CN113505470A - Novel non-Gaussian random wave simulation method - Google Patents

Novel non-Gaussian random wave simulation method Download PDF

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CN113505470A
CN113505470A CN202110652330.9A CN202110652330A CN113505470A CN 113505470 A CN113505470 A CN 113505470A CN 202110652330 A CN202110652330 A CN 202110652330A CN 113505470 A CN113505470 A CN 113505470A
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宋宪仓
王树青
杜君峰
郭远志
陶伟
侯宇瑶
吕泽宇
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Abstract

The invention discloses a novel non-Gaussian random wave simulation method, which comprises the steps of generating super-long time sequence Gaussian random waves according to a wave spectrum, constructing a novel nonlinear amplitude modulation model by taking a crest value and a deviation value of a target non-Gaussian random wave as an initial crest value and a deviation value, and carrying out one-time integral modulation on the super-long time sequence Gaussian random waves; extracting the phase of the modulated random wave, and combining the phase with the wave spectrum to generate a non-Gaussian random wave; evaluating the crest value and the deviation value of the non-Gaussian random wave, comparing the crest value and the deviation value with the target crest value and the deviation value, finely adjusting the input crest value and the deviation value according to the relation between the crest value and the target deviation value, building a novel non-linear amplitude modulation model again, and integrally modulating the Gaussian random wave again; repeating the steps to obtain the non-Gaussian random waves meeting the requirements. The invention has higher simulation efficiency, ensures the consistency of the random wave energy distribution before and after modulation, and has higher precision.

Description

Novel non-Gaussian random wave simulation method
Technical Field
The invention belongs to the field of ocean engineering, and particularly relates to a novel non-Gaussian random wave simulation method.
Background
A large amount of wave observation data show that random waves in an actual wave field are influenced by factors such as terrain, water depth and wave direction, the probability distribution of the wave surface elevation does not strictly obey Gaussian distribution, and the random waves in the actual wave field have certain non-Gaussian property. Compared with Gaussian waves, the non-Gaussian random waves have higher probability of occurrence of waves with small amplitude and waves with large amplitude, and are easier to cause one-time damage and long-term accumulated fatigue damage of the structure. In engineering, the actual non-Gaussian random waves are simplified into Gaussian random waves for design analysis, so that the structural response prediction and safety evaluation are inaccurate, and the structural safety hidden danger is formed.
Research shows that the probability distribution of the elevation of the wave surface of the random wave is not only related to the energy distribution of the random wave, but also closely related to the phase distribution of the random wave. For Gaussian random waves, their phases are independent of each other and uniformly distributed in the [0, 2 π ] range. Unlike gaussian random waves, the phases of non-gaussian random waves are not independent of each other, but have a certain dependence. Therefore, in order to generate non-Gaussian random waves, on one hand, the amplitude of the Gaussian random waves is modulated to increase the probability of the generation of the wave surface elevations of the waves with large amplitude and small amplitude, and the non-Gaussian waves meeting the requirements are obtained after a plurality of iterations; and on the other hand, the phase of the random wave can be modulated according to a certain relation from the phase relation of the random wave, the kurtosis value and skewness value of the random wave are gradually changed, and the non-Gaussian random wave meeting the requirements is obtained after a large number of iterations.
The zero memory nonlinear conversion method is a typical method for generating non-Gaussian random waves by changing the amplitude distribution of random waves, can integrally modulate the amplitude of the random waves of an ultra-long time sequence to enable the random waves to be quickly close to target non-Gaussian random waves, and has high calculation efficiency. In the design and analysis process of the ocean engineering structure, a wave spectrum is usually used as an input condition, a one-to-one correspondence relationship exists between the energy distribution of the wave spectrum and input wave parameters, and the change of the energy distribution of random waves can cause the change of the wave parameters corresponding to the random waves, so that the wave parameters adopted in the design and analysis are inconsistent with the expected wave parameters, the change of the energy distribution of the random waves in the design and analysis of the ocean engineering structure is not allowed, and the practicability of the method is limited.
The non-gaussian random wave simulation method based on phase quadratic modulation is a typical method for generating non-gaussian random waves by changing the phase relation of random waves. The method generates the random waves in a form of combining the random phase and the wave spectrum in the iteration process, the energy distribution of the random waves before and after modulation can be ensured to be consistent, but the method only can modulate one group of phases each time, and the influence of single phase modulation on the peak value and the deviation value of the random waves is very small, so that a large amount of iterations are needed to obtain the non-Gaussian random waves meeting the requirements, and the more data points in the random waves and the stronger non-Gaussian property are, the more times of the iterations are needed, so the calculation efficiency of the method needs to be improved urgently. In addition, ocean waves are generally narrow-band processes, energy distribution is concentrated, phases available for modulation are relatively few, and the non-Gaussian wave simulation method based on phase modulation is not ideal in effect of simulating narrow-band non-Gaussian random waves. Therefore, it is highly desirable to develop a non-gaussian random wave simulation method capable of rapidly generating a wave with a predetermined target kurtosis value and skewness value.
Disclosure of Invention
The invention aims to develop a novel non-Gaussian random wave simulation method aiming at the defects of the existing non-Gaussian random wave simulation method and combining the advantages of the existing method, so that the random wave energy distribution is not changed, the simulation efficiency is higher, the limitation of changing the random wave energy distribution by the traditional zero-memory nonlinear conversion method is broken through, and the defect of low calculation efficiency of the traditional phase modulation-based method is overcome.
In order to achieve the purpose, the invention is realized by the following technical scheme:
a novel non-Gaussian random wave simulation method comprises the following steps:
step S1, utilizing the effective wave height HsAnd over zero period TzGenerating a wave spectrum, and dispersing the wave spectrum according to a sampling theorem to obtain the amplitude of random waves
Figure RE-GDA0003255608350000021
And generate [0, 2 π]Random phase independent of each other in range
Figure RE-GDA0003255608350000022
Combining the discrete amplitude value and random phase of the wave spectrum to generate super-long time sequence Gaussian random waves
Figure RE-GDA0003255608350000023
Wherein t is a time variable, N is the discrete amplitude number of the wave spectrum,
Figure RE-GDA0003255608350000024
is a wave spectrum omegaiValue corresponding to frequency, Δ ωiIs the wave frequency interval, omegaiIs the ith wave frequency; by kurtosis value K of target non-Gaussian wavetSum deviation value StAs initial input kurtosis value and skewness value, a novel nonlinear amplitude modulation model is constructed, and the model is used for carrying out one-time initial overall modulation on the Gaussian random waves of the super-long time sequence;
step S2, extracting the phase of the modulated random wave
Figure RE-GDA0003255608350000025
The amplitude value of the wave spectrum after the wave spectrum is dispersed
Figure RE-GDA0003255608350000031
Combining to generate non-Gaussian random wave
Figure RE-GDA0003255608350000032
Step S3, evaluating the kurtosis value K and skewness value S of newly generated non-Gaussian random waves, and comparing the kurtosis value K with the target kurtosis value KtSum deviation value StComparing, calculating difference value delta K and delta S, and when kurtosis value K and skewness value S of non-Gaussian random wave are greater than target kurtosis value KtSum deviation value StWhen the peak value K and the skewness value S of the non-Gaussian random waves are smaller than the target peak value K, subtracting delta K/2 and delta S/2 from the target peak value and the skewness value to serve as input peak values and skewness values to construct a novel non-linear amplitude modulation model, and when the peak value K and the skewness value S of the non-Gaussian random waves are smaller than the target peak value KtSum deviation value StIn the process, the target kurtosis value and the skewness value plus delta K/2 and delta S/2 are used as input kurtosis value and skewness value to construct a novel nonlinear amplitude modulation model, and the newly constructed novel nonlinear amplitude modulation model is utilized to carry out integral modulation on the ultralong time sequence Gaussian random waves again;
and step S4, repeating the steps S2-S3 until a non-Gaussian random wave meeting the requirement is generated.
Further, the purpose of the invention can be realized by the following technical scheme:
a novel non-gaussian random wave simulation method, wherein the novel nonlinear amplitude modulation model in step S1 is as follows:
step S11, when the kurtosis value of the target non-Gaussian random wave is larger than 3.0, namely the target non-Gaussian wave is a super-Gaussian random wave, a nonlinear amplitude modulation model with the kurtosis value K and the skewness value S as input parameters
Figure RE-GDA0003255608350000033
Wherein
Figure RE-GDA0003255608350000034
Figure RE-GDA0003255608350000035
μ is Gaussian random wave ηgMean value of (a) is a Gaussian random wave etagStandard deviation of [, ]gIs the elevation of the wave surface of the Gaussian random wave.
Step S22, when the kurtosis value of the target non-Gaussian random wave is less than 3.0, namely the target non-Gaussian wave is a sub-Gaussian random wave, the nonlinear amplitude modulation model with the kurtosis value K and the skewness value S as input parameters is
Figure RE-GDA0003255608350000036
Wherein
Figure RE-GDA0003255608350000037
Figure RE-GDA0003255608350000038
A novel non-Gaussian random wave simulation method is provided, wherein the wave spectrum in the step S1 is
Figure RE-GDA0003255608350000039
Figure RE-GDA00032556083500000310
Where ω is the wave frequency, α is the regularization coefficient, ωpIs the spectral peak frequency, gamma is the spectral peak increasing factor, and sigma is the peak type coefficient.
A novel non-gaussian random wave simulation method, wherein in step S1, the super-long time is: 3 hours, one hundred and several thousand data points.
Has the advantages that:
in step S1, in order to make the kurtosis value and skewness value of the modulated non-gaussian random wave quickly approach the target kurtosis value and skewness value, the novel nonlinear amplitude modulation model provided by the invention can perform one-time integral modulation on the ultralong time series gaussian random wave, and quickly change the amplitude distribution of the random wave, thereby changing the phase relationship of the random wave related to the random wave, and having very high calculation efficiency.
In step S2, in order to ensure that the energy distribution of the modulated non-Gaussian random wave is consistent with the energy distribution of the Gaussian random wave before modulation, the invention utilizes the phase of the modulated random wave
Figure RE-GDA0003255608350000041
And amplitude a after wave spectrum dispersioniThe combination generates non-gaussian random waves.
For the ultrahigh Gaussian random waves, the wave surface elevation of part of the waves can be obviously increased by the nonlinear conversion model, the wave surface elevation of part of the waves can be slightly reduced, and after the action of the nonlinear amplitude modulation model, the probability of the occurrence of large-amplitude waves and small-amplitude waves in the random waves is obviously increased, so that the random waves have obvious ultrahigh Gaussian characteristics.
For sub-Gaussian random waves, the nonlinear amplitude modulation model can obviously reduce the wave surface elevation of large-amplitude waves, and slightly increase the wave surface elevation of small-amplitude waves, and after the action of the nonlinear amplitude modulation model, the probability of the large-amplitude waves and the small-amplitude waves in the random waves is obviously reduced, so that the random waves have obvious sub-Gaussian characteristics.
Through one-time integral modulation, the crest value and the skewness value of the random wave can be rapidly close to the target crest value and the skewness value, compared with the traditional non-Gaussian wave simulation method based on phase modulation, the iterative modulation times are reduced from thousands of times of the traditional method to 3-5 times, and the simulation efficiency is very high.
Modulation parameter c in novel nonlinear amplitude modulation model3And c4The method is peculiar to the invention, has essential difference with parameters in the traditional non-linear model, and the modulation parameters in the novel non-linear amplitude modulation model are different along with different properties (sub-Gaussian or super-Gaussian random waves) of the simulated non-Gaussian random waves, thereby ensuring that the non-Gaussian random wave simulation method of the invention can carry out simulation on the super-Gaussian and sub-Gaussian random wavesAnd the limitation that the traditional nonlinear model can only simulate super-Gaussian random waves is broken through by effect simulation.
Compared with the prior art, the nonlinear amplitude modulation model is used for carrying out one-time integral modulation on the Gaussian random waves of the ultra-long time sequence, the amplitude distribution characteristic and the random phase relation of the random waves are changed rapidly, the number of times of simulation iteration can be reduced from thousands of times of the traditional method to 3-5 times, and the simulation efficiency is higher; compared with the traditional non-Gaussian wave simulation method based on nonlinear conversion, the method adopts a mode of combining the phase and the wave spectrum to generate the non-Gaussian random wave, ensures the consistency of the energy distribution of the random wave before and after modulation, and has very high calculation efficiency and higher precision while ensuring that the energy distribution of the random wave is unchanged; the invention can effectively simulate ultrahigh Gaussian, sub-Gaussian and non-Gaussian random waves with skewness values not equal to zero, and has great engineering application value.
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In order to more clearly illustrate the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments will be briefly described below. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.
FIG. 1 is a block flow diagram of a method provided by the present invention;
fig. 2 is a block diagram of a process of constructing a nonlinear amplitude modulation model in step S1 shown in fig. 1;
FIG. 3 is a schematic diagram of wave spectrum dispersion;
FIG. 4 is a plot of the wave surface elevations of non-Gaussian and Gaussian waves with different kurtosis values and skewness values;
FIG. 5 shows the energy distributions of non-Gaussian and Gaussian waves with different kurtosis and skewness values.
Detailed Description
Firstly, carrying out one-time integral modulation on Gaussian random waves by using a novel nonlinear amplitude modulation model, then extracting the phase of the modulated random waves, and combining the extracted phase with a wave spectrum to generate the non-Gaussian random waves. The method has very high calculation efficiency, can ensure that the energy distribution of the random waves is not changed before and after modulation, can effectively simulate ultrahigh Gaussian, sub-Gaussian and non-Gaussian random waves with skewness values not equal to zero, and has high practical value. The present invention will be further described with reference to specific examples.
Referring to fig. 1, which is a flow chart of the method of the present invention, a novel non-gaussian random wave simulation method includes the following steps:
step S1, utilizing the effective wave height HsAnd over zero period TzGenerating a wave spectrum
Figure RE-GDA0003255608350000051
In the formula, omega is wave frequency; alpha is a regularization coefficient; omegapIs the spectral peak frequency; gamma is a spectral peak rising factor, and sigma is a peak type coefficient; dispersing the wave spectrum according to the sampling theorem to obtain the amplitude of the random wave
Figure RE-GDA0003255608350000061
And generate [0, 2 π]Random phase independent of each other in range
Figure RE-GDA0003255608350000062
Combining the discrete amplitude value and random phase of the wave spectrum to generate super-long time sequence Gaussian random waves
Figure RE-GDA0003255608350000063
Wherein y is a time variable, N is the number of discrete amplitude values of the wave spectrum,
Figure RE-GDA0003255608350000064
is a wave spectrum omegaiValue corresponding to frequency, Δ ωiIs the wave frequency interval, omegaiIs the ith wave frequency; by kurtosis value K of target non-Gaussian wavetSum deviation value StAs initial input kurtosis value and skewness value, construct new-type NOTLinear amplitude modulation model, refer to fig. 2;
the novel nonlinear amplitude modulation model is as follows: step S11, when the kurtosis value of the target non-Gaussian random wave is larger than 3.0, namely the target non-Gaussian wave is a super-Gaussian random wave, a nonlinear amplitude modulation model with the kurtosis value K and the skewness value S as input parameters
Figure RE-GDA0003255608350000065
Wherein
Figure RE-GDA0003255608350000066
μ is Gaussian random wave ηgMean value of (a) is a Gaussian random wave etagStandard deviation of [, ]gIs the elevation of the Gaussian random wave surface;
step S22, when the kurtosis value of the target non-Gaussian random wave is less than 3.0, namely the target non-Gaussian wave is a sub-Gaussian random wave, the nonlinear amplitude modulation model with the kurtosis value K and the skewness value S as input parameters is
Figure RE-GDA0003255608350000067
Wherein
Figure RE-GDA0003255608350000068
Figure RE-GDA0003255608350000069
Carrying out one-time initial integral modulation on the Gaussian random waves of the super-long time sequence by using the model;
step S2, extracting the phase of the modulated random wave
Figure RE-GDA00032556083500000610
The amplitude value of the wave spectrum after the wave spectrum is dispersed
Figure RE-GDA00032556083500000613
Combining to generate non-Gaussian random wave
Figure RE-GDA00032556083500000612
Step S3, evaluating the kurtosis value K and skewness value S of newly generated non-Gaussian random waves, and comparing the kurtosis value K with the target kurtosis value KtSum deviation value StComparing, calculating difference value delta K and delta S, and when kurtosis value K and skewness value S of non-Gaussian random wave are greater than target kurtosis value KtSum deviation value StWhen the peak value K and the skewness value S of the non-Gaussian random waves are smaller than the target peak value K, subtracting delta K/2 and delta S/2 from the target peak value and the skewness value to serve as input peak values and skewness values to construct a novel non-linear amplitude modulation model, and when the peak value K and the skewness value S of the non-Gaussian random waves are smaller than the target peak value KtSum deviation value StIn the process, the target kurtosis value and the skewness value plus delta K/2 and delta S/2 are used as input kurtosis value and skewness value to construct a novel nonlinear amplitude modulation model, and the newly constructed novel nonlinear amplitude modulation model is utilized to carry out integral modulation on the ultralong time sequence Gaussian random waves again;
and step S4, repeating the steps S2-S3 until a non-Gaussian random wave meeting the requirement is generated.
The invention carries out one-time integral modulation on the ultralong time sequence Gaussian random waves to enable the waves to be quickly close to the target non-Gaussian random waves, has higher calculation efficiency, and simultaneously generates the non-Gaussian random waves by utilizing the phase of the modulated random waves and the amplitude after the wave spectrum is dispersed, thereby ensuring the energy distribution characteristics of the random waves before and after modulation to be consistent. In addition, the method can effectively simulate super-Gaussian waves, sub-Gaussian waves and non-Gaussian random waves with skewness values not being zero, and has strong engineering practicability.
In this embodiment, the ultra-long time is: 3 hours, one hundred and several thousand data points. In ocean engineering, storm surge is often used as a design environmental load, a wave spectrum is used for describing energy distribution of the storm surge, the duration of one storm surge is generally 3 hours, in a few cases, the duration can reach 6 hours or even 9 hours, the sampling time interval of a wave surface is generally 0.1s (or even smaller), the estimation is carried out in 3-hour time, and 108000 data points exist in the process of one storm surge.
For more clearly illustrating the technical effects of the present invention, a wave spectrum dispersion diagram is shown in fig. 3, taking a sea state with an effective wave height of 7.5m and an average zero crossing period of 14.5s as an example; sub-gaussian random waves with a kurtosis value of 2.0 and super gaussian random waves with kurtosis values of 4.0 and 6.0, and non-gaussian waves with skewness values of-0.5 and 0.5, respectively, were simulated. The wave surface process of the non-gaussian random wave and the gaussian wave with different kurtosis values and skewness values is shown in fig. 4, and the energy distribution of the non-gaussian random wave and the gaussian wave with different kurtosis values and skewness values is shown in fig. 5.
And (4) conclusion: the comparison result shows that the wave crest and the wave trough of partial wave surface of the Gaussian random wave are obviously increased after the Gaussian random wave is acted by the nonlinear amplitude modulation model, the wave crests and the wave troughs of other parts are slightly reduced, obvious non-Gaussian property is presented, and the energy distribution of the non-Gaussian random wave generated after modulation is completely the same as that of the Gaussian wave. Comparing Gaussian waves with non-Gaussian random waves can find that obvious phase difference exists between the newly generated non-Gaussian waves and the Gaussian waves, which shows that amplitude modulation is carried out by the nonlinear amplitude modulation model, the phase relation of the random waves can be changed rapidly, and therefore the kurtosis value and the skewness value of the random waves are enabled to be close to the target kurtosis value and the skewness value rapidly. In addition, the invention can simulate the super-Gaussian random wave and has good effect on the sub-Gaussian random wave.
In conclusion, the non-Gaussian random wave simulation method has high calculation efficiency, can ensure that the energy distribution characteristic of random waves is unchanged, can effectively simulate ultrahigh Gaussian waves, sub-Gaussian waves and non-Gaussian random waves with skewness values not being zero, and has high engineering practical value.
Although the present invention has been described with reference to specific embodiments, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.

Claims (4)

1. A novel non-Gaussian random wave simulation method is characterized by comprising the following steps:
step S1, utilizing the effective wave height HsAnd over zero period TzGenerating a wave spectrum, and dispersing the wave spectrum according to a sampling theorem to obtain the amplitude of random waves
Figure RE-FDA0003255608340000011
And generate [0, 2 π]Random phase independent of each other in range
Figure RE-FDA0003255608340000012
Combining the discrete amplitude value and random phase of the wave spectrum to generate super-long time sequence Gaussian random waves
Figure RE-FDA0003255608340000013
Wherein t is a time variable, N is the discrete amplitude number of the wave spectrum,
Figure RE-FDA0003255608340000014
is the frequency spectrum omegaiWave spectrum value of frequency response, delta omegaiFor wave frequency interval, Δ ωiIs the ith wave frequency; with kurtosis value K of target non-Gaussian random wavetSum deviation value StAs initial input kurtosis value and skewness value, a novel nonlinear amplitude modulation model is constructed, and the model is used for carrying out one-time initial overall modulation on the Gaussian random waves of the super-long time sequence;
step S2, extracting the phase of the modulated random wave
Figure RE-FDA0003255608340000015
The amplitude value of the wave spectrum after the wave spectrum is dispersed
Figure RE-FDA0003255608340000016
Combining to generate non-Gaussian random wave
Figure RE-FDA0003255608340000017
Step S3, evaluating the kurtosis value K and skewness value S of newly generated non-Gaussian random waves, and comparing the kurtosis value K with the target kurtosis value KtSum deviation value StComparing, calculating difference value delta K and delta S, and when kurtosis value K and skewness value S of non-Gaussian random wave are greater than target kurtosis value KtSum deviation value StWhen the peak value K and the skewness value S of the non-Gaussian random waves are smaller than the target peak value K, subtracting delta K/2 and delta S/2 from the target peak value and the skewness value to serve as input peak values and skewness values to construct a novel non-linear amplitude modulation model, and when the peak value K and the skewness value S of the non-Gaussian random waves are smaller than the target peak value KtSum deviation value StIn the process, the target kurtosis value and the skewness value plus delta K/2 and delta S/2 are used as input kurtosis value and skewness value to construct a novel nonlinear amplitude modulation model, and the newly constructed novel nonlinear amplitude modulation model is utilized to carry out integral modulation on the ultralong time sequence Gaussian random waves again;
and step S4, repeating the steps S2-S3 until a non-Gaussian random wave meeting the requirement is generated.
2. The novel non-gaussian random wave simulation method according to claim 1, wherein the novel nonlinear amplitude modulation model in step S1 is as follows:
step S11, when the kurtosis value of the target non-Gaussian random wave is larger than 3.0, namely the target non-Gaussian wave is a super-Gaussian random wave, a nonlinear amplitude modulation model with the kurtosis value K and the skewness value S as input parameters is
Figure RE-FDA0003255608340000018
Wherein
Figure RE-FDA0003255608340000019
Figure RE-FDA0003255608340000021
μ is Gaussian random wave ηgMean value of (a) is a Gaussian random waveηgStandard deviation of [, ]gIs the elevation of the Gaussian random wave surface;
step S22, when the kurtosis value of the target non-Gaussian random wave is less than 3.0, namely the target non-Gaussian wave is a sub-Gaussian random wave, the nonlinear amplitude modulation model with the kurtosis value K and the skewness value S as input parameters is
Figure RE-FDA0003255608340000022
Wherein
Figure RE-FDA0003255608340000023
Figure RE-FDA0003255608340000024
3. The method according to claim 1, wherein the wave spectrum in step S1 is the wave spectrum
Figure RE-FDA0003255608340000025
Where ω is the wave frequency, α is the regularization coefficient, ωpIs the spectral peak frequency, gamma is the spectral peak increasing factor, and sigma is the peak type coefficient.
4. The method according to claim 1, wherein in step S1, the super-long time is: 3 hours, one hundred and several thousand data points.
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CN116227242A (en) * 2023-05-09 2023-06-06 中国海洋大学 Random irregular wave simulation method based on white noise filtering

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