A High-Precision Reconstruction Method of Wave Spectrum Based on Extreme Retention Number Model

Abstract

This invention relates to the field of marine engineering technology and provides a high-precision wave spectrum reconstruction method based on a polar residue model. The method involves obtaining initial wave spectrum data, performing dimensionless processing on the initial wave spectrum data to obtain dimensionless wave spectrum data, performing an inverse Fourier transform on the dimensionless wave spectrum data, and calculating the autocorrelation function of the wave spectrum data. The autocorrelation function of the wave spectrum data is then decomposed into a complex exponential function to determine the polar residue model of the wave spectrum data's autocorrelation function. Based on the polar residue model of the wave spectrum data's autocorrelation function, the polar residue model of the dimensionless wave spectrum data is determined. Finally, based on the polar residue model of the dimensionless wave spectrum data, the wave spectrum is reconstructed. The method provided by this invention has the advantages of high reconstruction accuracy and high computational efficiency.

Description

Technical Field

[0001] This invention relates to the field of marine engineering technology, and specifically to a high-precision wave spectrum reconstruction method based on a polar residue number model. Background Technology

[0002] The wave spectrum is a core mathematical model describing the distribution of wave-related quantities relative to frequency. It is defined as the variance spectrum of wave heave, reflecting the wave energy distribution characteristics by statistically analyzing the variance of each frequency component. As a fundamental environmental parameter in the field of marine engineering, it is widely used in the dynamic analysis of various marine engineering structures such as ships, oil and gas platforms, and wave energy devices.

[0003] Spectral analysis of wave-induced motion of offshore structures and numerical simulation of wave time history are important research contents in the dynamic analysis of offshore structures. To achieve efficient and high-precision implementation of these tasks, wave spectrum reconstruction research has received widespread attention in the industry. Approximating the wave spectrum as a filter is a mainstream technology in the offshore engineering industry, with common methods including autoregressive digital filters (AR digital filters), moving average digital filters (MA digital filters), and autoregressive moving average analog filters (ARMA digital filters). Digital filters are often limited by the ill-conditioned problem of polynomial root finding; the filter order and sampling frequency have a significant impact on filter design and are difficult to control. Analog filters are analytical filters, using a pre-defined filter characterization model, such as a bilinear two-stage cascaded filter. However, limited by the pre-defined theoretical model of the filter, the predetermined model has limitations in accurately representing the actual wave spectrum, especially in the low-frequency and high-frequency parts of the spectrum, resulting in large fitting errors and insufficient accuracy. High-precision analytical wave spectrum reconstruction technology remains a significant challenge for the industry. Summary of the Invention

[0004] The purpose of this invention is to solve the above-mentioned technical problems and provide a high-precision wave spectrum reconstruction method based on the extreme residue model.

[0005] To achieve the above objectives, some embodiments of the present invention provide the following technical solutions:

[0006] A high-precision wave spectrum reconstruction method based on a polar residue model includes the following steps:

[0007] S1: Obtain initial wave spectrum data For the initial wave spectrum data Dimensionless processing is performed to obtain dimensionless wave spectrum data. ;

[0008] S2: For the dimensionless wave spectrum data Perform inverse Fourier transform and calculate the autocorrelation function of the wave spectrum data. ;

[0009] S3: Autocorrelation function of the wave spectrum data Perform complex exponential decomposition to determine the autocorrelation function of the wave spectrum data. Retention number representation model ;

[0010] S4: Autocorrelation function based on the wave spectrum data Retention number representation model Determine dimensionless wave spectrum data The residual number model;

[0011] S5: Based on dimensionless wave spectrum data Extreme retention number model to reconstruct wave spectrum .

[0012] In some embodiments of the present invention, the initial wave spectrum data... Dimensionless processing is performed to obtain dimensionless wave spectrum data. The methods include:

[0013] Based on the initial wave spectrum data Data is collected to determine spectral peaks. The maximum value among these peaks is then selected, and the frequency of that maximum value is determined. Calculate the peak frequency of the spectrum Corresponding spectral values ;

[0014] Using spectral peak frequency Corresponding spectral values Wave spectrum data The data is dimensionless, including:

[0015] ;

[0016] in, The frequency of the wave spectrum, , where is a dimensionless, dimensionless frequency, indicated by a superscript. Represents a dimensionless function or variable.

[0017] In some embodiments of the present invention, the dimensionless wave spectrum data is... Perform inverse Fourier transform and calculate the autocorrelation function of the wave spectrum data. The methods include:

[0018] ;

[0019] in, It is an imaginary number.

[0020] In some embodiments of the present invention, the determination of the autocorrelation function of the wave spectrum data is described. Retention number representation model The steps include:

[0021] The autocorrelation function is decomposed, and the autocorrelation function is... Represented as the sum of multiple complex exponential functions:

[0022] ;

[0023] exist Based on the sum of multiple complex exponential functions, the autocorrelation function is... Perform a Laplace transform to obtain the autocorrelation function. Laplace field residual number representation model:

[0024] ;

[0025] in, It is the autocorrelation function Laplace transform, It is a Laplace variable. It is the extreme point. It is a residue. These are the pole and residue indices. It represents the number of poles and residues.

[0026] In some embodiments of the present invention, the determination of dimensionless wave spectrum data The steps of the extreme residue model include:

[0027] Residue characterization model based on autocorrelation function ,make , obtain the function Frequency domain representation function:

[0028] ;

[0029] Based on the frequency domain characterization function The dimensionless wave spectrum was obtained. The model for representing the extreme residue number:

[0030] ;

[0031] in, This indicates the operation of taking the real part. It is pi (π).

[0032] In some embodiments of the present invention, the reconstructed wave spectrum The steps include:

[0033] .

[0034] The wave spectrum high-precision reconstruction method based on the extreme residue number model proposed in this invention has the advantages of high efficiency, high precision, and strong versatility compared with the prior art. Specifically, the beneficial effects of the technical solution of this invention are as follows:

[0035] 1. By using dimensionless wave spectrum for spectral reconstruction, this invention has the universality to apply to any form of wave spectrum and any spectral parameters.

[0036] 2. By using the extreme residue model to reconstruct the spectrum, the ill-conditioned problems of traditional numerical fitting techniques and the limitation of fitting accuracy by a specific spectrum model are avoided, resulting in higher reconstruction accuracy and computational efficiency. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart of the high-precision wave spectrum reconstruction method based on the extreme residue number model of the present invention;

[0039] Figure 2 The dimensionless PM wave spectrum determined in the embodiments of the present invention;

[0040] Figure 3 The autocorrelation function of the dimensionless PM wave spectrum calculated by the method of this invention;

[0041] Figure 4 This is a comparison diagram of the dimensionless PM wave spectrum autocorrelation function and the wave spectrum autocorrelation function reconstructed by the polar residue model in this invention;

[0042] Figure 5 This is a comparison diagram of the dimensionless PM wave spectrum reconstructed using the extreme residue number model obtained by the method of this invention and the real dimensionless PM wave spectrum.

[0043] Figure 6 The method of the present invention is obtained A comparison of the PM wave spectrum reconstructed using the extreme residue number model and the actual PM wave spectrum at m / s. Detailed Implementation

[0044] To make the technical problems to be solved, the technical solutions, and the beneficial effects of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0045] The prefixes such as "first" and "second" used in this application embodiment are merely for distinguishing different descriptive objects and do not limit the position, order, priority, quantity, or content of the described objects. The use of ordinal numbers and other prefixes used to distinguish descriptive objects in this application embodiment does not constitute a limitation on the described objects. The description of the described objects is given in the claims or the context of the embodiments, and should not constitute unnecessary restrictions due to the use of such prefixes. Furthermore, in the description of this embodiment, unless otherwise stated, "multiple" means two or more.

[0046] The technical solutions of the embodiments of this application will be described below with reference to the accompanying drawings. In the description of the embodiments of this application, unless otherwise stated, " / " means "or," for example, A / B can mean A or B; the term "and / or" in this document is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone.

[0047] In the embodiments provided in this application, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0048] This invention proposes a high-precision wave spectrum reconstruction method based on the extreme residue number model, which includes the following steps.

[0049] S1: Obtain initial wave spectrum data For the initial wave spectrum data Dimensionless processing is performed to obtain dimensionless wave spectrum data. .

[0050] It should be understood that wave spectrum data The forms of expression are diverse, including PM spectrum, JONSWAP spectrum, and Büchner spectrum.

[0051] For example, the following PM wave spectrum can be selected:

[0052]

[0053] Among them, coefficient ,coefficient , It is the gravitational acceleration constant. This refers to the wind speed at a height of 19.4 meters above sea level; in some embodiments, the coefficient... Sum of coefficients Alternatively, you can choose to use other expressions.

[0054] The expression for the peak frequency of the PM wave spectrum is:

[0055] ;

[0056] Therefore, coefficient It can also be expressed as: Substitute it into the above PM wave spectrum From the expression, we get:

[0057] .

[0058] Dimensionless processing of spectral data transforms "unit-based energy density" into "unitless relative spectra," allowing spectra from different sea states and dimensions to be compared or applied to theoretical models on the same "universal curve." This eliminates the "incomparability" and "distortion" caused by differences in dimensions, units, and numerical scales, making the relationships, patterns, and model training of the data itself purer and more stable.

[0059] In some embodiments of the present invention, the initial wave spectrum data... Dimensionless processing is performed to obtain dimensionless wave spectrum data. The methods include:

[0060] Based on the initial wave spectrum data Data is collected to determine spectral peaks. The maximum value among these peaks is then selected, and the frequency of that maximum value is determined. Calculate the peak frequency of the spectrum Corresponding spectral values ;

[0061] Using spectral peak frequency Corresponding spectral values Wave spectrum data The data is dimensionless, including:

[0062] ;

[0063] in, The frequency of the wave spectrum, , where is a dimensionless frequency, superscript Represents a dimensionless function or variable.

[0064] For PM wave spectrum, dimensionless wave spectrum data The expression is:

[0065] .

[0066] It should be understood that wave spectrum data contains multiple peaks, which are represented as spectral peaks in the spectral data. To achieve dimensionless processing of the spectral data, the frequency of the spectral peak with the most representative maximum value is selected. It assists in dimensionless processing.

[0067] Figure 1 Displayed dimensionless wave spectrum The curve has a frequency range from 0 to 32.767 rad / s, with a frequency interval of 0.001 rad / s.

[0068] S2: For dimensionless wave spectrum data Perform inverse Fourier transform and calculate the autocorrelation function of the wave spectrum data. .

[0069] The autocorrelation function is a mathematical tool that measures the similarity between a random signal or time series and itself at different time lags. In wave data analysis, it can be used to: extract the main period information of waves, check the stationarity of data, and perform preliminary verification for spectral estimation.

[0070] In some embodiments of the present invention, dimensionless wave spectrum data are used. Perform inverse Fourier transform to calculate the autocorrelation function of the wave spectrum data. The methods include:

[0071] ;

[0072] in, It is an imaginary number.

[0073] S3: Autocorrelation function of wave spectrum data Perform complex exponential decomposition to determine the autocorrelation function of the wave spectrum data. Retention number representation model .

[0074] In some embodiments of the present invention, the autocorrelation function of wave spectrum data is determined. Retention number representation model The steps include:

[0075] Decompose the autocorrelation function and divide the autocorrelation function Represented as the sum of multiple complex exponential functions:

[0076] ;

[0077] exist Based on the sum of multiple complex exponential functions, the autocorrelation function is... Perform a Laplace transform to obtain the autocorrelation function. Laplace field residual number representation model:

[0078] ;

[0079] in, It is the autocorrelation function Laplace transform, It is a Laplace variable. It is the extreme point. It is a residue. These are the pole and residue indices. It represents the number of poles and residues.

[0080] like Figure 2 As shown, the wave spectrum autocorrelation function The time range is from 0 to 49.6626 s, with a time interval of 0.1917 s. The Prony-SS complex exponential signal decomposition method is used to... Decompose and determine Number of poles ,pole The corresponding residue .

[0081] like Figure 3 As shown, the reconstructed autocorrelation function and the true autocorrelation function are in good agreement.

[0082] S4: Autocorrelation function based on wave spectrum data Retention number representation model Determine dimensionless wave spectrum data The extreme residue model.

[0083] In some embodiments of the present invention, dimensionless wave spectrum data is determined. The steps of the extreme residue model include:

[0084] Residue characterization model based on autocorrelation function ,make , obtain the function Frequency domain representation function:

[0085] ;

[0086] Based on frequency domain characterization function The dimensionless wave spectrum was obtained. The model for representing the extreme residue number:

[0087] ;

[0088] in, This indicates the operation of taking the real part. It is pi (π).

[0089] S5: Based on dimensionless wave spectrum data Extreme retention number model to reconstruct wave spectrum .

[0090] In some embodiments of the present invention, the wave spectrum is reconstructed. The steps include:

[0091] .

[0092] Based on the calculated poles and residue values ​​of the autocorrelation function, the dimensionless wave spectrum reconstructed using the sixth-order extreme residue model is determined. Its relationship with the true dimensionless wave spectrum See comparison Figure 4 The two are quite consistent.

[0093] Based on the calculated poles and residue values ​​of the autocorrelation function, the dimensionless wave spectrum reconstructed using the sixth-order extreme residue model is determined. Its relationship with the true dimensionless wave spectrum See comparison Figure 4 The two are quite consistent.

[0094] In this example, let m / s, the polar residue number model corresponding to this wind speed can be used to reconstruct the wave spectrum. .

[0095] Figure 5 A comparison chart showing the PM wave spectrum reconstructed by the extreme residue number model and the actual PM wave spectrum is presented. The two are in good agreement, verifying the effectiveness and high accuracy of the invention. Similarly, for any wind speed input or any wave spectrum form, the invention can quickly obtain the reconstructed wave spectrum value.

[0096] This invention proposes a high-precision wave spectrum reconstruction method based on the extreme residue number model. By using a dimensionless wave spectrum for wave spectrum reconstruction, this invention has the universality to apply to any form of wave spectrum and any spectral parameters. In addition, by using the extreme residue number model to reconstruct the wave spectrum, this invention avoids the ill-conditioned problem of numerical fitting in traditional techniques and the limitation of fitting accuracy by a specific wave spectrum model, thus achieving higher reconstruction accuracy and computational efficiency.

[0097] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. It should be noted that any modifications, equivalent substitutions, and improvements made by those skilled in the art within the spirit and principles of the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of this patent application should be determined by the scope of the appended claims.

Claims

1. A high-precision wave spectrum reconstruction method based on a polar residue model, characterized in that, Includes the following steps: S1: Obtain initial wave spectrum data For the initial wave spectrum data Dimensionless processing is performed to obtain dimensionless wave spectrum data. ; S2: For the dimensionless wave spectrum data Perform inverse Fourier transform and calculate the autocorrelation function of the wave spectrum data. ; S3: Autocorrelation function of the wave spectrum data Perform complex exponential decomposition to determine the autocorrelation function of the wave spectrum data. Retention number representation model ; S4: Autocorrelation function based on the wave spectrum data Retention number representation model Determine dimensionless wave spectrum data The residual number model; S5: Based on dimensionless wave spectrum data Extreme retention number model to reconstruct wave spectrum .

2. The high-precision wave spectrum reconstruction method based on the extreme residue number model according to claim 1, characterized in that, For the initial wave spectrum data Dimensionless processing is performed to obtain dimensionless wave spectrum data. The methods include: Based on the initial wave spectrum data Data is collected to determine spectral peaks. The maximum value among these peaks is then selected, and the frequency of that maximum value is determined. Calculate the peak frequency of the spectrum Corresponding spectral values ; Using spectral peak frequency Corresponding spectral values Wave spectrum data The data is dimensionless, including: ； in, The frequency of the wave spectrum, , where is a dimensionless frequency, superscript Represents a dimensionless function or variable.

3. The high-precision wave spectrum reconstruction method based on the extreme residue model according to claim 2, characterized in that, For the dimensionless wave spectrum data Perform inverse Fourier transform and calculate the autocorrelation function of the wave spectrum data. The methods include: ； in, It is an imaginary number.

4. The high-precision wave spectrum reconstruction method based on the extreme residue model according to claim 3, characterized in that, The autocorrelation function for determining the wave spectrum data Retention number representation model The steps include: The autocorrelation function is decomposed, and the autocorrelation function is... Represented as the sum of multiple complex exponential functions: ； exist Based on the sum of multiple complex exponential functions, the autocorrelation function is... Perform a Laplace transform to obtain the autocorrelation function. Laplace field residual number representation model: ； in, It is the autocorrelation function Laplace transform, It is a Laplace variable. It is the extreme point. It is a residue. These are the pole and residue indices. It represents the number of poles and residues.

5. The high-precision wave spectrum reconstruction method based on the extreme residue model according to claim 4, characterized in that, The determination of dimensionless wave spectrum data The steps of the extreme residue model include: Residue characterization model based on autocorrelation function ,make , obtain function Frequency domain representation function: ； Based on the frequency domain characterization function The dimensionless wave spectrum was obtained. The model for representing the extreme residue number: ； in, This indicates the operation of taking the real part. It is pi (π).

6. The high-precision wave spectrum reconstruction method based on the extreme residue model according to claim 5, characterized in that... The reconstructed wave spectrum The steps include: 。

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