A method for extrapolating the extreme values ​​of time-domain wave loads based on truncated samples and three-parameter distribution.

Abstract

This invention relates to a method for extrapolating the extreme values ​​of time-domain wave loads based on truncated samples and a three-parameter distribution. The method comprises the following steps: extracting amplitude samples from the original time history; removing a predetermined number of smaller amplitude samples to obtain truncated samples (x1, x2, ... x...). m The cutoff sample (x1, x2, ... x) obtained by fitting the three-parameter generalized extreme value distribution G(x; σ, γ, μ) is selected. m The method involves estimating the scale parameter σ, shape parameter γ, and position parameter μ using the probability weighted moments method, and obtaining the corresponding extrapolated extreme values ​​X of the wave load. This invention provides an extrapolation method for wave load extreme values ​​that balances rationality, stability, and accuracy. Compared with existing technologies, the positive advancements of this invention are: it has the advantages of reasonable amplitude extraction, appropriate distribution function selection, and high extrapolation accuracy. While ensuring accurate and stable fitting of wave load samples, it can conveniently perform extreme value extrapolation.

Description

Technical Field

[0001] This invention relates to a method for extrapolating the extreme values ​​of time-domain wave loads on ships, belonging to the field of ship structural design. Background Technology

[0002] The extreme values ​​of wave loads are crucial to the structural strength of hulls during the ship design phase. In determining the extreme values ​​of wave loads using time-domain wave loads and mathematical statistics, the following three factors significantly influence the accuracy of the extrapolated extreme values: the extraction of the wave load time-history amplitude, the selection of the distribution function to which the extracted samples conform, and the method for estimating the parameters in the distribution function.

[0003] Firstly, when the wave load time history contains both low-frequency wave components and high-frequency hydroelastic components, the local zero-crossing part in the high-frequency component will directly lead to an increase in the number of responses in the wave load time history, thereby affecting the size of the average zero-crossing period and the distribution characteristics of the response.

[0004] Secondly, the two-parameter distribution is generally chosen for the distribution function because it has fewer distribution parameters and the parameter estimation method is simple. However, since the two-parameter distribution omits the position parameter, it cannot adapt well to the extrapolation of the extreme values ​​of wave loads, and its parameter adaptability is far inferior to that of the three-parameter distribution of the same type.

[0005] Finally, if a three-parameter distribution function is chosen, the quality of parameter estimation is closely related to the selection of the estimation method. For example, commonly used methods such as maximum likelihood estimation and least squares method require setting initial values ​​and iterative solutions, which are complex calculation processes. If the initial values ​​are not set appropriately, the solution will fail. In addition, conventional fitting methods usually focus on fitting the smaller part of the sample amplitude, making it difficult to take into account the larger part of the sample amplitude. This will directly lead to insufficient accuracy in extrapolating the extreme values ​​when the exceedance probability is small. Summary of the Invention

[0006] The technical problem to be solved by this invention is that the existing extrapolation methods for ship time-domain wave load extrema have unreasonable amplitude extraction, inappropriate selection of distribution functions, and insufficient extrapolation accuracy.

[0007] To solve the above-mentioned technical problems, the technical solution of the present invention is to provide a method for extrapolating the extreme values ​​of time-domain wave loads based on truncated samples and three-parameter distribution, characterized by comprising the following steps:

[0008] Step 1: Perform low-pass filtering on the wave load time history within a certain time period to filter out the high-frequency hydroelastic components. Then, extract the zero-crossing time from the remaining low-frequency wave components and extract the amplitude samples of the original time history based on the obtained zero-crossing time.

[0009] Step 2: Remove a set number of samples with smaller amplitudes to obtain the truncated samples (x1, x2, ... x). m ), where m is the number of samples;

[0010] Step 3: Use the truncated sample (x1, x2, ... x) obtained by fitting the three-parameter generalized extreme value distribution G(x; σ, γ, μ) m ), where x is the fitted variable, and σ, γ, and μ are the scale parameter, shape parameter, and position parameter, respectively;

[0011] Step 4: Estimate the scale parameter σ, shape parameter γ, and position parameter μ using the probabilistic weighted moments method;

[0012] Step 5: Given the design probability P (x≥X), the extrapolated extreme value X of the wave load is shown in the following formula:

[0013] Preferably, in step 1, the certain time period is at least 3 to 5 hours.

[0014] Preferably, in step 2, after the extracted amplitude samples are sorted in ascending or descending order, a set number of smaller amplitude samples are removed.

[0015] Preferably, in step 2, the truncated samples (x1, x2, ... x) m The number of samples was taken as 20% of the total sample size.

[0016] Preferably, in step 3, the three-parameter generalized extreme value distribution G(x; σ, γ, μ) is expressed as:

[0017] Preferably, in step 4, the probability weighted moment method uses the k-th order excess probability weighted moment expressed in terms of distribution parameters as shown in equation (1), where k is a non-negative integer:

[0018]

[0019] In equation (1), Γ() is the gamma function.

[0020] Preferably, substituting k = 0, 1, 2 into the k-th order excess probability weight moment yields the following system of equations (2):

[0021]

[0022] Solving the equation shown in (2) yields the unique shape parameter γ, scale parameter σ, and position parameter μ.

[0023] Preferably, for truncated samples (x1, x2, ... x... mM in the system of equations shown in equation (2) 1,0,0 M 1,1,0 M 1,2,0 It can be obtained from the following formula (3):

[0024]

[0025] In equation (3), x j To truncate the sample (x1, x2, ... x m The j-th sample in ).

[0026] Preferably, when solving the equation shown in equation (2), the iterative method is used to calculate the equation in equation (2). The transcendental equation contained in the equation yields the unique shape parameter γ; based on this, the unique scale parameter σ and position parameter μ are obtained through the other two equations in equation (2), and the three-parameter generalized extremum distribution G(x; σ, γ, μ) is thus determined.

[0027] Preferably, the iterative method is the Brent iteration method.

[0028] This invention provides a method for extrapolating wave load extrema that balances rationality, stability, and accuracy. Compared with existing technologies, the positive improvements of this invention are: it has the advantages of reasonable amplitude extraction, appropriate distribution function selection, and high extrapolation accuracy; while ensuring accurate and stable fitting of wave load samples, it can conveniently perform extremum extrapolation. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of wave load time-history amplitude extraction according to a preferred embodiment of the present invention. Detailed Implementation

[0030] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various alterations or modifications to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0031] This invention provides a method for extrapolating the extreme values ​​of time-domain wave loads on ships, comprising the following steps:

[0032] Step 1: Perform low-pass filtering on the original 3-hour wave load time history to remove high-frequency hydroelastic components. Then, extract the zero-crossing time from the remaining low-frequency wave components. Based on the obtained zero-crossing time, extract amplitude samples from the original time history, selecting the time history from 1414 to 1475 seconds in the middle. Figure 1As shown, the solid line represents the original time history, the dashed line represents the time history of the filtered low-frequency wave components, the dots represent the extracted zero-crossing moments, the squares represent the extracted peak samples, and the triangles represent the extracted valley samples.

[0033] Step 2: Taking the peak samples in the amplitude samples as an example, sort the extracted 893 peak samples in ascending order, and then remove the smaller amplitude samples that account for 20% of the total number of peak samples to obtain the truncated samples (x1, x2, ... x). m The sample size m is 715;

[0034] Step 3: Use the truncated sample (x1, x2, ... x) obtained by fitting the three-parameter generalized extreme value distribution G(x; σ, γ, μ) as shown in equation (1). m ):

[0035]

[0036] In equation (1), x is the fitting variable, and σ, γ, and μ are the scale parameter, shape parameter, and position parameter, respectively.

[0037] Step 4: Estimate the three parameters σ, γ, and μ of the above distribution using the probability weighted moment method. This includes the following steps:

[0038] Step 401: To avoid large estimation errors caused by higher-order factors of sample values ​​and to obtain better fitting results, the k-th (non-negative integer) order excess probability weight moments expressed in terms of distribution parameters, as shown in equation (2), are usually used.

[0039]

[0040] In equation (2), Γ() is the gamma function.

[0041] Step 402: Since three parameters need to be determined, k = 0, 1, 2 are substituted into equation (2) above to obtain the system of equations (3) for calculating σ, γ, and μ:

[0042]

[0043] Step 403: For the 715 extracted peak samples, M is contained in the system of equations shown in equation (3). 1,k,0 (k=0,1,2) can be conveniently obtained from equation (4):

[0044]

[0045] In equation (4), x j To truncate the sample (x1, x2, ... x m The j-th sample in ).

[0046] Calculation yields M1,0,0 It is 6.12×10 9 M 1,1,0 3.65×10 9 M 1,2,0 2.65×10 9 .

[0047] Step 404: Using the Brent iteration method, calculate the transcendental equation contained in equation (3), and obtain the unique shape parameter γ as -0.14. Based on this, the unique scale parameter σ is obtained as 1.91 × 10⁻⁶ using the other two equations. 9 The position parameter μ is 5.25 × 10⁻⁶. 9 Thus, the three-parameter generalized extreme value distribution G(x; σ, γ, μ) is determined.

[0048] Step 5: Given the design probability P(x≥X)=10 -8 Under these conditions, the extrapolated extreme value X of the corresponding wave load is:

Claims

1. A method for extrapolating the extreme values ​​of time-domain wave loads based on truncated samples and a three-parameter distribution, characterized in that, Includes the following steps: Step 1: Perform low-pass filtering on the wave load time history within a certain time period to filter out the high-frequency hydroelastic components. Then, extract the zero-crossing time from the remaining low-frequency wave components and extract the amplitude samples of the original time history based on the obtained zero-crossing time. Step 2: Remove a set number of samples with smaller amplitudes to obtain the truncated samples (x1, x2, ... x). m ), where m is the number of samples; Step 3: Use the truncated sample (x1, x2, ... x) obtained by fitting the three-parameter generalized extreme value distribution G(x; σ, γ, μ) m ), where x is the fitted variable, and σ, γ, and μ are the scale parameter, shape parameter, and position parameter, respectively; Step 4: Estimate the scale parameter σ, shape parameter γ, and position parameter μ using the probabilistic weighted moments method, wherein the probabilistic weighted moments method uses the k-th order overprobabilistic weighted moments expressed in terms of distribution parameters as shown in Equation (1), where k is a non-negative integer: In equation (1), Γ() is the gamma function; Substituting k = 0, 1, 2 into the k-th order excess probability weight moment, we obtain the following system of equations (2): Solving the equation shown in equation (2) yields the unique shape parameter γ, scale parameter σ, and position parameter μ; For the truncated sample (x1, x2, ... x) m M in the system of equations shown in equation (2) 1,0,0 M 1,1,0 M 1,2,0 It can be obtained from the following formula (3): In equation (3), x j To truncate the sample (x1, x2, ... x m The j-th sample in ); When solving the equation shown in equation (2), the iterative method is used to calculate the equation in equation (2). The transcendental equation contained in the equation yields the unique shape parameter γ; based on this, the unique scale parameter σ and position parameter μ are obtained through the other two equations in equation (2), and the three-parameter generalized extreme value distribution G(x; σ, γ, μ) is thus determined. Step 5: Given the design probability P (x≥X), the extrapolated extreme value X of the wave load is shown in the following formula:

2. The time-domain wave load extremum extrapolation method based on truncated samples and three-parameter distribution as described in claim 1, characterized in that, In step 1, the specified time period is at least 3 to 5 hours.

3. The time-domain wave load extremum extrapolation method based on truncated samples and three-parameter distribution as described in claim 1, characterized in that, In step 2, the extracted amplitude samples are sorted in ascending or descending order, and then a set number of smaller amplitude samples are removed.

4. The time-domain wave load extremum extrapolation method based on truncated samples and three-parameter distribution as described in claim 3, characterized in that, In step 2, the truncated samples (x1, x2, ... x) m The number of samples was taken as 20% of the total sample size.

5. The time-domain wave load extremum extrapolation method based on truncated samples and three-parameter distribution as described in claim 1, characterized in that, In step 3, the three-parameter generalized extremum distribution G(x; σ, γ, μ) is expressed as:

6. The time-domain wave load extremum extrapolation method based on truncated samples and three-parameter distribution as described in claim 1, characterized in that, The iterative method is the Brent iteration method.

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