A multi-site joint extreme value prediction and verification method for ocean environment design parameters

Abstract

The present invention discloses a method for predicting and testing the multi-site joint extreme value of a marine environment design parameter, and the steps are as follows: obtaining historical data of several years measured by multiple sites in a region or a sea area, determining the maximum marine environmental element value of each observation site in each independent storm process, and forming sample analysis data; fitting the generalized Pareto distribution after selecting a threshold for the sample analysis data, and calculating the design value corresponding to the corresponding return period; combining the sample analysis data of multiple sites in the selected area, selecting a unified order statistic, analyzing the correlation, performing Laplace marginal transformation, and establishing a multi-site conditional extreme value model; using the conditional extreme value model to calculate the probability of the corresponding extreme condition exceeding the design value. The method described in the present invention quantifies the probability of failure of the extreme value estimation of the return period to a certain extent, and can be used as a test method for the design value of the marine environment parameter under extreme conditions, which is beneficial to the prevention and control of marine disasters and the improvement of the design safety of marine structures.

Description

Technical Field

[0001] The invention relates to ocean and coastal engineering technology, in particular to a multi-site joint extreme value prediction and testing method for ocean environment design parameters. Background Art

[0002] Marine environmental design parameters refer to a series of environmental factors that must be considered when designing marine structures, such as wind, waves, and tides. In order to ensure the service life of the designed structure, such design parameters are usually interpreted in the form of once in N years. In recent years, with global warming, various marine disasters have occurred frequently, causing great damage to marine structures. Therefore, it is imperative to use a large amount of historical data to estimate possible extreme disaster events in the future to ensure the safety of marine and coastal structures.

[0003] Extreme value theory is a powerful statistical method that can provide statistical models for rare natural disaster events. Through extreme value theory, the size of extreme marine disaster data that occurs once in many years can be calculated, such as "once in 50 years" and "once in 100 years" wave height, wind speed, etc. There are two common explanations for the recurrence level with a recurrence period of T years: (i) waiting time: the average waiting time before the next event occurs is T years (ii) number of events: the average number of events that occur in a T-year period is 1. Extreme data are often referred to when designing marine structures to resist extreme disasters that may occur in the future.

[0004] The most widely used method for inferring the extreme values of marine environmental design parameters is the annual extreme value method, which selects the largest sample data of each year as the analysis data to form an extreme value data set, and then fits the extreme distribution families such as the generalized extreme value distribution (GEV) and the Gumbel distribution. The distribution parameters are fitted through the selected data and the extreme values corresponding to the corresponding return period are calculated by extrapolation. This method ignores a large amount of data and cannot well reflect the uncertainty of marine environmental elements in the selected area. Another method is the over-threshold method (POT), but the over-threshold method needs to ensure the independence and extremeness of the data. The currently used POT method cannot simultaneously ensure the independence and extremeness of the data.

[0005] At present, the calculation of marine environmental design parameters is highly dependent on the historical data of a single observation site. However, extreme events between different sites are often correlated. It is urgent to effectively utilize this correlation to improve the inference accuracy of the extreme values of the recurrence period of marine environmental design parameters. Summary of the invention

[0006] Purpose of the invention: The purpose of the present invention is to provide a multi-site joint extreme value prediction and verification method for marine environmental design parameters, so as to improve the prediction reliability of the recurrence period of marine environmental elements, and use the extreme dependence of multiple sites to give a conditional probability corrected prediction value.

[0007] Technical solution: A multi-site joint extreme value prediction and verification method for ocean environment design parameters according to the present invention includes the following steps:

[0008] (1) Data collection: Use Python, R language, Matlab, etc. to crawl and obtain the measured data of multiple observation stations in the selected ocean area over the years and integrate them;

[0009] (2) Data preprocessing: Analyze data missing, perform multiple interpolation on the obtained data to form complete historical data;

[0010] (3) Selection of independent storm process data: For the data measured at a single observation station after preprocessing, use the extreme value index diagram and the generalized Pareto distribution parameter stability diagram to select a lower threshold u 1i , assuming that the ocean environment elements exceeding u 1i within X hours belong to the same storm process and are grouped into one category, select the maximum value in each category to form sample analysis data;

[0011] (4) Single-site extreme value prediction: After using the mean residual life diagram to select a larger threshold u 2i for the analysis data selected in the independent storm process, fit the data exceeding u 2i to the generalized Pareto distribution, use the maximum likelihood estimation method to estimate the parameters of the generalized Pareto distribution, and calculate the extreme values corresponding to the corresponding return periods;

[0012] After using the mean residual life diagram to select a larger threshold u 2i for the analysis data selected in the independent storm process, fit the data exceeding u 2i to the generalized Pareto distribution, use the maximum likelihood estimation method to estimate the parameters of the generalized Pareto distribution, and the formula is as follows:

[0013]

[0014] Among them, ξ is the shape parameter of the Pareto distribution, σ is the scale parameter of the Pareto distribution, and l(σ,ξ) represents the maximum likelihood estimation;

[0015] Calculate the extreme values corresponding to the corresponding return periods, and the formula is as follows:

[0016]

[0017] Among them, z m represents the extreme value under a specific return period m, and λ u represents the number of times the extreme value appears on average per year after the secondary threshold selection.

[0018] (5) Selection of multi-site order statistics: Based on the independent storm process, the analysis data of all sites in the selected area are obtained. The analysis data of all sites are sorted from large to small respectively, the order statistic k of this area is determined, and the first k (k is less than the length of the sample analysis data of the observation points of all stations) analysis data of all sites in this area are selected to form a multi-site sample analysis data group;

[0019] (6) Establishment of multi-site joint extreme condition model: Using u corresponding to each site 2i as the marginal threshold, after performing Laplace marginal transformation on each site in the multi-site analysis data group and setting the dependence proportion value y (0 < y < 1), a multi-site conditional extreme value model (CEM) of the selected area is established, and the extreme value dependence relationship between multi-sites is estimated by using the extreme value structure parameter a of the CEM model;

[0020] Let X = (X1,..., X d ) be a d-dimensional random variable with arbitrary marginal distributions. Let F i represent the estimate of the i-th marginal distribution function, G represent the distribution function of the to-be-determined standardized marginal distribution. The original vector variable X is transformed into Y = (Y1,…, Y d ), which is a variable with standardized marginal distributions through the use of the probability integral transformation, as follows:

[0021] Y i = G -1 (F i (X i )), i = 1,..., d (3)

[0022] F i is the marginal empirical distribution function of the data. In this case, Equation (3) is also called the rank transformation, or a semi-parametric model that uses the empirical distribution below the threshold and the fitted GPD model of the distribution tail above the threshold;

[0023] Y i is the required conditional variable, Y -i is the remainder representing the vector Y excluding the i-th component. The method of the conditional extreme value method conditions on Y i being higher than a high threshold t, and models the conditional dependence of the remaining Y i based on the observed values of Y -i > t; the form of the regression model of the conditional dependence structure depends on the exact choice of G in Equation (3);

[0024] If G is the Laplace distribution function, Y is the marginal Laplace distribution function; under the condition that the variable Y i exceeds the high threshold t, the conditional extreme value model of the remaining variable Y -i adopts the following form:

[0025]

[0026] Z |i is the vector residual, and the (d - 1)-dimensional parameter vectors α |i and β |i satisfy (α |i , β |i ) ∈ (-∞, 1) d-1 , where α |i , related to Y j , j ∈ {1,..., d}, j is not equal to i, then 0 < α j|i ≤1 and -1 ≤ α j|i < 0 respectively correspond to the positive correlation and negative correlation between the large values of Y j and Y i ; in the case of using the Laplace margin, the structure of the correlation model is greatly simplified, and in this case, a single model structure is sufficient for the extreme dependence between the selected regional sites.

[0027] (7) Extreme conditional probability prediction: Calculate the probability that other sites exceed the marine environmental design parameters under extreme conditions at a certain site through the multi-site conditional extreme value model (CEM) to verify the safety of the selected corresponding design values of the structure.

[0028] A computer storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the above-mentioned multi-site joint extreme value prediction and verification method for marine environmental design parameters.

[0029] A computer device, including a storage, a processor, and a computer program stored on the storage and executable on the processor, and when the processor executes the computer program, it implements the above-mentioned multi-site joint extreme value prediction and verification method for marine environmental design parameters.

[0030] Beneficial effects: Compared with the prior art, the present invention has the following advantages: The method of the present invention ensures the extremity of the selected extreme value data, quantifies the failure probability of the return period extreme value estimation to a certain extent, and can be used as a verification method for the design values of marine environmental parameters under extreme conditions, which is beneficial to the prevention and control of marine disasters and the improvement of the design safety of marine structures. Description of the Drawings

[0031] Figure 1 The flow chart of the steps of the method of the present invention;

[0032] Figure 2 The extreme value index diagram and the generalized Pareto distribution parameter stability diagram; among them, Figure (a) is the extreme value index estimation diagram, and Figure (b) is the generalized Pareto distribution parameter stability diagram;

[0033] Figure 3 Data graph after clustering by selecting threshold u1;

[0034] Figure 4 Average remaining life graph;

[0035] Figure 5 Generalized Pareto distribution fitting effect test graph; among them, Figure (a) is the cumulative probability distribution graph, and Figure (b) is the quantile test graph;

[0036] Figure 6 Spearman correlation coefficient graph;

[0037] Figure 7 Conditional extreme value model prediction graph. Specific implementation manner

[0038] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0039] As Figure 1 shown, a multi-site joint extreme value prediction and test method for marine environment design parameters includes the following steps:

[0040] 1. Data collection: Historical data of hourly tide levels at two stations along the coast of a certain area from 2005 to 2020 was collected using R language.

[0041] 2. Data preprocessing: It was observed from Table 1 that the missing historical tide level data at this location is very few and does not affect the extreme value analysis. Multiple interpolation was performed on the missing data in Table 1.

[0042] Table 1 Historical data of two tide level stations in a certain area

[0043]

[0044] 3. Selection of independent storm process data: Taking Station 1 as an example for single-site extreme value analysis, first draw the extreme value index graph and the generalized Pareto distribution parameter stability graph of Station 1. As Figure 2 shown, select a suitable threshold u 11 = 355 cm. The tide level data exceeding u 11 within 60 hours is regarded as the same storm process. Select the maximum value in each storm process to form the sample analysis data. Station 1 generated a total of 257 storm processes with tide levels exceeding 355 cm between 2005 and 2020, and the maximum tide level value during this period was 466 cm. Figure 3 shows the scatter distribution graph of the tide level data of Station 1 after the selection of the independent storm process. Perform the same operation on Station 2 to select the threshold u 12 = 315 cm. Table 2 shows the description of the sample analysis data of the two stations.

[0045] Table 2 Multi-site sample data

[0046]

[0047] 4. Single-site extreme value prediction:

[0048] Select the second threshold u from the sample analysis data of Site 1 21 , Figure 4 is the average remaining life graph of Site 1. Select a stable threshold u that can maintain the data volume 21 = 375 cm.

[0049] Use the Generalized Pareto Distribution to fit the data, and use the maximum likelihood estimation method in Equation (1) to estimate the parameters of the distribution. Perform the same operation on Site 2. Select u from the sample analysis data of Site 2 22 = 332 cm. The parameter estimation results of Site 1 and Site 2 are shown in Table 3.

[0050] Table 3 Parameter estimation results of Site 1 and Site 2

[0051]

[0052] Using formula (2), calculate the design tide level heights of Site 1 and Site 2 with a 100-year return period to be 499 cm and 391 cm respectively. The extreme value fitting effect of Site 1 is shown in Figure 5 , indicating that the Pareto distribution effect fitted by the extreme value data selection method of the present invention is very good.

[0053] 5. Selection of order statistic k

[0054] Sort the sample analysis data of the two sites from largest to smallest, and select k = 200 according to the lengths of the sample analysis data of the two sites to form the multi-site sample analysis data group in Table 4.

[0055] Table 4 Multi-site sample analysis data group

[0056] Observation point k Maximum value Minimum value Mean value Station 1 200 466 360 374 Station 1 200 372 318 329

[0057] 6. Multi-site joint conditional extreme value modeling: Use the multi-site sample analysis data group in Table 4, Figure 6 Draw the Spearman pairwise correlation graph of the extreme tide level data of the two sites in, and it can be seen that there is a strong correlation between the extreme tide level data of the two observation sites. Perform the Laplace marginal transformation according to formulas (3) and (4). Select the dependence ratio value y = 0.75, with the respective u of the two sites 2iAs a marginal threshold, a conditional extreme value model (CEM) of extreme data of tidal levels at two stations is established. Table 5 shows the extreme value dependence structure parameter a of the established CEM model. The extreme value structure parameter a represents the extreme influence on other stations in the region conditional on one observation point. Table 5 gives the estimation results of the extreme value structure parameters of the two-station CEM model.

[0058] Table 5 Extreme value structure parameter a of Station 1 and Station 2

[0059] Station 2 Taking Station 1 as the condition 0.2034 Station 1 Taking Station 2 as the condition 0.1812

[0060] 7. Extreme conditional probability prediction: Table 6 conducts a probability analysis of the design tidal level value with a 100-year return period calculated in the prediction of the tidal level exceeding the single-point extreme value under extreme conditions using the established CEM model. Under given conditions, the CEM model will extrapolate and calculate the exceedance probability. Figure 7 The data prediction diagram of Station 1 under extreme conditions of the CEM model is given. Extreme value conditions Q99.792 and Q99.790 are set at Station 1 and Station 2 respectively. Here, Q refers to the quantile of the sample analysis data after the order statistic k is selected for the corresponding station.

[0061] For example, under the extreme tidal level condition Q99.792 of Station 1 given, 1000 expected tidal level data values are generated using the CEM model and Monte Carlo simulation. The mathematical expectation of these 1000 data values reaches the design tidal level value of 499 cm with a 100-year return period at Station 1. At this time, the probability that the tidal level at Station 2 exceeds its design tidal level value of 391 cm with a 100-year return period reaches 0.151. This shows that when Station 1 reaches or approaches the extreme tide with a 100-year return period, the probability that the tidal level at Station 2 exceeds its design tidal level value in a period of time after that is not high, indicating that the single-point prediction result meets the basic requirements. Figure 7 The prediction diagram of the CEM model conditional on Station 1 > Q99.792 is shown.

[0062] Table 6 Probability of exceeding the design tidal level value under extreme conditions

[0063]

Claims

1. A multi-site joint extreme value prediction and verification method for ocean environment design parameters, characterized in that Including the following steps: (1) Data collection: The crawler obtains and integrates the measured data of multiple observation stations in the selected ocean area over the years; (2) Data preprocessing: Analyze data missingness, perform multiple interpolations on the obtained data to form complete historical data; (3) Independent storm process data selection: For the data measured at a single observation site after preprocessing, a lower threshold u is selected using the extreme value index plot and the generalized Pareto distribution parameter stability plot. 1i , assuming that the marine environmental elements exceeding u occurring within X hours 1i belong to the same storm process and are grouped into one category, and the maximum value in each category is selected to form the sample analysis data; (4) Single-site extreme value prediction: After selecting a relatively large threshold u using the mean residual life graph for the analysis data selected during an independent storm process, fit the data exceeding u to the generalized Pareto distribution, estimate the parameters of the generalized Pareto distribution using the maximum likelihood estimation method, and calculate the extreme values corresponding to the corresponding return periods; 2i After that, for the data exceeding u 2i fit to the generalized Pareto distribution, estimate the parameters of the generalized Pareto distribution using the maximum likelihood estimation method, and calculate the extreme values corresponding to the corresponding return periods; (5) Selection of multi-station order statistics: According to the independent storm process, obtain the analysis data of all stations in the selected area, sort the analysis data of all stations from large to small respectively, determine the order statistic k of this area, and select the top k analysis data of all stations in this area to form a multi-station sample analysis data group; (6) Establishment of multi-site combined extreme condition model: Using the u corresponding to each site 2i as the marginal threshold, perform Laplace marginal transformation on each site in the multi-site analysis data group and set the dependence ratio value y to establish a multi-site conditional extreme value model for the selected area, and use the extreme value structure parameter a of the CEM model to estimate the extreme value dependence relationship between multiple sites; (7) Extreme condition probability prediction: Calculate the probability that other stations exceed the ocean environment design parameters under extreme conditions at a certain station through the multi-station conditional extreme value model to verify the safety of the selected corresponding design values of the structure.

2. The multi-site joint extreme value prediction and verification method for marine environment design parameters according to claim 1, characterized in that The specific content of step (4) is as follows: Select a relatively large threshold \(u\) using the mean residual life plot for the analysis data selected during an independent storm process 2i After that, fit the data exceeding \(u\) 2i to the generalized Pareto distribution, and estimate the parameters of the generalized Pareto distribution using the maximum likelihood estimation method. The formula is as follows: Among them, ξ is the shape parameter of the Pareto distribution, σ is the scale parameter of the Pareto distribution, and l(σ,ξ) represents the maximum likelihood estimate; Calculate the extreme value corresponding to the corresponding recurrence period, and the formula is as follows: Among them, z m represents the extreme value under a specific recurrence period m, and λ u represents the number of occurrences of the extreme value after the secondary threshold selection per year on average.

3. The multi-site joint extreme value prediction and verification method for marine environment design parameters according to claim 1, wherein The specific content of step (6) is as follows: Let \(X=(X_1,\ldots,X d )\) be a \(d -\)dimensional random variable with arbitrary marginal distributions. Let \(F i \) denote the estimate of the \(i -\)th marginal distribution function, and \(G\) denote the distribution function of the standardized marginal distribution to be determined. The original vector variable \(X\) is transformed into \(Y=(Y_1,\ldots,Y d )\), which is a variable with standardized marginal distributions by using the probability integral transformation as follows: Y i = G -1 (F i (X i )), i = 1, ..., d (3) F i is the marginal empirical distribution function of the data. In this case, Equation (3) is also called the rank transformation or a semi-parametric model that uses the empirical distribution below the threshold and the fitted GPD model of the distribution tail above the threshold. Y i is the required conditional variable, Y -i is the remainder indicating that the vector Y does not include the i-th component. The method of the conditional extreme value method is conditional on Y i being higher than a certain high threshold t, and based on the observations of Y i >t to model the conditional dependence of the remaining Y -i The form of the regression model of the conditional dependence structure depends on the exact choice of G in Equation (3); If G is the Laplace distribution function and Y is the marginal Laplace distribution function; under the condition that the variable Y i exceeds the high threshold t, the conditional extreme value model of the remaining variable Y -i takes the following form: Z |i is the vector residual, the (d - 1)-dimensional parameter vectors α |i and β |i satisfy (α |i , β |i ) ∈ (-∞, 1) d-1 , where, α |i , is related to Y j , j ∈ {1,..., d}, j is not equal to i, then 0 < α j|i ≤ 1 and -1 ≤ α j|i < 0 respectively correspond to the positive and negative correlations between the large values of Y j and Y i ; in the case of using the Laplace margin, the structure of the correlation model is greatly simplified, in which case a single model structure is sufficient for the extreme dependence between the selected regional sites.

4. A computer storage medium, on which a computer program is stored, characterized in that, When the computer program is executed by the processor, it implements a multi-station joint extreme value prediction and test method for ocean environment design parameters as described in any one of claims 1-3.

5. A computer device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements a multi-station joint extreme value prediction and test method for ocean environment design parameters as described in any one of claims 1-3.

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