CN107490464B - The back wave separation method of Nonlinear Wave based on addition of waveforms principle - Google Patents
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Abstract
The invention discloses a kind of back wave separation methods of Nonlinear Wave based on addition of waveforms principle, the incidence wave of enough durations is measured by using the fixed wave height recorder of single branch and composite wave that incidence wave is superimposed with back wave, applied waveforms linear superposition theorem, and consider that the incidence wave that wave flume is made has excellent stability and repeatability, incidence wave is directly subtracted so from composite wave, it can be obtained reflection configuration, to achieve the purpose that separate back wave.This method only needs the measuring instrument individually fixed, and is suitable for linear and any high-order nonlinear rule wave problem.Measurement method is simple, and solution procedure is easy, and improves back wave separative efficiency.
Description
Technical Field
The invention belongs to the technical field of ocean engineering, and particularly relates to a reflected wave separation method of nonlinear waves based on a waveform superposition principle.
Background
When the wave propagation encounters a large object, the wave is reflected. The reflected wave and the incident wave are superposed before the structure to form a composite wave. The reflection coefficient is one of the important parameters in the laboratory study of the hydrodynamic performance of breakwaters. The reflected wave is separated from the synthesized waveform, and the method has important significance for the research of the hydrodynamic performance of the breakwater. Currently, there are two main types of methods for separating the reflected waves: the separation method is applicable only to linear waves and the separation method is applicable to nonlinear waves. Two-point method, three-point method and multi-point method are commonly used for the separation method of linear waves, namely: measuring the synthesized waveform by using two fixed wave height meters, three wave height meters or more fixed wave height meters, and analyzing and processing the synthesized waveform by methods such as Fourier transform, wavelet transform, least square method and the like to obtain the wave height and phase of the reflected wave; there is also a method of measuring by using a moving single wave height meter, and the reflected wave height is calculated by using the Doppler effect. For the reflected wave separation method of nonlinear waves, the nonlinear incident waves and the reflected waves are assumed to be formed by superposition of basic waveforms, high-order free waves and constraint waves, increased variables require that at least 4 waves of synthetic wave data measured by a wave height instrument can be solved, and due to the fact that determination of high-order wavelengths is approximate, considered nonlinearity can obtain results with high precision for second-order equi-mild nonlinear situations, but errors exist for the high-order nonlinear situations. In summary, the current waveform separation method, either the measurement instrument or the analysis method, is relatively complex: a plurality of measuring instruments or movable measuring instruments are required to be adopted for data acquisition, and the measuring method is complex; in the analysis process, the number of unknowns is large, the solution is complex, in addition, the hypothesis exists in the separation process, and the result precision in the application range is higher.
Disclosure of Invention
The invention aims to provide a reflected wave separation method of nonlinear waves based on a waveform superposition principle, which can solve the defects of the traditional reflected wave separation method, has simple measurement method and easy solving process, is suitable for linear and random high-order nonlinear regular wave problems, and improves the reflected wave separation efficiency.
The purpose of the invention is realized by the following technical scheme, which comprises the following steps:
firstly, arranging experimental equipment in a wave water tank of a laboratory according to the sequence of wave making equipment, a wave height instrument and a reflection model, connecting the wave height instrument with a data processor, and respectively carrying out two sets of wave making tests with the same wave making parameters when a reflection model is not available and when the reflection model is available;
secondly, measuring the waveform data of the two wave-making tests in the step one by using a single fixed wave height instrument to obtain the waveform data without a reflection model and the waveform data with the reflection model;
thirdly, determining the time period of the incidence waveform and the reflection waveform in the waveform with the reflection model in the second step;
fourthly, separating reflected waves of the waveforms with the reflection models in the second step by applying a waveform linear superposition principle;
fifthly, determining parameters of the reflected waveform in the waveform obtained in the step four.
According to the scheme, the experimental equipment in the step one comprises: the wave making device comprises wave making equipment, a wave height instrument, a reflection model, a wave water tank and a data processor. The wave-making equipment is controlled by a servo motor and is used for generating required waves, and the wave-making stability and the repeatability error of the wave-making equipment are within 5 percent; the wave height instrument is used for acquiring wave data and transmitting the data to the data processor to obtain a oscillogram, and the measurement error of the wave height instrument is within 0.5 percent; the reflection model is a single flat plate vertically penetrating through the water surface, is arranged perpendicular to the incident wave direction and is used for reflecting waves to obtain synthetic waves.
According to the scheme, when the reflection model exists in the step two, the waveform measured by the wave height meterIs formed by incident wave formsCombined waveform of incident wave and reflected waveTwo-stage composition, which can be expressed as follows:
to synthesize the waveformIs to enterWave-shaped jetAnd the reflected waveformCan be expressed as:
substituting the formula (2) into the formula (1) to obtain the reflection waveformExpression:
wherein,represents t0～teThe waveform of the single wave height meter in the time period when the reflection model exists,represents t0～t1The incident waveform of the time segment is,represents t1～teThe resultant waveform of the time segment is,represents t1～teThe incident waveform in the time-segment composite wave,represents t1～teTime slot deviceA reflected waveform in the wave.
T is the time when a reflection model exists because the stability of water tank wave generation is good0～teIncident waveform of time segmentCan be written as:
substituting the formula (4) into the formula (3) to obtain a reflection waveformThe expression is as follows:
this formula is used to separate the reflected waveforms in step four
Waveform without reflection modelThe entire period is the incident waveform, i.e.:
wherein,represents t0～teWaveform without reflection model of single wave height measurement of time period,representing time t without reflection model0～teIncident waveform of a time segment.
According to the scheme, the time period of the incident wave in the third step is the time period of the overlapping part of the waveform when the reflection model exists and the waveform when the reflection model does not exist in the second step: t is t0～t1The time period immediately following the time period is the time period of the incident wave and the reflected wave, however, the time period of the superimposed wave is limited and is taken as: t is t1～teTime periods, since multiple reflections may subsequently occur.
According to the scheme, the waveform linear superposition principle in the fourth step refers to that: when several lines of waves propagate in the medium at the same time, the propagation characteristics including wavelength, frequency, waveform and wave speed are not influenced by the existence of other waves. In the meeting region, the combined vibration is the superposition of the partial vibrations. The waveform with the reflection modelThe reflected wave is separated by adopting the formula (5) in the step two. (5) Incident wave form in the formulaObtained by the following two ways:
a. due to the good repeatability of the wave making of the water tank, the incident wave in the wave form of the reflection modelIncident wave in the absence of a reflection modelThe superposition is better, namely:
wherein,representing t with a reflection model0～teThe incident wave of the time segment is,representing time t without reflection model0～teIncident wave of a time segment.
b. T which cannot be directly measured in a synthesized waveform with a reflection model due to good stability of water tank wave generation1～teIncident wave of a time segmentCan be formed by t0～t1Incident waveform of time segmentRepeating the waveform over time, thus deforming (4) as:
wherein N satisfies Nt1＝te。
And the waveform of the reflection modelAnd incident waveformApplied to the formula (5), i.e. the reflected waveform can be separated
According to the scheme, the reflected waveform obtained in the step five is taken as the part with stable waveform after the reflected wave appears in the waveform obtained in the step four.
The result accuracy depends on the stability and repeatability of the water tank wave generation and the measurement accuracy of the wave height meter, and the application range of the method is related to whether the experiment can obtain the incident wave and the synthetic wave with enough duration or not, and is related to whether the wave is broken or not and whether the incident wave is perpendicularly incident to the reflection model or not.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a novel method suitable for reflected wave separation of high-order nonlinear waves, which only needs a single fixed measuring instrument, fully utilizes incident wave data provided by the single measuring instrument and synthetic wave data of reflected waves and incident waves superposed on each other based on a waveform superposition principle, and can process any high-order nonlinear wave problem. The measuring method is simple, the solving process is easy, and the efficiency of waveform separation of reflected waves is improved.
Drawings
Fig. 1 is a schematic structural diagram of the wave generating device of the present invention.
Fig. 2 is a waveform diagram with a reflection model.
Fig. 3 is a waveform diagram of a reflection-free model.
Fig. 4 is a waveform diagram processed by the waveform superposition principle.
In the figure: 1. wave making equipment, 2 wave height instrument, 3 reflection model, 4 wave water tank, 5 data processor, and 6 reflection waveform position.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
The invention comprises the following steps:
the method comprises the following steps: the experimental equipment is well arranged in a wave water tank 4 of a laboratory according to the sequence of a wave generating device 1, a wave height instrument 2 and a reflection model 3, the wave height instrument 2 is connected with a data processor 5, and wave generating tests with the same wave generating parameters of two groups of wave generating devices without the reflection model 3 and with the reflection model 3 are respectively carried out as shown in figure 1.
"Experimental facilities" include: the wave generating device comprises a wave generating device 1, a wave height gauge 2, a reflection model 3, a wave water tank 4 and a data processor 5. The wave-making equipment 1 is controlled by a servo motor and is used for generating required waves, and the wave-making stability and the repeatability error of the wave-making equipment are within 5 percent; the wave height instrument 2 is used for acquiring wave data and transmitting the data to the data processor 5 to obtain a oscillogram, and the measurement error of the wave height instrument 2 is within 0.5 percent; the reflection model 3 is a single flat plate vertically penetrating through the water surface, is installed perpendicular to the incident wave direction, and is used for reflecting waves to obtain synthetic waves.
Step two: and (3) measuring the waveform data of the two wave making tests in the step one by using the single fixed wave height instrument 2 to obtain the waveform data without the reflection model 3 and the waveform data with the reflection model 3.
FIG. 2 is a waveform with a reflection model 3Is formed by incident wave formsCombined waveform of incident wave and reflected waveTwo-part composition, which can be expressed as follows:
to synthesize the waveformIs an incident wave formAnd the reflected waveformThe overlay, can be expressed as:
substituting the formula (2) into the formula (1) to obtain the reflection waveformExpression:
wherein,represents t0～teThe waveform of the reflection model 3 measured by the single wave height indicator 2 of the time period,represents t0～t1The incident waveform of the time segment is,represents t1～teThe resultant waveform of the time segment is,represents t1～teThe incident waveform in the time-segment composite wave,representst1～teTime segments the reflected waveform in the composite wave.
T when there is the reflection model 3 because the stability of the wave generated by the wave water tank 4 is good0～teIncident waveform of time segmentCan be written as:
substituting the formula (4) into the formula (3) to obtain a reflection waveformThe expression is as follows:
this formula is used to separate the reflected waveforms in step four
FIG. 3 is a waveform of a case where there is no reflection model 3Can be expressed as:
wherein,represents t0～teWaves without reflection model 3 measured by single wave height meter 2 for time periodIn the shape of a square,representing the time t of the model 3 without reflection0～teIncident waveform of a time segment.
Step three: and determining the time period of the incident waveform and the reflected waveform in the waveform with the reflection model 3 in the step two.
The time period of the incident wave is the time period of the overlapping part of the waveform when the reflection model 3 exists and the waveform when the reflection model 3 does not exist in the step two: t is t0～t1The time interval immediately following the time interval is the time interval during which the incident wave and the reflected wave are superposed, however, the time interval of the superposed wave is limited and is taken as t1～teTime periods, since multiple reflections may subsequently occur.
Specifically, in the present embodiment, in comparison with fig. 2 and 3, in the first 6s period, the waveform of the synthesized wave in the case where the reflection model 3 exists and the waveform in the case where the reflection model 3 does not exist overlap each other well, and therefore, the period can be regarded as the period of the incident waveform.
After 6s, the difference between the two waveforms and the phase is obvious, and a reflection phenomenon exists. Considering that the wave front of the incident wave is also reflected by the reflection model 3 and the first peak rises after 8s in fig. 2, it indicates that the reflected wave should appear after 8 s.
Step four: and (5) separating the reflected wave from the waveform with the reflection model 3 in the step two by applying a waveform linear superposition principle.
The principle of waveform linear superposition refers to: when several lines of waves propagate in the medium at the same time, the propagation characteristics including wavelength, frequency, waveform and wave speed are not influenced by the existence of other waves. In the meeting region, the combined vibration is the superposition of the partial vibrations. Waveform with reflection model 3The reflected wave is separated by direct measurement in the second stepAdopts the formula (5) in the step two. (5) Incident wave form in the formulaObtained by the following two ways:
a. because the repeatability of the wave making of the water tank is better, namely in the process of making the wave for many times under the same control signal, the period and wave height of each wave made have good identity, and the incident wave in the wave form when the reflection model 3 existsIncident wave with no reflection model 3The superposition is better, namely:
wherein,representing t with the reflection model 30～teThe incident wave of the time segment is,representing the time t of the model 3 without reflection0～teIncident wave of a time segment.
b. Because the stability of the water tank wave making is better, namely in the process of one wave making under the same control signal, the period and wave height of the wave made are kept stable for a long time, and t which can not be directly measured in the synthesized waveform when the reflection model 3 exists1～teIncident wave of a time segmentCan be formed by t0～t1Incident waveform of time segmentRepeating the waveform over time, so that equation (4) is transformed as:
wherein N satisfies Nt1＝te。
And the waveform of the reflection model 3And incident waveformApplied to the formula (5), i.e. the reflected waveform can be separated
Specifically, in this embodiment, the waveform when the reflection model 3 exists is the waveform obtained when the reflection model 3 exists in the second step, that is, the waveform shown in fig. 2, the incident waveform in this waveform is the incident waveform before 6s obtained in the third step, and the incident waveform in the whole time period is to be obtained, and since the wave generated by the wave water tank 4 has good stability and repeatability, the following two methods can be used for processing:
a. in step two, the incident waveform over the entire time period can be represented by the waveform of the non-reflection model 3, i.e., as shown in fig. 3.
b. In step three, the obtained incident waveform before 6s is taken as the proper length, and one waveform repetition is performed on the whole time period, so that the incident waveform on the whole time period is obtained.
When the stability and repeatability of wave generation in the wave water tank 4 are good, the incident waveforms obtained by the above two methods are basically the same over the whole time period, so this embodiment will take the method (1) as an example to obtain the incident waveform over the whole time period, that is, as shown in fig. 3, and apply the waveform with the reflection model 3 and the incident waveform to the formula (5), that is, to obtain the desired reflection waveform, as shown in fig. 4.
Step five: and determining parameters of the reflected waveform in the waveform obtained in the step four.
The reflected waveform should be the portion of the waveform obtained in step four where the waveform is stable after reflection.
Specifically, in this embodiment, fig. 4 is a reflected waveform obtained by separating the superimposed wave by applying the waveform superimposing principle, and as shown in fig. 4 and known by combining the time period of occurrence of the reflected wave determined in step three, the reflected wave before 8s is the wave front of the incident wave; the reflection waveform of the reflection model 3 appears after 8s, there is a stable reflection waveform after 10s, and further, the waveform may contain multiple reflection waves. Therefore, the waveform of the black frame identification area 6 in fig. 4 should be selected as the reflection waveform of the reflection model 3.
The embodiments of the present invention have been described in detail, but the description is only for the preferred embodiments of the present invention and should not be construed as limiting the scope of the present invention.
Claims (5)
1. A reflected wave separation method of nonlinear waves based on a waveform superposition principle is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
firstly, arranging the experimental equipment in a wave water tank of a laboratory according to the sequence of wave generation equipment (1), a wave height instrument (2) and a reflection model (3), connecting the wave height instrument (2) with a data processor (5), and respectively carrying out two sets of wave generation tests with the same wave generation parameters when no reflection model (3) and a reflection model (3) exist;
secondly, measuring the waveform data of the two wave-making tests in the step one by using a single fixed wave height instrument (2) to obtain the waveform data without the reflection model (3) and the waveform data with the reflection model (3);
thirdly, determining the time period of incidence waveform and reflection waveform in the waveform with the reflection model (3) in the second step;
fourthly, separating reflected waves from the waveforms with the reflection models (3) in the second step by applying a waveform linear superposition principle;
fifthly, determining parameters of the reflected waveform in the waveform obtained in the step four;
when the reflection model (3) exists in the step two, the wave height instrument (2) obtains the measured waveformIs formed by incident wave formsCombined waveform of incident wave and reflected waveTwo-stage composition, which can be expressed as follows:
to synthesize the waveformIs an incident wave formAnd the reflected waveformCan be expressed as:
substituting the formula (2) into the formula (1) to obtain the reflection waveformExpression:
wherein,represents t0～teThe waveform of the single wave height meter (2) in the time period when the reflection model (3) exists,represents t0～t1The incident waveform of the time segment is,represents t1～teThe resultant waveform of the time segment is,represents t1～teThe incident waveform in the time-segment composite wave,represents t1～teA reflected waveform in the time-segment synthesized wave;
t when the reflection model (3) is provided because the stability of wave generation of the wave water tank (4) is better0～teIncident waveform of time segmentCan be written as:
substituting the formula (4) into the formula (3) to obtain a reflection waveformThe expression is as follows:
this formula is used to separate the reflected waveforms in step four
Waveform without reflection model (3)The entire period is the incident waveform, i.e.:
wherein,represents t0～teWaveform of a single wave height meter (2) in a time period without a reflection model (3),representing t without reflection model (3)0～teIncident waveform of a time segment.
2. The method for separating reflected waves of nonlinear waves based on the waveform superposition principle as claimed in claim 1, wherein: the "experimental facility" described in step one comprises: the wave generation device (1), the wave height instrument (2), the reflection model (3), the wave water tank (4) and the data processor (5); the wave generating equipment (1) is controlled by a servo motor and is used for generating required waves, and the wave generating stability and the repeatability error of the wave generating equipment are within 5 percent; the wave height instrument (2) is used for acquiring wave data and transmitting the data to the data processor (5) to obtain a oscillogram, and the measurement error of the wave height instrument (2) is within 0.5%; the reflection model (3) is a single flat plate vertically penetrating through the water surface, is arranged perpendicular to the incident wave direction, and is used for reflecting waves to obtain synthetic waves.
3. The reflected wave separation method of a nonlinear wave based on the waveform superposition principle according to claim 1 or 2, characterized in that: the time period of the incident wave in the third step is the time period of the overlapping part of the waveform when the reflection model (3) exists and the waveform when the reflection model (3) does not exist in the second step: t is t0～t1The time interval immediately following the time interval is the time interval during which the incident wave and the reflected wave are superposed, however, the time interval of the superposed wave is limited and is taken as t1～teTime periods, since multiple reflections may subsequently occur.
4. The method for separating reflected waves of nonlinear waves based on the waveform superposition principle as claimed in claim 3, wherein: the waveform linear superposition principle in the fourth step refers to that: when several lines of waves propagate in the medium at the same time, the propagation characteristics of the waves, including wavelength, frequency, waveform and wave speed, are not influenced by the existence of other waves; in the meeting region, the combined vibration is the superposition of the sub-vibrations; the waveform when the reflection model (3) exists is directly measured in the second step, and the reflected wave is separated by adopting the formula (5) in the second step; (5) incident wave form in the formulaObtained by the following two ways:
a. due to the good repeatability of the wave making of the water tank, the incident wave in the wave form of the reflection model (3)And a reflection-free model (3)) Incident wave of timeThe superposition is better, namely:
wherein,represents t with the reflection model (3)0～teThe incident wave of the time segment is,representing t without reflection model (3)0～teAn incident wave of a time segment;
b. t which cannot be directly measured in the synthesized waveform with the reflection model (3) due to the good stability of water tank wave generation1～teIncident wave of a time segmentCan be formed by t0～t1Incident waveform of time segmentRepeating the waveform over time, so that equation (4) is transformed as:
wherein N satisfies Nt1＝te，
And the waveform of the reflection model (3) is measuredAnd incident waveformApplied to the formula (5), i.e. the reflected waveform can be separated
5. The method for separating reflected waves of nonlinear waves based on the waveform superposition principle as claimed in claim 4, wherein: and the reflected waveform in the step five is taken as the part of the waveform obtained in the step four, which has stable waveform after the reflected wave appears.
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