CN107256280A - Ship joins the method for soaking transverse cutting head probability under a kind of calculating random sea condition - Google Patents
Ship joins the method for soaking transverse cutting head probability under a kind of calculating random sea condition Download PDFInfo
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Abstract
The present invention relates to a kind of method for calculating ship ginseng soaking transverse cutting head probability under random sea condition, including：Set up ship ginseng soaking single-degree-of-freedom rolling motion equation, i.e. mathematics vibration equation；Set up and ship righting arm function is solved based on strip theory, for obtaining the ship righting arm in mathematics vibration equation；Random Wave forced excitation torque is solved using corrugated angle, for obtaining the wave forced excitation torque in mathematics vibration equation；Random sea condition is handled using spectral analysis method, for obtaining the arbitrary excitation in mathematics vibration equation；Applied energy envelope curve stochastic averaging solves mathematics vibration equation, obtains the probability distribution of ship rolling response.
Description
Technical field
The invention belongs to transport, the technical field such as information, be related to motor imagination forecast of the ship under true random sea condition.
Background technology
At present, the direction with marine transportation ship increasingly towards maximization, high-tech, high performance is developed, complete
Whole stability requirement, which turns into, ensures the important foundation of security of shipping, the mandatory legal requirements also built as Ship Design.It is many
Well known, beam wind and athwart sea are the extreme danger sea situations of ship's navigation, and sway motion of the ship under the sea situation is to cause ship
The main cause toppled.People's all primary studies have paid close attention to this problem all the time, up to the present, are obtained for it
A large amount of and in-depth study achievement.But, by the observation to complete ship casualty and statistics, as a result show, completely
The casualty of ship has half to be the operational configuration for occurring to be in vertical wave or oblique wave in ship unexpectedly, and for a long time, ship
It when meeting with severe high sea sea situation, all can avoid directly bearing horizontal storm load as far as possible, and select ship to adjust
For vertical wave navigation or steaming with the sea on the bow or quarter, this also allows for stability loss problem of the ship in vertical wave and oblique wave and highlighted further.According to
Current progress understands that, even if stability of the ship in hydrostatic meets stability weighing apparatus alignment request, ship is in vertical wave or steaming with the sea on the bow or quarter
When, one of the reason for still occurring wide-angle rolling or even topple, is exactly that ship there occurs Parametric Rolling.
It is used as a typical case of Parametric Rolling phenomenon, in October, 1998, C11 grades of container ship " APL of Panamax
CHINA " numbers have suffered from severe stormy weather in the way for sailing for Seattle from Kaohsiung, slow down in captain according to conventional selection and meet
Extremely violent rolling motion is still generated after wave navigation, roll angle has been even up to 35 degree to 40 degree, and accident is straight
Connect result in 1/3rd container lose, 1/3rd container damage.
The ship particularly navigated by water in oblique wave, the ship is in addition to may be by parametric excitation, due to the presence of course angle,
The side of a ship of its each cross section or so two can have that certain wave surface height is poor, therefore the ship also suffers from horizontal wave and forces sharp
Encourage, i.e., acted on simultaneously by ginseng-strong joint incentive, at this moment the rolling phenomenon of ship also just becomes increasingly complex.
For the ship of steaming with the sea on the bow or quarter in regular ripple, it can more accurately try to achieve ship by numerical simulation method and exist
Steady roll angle under a certain specific wave condition (wavelength L, wave height H).But for true random sea condition, we not can determine that
The specific wave situations that ship is suffered from after going to sea, therefore ginseng of the simple numerical simulation ship under a certain group of random seed number-
The time history curve of soaking transverse cutting head, and without too big realistic meaning, inventor more pay attention to ship random ginseng-
The statistical nature of transverse cutting head under soaking, that is, the response probability distribution of ship is forecast.
The content of the invention
The present invention provides a kind of method for calculating ship ginseng-soaking transverse cutting head probability under random sea condition.The present invention's
Method can be with the probability distribution of ginseng of the Ship ' under true random sea condition-soaking rolling motion response.The present invention is used
Following technical scheme：
The method of ship ginseng-soaking transverse cutting head probability, comprises the following steps under a kind of calculating random sea condition：
First, ship ginseng-soaking single-degree-of-freedom rolling motion equation, i.e. mathematics vibration equation is set up：
Wherein, Φ is roll angle；IxxFor roll moment of inertia, Axx(ωn) it is rolling added moment of inertia；b1With b3Respectively line
Property damped coefficient and Nonlinear Cubic damped coefficient；Δ is displacement；G is acceleration of gravity；GZ is ship righting arm, by
Φ, η and Ψ are determined；M is wave forced excitation torque；
Under fixed coordinate system, it is η to be equal to the waveform expression formula of the long crested waves of captain at a time along the wavelength that x-axis is propagated
Cos (2 π x/L+ Ψ), wherein η are the fluctuating range of the long crested waves, and η ＞ 0 are crest, and η ＜ 0 are trough, and Ψ is the phase of ship and ripple
To position, span is [0-2 π].
2nd, set up and ship righting arm function is solved based on strip theory, for obtaining the ship in mathematics vibration equation
Righting arm GZ (Φ, η, Ψ)：
1) application Gauss is integrated, and obtaining ship rolling restoring moment is：
In formula,WithFor each immersion cross section centre of form B0Coordinate under reference frame, S (x ') is each leaching
Water Sectional Area, ρ is density of sea water, and L is between perpendicular, and β is course angle, and F (x ') is the barometric gradient in each cross section
Coefficient, its expression formula is：
In formula,For in ship hydrostatic during erectility each cross section waterline breadth, d (x ') is upright in ship hydrostatic
The drinking water in each cross section during state, k is wave number.
2) GZ (Φ, η, Ψ) is expanded into the multinomial on roll angle Φ and the combining form of Fourier space, used
Least square method carries out four-dimensional fitting to GZ (Φ, η, Ψ), obtains fitting parameter qi(i=1,2,3).
GZapp(Φ, η, Ψ)=q1Φ+q2Φ3+q3ηcΦ
3rd, Random Wave forced excitation torque is solved using corrugated angle, it is strong for obtaining the wave in mathematics vibration equation
Compel excitation moment M.
Wherein, q0For the metacentric height GM of ship.
4th, zero dimension processing is carried out for ship ginseng-soaking rolling motion equation, obtains the mathematics of nondimensional simplification
Vibration equation.
By GZapp(Φ, η, Ψ) substitutes into ship ginseng-soaking rolling motion equation, order with Mηc=ξt, and other side
The processing of Cheng Jinhang zero dimensions, is obtained：
Wherein,
5th, random sea condition is handled using spectral analysis method, for obtaining the arbitrary excitation in mathematics vibration equation ηc=
ξt：
1) rise of random seaway corrugated is processed as Narrow―band random process, according to this representation of the Lay of Narrow―band random process,
The significant wave surface function Z of true sea situationeffThere is following analytical expression in (x, t)：
Zeff(x, t)=ηc(t)cos(2πx/L)-ηs(t)sin(2πx/L)
Wherein ηsAnd η (t)c(t) it is random process；
2) the accurate approximate random sea situation of second order controlled autoregressive moving average model is used, i.e., using CARMA (2,1) process
The approximate known ocean wave spectrum of spectral density function, so as to obtain describing another key character parameter --- the auto-correlation of random sea condition
Function.
6th, applied energy envelope curve stochastic averaging solves mathematics vibration equation, obtains the probability distribution of ship rolling response.
The present invention can be applied at following two aspects：
1) the Ship Design stage, the ocean wave spectrum in marine site is navigated by water by the plan of design ship, can forecast that the design ship exists
When planning marine site navigation, roll angle exceedes the probability of a certain limiting value, if the probability is excessive, you can think that the ship is easy
Generation Parametric Rolling is, it is necessary to readjust design vessel type.
2) the ship's navigation stage, captain can be assisted to go out for drill ship decision-making.If ship is prominent to suffer severe sea condition, captain is determining
Deceleration is head sea before navigation, can forecast that ship roll angle exceedes the general of a certain limiting value under the severe sea condition rapidly by the present invention
Rate, then by suitably adjusting the speed of a ship or plane, course, avoid the experience frequency range for easily occurring Parametric Rolling phenomenon.
The technique effect of the present invention is as follows：
1) rapidity
Forecast ship joins-soaking transverse cutting head probability distribution at random, and Normal practice is to apply Monte Carlo principle, largely
Count under different random seed number, the prolonged transverse cutting head time history curve of ship that numerical simulation is obtained.By to sound
Answer sample value to be counted, obtain the interval probability of each roll angle of transverse cutting head.The accuracy of this method, be with statistics
Based on amount, i.e., it can inevitably sacrifice time efficiency.
And processing of the present invention to random sea condition is the expression formula based on ocean wave spectrum, rather than random seed number, any specific
The unique feature ocean wave spectrum of sea situation correspondence, therefore need not compute repeatedly, greatly improve calculating speed.It can also avoid simultaneously because random
Seed number deficiency (true sea situation can not be fully described) and produce error.
2) accuracy
The present invention is based on non-linear stochastic kinetic theory.Different from method for numerical simulation, the present invention is based on rigorous
The computational methods that mathematical derivation process is provided, result of calculation possesses higher accuracy.
3) generality
The present invention solves the essence of Ship's response probability, i.e. its mathematics vibration equation of Analytical Solution.The change of ship type and sea situation
Change can't influence the theory deduction process of equation solution, therefore, and the present invention is applied to any ship type under any random sea condition
Ginseng-soaking transverse cutting head probability solve, and any specially treated, highly versatile need not be carried out.
Brief description of the drawings
Fig. 1 numerical solution righting arm function GZ (Φ, η, Ψ) flow chart
Fig. 2 solves stationary probabilitydistribution function pst(H) flow chart
Fig. 3 C11 container ship molded lines
Fig. 4 righting arms curved surface (Ψ=0)
The three-dimensional fitting result and numerical result comparison diagram of Fig. 5 righting arm functions, pair of (a) on (Φ, Ψ)
Than result (η=10m)；(b) comparing result (Ψ=0rad) on (Φ, η)
Fig. 6 waves spectrum density is decomposed
Fig. 7 random processes ηc(t) fitting effect of spectral density function and CARMA (2,1)
Probability density functions of the Fig. 8 on energy H
Probability density functions of the Fig. 9 on ship max roll (angle) b under particular energy value H
Embodiment
The present invention is described in detail below
First, ship ginseng-soaking single-degree-of-freedom rolling motion equation, i.e. mathematics vibration equation is set up.
Wherein, Φ is roll angle；IxxFor roll moment of inertia, Axx(ωn) it is rolling added moment of inertia；b1With b3Respectively line
Property damped coefficient and Nonlinear Cubic damped coefficient；Δ is displacement；G is acceleration of gravity；GZ is ship righting arm, by
Φ, η and Ψ are determined；M is wave forced excitation torque.
Under fixed coordinate system, it is η to be equal to the waveform expression formula of the long crested waves of captain at a time along the wavelength that x-axis is propagated
Cos (2 π x/L+ Ψ), wherein η are the fluctuating range (η ＞ 0 are crest, and η ＜ 0 are trough) of the long crested waves, and Ψ is the phase of ship and ripple
To position, span is [0-2 π].
2nd, ship righting arm function is solved based on strip theory, for obtaining the recuperability in mathematics vibration equation
GZ (Φ, η, Ψ).
1) application Gauss is integrated, and obtaining ship rolling restoring moment is：
In formula,WithFor each immersion cross section centre of form B0Coordinate under reference frame, S (x ') is each leaching
Water Sectional Area, ρ is density of sea water, and L is between perpendicular, and β is course angle, and F (x ') is the barometric gradient in each cross section
Coefficient, its expression formula is：
In formula,For in ship hydrostatic during erectility each cross section waterline breadth, d (x ') is upright in ship hydrostatic
The drinking water in each cross section during state, k is wave number.
2) GZ (Φ, η, Ψ) is expanded into the multinomial on roll angle Φ and the combining form of Fourier space, used
Least square method carries out four-dimensional fitting to righting arm function GZ (Φ, η, Ψ), obtains fitting parameter qi(i=1,2,3).
GZapp(Φ, η, Ψ)=q1Φ+q2Φ3+q3ηcΦ
3rd, Random Wave forced excitation torque is solved using corrugated angle, for obtaining forcing power in mathematics vibration equation
Item M.
Wherein, q0For the metacentric height GM of ship.
4th, zero dimension processing is carried out for ship ginseng-soaking rolling motion equation, obtains the mathematics of nondimensional simplification
Vibration equation.
By GZapp(Φ, η, Ψ) substitutes into ship ginseng-soaking rolling motion equation, order with Mηc=ξt, and other side
The processing of Cheng Jinhang zero dimensions, is obtained：
Wherein,
6th, random sea condition is handled using spectral analysis method, for obtaining the arbitrary excitation in mathematics vibration equation ηc=ζt
(with GZ (Φ, η, Ψ and M are relevant).
1) rise of random seaway corrugated is processed as Narrow―band random process, this representation can by the Lay of Narrow―band random process
Know, the significant wave surface function Z of true sea situationeffThere is following analytical expression in (x, t)：
Zeff(x, t)=ηc(t)cos(2πx/L)-ηs(t)sin(2πx/L)
Wherein ηsAnd η (t)c(t) it is random process.Without using the expression-form of harmony superposition, so as to enormously simplify
Follow-up analysis process；
2) physical accidental process is described using mathematical method.The present invention using probabilistic model, (slide by second order controlled autoregressive
Averaging model) accurate approximate random sea situation, i.e., using the approximate known ocean wave spectrum of spectral density function of CARMA (2,1) process, from
And obtain describing another key character parameter --- the auto-correlation function of random sea condition.
6th, applied energy envelope curve stochastic averaging solves mathematics vibration equation, obtains the probability distribution of ship rolling response.
Based on flow chart 2, can obtain ship join at random-soaking under transverse cutting head stationary probabilitydistribution function pst
(H)、pst(b), by stationary probabilitydistribution function in a certain angular rangeInterior integration, can further obtain b (H) at the angle
Probability in the range of degree.
Illustrated with reference to embodiment.
C11 grades of container ships belong to easily occur Parametric Rolling phenomenon " unconventional " ship type, using C11 container ships as
Example, specifically studies it in 30 ° of feature wave height 3m, characteristic wavelength 262m ITTC ocean wave spectrums and course angle, speed of a ship or plane 1.43m/s ship
Transverse cutting head probability density function under oceangoing ship navigational parameter.The principal dimensions of the known ship and molded lines such as Fig. 3.
The C11 container ship principal dimensions of table 1
The numerical simulation C11 containers in the range of Φ ∈ [- 0.6 0.6] rad, η ∈ [- 10 10] m, Ψ ∈ [0 2 π] rad
The righting arm function GZ (Φ, η, Ψ) of ship, obtains the righting arm function GZ (Φ, η, Ψ) when different Φ, η and Ψ, Fig. 4 row
Change curved surface of the righting arm function on variable Φ and η when having gone out Ψ=0rad.
Fitting parameter q is asked for using least square method to above-mentioned righting arm function GZ (Φ, η, Ψ)i(i=1,2,3),
Obtain q1=2.164, q2=-1.7753, q3=-0.1061.The partial 3-D fitted figure picture of C11 container ships is as shown in Figure 5.
By fitting parameter qi(i=1,2,3) and C11 container ships principal dimensions (table 1), obtains zero dimension mathematics vibration equation
Each term coefficient be respectivelyWherein,With
Characteristic wavelength and course angle are relevant.
From the 8th international towing basin meeting (ITTC) ocean wave spectrum in 1978 as outside marine environment, work as characteristic wave
When high 3m, characteristic wavelength 262m, ship speed are that 1.43m/s, course angle are 30 °, it can obtain：
2) the ocean wave spectrum S (ω under frequency are met withe) the random process η that is decomposited with itsAnd η (t)c(t) spectral density function
Sηs(ωe) and Sηc(ωe)
3) application CARMA (2,1) process fitting random process ηc(t) fitting result chart and fitting coefficient, are obtained：
Table 2 CARMA (2,1) fitting coefficient
By systematic parameter A1、A2、B1, the auto-correlation function of random process is can obtain, it is relevant with time interval, specifically
Expression formula is as follows：
Wherein, τ is time interval, μ1,2Expression formula be：
By energy envelope curve stochastic averaging, and according to flow chart 2, C11 container ships are obtained under random ginseng-soaking
Transverse cutting head probability density function pst(H)、pst(b) as shown in Figure 8.
By probability density function in a certain angular rangeInterior integration, can finally give b (H) in the angular range
Probability.
Claims (1)
1. a kind of method for calculating ship ginseng-soaking transverse cutting head probability under random sea condition, comprises the following steps：
First, ship ginseng-soaking single-degree-of-freedom rolling motion equation, i.e. mathematics vibration equation is set up：
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Wherein, Φ is roll angle；IxxFor roll moment of inertia, Axx(ωn) it is rolling added moment of inertia；b1With b3Respectively linear resistance
Buddhist nun's coefficient and Nonlinear Cubic damped coefficient；Δ is displacement；G is acceleration of gravity；GZ is ship righting arm, by Φ, η and
Ψ is determined；M is wave forced excitation torque；
Under fixed coordinate system, it is η cos to be equal to the waveform expression formula of the long crested waves of captain at a time along the wavelength that x-axis is propagated
(2 π x/L+ Ψ), wherein η is the fluctuating range of the long crested waves, and η ＞ 0 are crest, and η ＜ 0 are trough, and Ψ is the relative position of ship and ripple
Put, span is [0-2 π]；
2nd, set up and ship righting arm function is solved based on strip theory, restored for obtaining the ship in mathematics vibration equation
Arm of force GZ (Φ, η, Ψ)：
1) application Gauss is integrated, and obtaining ship rolling restoring moment is：
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In formula,For in ship hydrostatic during erectility each cross section waterline breadth, d (x ') be ship hydrostatic in erectility
When each cross section drinking water, k is wave number；
2) GZ (Φ, η, Ψ) is expanded into the multinomial on roll angle Φ and the combining form of Fourier space, using minimum
Square law carries out four-dimensional fitting to GZ (Φ, η, Ψ), obtains fitting parameter qi(i=1,2,3)；
GZapp(Φ, η, Ψ)=q1Φ+q2Φ3+q3ηcΦ
3rd, Random Wave forced excitation torque is solved using corrugated angle, forces sharp for obtaining the wave in mathematics vibration equation
Encourage torque M；
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</mrow>
</mrow>
Wherein, q0For the metacentric height GM of ship；
4th, zero dimension processing is carried out for ship ginseng-soaking rolling motion equation, obtains the mathematics vibration of nondimensional simplification
Equation；
By GZapp(Φ, η, Ψ) substitutes into ship ginseng-soaking rolling motion equation, order with Mηc=ξt, and equation is carried out
Zero dimension processing, is obtained：
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1
Wherein,
5th, random sea condition is handled using spectral analysis method, for obtaining the arbitrary excitation in mathematics vibration equation ηc=ξt：
1) rise of random seaway corrugated is processed as Narrow―band random process, according to this representation of the Lay of Narrow―band random process, truly
The significant wave surface function Z of sea situationeffThere is following analytical expression in (x, t)：
Zeff(x, t)=ηc(t)cos(2πx/L)-ηs(t)sin(2πx/L)
Wherein ηsAnd η (t)c(t) it is random process；
2) the accurate approximate random sea situation of second order controlled autoregressive moving average model is used, i.e., using the spectrum of CARMA (2,1) process
The approximate known ocean wave spectrum of density function, so as to obtain describing another key character parameter --- the auto-correlation letter of random sea condition
Number；
6th, applied energy envelope curve stochastic averaging solves mathematics vibration equation, obtains the probability distribution of ship rolling response.
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| CN108153976A (en) * | 2017-12-25 | 2018-06-12 | 重庆华渝电气集团有限公司 | The emulation mode and host computer of naval vessel rolling motion in a kind of wave |
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| CN108549616A (en) * | 2018-02-28 | 2018-09-18 | 哈尔滨工程大学 | The forecasting procedure that ship based on G-N wave models substantially moves in severe sea condition |
| CN108549616B (en) * | 2018-02-28 | 2021-11-23 | 哈尔滨工程大学 | Forecasting method for large-amplitude motion of ship in severe sea condition based on G-N wave model |
| CN109187062A (en) * | 2018-08-22 | 2019-01-11 | 北京强度环境研究所 | A kind of on-board equipment life profile formulating method on duty |
| CN110717216A (en) * | 2019-08-30 | 2020-01-21 | 南京航空航天大学 | Method for forecasting rolling response of helicopter with flexible air bag under irregular wave |
| CN112446178A (en) * | 2020-11-26 | 2021-03-05 | 天津大学 | Ship wave-riding nonlinear dynamics analysis method in regular wave |
| CN112446178B (en) * | 2020-11-26 | 2022-04-08 | 天津大学 | Ship wave-riding nonlinear dynamics analysis method in regular wave |
| CN113095011A (en) * | 2021-04-23 | 2021-07-09 | 沪东中华造船(集团)有限公司 | Container ship binding force estimation method considering parameter rolling |
| CN113095011B (en) * | 2021-04-23 | 2023-11-07 | 沪东中华造船(集团)有限公司 | Container ship binding force prediction method considering parameter rolling |
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