CN111611650A - Method, computer-readable storage medium, and apparatus for determining hydrodynamic derivative - Google Patents

Method, computer-readable storage medium, and apparatus for determining hydrodynamic derivative Download PDF

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CN111611650A
CN111611650A CN202010421375.0A CN202010421375A CN111611650A CN 111611650 A CN111611650 A CN 111611650A CN 202010421375 A CN202010421375 A CN 202010421375A CN 111611650 A CN111611650 A CN 111611650A
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王晓原
夏媛媛
姜雨函
朱慎超
王芳涵
王赞恩
陈钒烨
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Navigation Brilliance Qingdao Technology Co Ltd
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Abstract

The invention belongs to the technical field of simulation analysis, and particularly relates to a method for determining a hydrodynamic derivative, a computer-readable storage medium and equipment. The method comprises the following steps: establishing a fixed coordinate system fixed on a space and a movable coordinate system fixed on a ship, and establishing a speed conversion relation according to the relation between the fixed coordinate system and the movable coordinate system; according to the MMG motion model, sequentially establishing a three-degree-of-freedom operation equation, a ship hydrodynamic equation and a ship motion equation; performing a ship model experiment based on the ship motion equation to obtain ship model experiment data; and fitting the ship model experimental data by using a second-order adjacent regression method to obtain the hydrodynamic derivative of the ship. The method has the advantages of low technical requirement, short time period and low cost; compared with a simple empirical formula for determining the hydrodynamic derivative, the method is higher in accuracy.

Description

Method, computer-readable storage medium, and apparatus for determining hydrodynamic derivative
Technical Field
The invention belongs to the technical field of simulation analysis, and particularly relates to a method for determining a hydrodynamic derivative in a ship maneuverability model modeling process, a computer-readable storage medium and computer equipment.
Background
With the development of the shipping industry, new ships and intelligent ships gradually attract wide attention, and whether the handling performance of the ships meets the requirement of safety is always a topic of great attention. Forecasting the maneuvering performance is a very important work, and the methods for forecasting the maneuverability of a ship mainly comprise 4 methods: an empirical formula method, a constraint test method, a numerical simulation method based on CFD, and a ship control motion mathematical model and computer simulation. The method of adopting the ship maneuvering motion mathematical model and the computer simulation is premised on the modeling of the ship maneuvering mathematical model; in the modeling process, determining numerous hydrodynamic derivatives in the mathematical model is a key step.
Currently, there are mainly 4 methods for determining the hydrodynamic derivative: the method is based on ship model test, the second is estimation by using an empirical formula, the third is a theoretical or numerical calculation method, and the fourth is the combination of free self-propelled ship model test and system identification. The method based on the ship model test is time-consuming and labor-consuming, and the test cost is expensive; the simple empirical formula causes low accuracy of the calculation result of the empirical formula due to large changes of the ship type. Therefore, a method for quickly and accurately determining hydrodynamic derivative is urgently needed in ship maneuverability simulation forecasting so as to improve the calculation precision of a ship maneuverability mathematical model.
Disclosure of Invention
Technical problem to be solved
In view of the defects and shortcomings in the prior art, the method for determining the hydrodynamic derivative in the ship maneuverability model modeling process is provided, and the problems that the period of time for determining the hydrodynamic derivative in the existing ship maneuverability model is long, the cost is high, and the accuracy of the calculation result of the ship maneuverability model is low are solved.
(II) technical scheme
In order to achieve the purpose, the invention adopts the following technical scheme:
in a first aspect, an embodiment of the present invention provides a method for determining a derivative of hydrodynamic force in a ship maneuverability model modeling process, including the following steps:
establishing a fixed coordinate system fixed on a space and a movable coordinate system fixed on a ship, and establishing a speed conversion relation according to the relation between the fixed coordinate system and the movable coordinate system;
according to the MMG motion model, establishing three-degree-of-freedom operation equations of the ship swaying speed, the surging speed and the heading angle speed, establishing a ship hydrodynamic equation according to the speed conversion relation and the three-degree-of-freedom operation equations, and establishing a ship motion equation according to the ship hydrodynamic equation;
performing a ship model experiment based on the ship motion equation to obtain ship model experiment data;
and fitting the ship model experimental data by using a second-order adjacent regression method to obtain the hydrodynamic derivative of the ship.
Compared with the prior art, the method for determining the hydrodynamic derivative in the ship control mathematical model has the advantages that the hydrodynamic derivative in the ship control mathematical model is determined, the model does not need to be trained, fitting can be directly carried out on the basis of ship model experiment data, the required hydrodynamic derivative is obtained, the technical requirement is low, the time period is short, and the cost is low. And compared with the method for determining the hydrodynamic derivative by using a simple empirical formula, the method has higher precision and is insensitive to abnormal values, and the defect of low precision of the empirical formula caused by large ship shape change is overcome.
Optionally, the speed conversion relationship is expressed according to the following formula:
v＝vm+xGr
wherein v is the ship swaying speed at the origin point under the moving coordinate system, r is the ship bow angular velocity, v is the ship bow angular velocitymThe ship swaying speed, x, at the center of gravity of the ship in the moving coordinate systemGAs a shipX-axis coordinate of the center of gravity of the ship.
Optionally, the ship hydrodynamic equation is expressed according to the following formula:
Figure BDA0002497005690000021
wherein m is the ship mass, u is the ship surging speed,
Figure BDA0002497005690000022
respectively the ship surging acceleration, the bow rocking angle acceleration IzGIs the moment of inertia, m, of the ship about the center of gravityxAnd myAdditional masses, J, for the vessel in the x-direction and y-direction, respectivelyzAn additional moment of inertia about the z-axis for the vessel; x, Y, NmRespectively the transverse hydrodynamic force, the longitudinal hydrodynamic force and the heading hydrodynamic moment on the ship.
Optionally, the ship motion equation is expressed according to the following formula:
Figure BDA0002497005690000034
Figure BDA0002497005690000031
Figure BDA0002497005690000032
wherein, XH' is a dimensionless value of the transverse hydrodynamic force to which the hull is subjected, YH' is a dimensionless value of longitudinal hydrodynamic force to which the hull is subjected, NH' is a dimensionless value of the yaw moment, R0' is a dimensionless value of the ship's straight running resistance, X 'vv、X′vr、X′rr、X′vvvv、Yv′、Yr′、Y′vvv、Y′vvr、Y′vrr、Y′rrr、N′v、N′r、N′vvv、N′vvr、N′vrr、N′rrrIs the hydrodynamic derivative of the vessel, r 'is a dimensionless value of the vessel's yaw rate, vm'is a dimensionless value for the vessel's sway speed.
Optionally, the fitting process of the ship model experimental data by using a quadratic proximity regression method includes:
performing first fitting according to the ship model experimental data to obtain a polynomial coefficient of first adjacent regression, and extracting data points with errors larger than a preset value in the first fitting process;
performing quadratic fitting according to the extracted data points to obtain polynomial coefficients of a second adjacent regression;
and carrying out weighted average on the polynomial coefficients of the first adjacent regression and the polynomial coefficients of the second adjacent regression so as to take the weighted average value as the polynomial coefficients of the fitting function.
The polynomial coefficient of the fitting function is determined through twice fitting, fitting accuracy can be improved, and the influence of data points with large errors on fitting results is reduced.
Optionally, the polynomial coefficients of the fitting function are calculated according to the following formula:
Figure BDA0002497005690000033
wherein, ctIs the polynomial coefficient of the fitting function, t is the polynomial degree, naIs the weight of the first neighbor regression, nbIs the weight of the second neighbor regression, atPolynomial coefficients obtained for first-order neighbor regression, btIs the polynomial coefficient obtained from the second neighbor regression.
Optionally, a vessel maneuverability model is also established from the hydrodynamic derivatives of the vessel.
The ship maneuverability model is established through the hydrodynamic derivative determined by the embodiment of the invention, the modeling period is shortened, and the rapidity and the accuracy of modeling can be realized.
In a second aspect, embodiments of the present invention provide a computer-readable storage medium, on which a program for determining a derivative of hydrodynamic force in a ship maneuverability model modeling process is stored, where the program is executed by a processor to implement the method for determining a derivative of hydrodynamic force in a ship maneuverability model modeling process described in the first aspect and various possible implementations thereof.
In a third aspect, an embodiment of the present invention provides a computer device, including a memory, a processor, and a program for determining a derivative of hydrodynamic force in a ship maneuverability model modeling process, stored in the memory and operable on the processor, where the processor implements the method for determining a derivative of hydrodynamic force in a ship maneuverability model modeling process, described in the first aspect and various possible implementations thereof, when the processor executes the program for determining.
For the descriptions of the second aspect, the third aspect and various implementations thereof in this application, reference may be made to the detailed description of the first aspect and various implementations thereof; in addition, for the beneficial effects of the second aspect, the third aspect and various implementation manners thereof, reference may be made to beneficial effect analysis in the first aspect and various implementation manners thereof, and details are not described here.
(III) advantageous effects
The invention has the beneficial effects that: according to the method for determining the hydrodynamic derivative in the ship maneuverability model modeling process, the computer readable storage medium and the equipment, ship model experiments are carried out by establishing a ship motion equation to obtain ship model experiment data, and the ship model experiment data are subjected to fitting processing by adopting a quadratic proximity regression method to obtain the hydrodynamic derivative of the ship, so that the technical effects of short time period and low cost in the determination process and high accuracy of the calculation result of the obtained hydrodynamic derivative for establishing the ship maneuverability model are achieved.
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The application is described with the aid of the following figures:
FIG. 1 is a schematic flow chart illustrating a method for determining derivatives of hydrodynamic forces during modeling of a vessel maneuverability model according to an embodiment of the present application;
FIG. 2 is a schematic diagram of a fixed coordinate system and a moving coordinate system of an MMG motion model according to an embodiment of the present application;
FIG. 3 is an exemplary graph of a first fit curve of lateral forces experienced by a bare hull in one embodiment of the present application;
FIG. 4 is an exemplary graph of a second fit curve of lateral forces experienced by a bare hull in one embodiment of the present application;
FIG. 5 is an exemplary graph of a fitted curve of a bare hull subjected to lateral forces in another embodiment of the present application;
FIG. 6 is an exemplary graph of a fitted curve of a bare hull subjected to longitudinal forces in another embodiment of the present application;
fig. 7 is an exemplary graph of a fitted curve of the yaw moment experienced by a bare hull in another embodiment of the present application.
Detailed Description
For the purpose of better explaining the present invention and to facilitate understanding, the present invention will be described in detail by way of specific embodiments with reference to the accompanying drawings.
Aiming at the problems that the determination time period of the hydrodynamic derivative is long, the cost is high and the accuracy of the calculation result of the ship maneuverability model is low in the existing ship maneuverability model modeling process, the embodiment of the invention provides a method for determining the hydrodynamic derivative in the ship maneuverability model modeling process. The method for determining the hydrodynamic derivative in the ship maneuverability model modeling process comprises the following steps:
establishing a fixed coordinate system fixed on a space and a movable coordinate system fixed on a ship, and establishing a speed conversion relation according to the relation between the fixed coordinate system and the movable coordinate system;
according to the MMG motion model, establishing three-degree-of-freedom operation equations of the ship swaying speed, the surging speed and the yawing angular speed, establishing a ship hydrodynamic equation according to the speed conversion relation and the three-degree-of-freedom operation equations, and establishing a ship motion equation according to the ship hydrodynamic equation;
performing a ship model experiment based on a ship motion equation to obtain ship model experiment data;
and fitting the ship model experimental data by using a quadratic proximity regression method to obtain the hydrodynamic derivative of the ship.
The method for determining the hydrodynamic derivative in the ship control mathematical model has the advantages of no need of training the model, low technical requirement, short time period and low cost; compared with a simple empirical formula for determining the hydrodynamic derivative, the method is higher in accuracy.
In order to better understand the above technical solutions, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the invention are shown in the drawings, it should be understood that the invention can be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
Fig. 1 is a schematic flow chart of a method for determining a hydrodynamic derivative in a mathematical model of a ship maneuvering motion according to an embodiment of the application. In order to more clearly explain the present invention, the steps in this embodiment will be described in detail with reference to fig. 1.
As shown in fig. 1, the method for determining the derivative of hydrodynamic force in the ship maneuverability modeling process includes the following steps:
and step S1, establishing a fixed coordinate system fixed on the space and a movable coordinate system fixed on the ship, and establishing a speed conversion relation according to the relation between the fixed coordinate system and the movable coordinate system.
That is, the MMG motion model coordinate system is determined first. The MMG motion model coordinate system is divided into a fixed coordinate system fixed on the space and a movable coordinate system fixed on the ship.
Fig. 2 is a schematic diagram of a fixed coordinate system and a moving coordinate system of an MMG motion model in an embodiment of the present application. As shown in FIG. 2, o0-x0y0z0The coordinate system represents a fixed coordinate system of space, x0-y0The plane representing the surface of the water at rest, z0The axis is perpendicular to the stationary water surface and is positive downwards.
o-xyz coordinate system representation is fixed atAccording to the dynamic coordinate system on the ship, the origin is located in a midship, the direction of the x axis pointing to the bow of the ship is positive, the direction of the y axis pointing to a starboard is positive, and the direction of the z axis perpendicular to the horizontal plane is positive downwards. The center of gravity of the ship has a coordinate (x) in an o-xyz coordinate system G0,0), ψ represents a heading angle, which is x-axis and x0The included angle of the axes, U being the speed of flight, the rudder angle, r being the angular velocity, U being the surge velocity, vmAs the swaying speed, xGIs the x-axis coordinate of the center of gravity of the vessel. In the two coordinate systems, the speed conversion relationship is shown in formula (1).
v＝vm+xGr (1)
Wherein v is the ship swaying speed at the origin under the moving coordinate system, r is the ship bow angular velocity, v is the ship bow angular velocitymIs the ship swaying speed, x, at the center of gravity of the ship in a moving coordinate systemGIs the x-axis coordinate of the center of gravity of the vessel.
The relationship between the resultant velocity and the surging and swaying velocities is shown in equation (2).
Figure BDA0002497005690000071
The drift angle calculation of the center of gravity of the ship is shown in formula (3).
β＝tan-1(-vm/u) (3)
And step S2, establishing three-degree-of-freedom operation equations of the ship swaying speed, the surging speed and the yawing angle speed according to the MMG motion model, establishing a ship hydrodynamic equation according to the speed conversion relation and the three-degree-of-freedom operation equations, and establishing a ship motion equation according to the ship hydrodynamic equation.
According to the MMG motion model, only the control motion of the ship on the water surface is considered, the influence of the rolling, pitching and heaving of the ship on the control motion is ignored, and an operation equation of three degrees of freedom of the rolling, pitching and yawing of the ship is established, as shown in a formula (4):
Figure BDA0002497005690000072
wherein m is the ship mass, u and v are ship surging at the origin respectivelyThe speed, the swaying speed, r is the bow angular velocity of the ship,
Figure BDA0002497005690000073
respectively the ship surging acceleration, the bow rocking angle acceleration, MzYaw moment of the vessel in the vicinity of the center of gravity, IzGMoment of inertia, F, for the vessel about the center of gravityx、FyThe resultant forces in the x direction and the y direction of the ship.
Fx、FyAnd MzCan be expressed as equation (5).
Figure BDA0002497005690000074
Wherein m isxAnd myRepresenting the additional mass of the vessel in the x-direction and y-direction, respectively, JzFor additional moment of inertia of the vessel about the z-axis, X, Y, NmRepresenting the transverse hydrodynamic force, the longitudinal hydrodynamic force and the yawing hydrodynamic moment experienced by the vessel acting in the x-direction and the y-direction, respectively.
By combining equations (1), (4) and (5), the ship hydrodynamic equation shown in equation (6) can be obtained by eliminating v.
Figure BDA0002497005690000081
Wherein m is the ship mass, u is the ship surging speed,
Figure BDA0002497005690000082
respectively the ship surging acceleration, the bow rocking angle acceleration IzGIs the moment of inertia, m, of the ship about the center of gravityxAnd myAdditional masses, J, for the vessel in the x-direction and y-direction, respectivelyzAn additional moment of inertia about the z-axis for the vessel; x, Y, NmRespectively the transverse hydrodynamic force, the longitudinal hydrodynamic force and the heading hydrodynamic moment on the ship.
The forces and moments are resolved according to the different locations acting on the vessel and can be expressed as equation (7)
Figure BDA0002497005690000083
Wherein, XH、YHRespectively representing the hydrodynamic forces, i.e. viscous hydrodynamic forces, N, acting on the bare hull part in the x-direction and in the y-directionHIndicating that the bare hull part is subjected to hydrodynamic torque; xP、YPRepresenting the reaction forces acting on the propeller output thrust in the x-direction and in the y-direction, respectively, NPRepresenting the reaction torque of the propeller output thrust.
When the ship is in navigation, the factors influencing the viscous hydrodynamic force and the torque comprise the geometric characteristics of the ship, the physical characteristics of the fluid and the motion state of the ship, and the ship is specified before the ship motion model is established, so that the geometric characteristics of the ship are known. In the process of establishing the mathematical model, the fluid physical characteristics can be regarded as constants by neglecting the change of the fluid characteristics, and in addition, the ship motion model is regarded as a quasi-constant motion without considering the influence of the ship acceleration on the viscous hydrodynamic coefficient. Based on the above assumptions, the viscous hydrodynamic forces experienced by a vessel while sailing are related only to the vessel speed.
Since the ship maneuvering model only considers the changes of the ship in three degrees of freedom in the horizontal plane, the viscous hydrodynamic force and the hydrodynamic moment can be expressed in the form of equation (8).
Figure BDA0002497005690000091
And (3) carrying out Taylor expansion on the formula (8) at the v-r-0 position to obtain a ship motion equation. Since the ship is symmetrical about the longitudinal section, when v and r change direction, the force X does not change in magnitude and directionHIs an even function of v, r, XHThe expression (2) does not contain the odd-numbered terms of v and r. Similarly, Y when v, r change signH、NHThe size is unchanged and the direction is changed, so that YH、NHThe expression (2) does not contain the even-numbered terms of v and r.
The motion parameters are then dimensionless. At present, two measurement standard units exist in the field of international universal ship motion mathematical models, namely a one-skimming system and a two-skimming system, and the one-skimming system is adopted in the embodiment. The MMG equation uses a non-dimensionalized basis for the system as shown in Table 1.
TABLE 1
Figure BDA0002497005690000092
In the table, ρ is the fluid (water) density, L is the length of the vessel, d is the draft of the vessel, and U is the speed of the vessel.
Dimensionless values of a physical quantity are represented by adding an apostrophe (X') to the upper right hand corner of the symbol for the physical quantity, which is numerically equal to the dimensionless value (original value) of the physical quantity divided by the base value of the physical quantity. After the parameters are dimensionless, a ship motion equation shown in equation (9) is established.
Figure BDA0002497005690000093
Wherein R is0' is the direct navigation resistance, X ' of a ship 'vv、X′vr、X′rr、X′vvvv、Yv′、Yr′、Y′vvv、Y′vvr、Y′vrr、Y′rrr、N′v、N′r、N′vvv、N′vvr、N′vrr、N′rrrIs the hydrodynamic coefficient of the ship, X'H、YH′、N′H、v′mR' are each XH、YH、NH、vmAnd a dimensionless value of r.
And step S3, carrying out ship model experiment based on the ship motion equation to obtain ship model experiment data.
The ship model is used as a physical simulation of the motion process of the real ship in water, and the selected ship model and the real ship meet main similar conditions, wherein the conditions comprise geometric similarity, quality similarity, motion similarity, hydrodynamic similarity and time scale relation. The data obtained by the ship model test can be applied to ships after dimensional transformation.
And carrying out a ship resistance test, and obtaining the direct sailing resistance of the ship through the ship resistance test.
And performing an oblique voyage test and a circular motion test, and obtaining hydrodynamic force and moment received by the ship and thrust output by the propeller through the oblique voyage test and the circular motion test.
The experiment of the hydrodynamic coefficient comprises a skew navigation experiment and a circular motion experiment, and the measured force comprises an inertia force part and a viscous hydrodynamic part. In the skew test and the circular motion test, the measured force can be expressed in the form of equation (10).
Figure BDA0002497005690000101
Wherein, X'mesRepresents the measured transverse force, Y 'received by the ship'mesRepresents the measured longitudinal force, N 'received by the ship'mesIndicating that the measured bow moment experienced by the vessel,
Figure BDA0002497005690000102
dimensionless value, X ', representing the transverse force to which the bare hull is subjected'PA dimensionless value representing the reaction force of the propeller output power in the X direction,
Figure BDA0002497005690000103
dimensionless value, Y ', representing the longitudinal force to which the bare hull is subjected'PA dimensionless value representing the reaction force of the propeller output power in the Y direction,
Figure BDA0002497005690000104
dimensionless value, N 'representing yaw moment'PA dimensionless value representing the reaction torque of the propeller output power.
In the ship test, the power output by the propeller can be measured.
Figure BDA0002497005690000105
Including viscous hydrodynamic and inertial portions, may be expressed in the form of equation (11).
Figure BDA0002497005690000111
Wherein the content of the first and second substances,
Figure BDA0002497005690000112
a dimensionless value representing the lateral force to which the bare hull is subjected,
Figure BDA0002497005690000113
a dimensionless value representing the longitudinal force to which the bare hull is subjected,
Figure BDA0002497005690000114
dimensionless values, m ', representing the yawing moment'y、m′x、v′m、r′、x′GRespectively, are dimensionless values of the corresponding physical quantities.
The equations (9) and (11) are combined to obtain the equation shown in the equation (12).
Figure BDA0002497005690000115
Wherein R is0Indicating straight running resistance.
Substituting the measured force into the formula (10), and calculating the force and moment applied to the ship model
Figure BDA0002497005690000116
And step S4, fitting the ship model experimental data by using a quadratic proximity regression method to obtain the hydrodynamic derivative of the ship.
According to the data obtained by calculation, fitting the measurement points of multiple tests, wherein a quadratic proximity regression method is adopted in the fitting method, and the quadratic proximity method is an improvement on the traditional proximity algorithm and specifically comprises the following steps:
performing first fitting according to the ship model experimental data to obtain a polynomial coefficient of first adjacent regression, and extracting data points with errors larger than a preset value in the first fitting process;
performing quadratic fitting according to the extracted data points to obtain polynomial coefficients of a second adjacent regression;
and carrying out weighted average on the polynomial coefficients of the first adjacent regression and the polynomial coefficients of the second adjacent regression so as to take the weighted average value as the polynomial coefficients of the fitting function.
Because the ship model experiment gives the speed, drift angle and yaw rate, the drift angle β and the swaying speed vmSince the relationship between the surging speed u and the following equation (3) is satisfied, when the surging speed is constant and the drift angle is small, the relationship between the surging speed and the drift angle is regarded as a proportional relationship shown in equation (13).
Figure BDA0002497005690000117
And the hydrodynamic derivative can be further deduced through the fitting relation between the drift angle beta and the transverse force, the longitudinal force and the heading moment borne by the ship body.
In this embodiment, the experimental data of the transverse hydrodynamic ship model is taken as an example, and fitting processing is performed by using a quadratic proximity regression method as an example for explanation.
Step 31, obtaining an unknown coefficient X 'through fitting of a quadratic neighbor regression method'vv、X′vr+m′+m′y、X′rr+x′Gm′、X′vvv。
In the formula (12), the first and second groups,
Figure BDA0002497005690000121
and
Figure BDA0002497005690000122
is a known term, R'0The dimensionless value of the direct navigation resistance can be obtained through a direct navigation test.
Referring to fig. 3, fig. 3 is a diagram illustrating an example of a first-time fitted curve of lateral force applied to a bare hull according to an embodiment of the present application, wherein the abscissa is drift angle β and the ordinate is vertical
Figure BDA0002497005690000123
The method is characterized in that a dimensionless value of force is obtained through ship model test measurement and calculation, scattered points represent points finally obtained through tests and formulas, a dotted line represents a fitting curve, and asterisks represent measurement points with large difference between a measured value and an expected value in regression.
The function of the first-fit curve can be expressed as equation (14).
Figure BDA0002497005690000124
Wherein the content of the first and second substances,
Figure BDA0002497005690000125
is a dimensionless value of the transverse force to which the bare hull is subjected, a1、a2、a3、a4Respectively, the polynomial coefficients of the first neighboring regression.
For the measurement points with larger difference between the measured value and the expected value in fig. 3, these measurement points are extracted and subjected to the second proximity regression. Referring to fig. 4, fig. 4 is a diagram illustrating an example of a second-order fitted curve of lateral forces experienced by a bare hull according to an embodiment of the present application; the abscissa in fig. 4 is a drift angle, the ordinate is a transverse hydrodynamic force to which the bare hull is subjected, the scatter points in the graph are points finally obtained through a test and a formula, an asterisk indicates a measurement point in the regression where a difference between a measured value and an expected value is large, a dotted line indicates a curve obtained through first fitting, and a dash-dot line indicates a curve obtained through second fitting.
The function of the second-fit curve can be expressed as equation (15).
Figure BDA0002497005690000126
Wherein the content of the first and second substances,
Figure BDA0002497005690000127
dimensionless value of transverse force to which the bare hull is subjected, b1、b2、b3、b4Is as followsPolynomial coefficients of quadratic neighbor regression.
Two regression equations are obtained by two adjacent regressions respectively corresponding to two groups of coefficients, and the first adjacent regression corresponds to naData points, second adjacent regression for nbCarrying out weighted average on the two groups of coefficients by using the data points, wherein the weight value of the first adjacent regression is naThe weight of the second neighbor regression is nbThe polynomial coefficient of the quadratic neighbor regression is calculated by equation (16).
Figure BDA0002497005690000131
Wherein, ctPolynomial coefficients for quadratic proximity regression, t is the polynomial degree, atPolynomial coefficients obtained for first-order neighbor regression, btIs the polynomial coefficient obtained from the second neighbor regression.
Finally, a polynomial equation obtained by quadratic proximity regression is obtained, as shown in formula (17).
Figure BDA0002497005690000132
From the conversion relationship between the drift angle and the swaying speed shown in the formula (13), the following can be obtained as shown in (18)
Figure BDA0002497005690000133
And obtaining corresponding coefficients by relating the coefficients to the swaying speed.
Figure BDA0002497005690000134
And finally, fitting the hydrodynamic coefficients of the longitudinal hydrodynamic force and the yawing moment is realized by adopting the same method.
FIG. 5 is an exemplary graph of a fitted curve of a bare hull subjected to a lateral force in another embodiment of the present application, FIG. 6 is an exemplary graph of a fitted curve of a bare hull subjected to a longitudinal force in another embodiment of the present application, and FIG. 7 is an exemplary graph of a fitted curve of a bare hull subjected to a longitudinal force in another embodiment of the present applicationThe horizontal axis is drift angle β, and the vertical axis is respectively drift angle β
Figure BDA0002497005690000135
(
Figure BDA0002497005690000136
A dimensionless value representing the lateral force to which the bare hull is subjected,
Figure BDA0002497005690000137
a dimensionless value representing the longitudinal force to which the bare hull is subjected,
Figure BDA0002497005690000138
a dimensionless value representing the heading moment), r 'represents a dimensionless value of the heading angular velocity, r' ═ 0 represents the skew test, r '═ -0.6 and r' ═ 0.6 represent the circular motion test, and the three curves in each figure are the fitting results under test conditions with different heading angular velocities. And fitting under different heading angular speeds to obtain hydrodynamic derivatives under different navigation conditions.
According to the data obtained by calculation, the measuring points of multiple tests are fitted, and a quadratic proximity regression method is adopted for fitting, so that the fitting precision is improved, and the influence of data points with larger errors on the fitting result can be reduced.
And step 32, determining the additional mass of the ship through a Zhoushanming empirical formula.
Dimensionless values m 'of additional mass of the vessel in the x-direction and y-direction in equations of motion of the vessel under hydrodynamic and inertial forces'x、m′yCan be obtained by using a Zhou Shou's empirical formula shown in formula (19).
Figure BDA0002497005690000141
Wherein, CbIs a rhombus coefficient, d is the design draft, B is the ship width, and L is the ship vertical line length.
And step S33, obtaining a polynomial coefficient based on the additional mass of the ship and the step S31, and determining the hydrodynamic derivative.
From hydrodynamic derivative X'vrFor example, X 'can be calculated by formula (20)'vr。
Figure BDA0002497005690000142
Other hydrodynamic derivatives can be calculated in the same way and will not be described here.
Optionally, in an embodiment of the application, the vessel maneuverability model is also built from hydrodynamic derivatives of the vessel. The ship maneuverability model is a three-degree-of-freedom ship maneuvering mathematical model established based on the MMG model, and the hydrodynamic derivative in the three-degree-of-freedom ship maneuvering mathematical model is determined by the method in the embodiment.
According to the embodiment of the invention, as the hydrodynamic derivative is determined by adopting the hydrodynamic derivative determination method in the embodiment, the ship model test data points are fitted, the technical requirement is low, a model does not need to be trained, and the required derivative can be obtained by directly fitting; therefore, the ship motion model is established according to the hydrodynamic derivative obtained by derivation, the time period is short, the cost is low, and the rapidness and the accuracy of modeling can be realized. Compared with a simple empirical formula, the ship model modeling method overcomes the defect of low accuracy of the empirical formula caused by large ship type change, and is short in modeling time, so that the research and development efficiency of the ship is improved.
Alternatively, in one embodiment, the hydrodynamic derivative is derived by using a quadratic proximity regression method, and the coefficient m is obtained by an empirical formulaxAnd myAnd establishing a ship maneuverability model for ship maneuverability simulation. The ship maneuverability model is established as shown in formula (21).
Figure BDA0002497005690000151
In the embodiment, compared with a simple empirical formula, the hybrid model based on the ship model test and the empirical formula makes up for the defect of low accuracy of the empirical formula caused by large ship shape change, and is short in modeling time, so that the research and development efficiency of the ship is improved.
In a second aspect, embodiments of the present invention provide a computer-readable storage medium, on which a program for determining a derivative of hydrodynamic force in a ship maneuverability model modeling process is stored, where the program is executed by a processor to implement the method for determining a derivative of hydrodynamic force in a ship maneuverability model modeling process described in the first aspect and various possible implementations thereof.
In a third aspect, an embodiment of the present invention provides a computer device, which includes a memory, a processor, and a determination program of a derivative of hydrodynamic force in a ship maneuverability model modeling process, stored in the memory and operable on the processor, where when the processor executes the determination program, the method for determining a derivative of hydrodynamic force in a ship maneuverability model modeling process according to the first aspect and various possible implementations thereof is implemented.
For the descriptions of the second aspect, the third aspect and various implementations thereof in this application, reference may be made to the detailed description of the first aspect and various implementations thereof; in addition, for the beneficial effects of the second aspect, the third aspect and various implementation manners thereof, reference may be made to beneficial effect analysis in the first aspect and various implementation manners thereof, and details are not described here.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions.
It should be noted that in the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word "comprising" does not exclude the presence of elements or steps not listed in a claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The invention may be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In the claims enumerating several means, several of these means may be embodied by one and the same item of hardware. The use of the terms first, second, third and the like are for convenience only and do not denote any order. These words are to be understood as part of the name of the component.
Furthermore, it should be noted that in the description of the present specification, the description of the term "one embodiment", "some embodiments", "examples", "specific examples" or "some examples", etc., means that a specific feature, structure, material or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, the claims should be construed to include preferred embodiments and all changes and modifications that fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention should also include such modifications and variations.

Claims (9)

1. A method for determining a hydrodynamic derivative in a ship maneuverability model modeling process is characterized by comprising the following steps of:
establishing a fixed coordinate system fixed on a space and a movable coordinate system fixed on a ship, and establishing a speed conversion relation according to the relation between the fixed coordinate system and the movable coordinate system;
according to the MMG motion model, establishing three-degree-of-freedom operation equations of the ship swaying speed, the surging speed and the heading angle speed, establishing a ship hydrodynamic equation according to the speed conversion relation and the three-degree-of-freedom operation equations, and establishing a ship motion equation according to the ship hydrodynamic equation;
performing a ship model experiment based on the ship motion equation to obtain ship model experiment data;
and fitting the ship model experimental data by using a second-order adjacent regression method to obtain the hydrodynamic derivative of the ship.
2. The method for determining the derivative of hydrodynamic force in a vessel maneuverability model modeling process of claim 1 wherein the speed transformation relationship is expressed according to the following formula:
v＝vm+xGr
wherein v is the ship swaying speed at the origin point under the moving coordinate system, r is the ship bow angular velocity, v is the ship bow angular velocitymThe ship swaying speed, x, at the center of gravity of the ship in the moving coordinate systemGIs the x-axis coordinate of the center of gravity of the vessel.
3. The method for determining derivatives of hydrodynamic forces in a vessel maneuverability model modeling process of claim 2 wherein said vessel hydrodynamic equation is expressed according to the following formula:
Figure FDA0002497005680000011
wherein m is the ship mass, u is the ship surging speed,
Figure FDA0002497005680000012
respectively the ship surging acceleration, the bow rocking angle acceleration IzGIs the moment of inertia, m, of the ship about the center of gravityxAnd myAdditional masses, J, for the vessel in the x-direction and y-direction, respectivelyzAn additional moment of inertia about the z-axis for the vessel; x, Y, NmRespectively the transverse hydrodynamic force, the longitudinal hydrodynamic force and the heading hydrodynamic moment on the ship.
4. The method for determining derivatives of hydrodynamic forces in a vessel maneuverability model modeling process of claim 3 wherein the vessel equations of motion are expressed according to the following formula:
Figure FDA0002497005680000021
Figure FDA0002497005680000022
Figure FDA0002497005680000023
wherein, XH' is a dimensionless value of the transverse hydrodynamic force to which the hull is subjected, YH' is a dimensionless value of longitudinal hydrodynamic force to which the hull is subjected, NH'is a dimensionless value of the yaw moment, R'0Is a dimensionless value, X ', of the direct navigation resistance of the ship'vv、X′vr、X′rr、X′vvvv、Yv′、Yr′、Y′vvv、Y′vvr、Y′vrr、Y′rrr、N′v、N′r、N′vvv、N′vvr、N′vrr、N′rrrIs the hydrodynamic derivative of the vessel, r 'is a dimensionless value of the vessel's yaw rate, vm'is a dimensionless value for the vessel's sway speed.
5. The method for determining hydrodynamic derivatives in a ship maneuverability model building process according to any of claims 1-4, wherein the fitting process of the ship model experimental data by quadratic proximity regression method comprises:
performing first fitting according to the ship model experimental data to obtain a polynomial coefficient of first adjacent regression, and extracting data points with errors larger than a preset value in the first fitting process;
performing quadratic fitting according to the extracted data points to obtain polynomial coefficients of a second adjacent regression;
and carrying out weighted average on the polynomial coefficients of the first adjacent regression and the polynomial coefficients of the second adjacent regression so as to take the weighted average value as the polynomial coefficients of the fitting function.
6. The method for determining the derivative of hydrodynamic force in a vessel maneuverability model modeling process of claim 5 wherein the polynomial coefficients of the fitting function are calculated according to the following formula:
Figure FDA0002497005680000024
wherein, ctIs the polynomial coefficient of the fitting function, t is the polynomial degree, naIs the weight of the first neighbor regression, nbIs the weight of the second neighbor regression, atPolynomial coefficients obtained for first-order neighbor regression, btIs the polynomial coefficient obtained from the second neighbor regression.
7. The method for determining hydrodynamic derivatives in a vessel maneuverability model building process of claim 1 wherein a vessel maneuverability model is also created based on the hydrodynamic derivatives of the vessel.
8. A computer-readable storage medium, on which a program for determining a derivative of hydrodynamic force in a vessel maneuverability model modeling process is stored, which program, when executed by a processor, implements a method for determining a derivative of hydrodynamic force in a vessel maneuverability model modeling process according to any of claims 1 to 7.
9. A computer apparatus comprising a memory, a processor and a program for determining derivatives of hydrodynamic forces during modeling of a vessel maneuverability model stored in the memory and operable on the processor, the processor when executing the program for determining implementing a method for determining derivatives of hydrodynamic forces during modeling of a vessel maneuverability model according to any of claims 1-7.
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