CN107490464A - The back wave separation method of Nonlinear Wave based on addition of waveforms principle - Google Patents

The back wave separation method of Nonlinear Wave based on addition of waveforms principle Download PDF

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CN107490464A
CN107490464A CN201710605897.4A CN201710605897A CN107490464A CN 107490464 A CN107490464 A CN 107490464A CN 201710605897 A CN201710605897 A CN 201710605897A CN 107490464 A CN107490464 A CN 107490464A
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msub
wave
msubsup
waveform
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CN107490464B (en
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吴静萍
何博
张敏
盘俊
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Wuhan University of Technology WUT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M10/00—Hydrodynamic testing; Arrangements in or on ship-testing tanks or water tunnels
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C5/00—Measuring height; Measuring distances transverse to line of sight; Levelling between separated points; Surveyors' levels

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Abstract

The invention discloses a kind of back wave separation method of the Nonlinear Wave based on addition of waveforms principle, the wave height recorder fixed by using single branch measures the composite wave that the incidence wave of enough durations and incidence wave are 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, reflection configuration can be obtained, so as to reach the purpose of separation back wave.This method only needs the measuring instrument of single fixation, suitable for linear and any high-order nonlinear rule ripple problem.Measuring method is simple, and solution procedure is easy, improves back wave separative efficiency.

Description

The back wave separation method of Nonlinear Wave based on addition of waveforms principle
Technical field
The invention belongs to field of ocean engineering, and in particular to a kind of Nonlinear Wave based on addition of waveforms principle Back wave separation method.
Background technology
When wave propagation meets with large-sized object, wave reflects.The ripple and incidence wave reflected is mutual before works Superposition, form composite wave.Under lab study breakwater hydrodynamic performance when, reflectance factor be important parameter of measurement it One.Back wave is separated from synthetic waveform, the research for breakwater hydrodynamic performance has great importance.Mesh Before, the method for separating back wave has two major classes：It is only applicable to the separation method of linear wave and point suitable for nonlinear wave From method.There are two-point method, line-of-sight course and multipoint method suitable for what the separation method of linear wave was commonly used, i.e.,：Use fixed two Wave height recorder, three wave height recorders or more branch wave height recorder measurement synthetic waveform, pass through Fourier transformation, wavelet transformation, least square The methods of method, analyzes and processing synthetic waveform, obtains the wave height and phase of back wave；Also measured using mobile single branch wave height recorder Method, utilize Doppler effect calculate reflection wave height.For the back wave separation method of nonlinear wave, it is assumed that non-linear incidence Ripple and back wave are formed by stacking by basic waveform and high-order free wave and constraint ripple, and increased variable requirement at least needs 4 The composite wave data of branch wave height recorder measurement could solve, and due to the determination of high-order wavelength exist it is approximate, consideration it is non-linear right The higher result of precision can be obtained in the mild nonlinear such as second order situation, but error be present for high-order nonlinear situation. In a word, current waveform separation method, either measuring instrument or analysis method are all more complicated：Need to use multiple measurements Instrument or moveable measuring instrument carry out data acquisition, and measuring method is complicated；Unknown number is more during analysis, solves multiple It is miscellaneous, and exist in separation process it is assumed that just higher to the result precision in the scope of application.
The content of the invention
It is an object of the invention to provide a kind of back wave separation method of the Nonlinear Wave based on addition of waveforms principle, energy Enough solves the above-mentioned deficiency of the waveform separation method of traditional reflective ripple, measuring method is simple, and solution procedure is easy, suitable for linear With any high-order nonlinear rule ripple problem, back wave separative efficiency is improved.
The purpose of the present invention is achieved through the following technical solutions, and is comprised the following steps：
First, experimental facilities is pacified according to the order of wave making epparatus, wave height recorder, reflection model in the wave flume in laboratory Put, and wave height recorder and data processor are connected, carry out areflexia model respectively and there are two groups during reflection model to make Wave parameter identical makes ripple experiment；
2nd, the wave height recorder fixed using single branch is made the Wave data that ripple is tested to two groups in step 1 and measured, and obtains Wave data during areflexia model and Wave data when having reflection model；
3rd, the period that incident waveform and reflection configuration occur is determined in the waveform for having reflection model of step 2；
4th, applied waveforms linear superposition theorem in step 2 to having waveform during reflection model to carry out dividing for back wave From；
5th, the parameter of reflection configuration is determined in the waveform obtained by step 4.
By such scheme, " experimental facilities " described in step 1 includes：Wave making epparatus, wave height recorder, reflection model, ripple Unrestrained tank and data processor.Wave making epparatus is by Serve Motor Control, and for producing required wave, it makes ripple stability and repetition Property error is within 5%；Wave height recorder is used to gather Wave Data, and passes data to data processor and obtain oscillogram, The measurement error of wave height recorder is within 0.5%；Reflection model is the single flat plate for penetrating the water surface vertically, perpendicular to incidence wave direction Installation, for reflecting wave, obtains composite wave.
By such scheme, in step 2 when having reflection model, the waveform of measurement obtained by wave height recorderIt is by incidence wave ShapeThe synthetic waveform being superimposed with incidence wave with back waveTwo sections of compositions, can be expressed as follows：
And synthetic waveformIt is incident waveformWith reflection configurationSuperposition, can be expressed as：
(2) formula is substituted into (1) formula, sorts out reflection configurationExpression formula：
Wherein,Represent t0~teWaveform when having a reflection model of single branch wave height recorder measurement of period,Generation Table t0~t1The incident waveform of period,Represent t1~teThe synthetic waveform of period,Represent t1~tePeriod closes Cheng Bozhong incident waveform,Represent t1~teReflection configuration in period composite wave.
Because tank is made, wave stability is preferable, therefore t when having a reflection model0~teThe incident waveform of period It can be written as：
(4) formula is substituted into (3) formula, the reflection configuration sorted outExpression formula is：
This formula is used to separate reflection configuration in step 4
Waveform during areflexia modelThe whole period is incident waveform, i.e.,：
Wherein,Represent t0~teWaveform during the areflexia model of single branch wave height recorder measurement of period,Represent T during areflexia model0~teThe incident waveform of period.
By such scheme, the period that incidence wave occurs in step 3 is waveform and nothing when having reflection model in step 2 The period of waveform intersection during reflection model：t0~t1Period, back to back period are incidence wave and back wave The period of superposition, but, the period of this superposition ripple is limited, is taken as：t1~tePeriod, because subsequently may Produce multiple reflection.
By such scheme, waveform linear superposition theorem described in step 4 refers to：Several train waves are propagated in medium simultaneously When, its propagation characteristic, which includes wavelength, frequency, waveform, velocity of wave, to be made a difference because of the presence of other ripples.In meeting area, It is a point superposition for vibration to close vibration.Waveform when having a reflection modelObtained, reflected by step 2 direct measurement The separation of ripple is to use (5) formula in step 2.(5) incident waveform in formulaObtained by following two approach：
A, it is preferable that the repeatability of ripple is made due to tank, the incidence wave in waveform when having reflection modelWith areflexia mould Incidence wave during typeOverlap preferably, that is, have：
Wherein,T when representative has reflection model0~teThe incidence wave of period,T when representing areflexia model0~ teThe incidence wave of period.
B, because tank is made, wave stability is preferable, can not t measured directly in synthetic waveform when having reflection model1~ teThe incidence wave of periodCan be by t0~t1The incident waveform of periodWaveform is carried out in time to repeat to obtain, because This deforms (4), is：
N meets Nt in formula1=te。
And by it is described have a reflection model when waveformAnd incident waveformApplied to (5) formula, you can isolate anti- Ejected wave shape
By such scheme, the reflection configuration described in step 5 is taken as gained waveform in step 4 and waveform after back wave occurs Stable part.
Its result precision depends on the measurement accuracy that tank makes wave stability, repeatability and wave height recorder, its scope of application With experiment whether can obtain enough durations incidence wave and composite wave it is relevant, and with whether wave broken, incidence wave whether It is relevant to impinge perpendicularly on reflection model.
Compared with prior art, the beneficial effects of the invention are as follows：The present invention proposes that one kind is applied to high-order nonlinear ripple Back wave separation new method, only need the measuring instrument of single fixation, based on addition of waveforms principle, make full use of single measurement The incidence wave data that instrument provides, and the composite wave data that back wave is superimposed with incidence wave, it is non-thread can to handle any high-order Property ripple problem.Measuring method is simple, and solution procedure is easy, improves the efficiency of the waveform separation of back wave.
Brief description of the drawings
Fig. 1 is the wave making epparatus structural representation of the present invention.
Fig. 2 is oscillogram when having reflection model.
Oscillogram when Fig. 3 is areflexia model.
Fig. 4 is the oscillogram after the processing of addition of waveforms principle.
In figure：1. wave making epparatus, 2. wave height recorders, 3. reflection models, 4. wave flumes, 5. data processors, 6. back waves The position of shape.
Embodiment
The present invention is described in detail with reference to the accompanying drawings and examples.
The present invention comprises the following steps：
Step 1：By experimental facilities according to wave making epparatus 1, wave height recorder 2, reflection model 3 in the wave flume 4 in laboratory Subsequent application it is good, and wave height recorder 2 and data processor 5 are connected, as shown in figure 1, carrying out the He of areflexia model 3 respectively There are two during reflection model 3 groups to make wave parameter identical and make ripple experiment.
" experimental facilities " includes：Wave making epparatus 1, wave height recorder 2, reflection model 3, wave flume 4 and data processor 5.Make Wave device 1 is by Serve Motor Control, and for producing required wave, it makes ripple stability and repeatability error within 5%；Wave High instrument 2 is used to gather Wave Data, and passes data to data processor 5 and obtain oscillogram, and the measurement error of wave height recorder 2 exists Within 0.5%；Reflection model 3 is the single flat plate for penetrating the water surface vertically, is installed perpendicular to incidence wave direction, for back wave Wave, obtain composite wave.
Step 2：The Wave data that the wave height recorder 2 fixed using single branch makes ripple experiment to two groups in step 1 measures, Wave data when obtaining areflexia model 3 and Wave data when having reflection model 3.
Fig. 2 is waveform when having reflection model 3It is by incident waveformThe conjunction being superimposed with incidence wave with back wave Into waveformTwo parts form, and can be expressed as follows：
And synthetic waveformIt is incident waveformWith reflection configurationSuperposition, can be expressed as：
(2) formula is substituted into (1) formula, sorts out reflection configurationExpression formula：
Wherein,Represent t0~teWaveform when having a reflection model 3 of single branch wave height recorder 2 measurement of period, Represent t0~t1The incident waveform of period,Represent t1~teThe synthetic waveform of period,Represent t1~tePeriod Incident waveform in composite wave,Represent t1~teReflection configuration in period composite wave.
Because wave flume 4 is made, wave stability is preferable, therefore t when having a reflection model 30~teThe incidence wave of period ShapeIt can be written as：
(4) formula is substituted into (3) formula, the reflection configuration sorted outExpression formula is：
This formula is used to separate reflection configuration in step 4
Waveform when Fig. 3 is areflexia model 3It can be expressed as：
Wherein,Represent t0~teWaveform during the areflexia model 3 of single branch wave height recorder 2 measurement of period,Generation T during table areflexia model 30~teThe incident waveform of period.
Step 3：The time that incident waveform and reflection configuration occur is determined in the waveform for having reflection model 3 of step 2 Section.
The period that incidence wave occurs is waveform when having reflection model 3 in step 2 and waveform during areflexia model 3 The period of intersection：t0~t1Period, back to back period are the period that incidence wave is superimposed with back wave, no Cross, the period of this superposition ripple is limited, is taken as t1~tePeriod, because may subsequently produce multiple reflection.
Specific to the present embodiment, comparison diagram 2 and Fig. 3, in preceding 6s period, the ripple of composite wave when having a reflection model 3 Waveform repeatability when shape and areflexia model 3 is preferable, therefore it can be assumed that is the period that this section is incident waveform.
After 6s, two waveforms and phase difference are obvious, and there is reflex.Also can in view of the wavefront of incidence wave Reflected by reflection model 3, and in fig. 2 after 8s first crest is uprushed, show that reflection configuration should appear in 8s After.
Step 4：Applied waveforms linear superposition theorem in step 2 to having waveform during reflection model 3 to carry out back wave Separation.
Waveform linear superposition theorem refers to：Several train waves are propagated in medium simultaneously when, its propagation characteristic includes wavelength, frequency Rate, waveform, velocity of wave will not make a difference because of the presence of other ripples.In meeting area, it is a point superposition for vibration to close vibration.Have anti- Penetrate waveform during model 3Obtained by step 2 direct measurement, the separation for carrying out back wave is to use (5) formula in step 2. (5) incident waveform in formulaObtained by following two approach：
A, the repeatability for making ripple due to tank preferably, i.e., repeatedly makes wave process, each secondary institute under identical control signal Making the cycle of ripple and wave height has good homogeneity, the incidence wave in waveform when having reflection model 3With areflexia mould Incidence wave during type 3Overlap preferably, that is, have：
Wherein,T when representative has reflection model 30~teThe incidence wave of period,When representing areflexia model 3 t0~teThe incidence wave of period.
B, because tank is made, wave stability is preferable, i.e., once makes wave process under same control signal, make ripple Cycle and wave height keep stable in a long time, can not t measured directly in synthetic waveform when having reflection model 31~te The incidence wave of periodCan be by t0~t1The incident waveform of periodCarry out waveform in time to repeat to obtain, therefore (4) formula is deformed, is：
N meets Nt in formula1=te。
And by it is described have a reflection model 3 when waveformAnd incident waveformApplied to (5) formula, you can isolate anti- Ejected wave shape
Ripple obtained by during specific to the waveform in the present embodiment, having during reflection model 3 to there is reflection model 3 in step 2 Shape, i.e., waveform shown in Fig. 2, incident waveform is the incident waveform before gained 6s in step 3 in this waveform, when obtaining whole Between section incident waveform, making ripple due to wave flume 4 has good stability and repeatability, can pass through following two methods Handled：
A, in step 2, the waveform when the incident waveform on the whole period can be with areflexia model 3 represents, i.e., such as Shown in Fig. 3.
B, in step 3, the incident waveform before gained 6s is taken into its suitable length, one is done on the whole period The repetition of individual waveform, so as to obtain the incident waveform on the whole period.
When wave flume 4 makes wave stability and repeatability is preferable, on the whole period obtained by both the above method Incident waveform is essentially the same, and therefore, such as the present embodiment will obtain the incident waveform on the whole period, i.e., by taking method (1) as an example Shown in Fig. 3, and will there are waveform during reflection model 3 and incident waveform to be applied to (5) formula, you can required reflection configuration is obtained, As shown in Figure 4.
Step 5：The parameter of reflection configuration is determined in the waveform obtained by step 4.
Reflection configuration should be taken as gained waveform in step 4 and the part of waveform stabilization after back wave occurs.
Specific in the present embodiment, Fig. 4 is the reflection configuration obtained after applied waveforms principle of stacking separates superposition ripple, such as Shown in Fig. 4 and combine knowable to the period that the back wave determined in step 3 occurs, be the reflection of incidence wave wavefront before 8s Ripple；Occur the reflection configuration of reflection model 3 after 8s, have stable reflection configuration after 10s, then backward, waveform may wrap Containing multiple reflection.Therefore, it should choose reflection configuration of the waveform of black surround identified areas 6 in Fig. 4 as the reflection model 3.
Embodiments of the invention are described in detail above, but the content is only presently preferred embodiments of the present invention, It is not to be regarded as the practical range for limiting the present invention.

Claims (6)

  1. A kind of 1. back wave separation method of the Nonlinear Wave based on addition of waveforms principle, it is characterised in that：Including following step Suddenly,
    First, in the wave flume in laboratory by experimental facilities according to wave making epparatus (1), wave height recorder (2), reflection model (3) Subsequent application is good, and wave height recorder (2) and data processor (5) are connected, and carries out areflexia model (3) respectively and has reflection Make wave parameter identical for two groups during model (3) and make ripple experiment；
    2nd, the wave height recorder (2) fixed using single branch is made the Wave data that ripple is tested to two groups in step 1 and measured, and obtains nothing Wave data during reflection model (3) and Wave data when having reflection model (3)；
    3rd, the period that incident waveform and reflection configuration occur is determined in the waveform for there are reflection model (3) of step 2；
    4th, applied waveforms linear superposition theorem carries out the separation of back wave to waveform when having reflection model (3) in step 2；
    5th, the parameter of reflection configuration is determined in the waveform obtained by step 4.
  2. 2. the back wave separation method of the Nonlinear Wave according to claim 1 based on addition of waveforms principle, its feature It is：" experimental facilities " described in step 1 includes：Wave making epparatus (1), wave height recorder (2), reflection model (3), wave water Groove (4) and data processor (5)；Wave making epparatus (1) is by Serve Motor Control, and for producing required wave, it makes ripple stability With repeatability error within 5%；Wave height recorder (2) is used to gather Wave Data, and passes data to data processor (5) Oscillogram is obtained, the measurement error of wave height recorder (2) is within 0.5%；Reflection model (3) is that the monolithic for penetrating the water surface vertically is put down Plate, installed perpendicular to incidence wave direction, for reflecting wave, obtain composite wave.
  3. 3. the back wave separation method of the Nonlinear Wave according to claim 1 or 2 based on addition of waveforms principle, it is special Sign is：In step 2 when having reflection model (3), the waveform of measurement obtained by wave height recorder (2)It is by incident waveform The synthetic waveform being superimposed with incidence wave with back waveTwo sections of compositions, can be expressed as follows：
    <mrow> <msubsup> <mi>&amp;eta;</mi> <mi>m</mi> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mn>1</mn> </msub> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;eta;</mi> <mi>c</mi> <mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    And synthetic waveformIt is incident waveformWith reflection configurationSuperposition, can be expressed as：
    <mrow> <msubsup> <mi>&amp;eta;</mi> <mi>c</mi> <mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;eta;</mi> <mrow> <mi>c</mi> <mo>.</mo> <mi>i</mi> </mrow> <mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;eta;</mi> <mrow> <mi>c</mi> <mo>.</mo> <mi>r</mi> </mrow> <mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    (2) formula is substituted into (1) formula, sorts out reflection configurationExpression formula：
    <mrow> <msubsup> <mi>&amp;eta;</mi> <mrow> <mi>c</mi> <mo>.</mo> <mi>r</mi> </mrow> <mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;eta;</mi> <mi>m</mi> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mn>1</mn> </msub> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>&amp;eta;</mi> <mrow> <mi>c</mi> <mo>.</mo> <mi>i</mi> </mrow> <mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,Represent t0~teWaveform when having reflection model (3) of single branch wave height recorder (2) measurement of period,Generation Table t0~t1The incident waveform of period,Represent t1~teThe synthetic waveform of period,Represent t1~tePeriod closes Cheng Bozhong incident waveform,Represent t1~teReflection configuration in period composite wave；
    Because wave flume (4) is made, wave stability is preferable, therefore t when having reflection model (3)0~teThe incidence wave of period ShapeIt can be written as：
    <mrow> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mn>1</mn> </msub> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;eta;</mi> <mrow> <mi>c</mi> <mo>.</mo> <mi>i</mi> </mrow> <mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    (4) formula is substituted into (3) formula, the reflection configuration sorted outExpression formula is：
    <mrow> <msubsup> <mi>&amp;eta;</mi> <mrow> <mi>c</mi> <mo>.</mo> <mi>r</mi> </mrow> <mrow> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;eta;</mi> <mi>m</mi> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    This formula is used to separate reflection configuration in step 4
    Waveform during areflexia model (3)The whole period is incident waveform, i.e.,：
    <mrow> <msubsup> <mi>&amp;eta;</mi> <mn>0</mn> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;eta;</mi> <mrow> <mn>0.</mn> <mi>i</mi> </mrow> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,Represent t0~teWaveform during areflexia model (3) of single branch wave height recorder (2) measurement of period,Generation T during table areflexia model (3)0~teThe incident waveform of period.
  4. 4. the back wave separation method of the Nonlinear Wave according to claim 3 based on addition of waveforms principle, its feature It is：The period that incidence wave occurs in step 3 is the waveform and areflexia model (3) when having reflection model (3) in step 2 When waveform intersection period：t0~t1Period, the back to back period be incidence wave be superimposed with back wave when Between section, but, the period of this superposition ripple is limited, is taken as t1~tePeriod, because may subsequently produce multiple Reflection.
  5. 5. the back wave separation method of the Nonlinear Wave according to claim 4 based on addition of waveforms principle, its feature It is：Waveform linear superposition theorem described in step 4 refers to：Several train waves are propagated in medium simultaneously when, its propagation characteristic bag Including wavelength, frequency, waveform, velocity of wave will not make a difference because of the presence of other ripples；In meeting area, it is a point vibration to close vibration Superposition；There is waveform during reflection model (3) to be obtained by step 2 direct measurement, the separation for carrying out back wave is used in step 2 (5) formula；(5) incident waveform in formulaObtained by following two approach：
    A, it is preferable that the repeatability of ripple is made due to tank, the incidence wave in waveform when there are reflection model (3)With areflexia mould Incidence wave during type (3)Overlap preferably, that is, have：
    <mrow> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>&amp;eta;</mi> <mrow> <mn>0.</mn> <mi>i</mi> </mrow> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,T when representative has reflection model (3)0~teThe incidence wave of period,T when representing areflexia model (3)0 ~teThe incidence wave of period；
    B, because tank is made, wave stability is preferable, can not t measured directly in synthetic waveform when having reflection model (3)1~te The incidence wave of periodCan be by t0~t1The incident waveform of periodCarry out waveform in time to repeat to obtain, therefore (4) formula is deformed, is：
    <mrow> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mi>e</mi> </msub> </mrow> </msubsup> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msubsup> <mi>&amp;eta;</mi> <mi>i</mi> <mrow> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>~</mo> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    N meets Nt in formula1=te,
    And by it is described have reflection model (3) when waveformAnd incident waveformApplied to (5) formula, you can isolate reflection Waveform
  6. 6. the back wave separation method of the Nonlinear Wave according to claim 5 based on addition of waveforms principle, its feature It is：Reflection configuration described in step 5 is taken as gained waveform in step 4 and the part of waveform stabilization after back wave occurs.
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