimation function is generated based on the AMISE minimization bandwidth calculation method and the Kendall correlation coefficient according to the sample information collected each time, and this multivariate kernel density estimation function is used to calculate the acceptance rate of the temporary characteristic component and the acceptance rate of the candidate sample, effectively avoiding the subjectivity and lack of adaptability problems brought by manually setting the bandwidth parameter, thereby reducing the risk of the accuracy of the acceptance rate calculated by the multivariate kernel density estimation function decreasing due to improper setting of the bandwidth parameter, and effectively ensuring the performance of the ship data sampling method.

[0185] Further, as Figure 9As shown, if the number of candidate result samples is at least 2, determine a subsample of the ship data parent sample from at least two candidate result samples according to the dispersion degree of each candidate result sample, including:

[0186] S610. If the number of candidate result samples is at least 2, calculate the standard deviation value of each group of candidate result samples respectively;

[0187] Specifically, if the number of candidate result samples is at least 2, calculate the standard deviation value of the candidate result samples of the ship data parent sample of ;

[0188] S620. Determine the candidate result sample with the smallest standard deviation value as the subsample of the ship data parent sample.

[0189] Among the S candidate result samples of the ship data parent sample , select the candidate result sample with the smallest standard deviation value as the subsample of the ship data parent sample , and update the ship data parent sample ;

[0190] The embodiments of the present invention provide the following simulation experiment data:

[0191] Table 1 is the test function set required for the simulation experiment. There are a total of 15 test functions, which are divided into 3 unimodal functions π 1 ~π 3 , 6 slightly locally optimal functions π 4 ~π 9 and 6 significantly locally optimal functions π 10 ~π 15 . For some functions, variable correlations are set, including only positive correlations between variables, only negative correlations between variables, and both positive and negative correlations between variables. For the other part of the functions, the variables are kept independent of each other.

[0192] Table 1 Test Functions

[0193]

[0194]

[0195] Table 2 shows 9 test functions π 1 , π 2 , π 4 , π 6 , π 8 , π 10 , π 11 , π 12 and π13 Meanwhile, different variance sizes are randomly set for each variable.

[0196] Table 2 Test functions (different distribution ranges between variables)

[0197]

[0198]

[0199] The performance of the evolutionary sampling algorithm is usually evaluated using the standard deviation and convergence. The normalization factor is calculated by the following formula (12) to observe the convergence of the algorithm. When λ converges to a stable value, we determine that the algorithm converges and obtains an optimal stable solution. Therefore, when the difference between λ in two adjacent iterations is less than a very small value, the algorithm can be determined to terminate.

[0200]

[0201] It can be seen from the following formula (13) that the standard deviation J can be used to represent the approximation degree between the distribution of the support sample set and the distribution of the target sample set. The smaller J is, the closer the distribution of the collected support sample set is to the distribution of the target sample set, and the higher the accuracy of the sample.

[0202]

[0203] where p(x) = λ * p * (x), p(x) represents the normalized output, and π(x) represents the target distribution. Data points uniformly distributed within the target domain are set to calculate the standard deviation.

[0204] The specific experimental settings are as follows: 300 random samples that conform to the range of each dimension are generated from the uniform distribution as the initial sample set, that is, N = 300; the number of iterations Iter = 300. In order for the evaluation index to show the differences between algorithms with different transfer density functions, we set an appropriate number of test points uniformly distributed within the domain to calculate the values of λ and J. At the same time, each test function is executed 30 times. Verify the influence of different values of the weight function parameter α in the single-component multiple-attempt evolutionary sampling (LCMTES) algorithm based on the Lévy distribution on the algorithm performance, and compare the performance with the adaptive single-component evolutionary sampling (LACES) algorithm based on the Lévy distribution when dealing with functions with the same and different distribution ranges between variables. Among them, the LACES algorithm is an evolutionary sampling algorithm based on the adaptive Lévy distribution that uses a component-by-component update strategy but does not use the multiple-attempt strategy in the ship data sampling method provided by the embodiments of the present invention for improvement.

[0205] Experiment 1: Select all the test functions in Table 1, set the parameters α = 0, α = 2.5 and α = [0, 2.5] of the weight function, verify the influence of different values of the parameter α of the weight function in the LCMTES algorithm on the algorithm performance, and compare the performance with the LACES algorithm in dealing with the same distribution range among variables. The abbreviations of the algorithms involved are as follows

[0206] LCMTES-1: The parameter α of the weight function is 0;

[0207] LCMTES-2: The parameter α of the weight function is 2.5;

[0208] According to Table 3, comparing the standard deviations of LCMTES-1, LCMTES-2 and the LCMTES algorithm, it can be seen that on unimodal functions, the performance of the LCMTES-1 algorithm can approximate or even slightly outperform the LCMTES-2 algorithm. Therefore, the method that only considers the target probability value in the current state for the weight value is applicable to unimodal functions. However, on functions with local optima, it can be clearly seen that the performance of the LCMTES-2 algorithm is better than that of the LCMTES-1 algorithm, achieving a reduction of 3.9% or more in the standard deviation on most functions. Therefore, for functions with local optima, compared with the function that only considers the target probability value in the current state for the weight value, the weight function setting that balances the jump distance from the current state and the probability under the target distribution π is more applicable. Since the LCMTES algorithm considers both α = 0 and α = 2.5 simultaneously, it can be clearly seen from Table 3 that the performance of the LCMTES algorithm is better than that of LCMTES-1 and LCMTES-2.

[0209] Compared with the LACES algorithm, it can be seen from Table 3 that on unimodal functions π 1 and π 3 , the standard deviations increase by 0.15 and 0.07, and the performance of the LACES algorithm is slightly better than that of the LCMTES algorithm. On functions with slightly local optima, for functions π 4 and π 5 , the standard deviations obtained by the LACES algorithm are slightly smaller than those of the LCMTES algorithm. For functions π 6 , π 7 and π 8 , the standard deviations of the LCMTES algorithm are slightly smaller. On functions with obvious local optima, the performance of the two algorithms is similar, and the difference in the standard deviation does not exceed 2%. In summary, when the differences among variables are the same, the performance of the LCMTES algorithm and the LACES algorithm is approximate.

[0210] Standard Deviations and Normalization Factors of the Last Generation of Samples in Table 3

[0211]

[0212]

[0213] Experiment 2: Select 9 test functions in Table 1 1 , 2 , 4 , 6 , 8 , 10 , 11 , 12 and 13 , and randomly set different variance sizes for each variable as shown in Table 2, and compare the performance of the LACES and LCMTES algorithms when dealing with functions with different distribution ranges between variables.

[0214] As can be seen from Table 4, on the unimodal functions 1 and 2 , the standard deviation of the LACES algorithm and the standard deviation of the LCMTES algorithm are approximately the same, and the difference between the two does not exceed 2%. For functions with local optima, from Figure 14 , Figure 16 , Figure 18 , Figure 20 , Figure 22 , Figure 24 and Figure 26 it can be clearly seen that the LCMTES algorithm not only shows a higher descent rate but also has a lower standard deviation, and its performance is significantly better than the LACES algorithm. For functions with slightly local optima, from Figure 15 , Figure 17 and Figure 19 it can be seen that compared with the LACES algorithm, the LCMTES algorithm has a faster convergence speed, and its standard deviation is reduced by 7.5% or more. For functions with obvious local optima, from Figure 21 , Figure 23 , Figure 25 and Figure 27 it can be seen that the LCMTES algorithm converges to the stable solution slightly slower than the LACES algorithm, but combined with Figure 20 , Figure 22 , Figure 24 and Figure 26 , it can be seen that the standard deviation of the LCMTES algorithm is significantly lower than that of the LACES algorithm. Compared with the LACES algorithm, the standard deviation of the LCMTES algorithm is reduced by more than 20%. In summary, when the target distribution is relatively simple, although there are differences in the variable range, the samples collected by the LACES algorithm can still have a good approximation effect on the target function. When the target function is relatively complex, the samples collected by the LCMTES algorithm can approximate the target distribution better than the LACES algorithm and have higher accuracy.

[0215] Standard Deviation and Normalization Factor of the Last Generation of Samples in Table 4

[0216]

[0217] It is understood that the above embodiments are merely exemplary embodiments adopted to illustrate the principles of the present invention, and the present invention is not limited thereto. For those of ordinary skill in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention, and these modifications and improvements are also regarded as the protection scope of the present invention.

Claims

1. A ship data sampling method, characterized in that: include: Acquire a parent sample of ship data for predicting ship stability, wherein the parent sample of ship data includes a plurality of parent sample feature components, and each parent sample feature component corresponds to a ship stability feature; Performing data augmentation processing on each of the parent sample feature components to obtain at least one candidate sample feature component corresponding to each of the parent sample feature components; Obtain at least one candidate sample of the parent sample of the ship data according to at least one candidate sample feature component corresponding to each of the parent sample feature components; Perform a rejection sampling operation on each of the candidate samples to obtain at least one candidate result sample of the ship data parent sample, wherein the number of the candidate result samples of the ship data parent sample, the number of the candidate samples of the ship data parent sample, and the number of the candidate sample feature components corresponding to each of the parent sample feature components are all equal; If the number of the candidate result samples is 1, determining that the candidate result sample is a subsample of the parent sample of the ship data; If the number of the candidate result samples is at least 2, determining one of the at least two candidate result samples as a sub-sample of the parent sample of the ship data according to the degree of dispersion of each candidate result sample; The parent sample of the ship data is updated according to the sub-sample, and the above steps are repeated until a preset number of iterations is met to obtain a final sample.

2. The method according to claim 1, characterized in that The step of performing data augmentation processing on each of the parent sample feature components to obtain at least one candidate sample feature component corresponding to each of the parent sample feature components includes: Generate at least two candidate feature components corresponding to each of the parent sample feature components according to at least two different proposal distributions; Obtaining at least one candidate sample feature component corresponding to each of the parent sample feature components according to at least one weight function and at least two candidate feature components corresponding to each of the parent sample feature components; The number of candidate sample feature components corresponding to each parent sample feature component is equal to the number of weight functions.

3. The method according to claim 2, characterized in that The step of obtaining at least one candidate sample feature component corresponding to each of the parent sample feature components according to at least one weight function and at least two candidate feature components corresponding to each of the parent sample feature components comprises: Selecting in turn at least two candidate feature components corresponding to each of the parent sample feature components according to at least two different weight functions to obtain at least two temporary feature components corresponding to each of the parent sample feature components, wherein the number of temporary feature components corresponding to each of the parent sample feature components is equal to the number of the weight functions; A rejection sampling operation is performed on each of the temporary feature components to obtain at least two candidate sample feature components corresponding to each of the parent sample feature components.

4. The method according to claim 3, characterized in that The step of selecting in sequence from the at least two candidate feature components corresponding to each of the parent sample feature components according to at least two different weight functions to obtain at least two temporary feature components corresponding to each of the parent sample feature components includes: Obtaining at least two different weight functions according to a result of adjusting a weight parameter of the weight function, wherein the weight parameter represents a bias of controlling the weight function; Respectively calculating the weight values ​​of each candidate feature component corresponding to each of the parent sample feature components under each of the weight functions; For each of the parent sample feature components, select the corresponding candidate feature components calculated by the same weight function as a group, and select a temporary feature component of the parent sample feature component from the corresponding candidate feature components by a random selection method according to the proportion of each group of weight values; After traversing each candidate feature component corresponding to each of the parent sample feature components, at least two temporary feature components corresponding to each of the parent sample feature components are obtained.

5. The method according to claim 3, characterized in that: The at least two different weight functions include: A weight function with a weight parameter of 0 and a weight function with a weight parameter of 2.

5.

6. The method according to claim 3, characterized in that: The step of performing a rejection sampling operation on each of the temporary feature components to obtain at least two candidate sample feature components corresponding to each of the parent sample feature components includes: Calculating the acceptance rate of each temporary feature component respectively; Generate random numbers in sequence, and if the generated random numbers are less than the acceptance rate of the corresponding temporary feature component, accept the temporary feature component as a candidate sample feature component of the corresponding parent sample feature component; If the generated random number is greater than or equal to the acceptance rate of the corresponding temporary feature component, then the temporary feature component is rejected as a candidate sample feature component of the corresponding parent sample feature component, and the parent sample feature component is determined as a candidate sample feature component; After traversing each temporary feature component corresponding to each parent sample feature component, at least two candidate sample feature components corresponding to each parent sample feature component are obtained.

7. The method according to claim 3, characterized in that The step of obtaining at least one candidate sample of the parent sample of the ship data according to at least one candidate sample feature component corresponding to each parent sample feature component comprises: Forming candidate samples of the parent sample of the ship data according to the candidate sample feature components selected based on the same weight function of each of the parent sample feature components; After traversing each candidate sample feature component corresponding to each parent sample feature component, at least two candidate samples of the parent sample of the ship data are obtained.

8. The method according to claim 1, characterized in that The step of performing a rejection sampling operation on each candidate sample to obtain at least one candidate result sample of the parent sample of the ship data comprises: Calculate the acceptance rate of each candidate sample respectively; Generate random numbers in sequence, and if the generated random numbers are less than the acceptance rate of the corresponding candidate samples, then accept the candidate samples as the candidate result samples of the parent samples of the ship data; If the generated random number is greater than or equal to the acceptance rate of the corresponding candidate sample, the candidate sample is rejected as the candidate result sample of the parent sample of the ship data, and the parent sample of the ship data is determined as the candidate result sample; After traversing each candidate sample of the parent sample of the ship data, at least one to-be-selected result sample of the parent sample of the ship data is obtained.

9. The method according to claim 8, characterized in that The respectively calculating the acceptance rate of each candidate sample comprises: Calculate the target bandwidth matrix of the multivariate kernel density estimation function based on the AMISE minimization bandwidth calculation method and the Kendall correlation coefficient; The acceptance rate of each candidate sample is calculated according to the target bandwidth matrix.

10. The method according to claim 1, characterized in that If the number of the candidate result samples is at least 2, determining a sub-sample of the parent sample of the ship data from at least two candidate result samples according to the discrete degree of each candidate result sample, comprising: If the number of the candidate result samples is at least 2, respectively calculate the standard deviation value of each group of the candidate result samples; The candidate result sample with the smallest standard deviation value is determined as the subsample of the parent sample of the ship data.

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