Ocean contouring method based on correlation structure and monte carlo simulation

Abstract

The application belongs to the technical field of marine engineering structure design and evaluation, and particularly relates to a marine contour line drawing method based on correlation structure and Monte Carlo simulation. Each factor variable parameter is modeled to obtain an edge distribution of each factor variable parameter; a joint probability model of the edge distribution and correlation structure is established for all factor variable parameters to obtain a joint distribution; a Monte Carlo method is used to amplify and generate more Monte Carlo synthetic joint samples about the factor variable parameter set; a failure probability corresponding to a return period is calculated based on a number of samples in a certain period in the Monte Carlo synthetic joint samples; the Monte Carlo synthetic joint samples are projected, and a threshold corresponding to a failure probability quantile is calculated to obtain a half-space region data set; and a marine contour line is obtained by taking an intersection of all angle half-space region data sets. The method can significantly reduce the directional distortion, and improve the physical interpretability, risk consistency and engineering applicability of the environmental contour line.

Description

Technical Field

[0001] This invention belongs to the field of marine engineering structure design and evaluation technology, and particularly relates to extreme value analysis and reliability design of offshore platforms, ships, and offshore wind turbines under combined wind-wave (and current) environments. Specifically, it involves a method for drawing ocean contour lines based on relevant structures and Monte Carlo simulation, that is, a modeling and calculation method that uses relevant structures to describe the parameter dependencies of multi-factor variables and combines Monte Carlo sampling to obtain ocean contour lines. Background Technology

[0002] Offshore structures operate under the influence of multiple variables, including wind, waves (and currents). In engineering, an "Ocean Contour" (also called an Environmental Contour) is often used to approximate extreme combined sea states with a given return period to reduce response calculations and decouple the environment from the structure. Current ocean contour methods are very general and vague. During construction, relevant domestic and Norwegian standards are often referenced. Traditional methods are often combined with IFORM: first, Rosenblatt transformation is used to map environmental variable parameters to an independent standard normal space, and then the radius of this space is taken as a reliability index. The circle is then transformed back to the original space to form an equal failure probability curve. However, since the transformation is generally nonlinear, the probability of the half-space outside the tangent in the original space is equal to the target failure probability. The properties are not guaranteed to hold true, and there may be an overestimation or underestimation of the probability of failure. Summary of the Invention

[0003] The purpose of this invention is to overcome the problem in the prior art where the probability of the half-space outside the tangent in the original space is equal to the probability of target failure. The properties are not guaranteed to hold true, and there may be overestimation or underestimation of the failure probability. A method for drawing ocean contours based on relevant structures and Monte Carlo simulation is provided.

[0004] In the first aspect, the method for drawing ocean contour lines based on relevant structures and Monte Carlo simulation includes the following steps:

[0005] S1: Model each factor variable parameter in the factor variable parameter set to obtain the marginal distribution of each factor variable parameter. The factor variable parameter set has at least wave height factor variable parameter and wave period factor variable parameter. S2: Based on the marginal distribution obtained in step S1, establish a joint probability model of the marginal distribution and correlation structure for all factor variable parameters to obtain the joint distribution of the factor variable parameter set; S3. Based on the joint distribution in S2, use the Monte Carlo method to amplify and generate more Monte Carlo synthetic joint samples about the parameter set of factor variables; S4. Number of samples within a certain period based on Monte Carlo synthetic joint samples Recurrence period The probability of failure; S5. Project the Monte Carlo synthetic joint sample based on each orientation angle, and calculate the threshold of the quantile corresponding to the failure probability based on the projected random variable. Obtain the half-space region data set based on the threshold; take all angles. The ocean outline is obtained based on the intersection of the half-space region data sets and the boundary of the intersection.

[0006] Preferably, in S1, a spliced ​​marginal distribution is used for each factor variable parameter: The portion below the threshold is the body. The factor variable parameters located in the body are empirically distributed and smoothed using kernel density. The portion of the factor variable parameters above the threshold is considered the tail. The excess is modeled using the generalized Pareto distribution (GPD) for the tail portion of the factor variable parameters.

[0007] Preferably, the threshold for each candidate Regarding the model quantile of this high quantile A comprehensive loss model is established based on the relative error index and the skewness index. The model quantile and the empirical quantile are input into the comprehensive loss model to obtain the corresponding comprehensive loss. Then, the threshold with the smallest comprehensive loss is selected as the final threshold.

[0008] Preferably, in SI, the wave height H s Perform edge distribution modeling to obtain information about wave height. H s Edge distribution; for wave period T p Modeling with a log-normal distribution yields information about the wave period. T p The marginal distribution.

[0009] Preferably, in S2, the relevant structural modeling specifically includes the following steps: S21. Sort each factor variable parameter in ascending order and calculate its rank to construct and obtain uniform pseudo-observation pairs located in the first interval; S22. Perform normal space mapping on each parameter in the uniform pseudo-observation pair to obtain the corresponding mapping parameters; S23. Obtain the correlation coefficients of the correlation structure based on all mapping parameters, and truncate the correlation coefficients within the second interval to obtain the joint correlation structure of the factor variable parameter set.

[0010] Preferably, the joint distribution of correlation structures includes at least one of the following: Gaussian correlation structure, t-correlation structure, Gumbel correlation structure, Clayton correlation structure, or Vine correlation structure joint distribution.

[0011] Preferably, S3 includes the following steps: S31. Construct a correlation matrix for the correlation coefficient, decompose it into a matrix, generate a standard normal vector, and then map it back to the first interval to obtain a uniform sample of the correlation of all factor variable parameters; S32. Input each parameter in the relevant uniform sample into the inverse function of the splicing edge distribution to obtain the parameters of the composite factor variable, and further obtain the Monte Carlo composite joint sample.

[0012] Preferably, S5 includes the following steps: S51. Take uniformly within [0, 2π). =360 azimuth angles ; S52. For each direction angle Linear projection of Monte Carlo synthetic joint samples; S53. For a given return period Tr, calculate the single-step failure probability pf, and take the (1-pf) quantile of the projection as the threshold in that direction; S54. Obtain the support tangents in the corresponding directions based on the threshold, and find the intersection of two adjacent support tangents to obtain the boundary point set; S55. Find the two-dimensional convex hull of the boundary point set to obtain a closed polygon arranged in vertex order, which serves as the ocean contour line for this recurrence period. Preferably, in S53, for After smoothing by circular moving average, proceed to S54.

[0013] The present invention also provides an electronic device, including a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, it implements the ocean contour drawing method based on correlation structure and Monte Carlo simulation described in this embodiment.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: The ocean contour mapping method based on correlation structure and Monte Carlo simulation described in this invention establishes a joint probability model of "marginal distribution + correlation structure" for each factor variable parameter in the factor variable parameter set. It then expands the sample using the Monte Carlo method and calculates ocean contours for different return periods. Compared to the traditional IFORM method, this invention does not first map environmental variables to a standard normal space and construct a reliable index contour before inversely transforming it back to the original variable space. Instead, it directly calculates the quantile thresholds corresponding to the target failure probability for the projected random variables in each direction within the original physical variable space, and forms the environmental contour by the envelope of the half-space data sets in each direction. Because this construction method directly constrains the failure probability in each direction, the resulting contour is superior to IFORM in terms of directional reliability consistency. The traditional IFORM method, after undergoing a nonlinear inverse transformation, may result in different actual failure probabilities corresponding to different directions in the original variable space, leading to both local bias towards danger and local bias towards conservatism. This invention can significantly reduce this type of directional distortion and improve the physical interpretability, risk consistency, and engineering applicability of the environmental contour. Meanwhile, the failure probabilities of the contour lines obtained by this invention are generally closer to the target failure probabilities in all directions, while the IFORM method shows significantly higher or lower values ​​than the target values ​​in some directions. The former indicates that IFORM underestimates the extreme environmental risks in that direction, while the latter indicates that IFORM is overly conservative in that direction. Therefore, this invention can reduce design deviations caused by directional distortion while ensuring the consistency of target reliability. Attached Figure Description

[0015] Figure 1 This is a comparison diagram of the combined form of the original data and the synthesized data of this application (coaxial and within the same range).

[0016] Figure 2 This is a schematic diagram of the ocean outline overlaid with 1 / 20 / 50 / 100 / 200 years against a background of synthetic scattering.

[0017] Figure 3 This is a schematic diagram showing the superposition and comparison of the edge histograms, fitted density curves, and synthesized histograms of Hs and Tp in this application.

[0018] Figure 4 This is a schematic diagram illustrating the quantitative demonstration of a window length of 9 in this application.

[0019] Figure 5 is a schematic diagram comparing the ocean contour drawing method based on relevant structure and Monte Carlo simulation in this application with the traditional IFORM. Figure 5a This is a schematic diagram comparing the ocean contour drawing method based on relevant structure and Monte Carlo simulation of this application with the traditional IFORM ocean contour drawing method. Figure 5bThis is a schematic diagram comparing the ocean contour drawing method based on relevant structures and Monte Carlo simulation of this application with the traditional IFORM area.

[0020] Figure 6 This is a schematic diagram comparing the failure probabilities in each direction of the ocean contour drawing method based on relevant structures and Monte Carlo simulation in this application with those of the traditional IFORM method.

[0021] Figure 7 This is a flowchart illustrating the ocean contour drawing method based on relevant structures and Monte Carlo simulation of this application. Detailed Implementation

[0022] The present invention will now be described in further detail with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0023] Unless otherwise specified, the terms "upper," "lower," "left," "right," "center," "inner," and "outer," etc., used in the description of specific embodiments of the present invention to indicate orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationship in which the product / equipment / device is usually placed during use. These terms are merely for the purpose of facilitating the description of the present invention or simplifying the description in specific embodiments, and for enabling those skilled in the art to quickly understand the solution, and do not indicate or imply that a particular device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship. Therefore, they should not be construed as limitations on the present invention.

[0024] Furthermore, the use of terms such as "horizontal," "vertical," "suspended," "parallel," and "coaxial" does not imply that the corresponding device / component / element must be absolutely horizontal, vertical, suspended, parallel, or coaxial. Slight tilt or deviation is permissible, as long as it does not affect the normal function of the relevant component. For example, "horizontal" simply means that its direction is more horizontal relative to "vertical," not that the structure must be perfectly horizontal; a slight tilt is acceptable. "Coaxial" means that two components are arranged as coaxially as possible, allowing them to move coaxially or approximately coaxially when their relative positions change. Alternatively, it can be simplified to mean that the corresponding device / component / element, when arranged in "horizontal," "vertical," "suspended," "parallel," or "coaxial" directions, can have an error / deviation of ±10% relative to the corresponding direction, more preferably within ±8%, more preferably within ±6%, more preferably within ±5%, and more preferably within ±4%. For example, the deviation in the "coaxial" direction is controlled within 0.2-1mm, preferably within 0.2-0.5mm. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its function in the solution of the present invention.

[0025] Furthermore, the use of terms such as "first," "second," and "third" in terminology is merely for distinguishing descriptions of identical or similar components and should not be interpreted as emphasizing or implying the relative importance of a particular component.

[0026] Furthermore, in the description of the embodiments of the present invention, "several", "more than", and "a number of" represent at least two. The number can be any number, such as two, three, four, five, six, seven, eight, or nine, and can even exceed nine.

[0027] Furthermore, in the description of the technical solution of this invention, unless otherwise explicitly specified / limited / restricted, the terms "set up," "install," "connect," "link," "provided with," "laid out," and "arranged" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to connection methods commonly used in the art, such as welding, riveting, bolting, and threaded connections. Such connections can be mechanical, electrical, or communication connections; they can be direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components.

[0028] Example 1 like Figure 1-7 The method for drawing ocean contour lines based on relevant structures and Monte Carlo simulation described in this embodiment includes the following steps: S1: Edge distribution modeling: Model each factor variable parameter in the factor variable parameter set to obtain the marginal distribution of each factor variable parameter, and obtain the cumulative distribution curve based on all marginal distributions. The factor variable parameters in the factor variable parameter set include at least wave height and wave period.

[0029] Let environmental factor variables be defined for each factor variable parameter. Then, model each factor variable parameter to obtain the marginal distribution of each factor variable parameter, and obtain the cumulative distribution curve based on the marginal distribution.

[0030] Specifically, preferably, environmental factor variable parameters are set. T is the transpose symbol, where d represents that there are d environmental factor variables, for example, in the two-dimensional case. It contains two factor variable parameters, namely H s Represents wave height and T p Representing the wave period, the target failure probability is .

[0031] With two-dimensional wave height H s Sum of waves T p For example, first, regarding wave height H s Perform edge distribution modeling and wave period analysis. T p Marginal distribution modeling is performed to obtain the marginal distributions for each factor variable parameter; then, the cumulative distribution curve (function) is obtained based on all the marginal distributions. Preferably, wave height can be controlled. H s Modeling was performed using methods such as Weiber distribution and Gumbel distribution.

[0032] Preferably, for wave period T p A log-normal distribution can be used for modeling.

[0033] A preferred example is that the wave height is often modeled using a three-factor variable parameter Weibull distribution, the wave period or wind speed is modeled using a log-normal distribution, or tail splicing is performed using POT-GPD to better model the tail data.

[0034] Taking the three-factor variable parameter Weiber distribution as an example (scale) ,shape ,Location The specific distribution function and probability density function are as follows:

[0035]

[0036] S2: Construct a joint distribution using related structural structures.

[0037] Based on the marginal distribution of each factor variable parameter obtained in step S1, the joint distribution of the first factor variable parameter set is obtained by modeling the relevant structural dependency structure. The first factor variable parameter set includes at least wave height factor variable parameters and wave period factor variable parameters. Specifically, preferably, based on the marginal distribution of each factor variable parameter obtained in S1, relevant structural dependency structure modeling is used to select relevant structures. Regarding the choice of correlation structure, Gaussian correlation, t-correlation, Gumbel correlation, Clayton correlation, or Vine correlation can be selected. The joint distribution should yield the joint distribution of parameters for at least two factor variables (including at least wave height and wave period). Joint distribution formula:

[0038] For example: Commonly used t-related structures: Let For degrees of freedom, correlation matrix ,but

[0039] The Gaussian correlation structure is suitable for symmetric, tailless correlations. The cumulative distribution function is...

[0040] in The standard normal cumulative distribution function is... For the correlation matrix multivariate normal cumulative distribution function The t-correlation structure is suitable for symmetric tail correlation. The cumulative distribution function of the t-correlation structure is:

[0041] It has degrees of freedom. Related The cumulative distribution function of the multivariate t.

[0042] Archimedes correlation structures are applicable to unilateral tail distributions. Specifically, they are divided into the Clayton distribution, suitable for left-tailed correlations, and the Gumbel distribution, suitable for right-tailed correlations. The Clayton correlation structure is expressed as follows:

[0043] Gumbel expressions are applicable to right-tailed dependencies, and the expression is:

[0044] S3 Related Structure Sampling.

[0045] Based on the joint distribution in S2, more Monte Carlo synthetic joint samples of wave height and wave period of the first factor variable parameter set are generated based on Monte Carlo. Specifically, preferably, based on the joint distribution of the above-mentioned factor variable parameters, more Monte Carlo synthetic joint samples of wave height and wave period of the above-mentioned factor variable parameters are generated.

[0046] For example, the previous joint distribution was for 10 years, but now, based on the above scheme, Monte Carlo synthetic joint samples for 20 years, 50 years, or even 100 years can be generated.

[0047] For example: the third step, Monte Carlo sampling. (Generation) One related structural sample, ; Different sampling methods are used for different related structural structures. Gaussian correlation structure: Generates normally distributed samples Then, the cumulative distribution function of the standard normal distribution is used to generate... Then, based on the corresponding marginal distribution, the target factor variable parameters are generated.

[0048] For t-correlation structures, according to the distribution Generate samples The parameters of the factor variables are obtained using the cumulative distribution function of the t-distribution. Then, the marginal distribution inverse cumulative distribution function is used to obtain samples of the target factor variable parameters.

[0049] S4 Failure Probability Calculation Annual sample number based on Monte Carlo synthetic joint samples and recurrence period Calculate the probability of failure: based on independent time intervals (typically 3 hours), annual sample size. Recurrence period Corresponding failure probability Or use calculate; For example, if the time step is 3 hours, the number of independent sea states per year is 365.25 * 8. For the return period... The failure probability corresponding to the year is

[0050] S5 direction tangent and half-space construction. For a given angle , thus obtaining the direction vector Calculate projection

[0051] The i-th Monte Carlo synthetic joint sample is in the direction Projection values ​​on Take the serial number Obtain the half-space data set. , represents all less than This corresponds to a specific set of data for wave height and wave period values.

[0052] S6 is constructed using Monte Carlo simulation of the envelope. Take the intersection of all angles (0-π) of the half-space , The boundary is the equivalent probability envelope under the above failure probability, i.e., the ocean contour line.

[0053] There is a joint distribution Sample Choose an angle Calculate projection .

[0054] Sort by projection in ascending order ,make Take the threshold This yields a half-space region data set, which represents the half-space region. .

[0055] For all Take the intersection Its boundary is the ocean outline.

[0056] In the above scheme, regarding the conversion between return period and failure probability, if sea state is calculated using 3-hour independent steps, then... The annual failure probability can be approximated as: Implementing this type of method requires first determining a reasonable joint environment model, which can be constructed using a factor variable parameterization model or based on empirical distributions and bootstrap methods.

[0057] In extreme marine conditions, for offshore platforms or offshore wind power, the values ​​on the ocean contour line are used as input conditions.

[0058] The following describes a preferred implementation of the method of the present invention in conjunction with an embodiment: using long-term sea state samples as input, a joint probability model of "marginal distribution + copula" is established for the significant wave height Hs and wave period Tp, and the samples are amplified by the Monte Carlo method and ocean contours with different return periods are calculated.

[0059] The program corresponding to this embodiment can run on a computer, and the input data is preferably a NumPy array file (.npy).

[0060] The following describes a preferred embodiment in detail: 1. Data Sources and Preprocessing (1) Data file and fields: The input file is a NumPy array file, which is a two-dimensional floating-point array. In this embodiment, two columns are used as joint factor variable parameters: namely, the effective wave height Hs and the wave period Tp.

[0061] (2) Cleaning rules: Perform validity screening on both Hs and Tp, and retain only samples that meet the condition of "finite value and greater than 0"; remove missing values, infinity and non-physical values ​​(such as negative or zero values). The cleaned samples are denoted as {(Hs_i, Tp_i)}, i=1,…,n.

[0062] (3) Plotting sampling: When the sample size is extremely large, in order to avoid slow plotting or occlusion, random sampling can be performed on the scatter plot or density plot; however, the contour calculation and Monte Carlo synthesis of the joint sample generation use the full synthetic data.

[0063] 2. Conversion of independent step size, annual equivalent sample size, and return period (1) Independent step length setting: Considering the correlation of wave sequence, this embodiment takes an independent step length of Δt = 6 hours.

[0064] (2) Annual equivalent sample size: Number of nearly independent samples within one year ≈365.25×(24 / Δt). When Δt = 6 hours, then ≈365.25×4≈1461.

[0065] (3) Single-step failure probability: For a given return period Tr (unit: years), this embodiment uses a failure probability pf = 1 / ( ·Tr).

[0066] (4) Recurrence period set: In this embodiment, the ocean outline corresponding to Tr∈{1, 20, 50, 100, 200} years is calculated.

[0067] 3. Marginal distribution modeling (body empirical distribution + tail GPD splicing) hybrid distribution To simultaneously ensure both "shape fidelity for common sea states" and "tail extrapolation for extreme sea states," this embodiment employs a spliced ​​marginal distribution for each factor variable parameter: Below the threshold, the data constitutes the body, and is modeled using at least one of empirical, parametric, semi-parametric, or non-parametric distributions. Parametric distributions include at least one of Weibull, Gamma, Lognormal, Rayleigh, Normal, or Gumbel distributions, while non-parametric distributions include at least one of empirical distributions, kernel density estimation distributions, or spline smoothing empirical distributions. Above the threshold, the data constitutes the tail, and the excess tail data is preferably modeled using the generalized Pareto distribution (GPD).

[0068] 3.1 Threshold Candidates and Tail Sample Number Constraints (1) Threshold Candidates: Threshold quantile candidate sets {0.95, 0.97, 0.98, 0.985} are set for the wave height Hs and the logarithmic period ln(Tp), respectively. For each candidate quantile... The threshold u is taken as the sample quantile corresponding to this quantile.

[0069] (2) Number of tail samples: To ensure the stability of GPD estimation, the number of tail samples above the threshold should be no less than 200 (which can be adjusted according to the data size). If a candidate threshold results in insufficient tail samples, the candidate will be automatically skipped.

[0070] 3.2 Wave height edge distribution (1) Partitioning: based on threshold The wave height sample is divided into a body (Hs≤ ) and tail (Hs> ).

[0071] (2) Cumulative distribution of body parts: The empirical distribution is formed by sorting the body parts samples. and according to body proportion Scaling yields: when h ≤ hour, This design can directly reproduce the empirically determined shape of the body, avoiding mismatch in the distribution of simple parameters in the main body area.

[0072] (3) Tail excess and GPD: Define tail excess z = h - (z>0), its distribution is fitted using GPD(z;ξ,β), so that when h> hour, .

[0073] 3.3 Periodic Tp Marginal Distribution The wave period Tp typically exhibits a significant right skew. To improve the numerical stability of the tail fitting, this embodiment first performs a logarithmic transformation Y=ln(Tp), and then fits the data in the Y domain using the same splicing strategy as Hs. Then, the marginal distribution of Tp is obtained through inverse transformation Tp=exp(Y). This approach can significantly reduce the ill-conditioned nature of long-tailed fitting and make the high quantile interval more controllable.

[0074] 3.4 Suppression of High-Plexicon Size "Overestimation" and Tail-Scale Self-calibration (1) Thick tail parameter constraint: To avoid the contour line being too high in the wave height direction, this embodiment sets a feasible range for the GPD shape parameter ξ: the ξ constraint for Hs is [-0.20, 0.30], and the ξ constraint for ln(Tp) is [-0.20, 0.35]. If the fitted ξ exceeds the limit, it is truncated to the boundary value.

[0075] (2) Threshold selection criterion: For each candidate threshold Calculate a set of higher quantiles p∈[ q u p φ ]( p φ Take the smaller of 0.9995 or 1-3 / n and compare the model quantiles. (p) and empirical quantile (p). Define the relative error index: Relative RMSE = sqrt(mean((( - ) / ( +ε))^2));Slightly larger measure = mean(max(0,( - ) / ( The overall loss is calculated as: Overall Loss = Relative RMSE + λ·Largest Metric, where λ = 3.5 in Hs and λ = 4.0 in ln(Tp). The threshold with the minimum overall loss is selected as the final threshold.

[0076] 4. Related structure modeling (taking Gaussian related structure as an example) (1) Obtaining pseudo-observations through rank transformation: Sort Hs and Tp in ascending order and calculate their ranks to construct... =(rank(Hs)-0.5) / n, =(rank(Tp)-0.5) / n, yielding a uniform pseudo-observation pair located in the first interval (0,1). , This step makes the relevant structure fitting more robust to edge errors.

[0077] (2) Normal space mapping: Let = , = ,in It is the standard normal quantile function.

[0078] (3) Correlation coefficient estimation: The maximum likelihood estimate of the Gaussian correlation structure can be given by the closed-form equation of the correlation coefficient, taking ρ = corr( , The correlation coefficient ρ is then truncated in the second interval [-0.98, 0.98] to ensure numerical stability and positive definiteness. This yields the joint correlation structure.

[0079] 5. Monte Carlo amplification to generate synthetic sea state samples (1) Synthesis Scale: To improve the stability of high quantile estimation, this embodiment generates a Monte Carlo synthetic joint sample equivalent to 200 years. The Monte Carlo synthetic joint sample size is... ≈200×1461≈2.92×10^5.

[0080] (2) Correlation structure sampling: Construct the correlation matrix R=[[1, ρ], [ρ, 1]], and perform its Cholesky decomposition R=LL^T to generate a two-dimensional standard normal vector. , ) = L·ε, where ε is the independent standard normal distribution. Then, by mapping u = Φ(Z) back to (0, 1), we obtain the relevant uniform samples ( , Cholesky decomposition is a matrix decomposition method.

[0081] (3) Edge inverse transformation: respectively , Inputting the inverse function (quantile function) of the splicing edge distribution yields the parameters of the composite factor variables: , Monte Carlo synthetic joint samples {( , )} is used for subsequent contour line calculation and visualization.

[0082] 6. Ocean contour line calculation (1) Directional discretization: uniformly selected within [0, 2π). =360 azimuth angles .

[0083] (2) Directional projection: For each direction Linear projection of the Monte Carlo synthetic joint samples: .

[0084] (3) Directional threshold: For a given return period Tr, calculate the single-step failure probability pf = 1 / (1461·Tr), and take the (1-pf) quantile of the projection as the threshold for that direction. .

[0085] (4) Ring smoothing: To suppress spikes caused by high quantiles in a limited number of samples, this embodiment uses... Perform circular moving average smoothing with a window length of 9.

[0086] (5) Construct boundary points from the intersection of tangents: Each direction corresponds to a supporting tangent. The boundary point set can be obtained by finding the intersection of two adjacent tangent lines.

[0087] (6) Convex Hull and Closure: Find the two-dimensional convex hull of the boundary point set to obtain a closed polygon arranged in vertex order, which serves as the ocean contour line for this recurrence period. This step can effectively eliminate local self-intersection or non-closure problems, ensuring the geometric consistency of the contour line.

[0088] The following is a detailed explanation of why the window length is set to 9 in the above scheme: like Figure 4 As shown, the selection criteria for the sliding window parameters are... This invention uses a circular sliding window averaging method to smooth the environmental contour support function C(θ). Through multi-dimensional verification using a quantitative index system and trade-off curve analysis, the optimal sliding window size is determined to be 9, based on the following specific criteria: Constructing a quantitative evaluation index system To quantify the smoothing effect, this invention defines two core evaluation metrics: Roughness R: The second-order circumferential root mean square of the support function C(θ), used to characterize the jaggedness and irregularity of the support function curve. The smaller R is, the smoother the curve is. Deviation D: The relative mean square deviation between the smoothed support function and the original support function. It is used to characterize the degree of shape distortion introduced by the smoothing operation. The smaller D is, the more faithful the smoothed contour is to the original distribution characteristics.

[0089] 2. Quantitative analysis of trade-off curves This invention calculates the above-mentioned indices by traversing the sliding window range [1, 31], and plots the roughness-deviation tradeoff curve. The results show that: Roughness R: When the window size increases from 1 to 9, R decreases rapidly (the rate of decrease is fastest from 1 to 5, and continues to decrease significantly from 5 to 9); after the window size is greater than 9, the marginal benefit of R decreases sharply, and the smoothing effect is not significantly improved. Deviation D: When the window size increases from 1 to 9, D hardly changes and the shape distortion is negligible; when the window size is larger than 9, D increases rapidly and the contour distortion is significantly aggravated.

[0090] The sliding window of 9 is located precisely at the inflection point of the tradeoff curve, achieving an optimal balance between sufficiently reducing roughness and minimizing shape distortion.

[0091] Figure 1 The "main region shape and related trends" used to examine the joint distribution are preserved. If the Monte Carlo composite joint sample shows a significantly longer tail or a shift of dense regions outward in the wave height direction relative to the original sample, it usually means that the wave height tail is too fat; this can be suppressed by tightening the upper bound of ξ, increasing the penalty coefficient λ, or enabling / enhancing the self-calibration of the tail scale β.

[0092] Figure 2 This is used to read the combined extreme combinations under different return periods. Theoretically, the longer the return period, the more the contour line expands outward while maintaining a closed and smooth shape. In this embodiment, the maximum / minimum coordinates of the contour line itself are used as the coordinate axis range when plotting, with an additional 6% boundary white space to ensure that the "full contour line is visible" and avoid only displaying a part of the contour line.

[0093] Figure 3 This is used for marginal consistency verification at the parameter level of a single-factor variable. The fitted curve should cover the shape of the original histogram and remain consistent in the right tail interval; the synthesized histogram should overlap with the original histogram as much as possible. If the right tail is significantly high, it indicates that the tail parameters still need further constraint or calibration; if the main body region has significant deviation, it is necessary to consider adjusting the threshold candidate set or adding a body smoothing / binning strategy.

[0094] 8. Summary of parameter settings

[0095] In the above solution of this embodiment, The independent step size Δt can be adjusted based on data correlation, for example, 3 hours or 12 hours; after adjustment, it needs to be updated synchronously. Convert to pf.

[0096] The number of contour directions and the smoothing window can be adjusted as needed: increasing the number of directions can improve geometric resolution, while increasing the smoothing window can reduce jagged edges but may lead to over-smoothing.

[0097] The relevant structure can be replaced with t-related structures, Clayton, Gumbel, etc. to enhance the tail-related characterization; the edge splicing structure remains unchanged to compare the effects of different relevant structures.

[0098] The method in this embodiment can be extended to environmental profiles with three-factor or multi-factor variable parameters (e.g., wind speed can be added). In this case, a high-dimensional correlation structure and multi-dimensional support function or equiprobability surface can be used for construction.

[0099] The ocean contour drawing method based on correlation structure and Monte Carlo simulation described in this embodiment performs extensive sampling of joint environmental factor variable parameters (such as wave height, wave period, wind speed, etc.) in the original environmental space; and samples each azimuth angle... Calculate the sample projection and select a threshold such that the proportion outside the threshold is P. f Based on this, a set of tangent half-spaces is obtained, and the intersection of all directions yields a convex set, the boundary of which is the ocean outline; this method does not require transformation of factor variables and parameters, and the interpretation is more intuitive.

[0100] The ocean contour drawing method based on correlation structure and Monte Carlo simulation described in this embodiment differs from the traditional IFORM method in that it does not first map environmental variables to a standard normal space and construct a reliable index contour before inversely transforming it back to the original variable space. Instead, it directly calculates the quantile threshold corresponding to the target failure probability for the projected random variables in each direction within the original physical variable space, and forms the environmental contour line by the envelope of the half-space data set in each direction.

[0101] Because this construction method directly constrains the failure probability in each direction, the resulting profile outperforms IFORM in terms of directional reliability consistency. Traditional IFORM methods, after undergoing a nonlinear inverse transformation, may result in different actual failure probabilities corresponding to different directions in the original variable space, leading to both local bias towards danger and local bias towards conservatism. This invention can significantly reduce this type of directional distortion, improving the physical interpretability, risk consistency, and engineering applicability of the environmental profile.

[0102] By comparing the failure probabilities of the method of this invention and the IFORM method in multiple directions, it can be seen that the failure probability of the profile obtained by this invention is generally closer to the target failure probability in all directions, while the IFORM method shows significantly higher or lower than the target value in some directions. The former indicates that IFORM underestimates the extreme environmental risk in that direction, while the latter indicates that IFORM is overly conservative in that direction. Therefore, this invention can reduce design deviations caused by directional distortion while ensuring the consistency of target reliability.

[0103] As shown in Figures 5 and 6, we use the ratio of actual failure probability to target value Pf in a certain direction to illustrate the superiority of the method. A ratio of 1 indicates that the actual failure probability is exactly equal to the target value Pf; a ratio greater than 1 indicates that the actual failure probability is greater than the target, and the risk is underestimated. Conversely, a ratio less than 1 indicates that the calculation in that direction is more conservative.

[0104] The verification results show that: like Figure 6 As shown, the failure probability ratio of the method of the present invention (green curve in the figure) is stable at around 1.0 in all directions with minimal fluctuation, indicating that the contour line precisely controls the target failure probability in all directions.

[0105] The failure probability ratio of the IFORM method (red curve in the figure) fluctuates significantly in all directions. Directions with a ratio greater than 1 indicate that IFORM underestimates the risk of extreme environments in that direction (the outline is too small, as shown by the red filled area in the figure); directions with a ratio less than 1 indicate that IFORM is overly conservative in that direction (the outline is too large, as shown by the pink filled area in the figure).

[0106] like Figure 5a As shown in the ocean contour line comparison diagram, for 20 / 50 / 100 / 200-year return periods, the contour lines (solid lines) obtained by the method of the present invention are slightly wider than the IFORM contour lines (dashed lines), that is, the range of extreme sea state (Tp, Hs) combinations covered by the present invention is larger.

[0107] like Figure 5b As shown, combined with the above failure probability verification results, it can be seen that the larger area of ​​the present invention is not due to excessive conservatism, but rather that the IFORM area is too small: the exceedance ratio of samples outside the IFORM outline is higher than the target Pf, indicating that the IFORM fails to cover the expected extreme sea conditions. The exceedance ratio of samples outside the outline of the present invention is consistent with the target Pf, indicating that the present invention precisely covers the correct range of extreme operating conditions.

[0108] In three dimensions (such as when wind speed is also considered), IFORM requires deriving the Rosenblatt transformation for three variables, which is very complex. The ocean contour drawing method based on correlation structure and Monte Carlo simulation described in this embodiment only requires sampling from the joint distribution and does not require deriving the transformation formula at all. Its method is far superior to IFORM in three-dimensional scenes.

[0109] Example 2 This embodiment provides an electronic device, including a processor and a memory. The memory stores a computer program, which, when executed by the processor, implements the ocean contour drawing method based on correlation structure and Monte Carlo simulation described in Embodiment 1.

[0110] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for drawing ocean contour lines based on relevant structures and Monte Carlo simulation, characterized in that, Includes the following steps: S1: Model each factor variable parameter in the factor variable parameter set to obtain the marginal distribution of each factor variable parameter. The factor variable parameter set has at least wave height factor variable parameter and wave period factor variable parameter. S2: Based on the marginal distribution obtained in step S1, establish a joint probability model of the marginal distribution and correlation structure for all factor variable parameters to obtain the joint distribution of the factor variable parameter set; S3. Based on the joint distribution in S2, use the Monte Carlo method to amplify and generate more Monte Carlo synthetic joint samples about the parameter set of factor variables; S4. Calculate the failure probability corresponding to the return period based on the number of samples in a certain period of the Monte Carlo synthetic joint sample; S5. Project the Monte Carlo synthetic joint sample based on each orientation angle, and calculate the threshold of the quantile corresponding to the failure probability based on the projected random variable. Obtain the half-space region data set based on the threshold; take all angles. The ocean outline is obtained based on the intersection of the half-space region data sets and the boundary of the intersection.

2. The method for drawing ocean contour lines based on correlation structure and Monte Carlo simulation according to claim 1, characterized in that, In S1, a concatenated marginal distribution is used for each factor variable parameter: The portion below the threshold is the body. The factor variable parameters located in the body are empirically distributed and smoothed using kernel density. The portion of the factor variable parameters above the threshold is considered the tail. The excess is modeled using the generalized Pareto distribution (GPD) for the tail portion of the factor variable parameters.

3. The method for drawing ocean contour lines based on correlation structure and Monte Carlo simulation according to claim 2, characterized in that, For each candidate threshold, a set of high quantiles is calculated, and the model quantiles and empirical quantiles for that high quantile are compared. A comprehensive loss model is established based on the relative error index and the skewness index. The model quantiles and empirical quantiles are input into the comprehensive loss model to obtain the corresponding comprehensive loss. Finally, the threshold with the smallest comprehensive loss is selected as the final threshold.

4. The method for drawing ocean contour lines based on correlation structure and Monte Carlo simulation according to claim 1, characterized in that, In S1, the wave height H s Perform edge distribution modeling to obtain information about wave height. H s Edge distribution; for wave period T p Modeling with a log-normal distribution yields information about the wave period. T p The marginal distribution.

5. The method for drawing ocean contour lines based on correlation structure and Monte Carlo simulation according to claim 1, characterized in that, In S2, the relevant structural modeling specifically includes the following steps: S21. Sort each factor variable parameter in ascending order and calculate its rank to construct and obtain uniform pseudo-observation pairs located in the first interval; S22. Perform normal space mapping on each parameter in the uniform pseudo-observation pair to obtain the corresponding mapping parameters; S23. Obtain the correlation coefficients of the correlation structure based on all mapping parameters, and truncate the correlation coefficients within the second interval to obtain the joint correlation structure of the factor variable parameter set.

6. The method for drawing ocean contour lines based on correlation structure and Monte Carlo simulation according to claim 5, characterized in that, The joint distribution of correlation structures includes at least one of the following: Gaussian correlation structure, t-correlation structure, Gumbel correlation structure, Clayton correlation structure, or Vine correlation structure joint distribution.

7. The method for drawing ocean contour lines based on correlation structure and Monte Carlo simulation according to claim 5, characterized in that, S3 includes the following steps: S31. Construct a correlation matrix for the correlation coefficient, decompose it into a matrix, generate a standard normal vector, and then map it back to the first interval to obtain a uniform sample of the correlation of all factor variable parameters; S32. Input each parameter in the relevant uniform sample into the inverse function of the splicing edge distribution to obtain the parameters of the composite factor variable, and further obtain the Monte Carlo composite joint sample.

8. The method for drawing ocean contour lines based on correlation structure and Monte Carlo simulation according to claim 1, characterized in that, S5 includes the following steps: S51. Take uniform values ​​in the range [0, 2π). =360 azimuth angles ; S52. For each direction angle Linear projection of Monte Carlo synthetic joint samples; S53. For a given return period Tr, calculate the single-step failure probability pf, and take the (1-pf) quantile of the projection as the threshold in that direction; S54. Obtain the support tangents in the corresponding directions based on the threshold, and find the intersection of two adjacent support tangents to obtain the boundary point set; S55. Find the two-dimensional convex hull of the boundary point set to obtain a closed polygon arranged in vertex order, which serves as the ocean outline for this recurrence period.

9. The method for drawing ocean contour lines based on correlation structure and Monte Carlo simulation according to claim 8, characterized in that, In S53, regarding... After smoothing by circular moving average, proceed to S54.

10. An electronic device comprising a processor and a memory, wherein the memory stores a computer program, characterized in that, When the computer program is executed by the processor, it implements the ocean contour drawing method based on correlation structure and Monte Carlo simulation as described in any one of claims 1 to 9.

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