Wave spectrum high-precision reconstruction method based on polar residue model

Abstract

The invention relates to the technical field of ocean engineering, and provides a wave spectrum high-precision reconstruction method based on a polar residue model. Obtaining initial wave spectrum data, and performing dimensionless processing on the initial wave spectrum data to obtain dimensionless wave spectrum data; inverse Fourier transform is carried out on the dimensionless wave spectrum data, and an autocorrelation function of the wave spectrum data is calculated; performing complex exponential decomposition on the autocorrelation function of the wave spectrum data, and determining a polar residue representation model of the autocorrelation function of the wave spectrum data; determining a polar residue model of the dimensionless wave spectrum data based on a polar residue representation model of an autocorrelation function of the wave spectrum data; and reconstructing a wave spectrum based on the polar residue model of the dimensionless wave spectrum data. The method provided by the invention has the advantages of high reconstruction precision and high calculation efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ocean engineering, and in particular to a high-precision wave spectrum reconstruction method based on a polar residue model. BACKGROUND

[0002] The wave spectrum is a core mathematical model describing the distribution of relevant quantities of each component wave with respect to frequency, which is defined as the variance spectrum of wave elevation, and reflects the energy distribution characteristics of waves by statistically analyzing the variance of each frequency component. As a basic environmental parameter in the field of ocean engineering, it is widely used in 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 marine structures and numerical simulation of wave time history are important research contents of marine structure dynamic analysis. In order to achieve efficient and high-precision development of the above work, the reconstruction of wave spectrum has attracted widespread attention in the industry. Approximating the wave spectrum as a filter is the mainstream technology in the marine industry, and common ones include autoregressive digital filter (AR digital filter), moving average digital filter (MA digital filter), and autoregressive moving average analog filter (ARMA digital filter). Digital filters are usually limited by the ill-conditioned problem of polynomial root finding, and the filter order and sampling frequency have a great influence on the filter design and are not easy to control. The analog filter is an analytical filter, which is characterized by a pre-defined filter model, such as a bilinear second-order cascade filter. However, due to the pre-defined theoretical model of the filter, there are limitations that the pre-defined model cannot accurately represent the actual wave spectrum, especially the low and high frequency parts of the wave spectrum, with large fitting errors and insufficient precision. High-precision analytical wave spectrum reconstruction technology is still an important challenge faced by the industry. SUMMARY

[0004] The present application aims to solve the above technical problems and provide a high-precision wave spectrum reconstruction method based on a polar residue model.

[0005] To achieve the above-mentioned purpose, in some embodiments of the present application, the following technical solutions are provided: A high-precision wave spectrum reconstruction method based on a polar residue model, comprising the following steps: S1: obtaining initial wave spectrum data , performing dimensionless processing on the initial wave spectrum data to obtain dimensionless wave spectrum data ; S2: performing inverse Fourier transform on the dimensionless wave spectrum data , and calculating the autocorrelation function of the wave spectrum data ; S3: calculating the autocorrelation function of the wave spectrum data Perform complex exponential decomposition to determine the autocorrelation function of the wave spectrum data The extreme residue characterization model ; S4: Autocorrelation function based on the wave spectrum data The extreme residue characterization model , determine the dimensionless wave spectrum data The extreme residue model of S5: Based on dimensionless wave spectrum data The extreme residue model reconstructs the wave spectrum .

[0006] In some embodiments of the present invention, the initial wave spectrum data Perform dimensionless processing to obtain dimensionless wave spectrum data The methods include: According to the initial wave spectrum data Data, determine the spectrum peak, take the maximum value of the spectrum peak in each spectrum peak, and determine the spectrum peak frequency of the maximum spectrum peak , calculate the peak frequency The corresponding spectrum value ; Use spectrum peak frequency The corresponding spectrum value Wave spectrum data The data is dimensionless processed, including: ; in, is the frequency of the wave spectrum, , is the dimensionless frequency, superscript Represents a dimensionless function or variable.

[0007] In some embodiments of the present invention, the dimensionless wave spectrum data Perform inverse Fourier transform and calculate the autocorrelation function of wave spectrum data The methods include: ; in, It is an imaginary number.

[0008] In some embodiments of the present invention, the autocorrelation function of the wave spectrum data is determined The extreme residue characterization model The steps include: Decompose the autocorrelation function and transform the autocorrelation function Expressed as the sum of multiple complex exponential functions: ; In the basis of the sum of the plurality of complex exponential functions expression, the autocorrelation function is subjected to Laplace transform, and the autocorrelation function Laplace domain pole residue representation model is obtained: ; Wherein, is the Laplace transform of the autocorrelation function , s is the Laplace variable, is the pole, is the residue, is the pole and residue number, is the pole and residue number, is the number of poles and residues.

[0009] In some embodiments of the application, the step of determining the pole residue model of the dimensionless wave spectrum data includes: Based on the residue representation model of the autocorrelation function , let , the frequency domain representation function of the function is obtained: ; Based on the frequency domain representation function , the pole residue representation model of the dimensionless wave spectrum is obtained: ; Wherein, represents the real part operation, is the circular constant.

[0010] In some embodiments of the application, the step of reconstructing the wave spectrum includes: .

[0011] The wave spectrum high-precision reconstruction method based on the pole residue model provided by the application has the technical effects of high efficiency, high precision and strong universality compared with the prior art. 1. The wave spectrum reconstruction is performed by using the dimensionless wave spectrum, so that the application has universal ability for any form of wave spectrum and any wave spectrum parameter. 2. The wave spectrum is reconstructed by using the pole residue model, which avoids the ill-conditioned problem of numerical fitting in the traditional technology and the limitation of fitting precision limited by specific wave spectrum model, and has higher reconstruction precision and calculation efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0012] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments or prior art description will be briefly introduced as follows. Obviously, the drawings in the following description only constitute some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of these drawings.

[0013] Figure 1 Flow chart of the high-precision wave spectrum reconstruction method based on the extreme value model of the present application; Figure 2 Non-dimensional P-M wave spectrum determined in the embodiments of the present application; Figure 3 Autocorrelation function of the non-dimensional P-M wave spectrum calculated by the method of the present application; Figure 4 Comparison chart of the autocorrelation function of the non-dimensional P-M wave spectrum and the autocorrelation function of the wave spectrum reconstructed by the extreme value model in the present application; Figure 5 Comparison chart of the non-dimensional P-M wave spectrum reconstructed by the extreme value model and the real non-dimensional P-M wave spectrum obtained by the method of the present application; Figure 6 Comparison chart of the P-M wave spectrum reconstructed by the extreme value model and the real P-M wave spectrum obtained by the method of the present application when the wave height is 0.5 m and the wave period is 10 s. Specific embodiments

[0014] In order to make the technical problems to be solved by the present application, technical solutions and beneficial effects more clearly understood, the present application will be further described in detail in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not used to limit the present application.

[0015] In the embodiments of the present application, the prefix words such as "first", "second" are only used to distinguish different description objects, and have no limiting effect on the position, order, priority, quantity or content of the described objects. The use of ordinal words such as ordinal words in the embodiments of the present application does not constitute a limitation on the described objects, and the description of the described objects should be referred to the description of the context in the claims or embodiments, and should not constitute redundant limitation because of the use of such prefix words. In addition, in the description of the embodiments, unless otherwise stated, the meaning of "a plurality of" is two or more.

[0016] ​With reference to the drawings and the embodiments of the present application, the technical solutions in the embodiments of the present application will be described. In the description of the embodiments of the present application, unless otherwise specified, " / " represents the meaning of or, for example, A / B can represent A or B; "and / or" in the present application is only a description of the association relationship of the associated objects, which means that there can be three kinds of relationships, for example, A and / or B, which can represent the three cases of A alone, A and B together, and B alone.

[0017] In several embodiments provided in the embodiments of the present application, it should be understood that the disclosed system and method can be implemented in other ways. For example, the above-described device embodiments are only schematic, for example, the division of the units is only a logical function division, and actual implementation can have another division manner, for example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the units shown or discussed can be indirect coupling or communication connection through some interface, device or unit, and can be electrical, mechanical or other forms.

[0018] The application provides a high-precision wave spectrum reconstruction method based on a polar residual model, comprising the following steps.

[0019] S1: obtaining initial wave spectrum data , the initial wave spectrum data is processed by dimensionless processing to obtain dimensionless wave spectrum data .

[0020] It should be understood that the expression form of the wave spectrum data is various, including P-M spectrum, JONSWAP spectrum, and Bousinesq spectrum.

[0021] For example, the following P-M wave spectrum can be selected:

[0022] wherein the coefficient , the coefficient , is the gravitational acceleration constant, is the wind speed at a height of 19.4 meters above the sea surface; in some embodiments, the coefficient and the coefficient can also be selected to use other expressions.

[0023] The expression of the peak frequency of the P-M wave spectrum is: ; Therefore, the coefficient can also be expressed as: , which is brought into the P-M wave spectrum above In the expression, we have: .

[0024] The dimensionless processing of the spectral data can change the "energy density with units" into the "relative spectrum without units", so that different sea states and different dimensional spectra can be compared on the same "universal curve" or applied to the theoretical model. Eliminate the "incomparable" and "distortion" caused by the difference of dimension, unit and numerical scale, so that the relationship, law or model training of the data itself becomes more pure and stable.

[0025] In some embodiments of the present application, the initial wave spectrum data is dimensionless processed to obtain dimensionless wave spectrum data The method comprises: According to the initial wave spectrum data data, determine the spectral peak, take the spectral peak maximum value in each spectral peak, and determine the spectral peak frequency of the spectral peak maximum value , calculate the wave spectrum value corresponding to the spectral peak frequency ; The wave spectrum data data is dimensionless processed using the spectral peak frequency corresponding to the wave spectrum value , including: ; Wherein, is the frequency of the wave spectrum, is the dimensionless frequency, and the superscript represents the dimensionless function or variable.

[0026] For the P-M wave spectrum, the expression of the dimensionless wave spectrum data is: .

[0027] It should be understood that the wave spectrum data will have multiple wave peaks, and the wave peak is reflected as a spectral peak on the spectral data. In order to complete the dimensionless processing of the spectral data, the spectral peak frequency of the spectral peak maximum value is selected to assist in the dimensionless processing.

[0028] Figure 1 The dimensionless wave spectrum curve is shown, wherein the frequency range is from 0 to 32.767 rad / s, and the frequency interval is 0.001 rad / s.

[0029] S2: The dimensionless wave spectrum data performing inverse Fourier transform, and calculating the autocorrelation function of the wave spectrum data .

[0030] The autocorrelation function is a mathematical tool to measure the similarity of a random signal or time series with itself at different time lags. In wave data analysis, it can be used to extract the main period information of the wave, check the stationarity of the data, and make preliminary verification for spectrum estimation.

[0031] In some embodiments of the present application, the dimensionless wave spectrum data performing inverse Fourier transform, and calculating the autocorrelation function of the wave spectrum data The method comprises the following steps: ; wherein, is an imaginary number.

[0032] S3: performing complex exponential decomposition on the autocorrelation function of the wave spectrum data to determine the pole-residue representation model of the autocorrelation function of the wave spectrum data .

[0033] In some embodiments of the present application, the step of determining the pole-residue representation model of the autocorrelation function of the wave spectrum data comprises the following steps: decomposing the autocorrelation function, and expressing the autocorrelation function as a sum of multiple complex exponential functions: ; On the basis of the sum of multiple complex exponential functions of performing Laplace transform on the autocorrelation function to obtain the Laplace domain pole-residue representation model of the autocorrelation function : ; wherein, is the Laplace transform of the autocorrelation function , is a Laplace variable, is a pole, is a residue, is a pole and residue number, is the number of poles and residues.

[0034] As shown in Figure 2 , wherein the wave spectrum autocorrelation function ​​The time range is from 0 to 49.6626 s, and the time interval is 0.1917 s. Decompose and determine The number of extreme points ,pole , the corresponding residue .

[0035] like Figure 3 As shown in Figure 3, the comparison results of the reconstructed autocorrelation function and the true autocorrelation function show that the two numerical values ​​are in good agreement.

[0036] S4: Autocorrelation function based on wave spectrum data The extreme residue characterization model , determine the dimensionless wave spectrum data The extreme residue model.

[0037] In some embodiments of the present invention, dimensionless wave spectrum data is determined The steps of the extreme residue model include: Residue representation model based on autocorrelation function ,make , we get the function Frequency domain characterization function of : ; Based on frequency domain characterization function , we get the dimensionless wave spectrum The extreme residue characterization model of : ; in, represents the real part operation, It is pi.

[0038] S5: Based on dimensionless wave spectrum data The extreme residue model reconstructs the wave spectrum .

[0039] In some embodiments of the present invention, the wave spectrum is reconstructed The steps include: .

[0040] According to the calculated autocorrelation function poles and residue values, the dimensionless wave spectrum reconstructed by the sixth-order pole residue model is determined. , which is consistent with the true dimensionless wave spectrum For comparison, see Figure 4 , the two are consistent well.

[0041] According to the calculated autocorrelation function pole and residue value, the dimensionless wave spectrum reconstructed by the six-order pole residue model is determined , and the comparison with the real dimensionless wave spectrum is shown in Figure 4 , and the consistency is good.

[0042] In this example, let m / s, the wave spectrum reconstructed by the pole residue model corresponding to the wind speed can be obtained.

[0043] Figure 5 The comparison between the P-M wave spectrum reconstructed by the pole residue model and the real P-M wave spectrum is shown, and the consistency is good, verifying the effectiveness and high precision of the present application. Similarly, for any wind speed input or any wave spectrum form, the present application can quickly obtain the reconstructed value of the corresponding wave spectrum.

[0044] The present application provides a wave spectrum high-precision reconstruction method based on a pole residue model, and the wave spectrum reconstruction is performed by using a dimensionless wave spectrum, so that the present application has universal ability for any form of wave spectrum and any wave spectrum parameter; in addition, the present application reconstructs the wave spectrum by using the pole residue model, avoids the ill-conditioned problem of numerical fitting in the prior art, and the fitting precision is limited by the specific wave spectrum model, and has higher reconstruction precision and calculation efficiency.

[0045] The above only describes the preferred embodiments of the present application and is not used to limit the present application, and it should be pointed out that for ordinary skilled persons in the art, any modification, equivalent replacement and improvement within the spirit and principles of the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the appended claims.

Claims

1. A high-precision wave spectrum reconstruction method based on the extreme residue model, characterized in that: The following steps are involved: S1: Obtain initial wave spectrum data , for the initial wave spectrum data Perform dimensionless processing to obtain dimensionless wave spectrum data ; S2: The dimensionless wave spectrum data Perform inverse Fourier transform and calculate the autocorrelation function of 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 The extreme residue characterization model ; S4: Autocorrelation function based on the wave spectrum data The extreme residue characterization model , determine the dimensionless wave spectrum data The extreme residue model of S5: Based on dimensionless wave spectrum data The extreme residue model reconstructs the wave spectrum .

2. The high-precision wave spectrum reconstruction method based on the extreme residue model according to claim 1 is characterized in that: The initial wave spectrum data Perform dimensionless processing to obtain dimensionless wave spectrum data The methods include: According to the initial wave spectrum data Data, determine the spectrum peak, take the maximum value of the spectrum peak in each spectrum peak, and determine the spectrum peak frequency of the maximum spectrum peak , calculate the peak frequency The corresponding spectrum value ; Use spectrum peak frequency The corresponding spectrum value Wave spectrum data The data is dimensionless processed, including: ； in, is the frequency of the wave spectrum, , is the dimensionless frequency, the 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 is characterized in that: The dimensionless wave spectrum data Perform inverse Fourier transform and calculate the autocorrelation function of 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 is characterized in that: Determining the autocorrelation function of the wave spectrum data The extreme residue characterization model The steps include: Decompose the autocorrelation function and transform the autocorrelation function Expressed as the sum of multiple complex exponential functions: ； exist Based on the expression of the sum of multiple complex exponential functions, the autocorrelation function Perform Laplace transform to obtain the autocorrelation function The Laplace domain extreme residue characterization model: ； in, is the autocorrelation function The Laplace transform of is the Laplace variable, It's the extreme, It is the remainder, are the pole and residue numbers, is the number of extreme points and residues.

5. The high-precision wave spectrum reconstruction method based on the extreme residue model according to claim 4 is characterized in that: Determining dimensionless wave spectrum data The steps of the extreme residue model include: Residue representation model based on autocorrelation function ,make , we get the function Frequency domain characterization function of : ； Based on the frequency domain characterization function , we get the dimensionless wave spectrum The extreme residue characterization model of : ； in, represents the real part operation, It is pi.

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

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