CN114003847B - Method for generating and modulating malformed wave and method for correcting spectrum - Google Patents
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Abstract
The invention discloses a generation and modulation method of an abnormal wave and a correction method of an abnormal wave spectrum, in the generation and modulation method of the abnormal wave, firstly, an irregular wave sequence is constructed, then extreme waves are constructed, then a single extreme large wave is inserted into the irregular wave sequence in a time domain, so that a wave sequence containing the abnormal wave is constructed, then the sequence is converted into a frequency domain through Fourier transformation, a wave-making signal is generated by multiplying a corresponding hydrodynamic coefficient, and the generated abnormal wave can be modulated by adjusting input parameters of the abnormal wave. The invention can realize the modulation of the malformed wave surface by the method, and keep other wave surface processes in the wave train unchanged; the correction method of the abnormal wave spectrum can ensure that the actual measurement spectrum of the abnormal wave and the target spectrum are well matched. The invention provides a powerful research means for exploring the interaction mechanism of the malformed wave and the structure.
Description
Technical Field
The invention relates to the technical field of physical oceanography, in particular to a generation and modulation method of malformed waves and a spectrum correction method.
Background
Malformed waves, also known as mad dog waves, devil waves, are a kind of super large waves present in the ocean, generally defined as H max≥2Hs(Hmax being the maximum wave height and H s being the effective wave height). The malformed wave contains huge energy, so that the malformed wave has huge damage to production platforms and ships in the ocean. Up to now, many ocean platform and vessel accidents caused by malformed waves have been recorded. From 1981 to 2000, over 200 large vessels were lost, most of which were considered to be due to malformed waves. Wherein Haver and Anderson report Draupner malformed wave induced failure of the Draupner jacket platform. The marine observation platform FINO-1 used for recording data is hit and damaged by the malformed wave at a position 18m away from the still water surface. More safety accidents caused by malformed waves can be found in the existing literature.
Malformed waves can suddenly appear at any water depth, any weather, including storm surge weather, and even calm water surfaces. According to the Rayleigh distribution, the probability of occurrence of malformed waves is 1/3000 under standard random wave sea conditions. However, a large number of actual observations indicate that the actual occurrence probability of the malformed wave is far greater than the theoretical value. The european "MaxWave" program aims to monitor wave conditions in severe weather by radar and in situ sensors, and by analyzing satellite monitoring data for 3 weeks in the south atlantic ocean, the presence of a large number of malformed waves was found, the maximum observed wave height reaching 25m, h max/Hs =2.9. Carlos analyzed storm surge data from 11, month 16 to 22, 7 days 1997 in North sea, and found 21 malformed waves. The malformed wave can be observed in various sea areas worldwide, clauss derives a probability density function of the extreme wave height based on Rayleigh statistics, and he finds that the probability of occurrence of the malformed wave (H msx≥2Hs) is 28%. At present, the malformed wave has attracted extensive attention from scholars at home and abroad and is considered in design.
Physical model testing is an important tool for exploring the mechanism of malformed wave-structure interaction because of the strong nonlinear interaction between malformed wave-structures. Luo, koh (reference 1) developed a model test to study the impact of the malformed wave on the tension leg platform, and discuss the wave surface characteristics of the incident malformed wave by adjusting the occurrence position of the malformed wave. Pan, liang (reference 2) experimentally compares the motion response of a surface moored floating square box in a malformed wave train and an irregular wave train, but the two wave trains only achieve the same spectrum. Houtani, waseda (reference 3) have conducted model tests in a towing tank to investigate the effect of three sister waves on an elastic container ship. By precisely controlling the trailer, the time of encounter of the model ship with the three sister waves can be precisely controlled and adjusted.
However, the effects of different malformed wave shapes have been rarely studied, and it has been pointed out in the prior art that malformed wave surface shapes may be an important factor in influencing the movement of structures. Furthermore, there is little research in the laboratory on how to control the shape of the malformed wave. Currently, due to the convenience and efficiency of the linear superposition model, the model is often used to generate malformed waves in the laboratory. In the linear superposition model, the wave train of the malformed wave is divided into two parts in the frequency domain: focused wave trains and random wave trains. In the focused wave train, the phases of the component waves are adjusted to enable all waves to reach the maximum value at the same point and at the same time, so that a single large wave is formed. Whereas in a random wave train, the initial phases of the constituent waves are random. But the randomness in the random wave trains is such that the final constituent misshapen wave trains are also random. In the frequency domain, it is difficult to specify parameters such as the wave height and period of the abnormal wave, and the shape of the abnormal wave cannot be adjusted. The superposition model is extended to three dimensions by Ueno, miyazaki (reference 4) and SCHMITTNER AND HENNIG (reference 5) et al, while taking into account the wave height spectrum and direction spectrum. Using the linear superposition model, a spurious wave is generated, which often deviates from the target value because the effects of nonlinear wave-wave interactions are not considered in the linear model.
Thus, clauss (reference 6), klein (reference 7) and Clauss AND SCHMITTNER (reference 8) propose an optimization method to reproduce the target malformed wave surface in the laboratory. The method adopts discrete wavelet transformation and subplex optimizing method, and after the coefficient of wavelet transformation is corrected and optimized, the characteristics of the malformed wave surface can be well matched with the target value. However, this optimization method has the disadvantage that the optimization process is time consuming, one working condition takes about 20 hours, and if one wants to explore the influence of a set of malformed wave parameters, it is obvious that the method is very inefficient; in addition, in the optimization process, the wave surface process at other moments is also modified, which is not beneficial to analyzing the influence of the partial wave surface characteristics of the malformed wave.
Reference is made to:
[1]Luo M,Koh CG,Lee WX,Lin P,Reeve DE.Experimental study of freak wave impacts on a tension-leg platform.Mar struct 2020;74:102821.
[2]Pan W,Liang C,Zhang N,Huang G.Experimental study on hydrodynamic characteristics of a moored square cylinder under freak wave(II:Frequency-domain study).Ocean Eng 2021;219:108452.
[3]Houtani H,Waseda T,Tanizawa K,Sawada H.Temporal variation of modulated-wave-train geometries and their influence on vertical bending moments ofa container ship.Appl Ocean Res 2019;86:128-40.
[4]Ueno M,Miyazaki H,Taguchi H,Kitagawa Y,Tsukada Y.Model experiment reproducing an incident offast ferry.J Mar Sci Technol 2013;18(2):192-202.
[5]Schmittner C,Hennig J,editors.Optimization of Short-Crested Deterministic Wave Sequences via a Phase-Amplitude Iteration Scheme.ASME 201231st International Conference on Ocean,Offshore and Arctic Engineering;2012;Rio de Janeiro,Brazil.
[6]Clauss G.The Taming of the Shrew:Tailoring Freak Wave Sequences for Seakeeping Tests.J Ship Res 2008;52:194-226.
[7]Klein M.The New Year Wave:Spatial Evolution of an Extreme Sea State.J Offshore MechArct Eng 2009;131.
[8]Clauss Gn,Schmittner C.Experimental Optimization of Extreme Wave Sequences for the Deterministic Analysis of Wave/Structure Interaction.J Offshore MechArct Eng 2007;129(1):61-7.
disclosure of Invention
The invention aims to solve the technical problems that in the prior art, the conventional method for generating the malformed wave is to linearly superimpose waves with different frequencies in a frequency domain, the generated malformed wave surface often deviates from a target value, and the malformed wave surface is inconvenient to modulate, and provides a method for generating and modulating the malformed wave; meanwhile, in order to keep the abnormal wave train consistent with the target spectrum in the frequency domain, the invention also provides a method for correcting the abnormal wave spectrum.
In order to achieve the above object, the present invention provides the following technical solutions:
A generation modulation method of malformed waves comprises the following steps:
Step one, constructing an irregular wave sequence as a basic wave train of a malformed wave train, wherein the irregular wave train is expressed as superposition of a plurality of linear waves;
constructing an extreme wave by adopting a trigonometric function with specified parameters, wherein the function analytic formula of the extreme wave is as follows:
Where EW is the extreme wavefront process; EH and EP are the wave height and period, respectively, of the extreme wave; tc is the time at which the extreme wave occurs; alpha 1＝ζcrest/EH,ζcrest is the peak of the extreme wave;
Inserting the extreme waves into the irregular wave train, smoothly inserting the extreme waves into the irregular wave train according to the designated time t c through a transition function, and forming a function analysis type of the abnormal wave train:
FWT＝IWE*TranF+EW*(1-TranF)
Wherein FWT is a wave train of malformed waves; tranF is the transition function;
Step four, the constructed malformed wave train is converted into a frequency domain through Fourier transformation to obtain the amplitude a ' i, the wave number k ' i and the wave circle frequency omega ' i of the malformed wave train, and then the function analytic expression of wave train information at the wave making plate is calculated through phase offset to generate a wave making driving signal, wherein the function analytic expression of the wave train information is as follows:
Wherein Fwm (x c, t) is wave train information at the waveplate; x c is the distance between the wave-making plate and the position where the malformed wave forms;
modulating the generated abnormal wave, adjusting the wave height EH and the period EP of the extreme wave in function analysis, and adjusting the shape of the abnormal wave contained in the irregular wave train; and adjusting different focusing times and focusing positions of the malformed wave by adjusting the malformed wave forming time tc in the function analysis of the step two extreme wave and the distance x c between the wave forming plate and the malformed wave forming position in the step four until the malformed wave is modulated into the needed waveform, the malformed wave with different focusing times and focusing positions.
According to the invention, an irregular wave sequence can be constructed, then extreme waves are constructed, then a single extreme large wave is inserted into the irregular wave sequence in a time domain, so that a wave sequence containing abnormal waves is constructed, then the sequence is converted into a frequency domain through Fourier transformation, and a wave generation signal is generated by multiplying a corresponding hydrodynamic coefficient. Due to the visualization and operability of the time domain, other special extreme waves such as malformed waves, three sister waves and the like can be conveniently constructed.
The invention provides a generation and modulation method of malformed waves, which can effectively generate expected extreme waves, including malformed waves and three sister waves, and has wider adaptability; the method can realize the modulation of the malformed wave surface and keep the other wave surface processes in the wave train unchanged. The method provides a powerful tool for exploring the interaction mechanism of ocean malformed waves and structures.
Preferably, in the first step, the irregular wave train is expressed as a function of superposition of several linear waves, and the expression is:
Wherein IWE (x, t) is an irregular wave-plane process; x and t represent position and time, respectively, x being a constant; subscript i represents the ith constituent wave; m represents the total number of constituent waves; a. k, ω and ε represent the amplitude, wavenumber, the frequency of the wave circle and the initial phase, respectively.
Preferably, the analytical formula of the transition function TranF in the third step is:
Preferably, the wave plate driving signal in the fourth step may be obtained by multiplying Fwm (x c, t) by a bessel transfer function, where the bessel transfer function is:
Wherein S 0 (t) is a driving signal of the wave generator, and h is the water depth.
The invention also provides a method for correcting the abnormal wave spectrum, which comprises the following steps:
step one, generating a malformed wave train according to the method for generating and modulating the malformed wave, wherein the generated malformed wave spectrum is a target spectrum S T(ωi;
step two, performing a physical model experiment, namely performing actual measurement on the abnormal wave train to obtain an actual measurement spectrum S M(ωi of the abnormal wave;
step three, carrying out spectrum correction, wherein a correction formula is adopted as follows:
Wherein S i1(ωi) is the input spectrum, S i2(ωi) is the modified malformed wave spectrum;
step four, introducing a relaxation factor lambda to obtain a corrected spectrum S' i2(ωi) after introducing the relaxation factor:
S′i2(ωi)＝λSi2(ωi)+(1-λ)Si1(ωi)；
Wherein: lambda is a relaxation factor, and takes on a value of 0-1;
And fifthly, taking the corrected spectrum S i2(ωi after the relaxation factor is introduced as an input spectrum S i1(ωi), repeating the steps two to four, and repeating the steps for a plurality of times to obtain a final corrected spectrum S' i2(ωi after the relaxation factor is introduced, thereby completing the correction of the abnormal wave spectrum.
The correction method of the abnormal wave spectrum provided by the invention can ensure that the actually measured spectrum and the target spectrum of the abnormal wave are well matched, and provides a powerful research means for exploring the interaction mechanism of the abnormal wave and the structure.
Preferably, the number of iterations in the fifth step is 3-5.
Preferably, the composition and the initial phase of the wave train of the malformed wave generated in the step one remain unchanged.
Preferably, the device for the physical model experiment in the second step comprises a water tank, wherein a push plate type wave generator is arranged at one end in the water tank, a bracket is arranged in the water tank, a plurality of wave height meters are arranged on the bracket at intervals, and each wave height meter is connected with a signal collector.
Preferably, the sampling frequency of the wave height meter is 50-100Hz, and the measurement accuracy is 0.05-0.1mm.
Preferably, the length of the pool is 40-60m, the width of the pool is 30-40m, and the interval between each wave height meter is 0.2-0.4m.
Compared with the prior art, the invention has the beneficial effects that:
1. The invention provides a generation and modulation method of malformed waves, which can effectively generate expected extreme waves, including malformed waves and three sister waves, and has wider adaptability; the method can realize the modulation of the malformed wave surface and keep the other wave surface processes in the wave train unchanged; the method provides a powerful tool for exploring the interaction mechanism of ocean malformed waves and structures;
2. The correction method of the abnormal wave spectrum provided by the invention can ensure that the actually measured spectrum and the target spectrum of the abnormal wave are well matched, and provides a powerful research means for exploring the interaction mechanism of the abnormal wave and the structure.
Description of the drawings:
FIG. 1 is a flow chart of a method for generating and modulating a malformed wave according to the present invention;
FIG. 2 is a graph of the extreme waves and transition functions of the present invention;
FIG. 3 shows a modified wave train and corresponding irregular wave trains constructed in accordance with the present invention;
FIG. 4 is a flow chart of a method for correcting a modified wave spectrum according to the present invention;
Fig. 5a is a front view of the arrangement of the physical model experiment in this example 2;
FIG. 5b is a top view of the device layout of the physical model experiment;
FIG. 6a is a graph showing the abnormal wave generated in the first working condition in the different random wave trains according to the present invention;
FIG. 6b is a graph showing the abnormal wave generated in the second working condition in the different random wave trains according to the present invention;
fig. 7 is a three sister wave train diagram (H s＝6.8cm,Tp =1.6 s) generated by the method for generating and modulating a malformed wave according to the present invention;
FIG. 8 is a graph comparing measured spectra to target spectra;
Fig. 9 is a graph of comparison between a misshapen wave train and a conventional wave train at different wave heights (T p =1.6 s);
Fig. 10 is a graph of comparison between a misshapen wave train and a conventional wave train under different periodic conditions (H s =6 cm);
Fig. 11 is a graph of different contrast of the malformed wave heights (H s＝8.2cm,Tp =1.9 s);
fig. 12 is a graph of different cycle comparisons of malformed waves (H s＝6cm,Tp =1.4 s);
fig. 13 is a graph of large peak and large trough comparison (H s＝6cm,Tp =1.4 s).
The marks in the figure:
1-wave making plate, 2-water pool, 3-support, 4-transverse plate, 5-wave height instrument and 6-wave eliminating net.
Detailed Description
The present invention will be described in further detail with reference to test examples and specific embodiments. It should not be construed that the scope of the above subject matter of the present invention is limited to the following embodiments, and all techniques realized based on the present invention are within the scope of the present invention.
Example 1
As shown in fig. 1, a method for generating and modulating a malformed wave includes the following steps:
step one, constructing an irregular wave sequence as a basic wave train of a malformed wave train, wherein the irregular wave train is expressed as superposition of a plurality of linear waves, and the function expression is as follows:
Wherein IWE (x, t) is an irregular wave-plane process; x and t represent position and time, respectively, x being a constant; subscript i represents the ith constituent wave; m represents the total number of constituent waves; a. k, ω and ε represent the amplitude, wavenumber, the frequency of the wave circle and the initial phase, respectively;
It should be noted that the initial phase of each component wave is random, and the application is specified by a "rand" function in MATLAB software, in which a set of random numbers is generated by a random seed (random seed) that is manually input. The amplitude can be calculated from the spectrum:
Wherein S (ω i) is the wave spectrum;
constructing an extreme wave by adopting a trigonometric function with specified parameters, wherein the function analytic formula of the extreme wave is as follows:
Where EW is the extreme wavefront process; EH and EP are the wave height and period, respectively, of the extreme wave; tc is the time at which the extreme wave occurs; alpha 1＝ζcrest/EH,ζcrest is the peak of the extreme wave;
in the second step, in order to achieve smooth transition between the extreme waves and the irregular wave trains in the third step, the above-mentioned function analysis is to add transition sections connected to the free water surface before and after the extreme waves. Wherein the extreme wave curve is shown in figure 2;
Step three, inserting extreme waves into the irregular wave train, smoothly inserting the extreme waves into the irregular wave train according to the designated time t c through a transition function, and forming a malformed wave train:
FWT＝IWE*TranF+EW*(1-TranF)#(4)
wherein FWT is the malformed wave train and TranF is the transition function, wherein the specific function resolution of the TranF transition function is as follows:
the mode of TranF transition functions is shown in fig. 2, and the constructed abnormal wave trains and the corresponding irregular wave trains are shown in fig. 3;
Generating a wave-making driving signal, namely obtaining the amplitude a ' i, the wave number k ' i and the wave circle frequency omega ' i of the malformed wave train through Fourier transformation to the frequency domain by the structured malformed wave train, and then calculating wave train information at the wave-making plate through phase deviation to generate the wave-making driving signal, wherein the function analytic formula of the wave train information is as follows;
Wherein Fwm (x c, t) is wave train information at the waveplate; x c is the distance between the wave-making plate and the position where the malformed wave forms;
The above-mentioned wave-making plate driving signal may be obtained by multiplying Fwm (x c, t) by a bessel transfer function, where the bessel transfer function is:
Wherein S 0 (t) is a driving signal of the wave generator, and h is the water depth.
Modulating the generated abnormal wave, adjusting the wave height EH and the period EP of the extreme wave in function analysis, and adjusting the shape of the abnormal wave contained in the irregular wave train; by adjusting the malformed waveform forming time tc in the formula 4 and the malformed waveform forming position x c in the formula 5, different focusing times and focusing positions of the malformed wave are adjusted until the malformed wave which is modulated into a required waveform shape and different focusing times and focusing positions. Specifically, by adjusting the wave height EH and the period EP of the extreme wave in expression 3, the abnormal wave shape included in the irregular wave train can be adjusted. The malformed wave height EH takes a negative value to generate a large wave trough. By adjusting the malformed waveform forming time tc in equation 4 and the malformed waveform forming position x c in equation 5, different malformed wave focusing times and focusing positions can be achieved. For the generation of a sister wave or other special wave surface, the generation can still be performed according to the steps, except that a single extreme wave in the formula 3 is replaced by a target wave.
The method can firstly construct an irregular wave sequence, then construct extreme waves, then insert a single extreme large wave into the irregular wave sequence in a time domain, thereby constructing a wave sequence containing abnormal waves, then convert the sequence into a frequency domain through Fourier transformation, and multiply the frequency domain by a corresponding hydrodynamic coefficient to generate a wave-making signal. Due to the visualization and operability of the time domain, other special extreme waves such as malformed waves, three sister waves and the like can be conveniently constructed.
The invention provides a generation and modulation method of malformed waves, which can effectively generate expected extreme waves, including malformed waves and three sister waves, and has wider adaptability; the method can realize the modulation of the malformed wave surface and keep other wave surface processes in the wave train unchanged; the method provides a powerful tool for exploring the interaction mechanism of ocean malformed waves and structures.
Example 2
As shown in fig. 4, embodiment 2 provides a method for correcting a malformed wave spectrum, which includes the steps of:
Step one, generating a malformed wave train according to the method for generating and modulating a malformed wave in the above embodiment 1, wherein the generated malformed wave spectrum is a target spectrum S T(ωi);
step two, performing a physical model experiment, namely performing actual measurement on the abnormal wave train to obtain an actual measurement spectrum S M(ωi of the abnormal wave;
step three, carrying out spectrum correction, wherein a correction formula is adopted as follows:
Wherein S i1(ωi) is the input spectrum, S i2(ωi) is the modified malformed wave spectrum;
step four, introducing a relaxation factor lambda to obtain a corrected spectrum S' i2(ωi) after introducing the relaxation factor:
S′i2(ωi)＝λSi2(ωi)+(1-λ)Si1(ωi)#(9)；
Wherein: lambda is a relaxation factor, and takes on a value of 0-1;
And fifthly, taking the corrected spectrum S 'i2(ωi after the relaxation factor is introduced as an input spectrum S i1(ωi), repeating the steps two to four, and repeating the steps for a plurality of times to obtain a final corrected spectrum S' i2(ωi after the relaxation factor is introduced, thereby completing the correction of the abnormal wave spectrum.
The correction method of the abnormal wave spectrum provided by the invention can ensure that the actually measured spectrum and the target spectrum of the abnormal wave are well matched, and provides a powerful research means for exploring the interaction mechanism of the abnormal wave and the structure.
The iteration times in the fifth step are 3-5 times. In the spectrum correction process, in order to make the nonlinear effect influence of wave-wave interaction more stable, the composition components and the initial phase of the malformed wave train generated in the step one remain unchanged.
As shown in figures 5a and 5b, the device for the physical model experiment in the second step comprises a pool 1, the length a of the pool 1 is 40-60m, the width b of the pool is 30-40m, the distance l between wave height meters 5 is 0.2-0.4m, the sampling frequency of the wave height meters is 50-100Hz, the measuring precision is 0.05-0.1mm, a push plate type wave-making plate 1 is arranged at one end in the pool 1, a bracket 3 is arranged in the pool 2, a plurality of wave height meters 5, such as 9-10 wave height meters 5 are arranged on the bracket 3 at intervals, and a signal collector is connected to each wave height meter 5.
Example 3
In this embodiment 3, a physical model experiment of a method for generating and modulating a malformed wave and a method for correcting a spectrum of the malformed wave is shown in fig. 5a, and fig. 5b, which is a plan view of an apparatus arrangement of the physical model experiment in this embodiment 2, wherein the physical model experiment includes a pool 2 and a wave-making plate 1 positioned at one end of the pool 2, and a capacitive wave height meter 5 is used to measure a wave surface time history, the measurement accuracy is 0.1mm, and the sampling frequency is 50Hz; a total of 9 wave height meters 5 are installed along the central line of the water tank 2, and the distance between the wave height meters 5 is 0.3m. The wave height meter 5# is 18m away from the wave making plate; the wave height gauge 5 is fixed to a designated position in the pool by a bracket 3 and a cross plate 4, wherein the cross plate 4 may be made of aluminum alloy plate. The water depth of this test is 0.7m. The total sampling time 164s and the malformed wave formation time tc were set to 50s. The wave spectrum adopts JONSWAP spectrum, and the total wave number M is 300. The random seed of the initial phase in step 1 is taken as "12" unless otherwise specified. The focusing position is taken at the position of the 5# wave height instrument, namely the initial value of x c is taken as 18m. After each test is completed, the water surface is calm under the action of the wave eliminating net 6, and the next test is performed. Since the time and location of occurrence of the malformed wave are also achievable in the linear superposition model, they are not discussed here. The method is mainly used for verifying the effectiveness of the method for generating the abnormal wave and observing the effect of adjusting the wave surface of the abnormal wave by the method.
The method provided by the invention is verified in the time domain and the frequency domain through the physical model test. Next, the actual measurement wave trains with different malformed wave shapes are compared, wherein the actual measurement wave trains comprise malformed wave sequences and corresponding irregular wave sequences, different malformed wave heights and periodic sequences, and large wave crest and large wave trough sequences, and the data displayed in the invention are all from a 5# wave height instrument. In order to make the displayed process line clearer, the invention selects a time period of 20-100s for display. The goodness of fit of the two wave sequences is evaluated by the determinable coefficients (equation 10) as follows:
wherein r 2 represents a determinable coefficient; zeta 1i and zeta 2i represent the rise of the wave surface at the i-th time of wave train 1 and wave train 2, respectively; representing the average value of the elevation of the wave surface of the second wave train; n represents the sample volume acquired. r 2 varies from 0 to 1, with a larger value indicating a better consistency of the two wave sequences.
The focus position of the actual malformed wave often deviates from the input value due to the influence of wave-wave nonlinear interactions, wave-making plate performance, and other factors. For different test conditions, the deviation is unstable, so that the x c needs to be adjusted according to the actual focusing position in the actual wave making process. During the test, it was found that: for the generation of large wave peaks, the position deviation is usually smaller than 1m, and the generation of the malformed wave at the preset position can be realized through 2-3 times of adjustment; however, for the generation of large valleys, the positional deviation is large, and more adjustments are required. The wave surface process shown in this section is the result of x c after adjustment, and the malformed wave is generated at the 5# wave height instrument position.
1. Method validity verification
Under different random seed conditions, the comparison of the time and wave surface and wave height of different actually measured malformed wave trains generated based on the method is shown in fig. 6a and 6b, wherein H is the down-zero-crossing statistical wave height. From the wave process line we can observe a sharp spike, which is consistent with the intuitive nature of the malformed wave.
As shown in fig. 6a, in condition 1, H max and ζ crest are 19.90cm and 12.73cm, respectively, and corresponding H max/Hs＝2.34,ζcrest/Hmax =0.64.
As shown in fig. 6b, in condition 2, H max and ζ crest are 18.60cm and 12.29cm, respectively, and corresponding H max/Hs＝2.19,ζcrest/Hmax =0.66. It can be seen that all parameters are satisfied by the global and local features of the malformed wave (H max＞2Hs,ξcrest＞0.6Hmax).
Fig. 7 shows a three sister wave generated based on this method. As can be seen from the process line, three consecutive abnormal large waves appear on the water surface. The wave heights of the three large waves are 13.94cm, 15.16cm and 13.40cm respectively, and the corresponding H max/Hs is 2.1, 2.2 and 2.0 respectively. All three waves meet the criteria for malformed wave H max≥2Hs.
Fig. 8 shows a comparison of the target spectrum and the corrected measured spectrum. It can be seen that the measured spectrum is well matched with the target spectrum after the spectrum correction. For condition one, the errors of the spectral peak frequency, spectral peak and spectral total energy were 0.00%, 6.44% and 0.39%, respectively. For condition two, the errors of the spectral peak frequency, the spectral peak and the total energy of the spectrum are 0.00%, 2.36% and 12.83%, respectively.
Therefore, the method provided by the invention can effectively generate malformed waves and trissister waves in a laboratory, and has good performance in time domain and frequency domain.
2. Abnormal wave generation result under different basic wave train conditions
Under the conditions of different spectral peak periods and effective wave heights, the comparison result of the malformed wave train and the corresponding irregular wave train is shown in fig. 9 and 10. Calculation of this subsection r 2 excludes the moment of occurrence of the malformed wave. It can be seen that the wavefront processes at other times are almost completely identical except for the moment of occurrence of the malformed wave. The maximum and minimum r 2 values are 0.962 and 0.884, respectively. The result shows that the method can insert extreme waves into an irregular wave train without influencing wave surface processes at other moments. This facilitates an accurate comparison of the interaction of the malformed wave and conventional waves with the structure.
3. Comparison of malformed wave waveform modulation results
The adjustment of the malformed wave waveform is achieved by adjusting the input parameters in the function analysis formula 3. The comparison of four different malformed wave heights is shown in fig. 11. The relative wave height range of the malformed wave generated based on the method is larger (H max/Hs =2.05-3.16), meanwhile, the wave surface process of the malformed wave period and other moments is highly consistent, the relative deviation of the malformed wave period is less than 3%, and any two wave trains r 2 are greater than 0.96. The comparison of four different malformed wave period results is shown in fig. 12, the generated malformed wave period range is (ep=1.48 s-1.84 s), meanwhile, the malformed wave heights and wave surface processes at other moments are consistent in height, the maximum relative deviation of the malformed wave heights is 2.7%, and any two wave columns r 2 are larger than 0.92. The comparison of the large peaks and large valleys is shown in FIG. 13, where the maximum peaks and the maximum valleys are 9.29cm and-7.38 cm, respectively. The wavefront process at other times is highly uniform, and the r 2 value of the two wavetrains is 0.86.
The results show that the method can effectively adjust the malformed waveform, and the wave surface process is unchanged at other moments in the process. By using the method, the interaction mechanism of different malformed wave shapes and structures can be explored.
The present invention proposes a new method for generating malformed waves in a laboratory. In this method, a malformed wave train is constructed by inserting a single extreme wave in the irregular wave train. Unlike the conventional linear superposition model, the construction of the wave trains of malformed waves is performed in the time domain. Other special wave surface forms, such as three sisters waves, can be conveniently generated due to operability in the time domain, and the shape of the malformed wave is easy to adjust. In addition, the invention also provides a spectrum correction method of the malformed wave train. And carrying out a physical model test to verify the method. The following conclusions were drawn:
① The method can effectively generate extreme waves in a laboratory, including malformed waves and three sister waves. The method provided by the invention corrects the abnormal wave spectrum, and the actually measured spectrum and the target spectrum are well matched.
② The method can conveniently adjust the shape of the local wave surface based on the visualization and operability of operation in the time domain. And the adjustment of the local waveform does not affect the wave surface process at other moments. The method is helpful for deep exploration of the interaction mechanism of the malformed wave-structure.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (10)
1. The generation and modulation method of the malformed wave is characterized by comprising the following steps: step one, constructing an irregular wave sequence as a basic wave train of a malformed wave train, wherein the irregular wave train is expressed as superposition of a plurality of linear waves; constructing an extreme wave by adopting a trigonometric function with specified parameters, wherein the function analytic formula of the extreme wave is as follows: Where EW is the extreme wavefront process; EH and EP are the wave height and period, respectively, of the extreme wave; tc is the time at which the extreme wave occurs; α1=ζ crest/EH, ζ crest being the peak of the extreme wave; step three, inserting the extreme waves into the irregular wave train, smoothly inserting the extreme waves into the irregular wave train according to the designated time tc through a transition function, and forming a function analysis formula of the abnormal wave train: fwt=iwe TranF +ew (1-TranF) where FWT is the wave train of malformed waves; tranF is the transition function; IWE is an irregular wave train; step four, converting the constructed malformed wave train into a frequency domain through a Fourier function to obtain an amplitude a ' i, a wave number k ' i and a wave circle frequency omega ' i of the malformed wave train, and calculating a function analytic formula of wave train information at a wave making plate through phase offset to generate a wave making driving signal, wherein the function analytic formula of the wave train information is as follows: /(I) Wherein Fwm (xc, t) is wave train information at the waveplate; xc is the distance between the wave-making plate and the position where the malformed wave forms; modulating the generated abnormal wave, adjusting the wave height EH and the period EP of the extreme wave in function analysis, and adjusting the shape of the abnormal wave contained in the irregular wave train; and adjusting different focusing times and focusing positions of the malformed wave by adjusting the malformed wave forming time tc in the function analysis of the step two extreme wave and the distance xc between the wave forming plate and the malformed wave forming position in the step four until the malformed wave is modulated into the needed waveform, the malformed wave with different focusing times and focusing positions.
2. The method of generating and modulating a malformed wave according to claim 1, wherein in the first step, the irregular wave train is expressed as a function of superposition of several linear waves, and the expression is: Wherein IWE (x, t) is an irregular wave-plane process; x and t represent position and time, respectively, x being a constant; subscript i represents the ith constituent wave; m represents the total number of constituent waves; a. k, ω and ε represent the amplitude, wavenumber, the frequency of the wave circle and the initial phase, respectively.
3. The method of generating and modulating a malformed wave according to claim 1, wherein the function analysis formula of the transition function TranF in the third step is:。
4. The method of generating and modulating a malformed wave according to claim 1, wherein the driving signal of the wave-making plate in the fourth step is obtained by multiplying Fwm (xc, t) by a bessel transfer function, where the bessel transfer function is: wherein S0 (t) is a driving signal of the wave generator, and h is the water depth.
5. A method for correcting a modified wave spectrum, comprising the steps of: step one, generating a malformed wave train according to the method for generating and modulating a malformed wave according to any one of claims 1 to 4, wherein the generated malformed wave spectrum is a target spectrum ST (ωi); step two, performing a physical model experiment, namely performing actual measurement on the abnormal wave train to obtain an actual measurement spectrum SM (omega i) of the abnormal wave; step three, carrying out spectrum correction, wherein a correction formula is adopted as follows: Where Si1 (ωi) is the input spectrum and Si2 (ωi) is the modified abnormal wave spectrum; step four, introducing a relaxation factor lambda to obtain a corrected spectrum S 'i2 (omega i) after the relaxation factor is introduced as S' i2 (omega i) =lambda Si2 (omega i) + (1-lambda) Si1 (omega i), wherein: lambda is a relaxation factor, and takes on a value of 0-1; and fifthly, taking the corrected spectrum S 'i2 (omega i) after the relaxation factor is introduced as an input spectrum Si1 (omega i), repeating the steps two to four, and repeating the steps for a plurality of times to obtain a final corrected spectrum S' i1 (omega i) after the relaxation factor is introduced, thereby completing the correction of the abnormal wave spectrum.
6. The method for correcting a modified wave spectrum according to claim 5, wherein the number of iterations in the fifth step is 3 to 5.
7. The method of claim 5, wherein the composition and the initial phase of the wave train of the malformed wave generated in the first step remain unchanged.
8. The method for correcting abnormal wave spectrum according to claim 5, wherein the device for physical model experiment in the second step comprises a water tank, wherein a push plate type wave generator is arranged at one end in the water tank, a bracket is arranged in the water tank, a plurality of wave height meters are arranged on the bracket at intervals, and each wave height meter is connected with a signal collector.
9. The method for correcting the abnormal wave spectrum according to claim 8, wherein the sampling frequency of the wave height meter is 50-100Hz, and the measuring precision is 0.05-0.1mm.
10. The method for correcting a modified wave spectrum according to claim 8, wherein the pool has a length of 40-60m and a width of 30-40m, and the pitch of each wave height meter is 0.2-0.4m.
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