Power spectrum analysis-based three-degree-of-freedom real-time motion simulation method and system for ship in sea waves

Abstract

The invention discloses a three-degree-of-freedom real-time motion simulation method and system of a ship in sea waves based on power spectrum analysis, and belongs to the technical field of ship and ocean engineering, and the method comprises the steps: obtaining sea wave data and basic parameters of the ship; establishing a sea wave simulation model based on a frequency density spectrum to obtain a sea wave spectrum; based on the sea wave spectrum and the ship basic parameters, establishing a power spectrum density function of ship swaying motion; establishing a kinetic equation of the ship swaying motion, and solving a coefficient of the kinetic equation of the ship swaying motion and a power spectral density function of the ship swaying motion according to the sea wave data and the ship basic parameters; and solving the kinetic equation of the ship swaying motion, and obtaining time calendar data of the three-degree-of-freedom swaying motion of the ship through inverse Fourier transform. By means of the method, simulation calculation of rolling, pitching and heaving three-degree-of-freedom motion of any ship type under any sea condition can be achieved, and manpower, material resource and financial resource input of ship model tests and real ship sea tests is saved.

Description

Technical Field

[0001] The present invention relates to the technical field of ship and ocean engineering, and particularly to a three-degree-of-freedom real-time motion simulation method and system for a ship in waves based on power spectrum analysis. Background Art

[0002] When a ship sails on the sea surface, in most cases, it will be disturbed by factors such as waves, sea winds, and ocean currents and generate swaying motions, which will cause the motion posture of the ship to change at all times, and may even cause slamming, splashing, overtopping, stalling, and propeller racing. In order to explore the motion law of a ship in waves, in the past, it was mainly carried out through ship model tests in a wave-making tank or full-scale sea trials. However, ship model tests not only require high costs, but also there are significant differences between the simulated environment and the combined action of wind, waves, and currents in the real sea conditions, making it difficult to accurately reflect the actual situation; although full-scale sea trials are carried out in the real ocean environment, they are accompanied by non-negligible risks, posing a serious threat to the safety of ships and personnel. Therefore, there is an urgent need for a ship motion research method that can accurately simulate the motion characteristics of various ship types under different sea conditions, does not rely too much on a large amount of measured data, and is real-time. Summary of the Invention

[0003] The purpose of this application is to overcome the defects of the prior art and provide a three-degree-of-freedom real-time motion simulation method and system for a ship in waves based on power spectrum analysis.

[0004] In the first aspect, this application provides a three-degree-of-freedom real-time motion simulation method for a ship in waves based on power spectrum analysis, including the following steps: Obtain wave data and basic ship parameters; According to the wave data, establish a wave simulation model based on the frequency density spectrum to obtain a wave spectrum; Based on the wave spectrum and the basic ship parameters, establish a power spectral density function of the ship's swaying motion to obtain the relationship between the ship's swaying motion and the wave spectrum; Establish a dynamic equation of the ship's swaying motion, and according to the wave data and the basic ship parameters, solve the coefficients of the dynamic equation of the ship's swaying motion and the power spectral density function of the ship's swaying motion; Based on the coefficients of the dynamic equation of the ship's swaying motion, solve the dynamic equation of the ship's swaying motion, and obtain the time history data of the three-degree-of-freedom swaying motion of the ship through inverse Fourier transform.

[0005] Optionally, the step of establishing a wave simulation model based on the frequency density spectrum according to the wave data to obtain a wave spectrum includes: According to the wave data, use the frequency density spectrum to establish a wave spectrum of irregular waves; Input the parameters of the wave spectrum of the irregular sea waves into the wave model, construct the sea wave simulation model based on the frequency density spectrum, and obtain the final sea wave spectrum.

[0006] Optionally, the formula of the wave spectrum of the irregular sea waves is as follows: where ω is the sea wave frequency, is the sea wave direction, is the frequency density spectrum, is the direction distribution function.

[0007] Optionally, the wave model is the Gerstner model.

[0008] Optionally, the frequency density spectrum includes the PM spectrum and the significant wave height.

[0009] Optionally, the formula of the power spectral density function of the ship's rolling motion is as follows: where, is the power spectral density function of the sea waves, that is, the final sea wave spectrum; is the sea wave direction; is the i th amplitude-frequency response operator of the rolling motion; is the angular frequency.

[0010] Optionally, the coefficients of the dynamic equation of the ship's rolling motion include: damping moment, inertia moment, and restoring moment.

[0011] Optionally, establishing the dynamic equation of the ship's rolling motion, and solving the coefficients of the dynamic equation of the ship's rolling motion and the power spectral density function of the ship's rolling motion according to the sea wave data and the ship's basic parameters includes: Establish the dynamic equation of the ship's rolling motion, and the dynamic equation of the ship's rolling motion includes: the dynamic equation of the ship's roll motion, the dynamic equation of the ship's pitch motion, and the dynamic equation of the ship's heave motion; Determine the damping moment through experiments, and the damping moment includes: the roll motion damping moment, the pitch motion damping moment, and the heave motion damping moment; Determine the inertia moment using the regression equation, and the inertia moment includes: the roll motion inertia moment, the pitch motion inertia moment, and the heave motion inertia moment; Determine the restoring moment according to the ship's basic parameters, and the restoring moment includes: the roll motion restoring moment, the pitch motion restoring moment, and the heave motion restoring moment; According to Froude theory, encounter frequency and correction coefficients are introduced to obtain disturbing moments, which include: disturbing moment of rolling motion, disturbing moment of pitching motion, and disturbing moment of heaving motion; the amplitude-frequency response operator of oscillatory motion is determined according to each coefficient, and the power spectral density function of ship oscillatory motion is obtained. The amplitude-frequency response operator of oscillatory motion includes: amplitude-frequency response operator of rolling motion, amplitude-frequency response operator of pitching motion, and amplitude-frequency response operator of heaving motion. The power spectral density function of ship oscillatory motion includes: power spectral density function of ship rolling motion, power spectral density function of ship pitching motion, and power spectral density function of ship heaving motion.

[0012] Optionally, the formula of the dynamic equation of the ship's oscillatory motion is as follows: Wherein, is the inertial moment of rolling motion, is the inertial moment of the rolling axis, is the added inertial moment of the rolling axis, is the damping moment of rolling motion, is the restoring moment of rolling motion, is the disturbing moment of rolling motion, is the rolling acceleration, is the rolling speed, is the rolling angle, is the inertial moment of pitching motion, is the inertial moment of the pitching axis, is the added inertial moment of the pitching axis, is the damping moment of pitching motion, is the restoring moment of pitching motion, is the disturbing moment of pitching motion, pitching acceleration, is the pitching speed, is the pitching angle, is the inertial moment of heaving motion, is the mass, is the added mass, is the damping moment of heaving motion, is the restoring moment of heaving motion, is the disturbing moment of heaving motion, is the heaving acceleration, is the heaving speed, is the heaving value.

[0013] In a second aspect, the present application also provides a three-degree-of-freedom real-time motion simulation system for a ship in waves based on power spectrum analysis. The three-degree-of-freedom real-time motion simulation system for a ship in waves based on power spectrum analysis includes: A data acquisition module for acquiring wave data and basic ship parameters; A wave simulation module for establishing a wave simulation model based on the frequency density spectrum according to the wave data and the basic ship parameters, and constructing a power spectral density function of the ship's rolling motion; A dynamic equation construction module for establishing a dynamic equation of the ship's rolling motion, determining coefficients, and solving the dynamic equation of the ship's rolling motion; A fitting analysis module for obtaining time history data of the ship's three-degree-of-freedom rolling motion according to the solution result of the dynamic equation of the ship's rolling motion and the power spectral density function of the ship's rolling motion, and performing curve fitting and analysis.

[0014] The present application provides a three-degree-of-freedom real-time motion simulation method and system for a ship in waves based on power spectrum analysis. By combining the frequency density spectrum and the Gestner model, a Gestner wave simulation model based on the frequency density spectrum is constructed, which can accurately simulate the complex shape and dynamic changes of waves under real sea conditions, overcome the limitations of traditional wave models, and provide a highly realistic marine environment basis for ship motion analysis; by establishing a power spectral density function of the ship's rolling motion, the internal physical connection between the ship's rolling motion and waves can be deeply analyzed, which helps to study the ship's motion characteristics; by constructing and solving the dynamic equation of the ship's rolling motion, the time history data of the ship's three-degree-of-freedom rolling motion under any sea conditions is obtained, and the actual motion state of the ship under different sea conditions can be accurately grasped, providing reliable decision-making support for ship navigation safety assessment, route planning, and ocean engineering operations.

[0015] To make the above features and advantages of the invention more obvious and understandable, specific embodiments are hereinafter given and described in detail in conjunction with the accompanying drawings as follows. Description of the Drawings

[0016] To more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the following will briefly introduce the drawings required for use in the description of the embodiments or related technologies. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0017] Figure 1 It is a flowchart of a three-degree-of-freedom real-time motion simulation method for a ship in waves based on power spectrum analysis provided in an embodiment of the present application.

[0018] Figure 2 This is the flowchart of step S40 in the three - degree - of - freedom real - time motion simulation method of a ship in waves based on power spectrum analysis provided in an embodiment of the present application.

[0019] Figure 3 This is the time - history data diagram of the rolling motion of the three - degree - of - freedom real - time motion simulation method of a ship in waves based on power spectrum analysis provided in an embodiment of the present application.

[0020] Figure 4 This is the time - history data diagram of the pitching motion of the three - degree - of - freedom real - time motion simulation method of a ship in waves based on power spectrum analysis provided in another embodiment of the present application.

[0021] Figure 5 This is the time - history data diagram of the heaving motion of the three - degree - of - freedom real - time motion simulation method of a ship in waves based on power spectrum analysis provided in another embodiment of the present application.

[0022] Figure 6 This is the structure diagram of the three - degree - of - freedom real - time motion simulation system of a ship in waves based on power spectrum analysis provided in another embodiment of the present application. Detailed implementation manners

[0023] To make the objectives and technical solutions of the embodiments of the present application clearer, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present application. Obviously, the described embodiments are some, but not all, of the embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the described embodiments of the present application without creative efforts shall fall within the scope of protection of the present application.

[0024] In real sea conditions, generally, the direction of ship navigation and the direction of wave propagation form a certain angle, and the ship will undergo six - degree - of - freedom swaying motions, namely linear reciprocating motions along the three coordinate axes and rotations around the three coordinate axes, that is, surge, sway, heave, roll, pitch, and yaw motions. Among them, the most important ones are roll, pitch, and heave. For example, an excessive roll amplitude may cause cargo displacement or even ship capsizing; pitching will change the draft of the ship, affecting the navigation speed and resistance; heaving will cause the ship to collide with the waves frequently, accelerating the wear of the ship's structure. The three - degree - of - freedom swaying motion of the present application includes the swaying motions of the ship's roll, pitch, and heave three degrees of freedom.

[0025] In one embodiment, please refer to Figure 1, this application provides a three-degree-of-freedom real-time motion simulation method for ships in waves based on power spectrum analysis. The three-degree-of-freedom real-time motion simulation method for ships in waves based on power spectrum analysis may include the following steps: Step S10 to Step S50.

[0026] Step S10: Obtain wave data and ship basic parameters.

[0027] Step S20: According to the wave data, establish a wave simulation model based on the frequency density spectrum to obtain the wave spectrum.

[0028] Step S30: Based on the wave spectrum and ship basic parameters, establish the power spectral density function of the ship's rolling motion to obtain the relationship between the ship's rolling motion and the wave spectrum.

[0029] Step S40: Establish the dynamic equation of the ship's rolling motion, and according to the wave data and ship basic parameters, solve the coefficients of the dynamic equation of the ship's rolling motion and the power spectral density function of the ship's rolling motion.

[0030] Step S50: Based on the coefficients of the dynamic equation of the ship's rolling motion, solve the dynamic equation of the ship's rolling motion, and obtain the time history data of the three-degree-of-freedom rolling motion of the ship through inverse Fourier transform.

[0031] In the three-degree-of-freedom real-time motion simulation method for ships in waves based on power spectrum analysis of this application, by establishing a wave simulation model based on the frequency density spectrum, the wave characteristics under real sea conditions can be accurately simulated; by establishing the power spectral density function of the ship's rolling motion, the internal relationship between the ship's rolling motion and the wave spectrum can be systematically quantified; through the dynamic equation of the ship's rolling motion, the influence of the ship's own characteristics and wave forces on the ship's rolling motion can be comprehensively considered, so that in the absence of real data, accurate ship rolling motion can still be obtained through reasonable theoretical derivation and calculation, overcoming the limitations of traditional measured data-dependent methods. In summary, this method can efficiently and accurately realize the real-time simulation of the three-degree-of-freedom motion of rolling, pitching, and heaving of any ship type under any sea conditions, providing a very valuable tool for the research and practice in the field of ship engineering and strongly promoting the development of related industries.

[0032] In Step S10, please refer to Figure 1 Step S10 in it to obtain wave data and ship basic parameters.

[0033] As an example, wave data can be obtained through devices and means such as ocean buoys, satellite remote sensing, and ocean observation stations. The wave data may include: wave frequency ω, wave direction etc. Among them, the wave frequency ω reflects the speed of wave fluctuations. Waves with different frequencies have different acting forces and influencing methods on the ship; the relative relationship between the wave direction and the ship's sailing direction determines the impact angle and acting effect of the waves on the ship. The waves are usually wind-generated waves, and the wave direction is usually consistent with the average wind direction.

[0034] As an example, the basic ship parameters can be obtained through ship design drawings, ship construction records, publicly available online data, and actual measurements, etc. The basic ship parameters may include: ship speed V , encounter angle (i.e., wave direction angle) , angular frequency ω, ship displacement D , draft d , ship width B , ship length L、 fluid density ρ , displacement volume ∇ etc. Among them, the speed V of the ship affects the interaction intensity and frequency between the ship and the waves. The draft d determines the depth and buoyancy distribution of the ship in the water and plays an important role in the stability and motion response of the ship. The ship width B and ship length L These dimensional parameters affect the moment of inertia and force-bearing area of the ship, etc.

[0035] In step S20, refer to Figure 1 step S20 therein, input the wave data, establish a wave simulation model based on the frequency density spectrum, and obtain the wave spectrum.

[0036] As an example, based on the obtained wave data, the irregular waves can be described as a wave spectrum , and the wave spectrum can be expressed by the following formula: where ω is the wave frequency, is the wave direction, is the frequency density spectrum, is the direction distribution function. The frequency density spectrum can be used to describe the energy distribution of the simulated waves at different frequencies.

[0037] Furthermore, integrating the wave spectrum over the entire bandwidth frequency and direction can reflect the total energy passed by the waves. The formula for the total energy of the waves is: where ω is the wave frequency, is the wave direction, is the wave spectrum, is the mean wave direction. Integrate the wave directions within a certain angular range around the mean wave direction and accumulate the wave energy at different frequencies and in different directions through double integration to obtain the total wave energy .

[0038] As an example, the frequency density spectrum may include the PM spectrum, the significant wave height, etc.

[0039] In one example, the PM spectrum can be used to describe the frequency density spectrum . The PM spectrum can simulate a fully developed ocean, which is an ocean where the variance of the wave height is basically stable and the energy acquisition and consumption are basically balanced. The frequency density spectrum described by the PM spectrum can be expressed by the following formula: where is the acceleration due to gravity; represents the mean wind speed at a height of 19.5 m above sea level, ω is the wave frequency, is the wave direction.

[0040] In another example, the significant wave height can be used to describe the frequency density spectrum and can be expressed by the following formula: where is the significant wave height, ω is the wave frequency, is the acceleration due to gravity, is the wave direction.

[0041] Furthermore, in order to simulate more general waves with diffracted wave interference, the directional distribution function is used to describe the distribution of wave energy around the mean wave direction . Usually, the wave direction , and the integral of the distribution function with respect to the wave direction is 1.

[0042] As an example, the directional distribution function can be expressed by the following formula: where is the wave direction, is the mean wave direction, c is a parameter, and the ITTC recommends selecting the parameter c = 1.

[0043] Furthermore, the total energy of the ocean waves is discretized and modeled to obtain the wave surface equation of the ocean waves, and the wave surface equation can be expressed by the following formula: where represents the wave surface height of the ocean waves at the spatial coordinate (x, y) at the moment t ; is the wave amplitude of the component wave, which is a coefficient related to the ocean waves and determines the amplitude size of different component ocean waves, , is the increment of the ocean wave frequency , is the increment of the direction angle , is the i th angular frequency, ; is the j th direction angle; k is the wave number; μ is a parameter related to the ocean wave direction ; x and y are the spatial coordinates of the ocean wave particles; t is the time; n , m are the number of discrete points.

[0044] Furthermore, since the frequency density spectrum can only reflect the height field of the ocean waves, and the ocean waves are relatively flat and cannot simulate the curled part of the ocean waves, which does not conform to the characteristics of the relatively steep wave crest / flatter wave trough of the ocean waves. Therefore, the Gerstner ocean wave model is used to further simulate the ocean waves. The data of the frequency density spectrum (such as parameters related to wave amplitude, frequency, direction, etc.) are used as the input of the Gerstner ocean wave model. The Gerstner ocean wave model processes and superimposes these input parameters according to its own dynamic equation, and outputs the three-dimensional positions of the ocean wave particles at different moments, thereby realizing the simulation of the ocean waves, making the relatively simple ocean wave form originally described only by the ocean wave spectrum become more realistic and complex through the Gerstner ocean wave model, presenting ocean waves with actual characteristics such as curling.

[0045] As an example, the Gerstner ocean wave model can describe the motion of ocean wave particles from a dynamic perspective. The ocean wave model is composed of the linear superposition of multiple different wave amplitudes and different angular frequencies. The three-dimensional discrete form of the ocean wave particles at time t can be expressed as: where the xy plane is defined as the plane when the water surface is stationary, zThe axis is perpendicular to the plane and points upward; each wave particle on the sea surface moves in a circular motion around its stationary position and x is the abscissa of the wave particle, which is used to determine the position of the wave particle in the xy plane along the horizontal direction; y is the ordinate of the wave particle, which is used to determine the position of the wave particle in the xy plane perpendicular to the abscissa direction; z is the height coordinate of the wave particle, which is used to represent the vertical height of the wave particle relative to the xy plane; is the abscissa of the wave particle when it is stationary; is the ordinate of the wave particle when it is stationary; is the height coordinate of the wave particle when it is stationary; is the amplitude of the component wave, which represents the maximum distance that the wave particle deviates from its stationary position during the propagation of a certain specific component wave. , is the increment of the wave frequency ; is the increment of the direction angle ; is the i th wave number, ; is the i th angular frequency, ; and it propagates in the xy plane along the x axis at an angle of , is the j th direction angle; n , m are the number of discrete points of the frequency density spectrum; is the i th initial phase. The Gerstner wave model outputs the three-dimensional position information of the wave particles at different times, thereby realizing the curling effect of the waves and more realistically simulating the wave form, providing an information basis for subsequent calculation of the wave interference force on the ship.

[0046] In step S30, please refer to step S30 in Figure 1 to establish the power spectral density function of the ship's rolling motion based on the wave spectrum of the sea waves and the basic parameters of the ship, and obtain the relationship between the ship's rolling motion and the said wave spectrum of the sea waves.

[0047] As an example, based on the wave spectrum of the sea waves and the basic parameters of the ship, the power spectral density function of the ship's rolling motion and the power spectral density function of the sea waves The relationship between them is used to obtain the power spectral density function of the ship's rolling motion : Among them, is the power spectral density function of the sea wave, is the i th amplitude-frequency response operator of the rolling motion, is the angular frequency, is the sea wave direction.

[0048] Furthermore, since the ship speed is not 0, the angular frequency can be converted into the encounter frequency , then the encounter frequency can be obtained by the following formula: Among them, is the ship speed; is the encounter angle, that is, the wave direction angle, which is the angle of the sea wave calculated based on the stern line, and the counterclockwise direction is positive; is the encounter frequency; is the angular frequency; is the gravitational acceleration.

[0049] As an example, based on the encounter frequency , the sea wave level can be regarded as constant, then the total energy of the sea wave remains unchanged, that is: Among them, is the encounter frequency, is the angular frequency, is the sea wave power spectral density based on the encounter frequency , is the sea wave power spectral density, is the sea wave direction. At this time, the power spectral density of the ship's rolling motion at the encounter frequency can be expressed as: Among them, is the th amplitude-frequency response operator of the rolling motion with the encounter frequency i as a variable, is the sea wave power spectral density function based on the encounter frequency , is the encounter frequency of the ship's rolling motion, is the sea wave direction.

[0050] In step S40, please refer toFigure 1 In step S40, a dynamic equation of the ship's rolling motion is established, and according to the wave data and the ship's basic parameters, the coefficients of the dynamic equation of the ship's rolling motion and the power spectral density function of the ship's rolling motion are solved.

[0051] As an example, please refer to Figure 2 , step S40 may include: steps S401 to S406.

[0052] Step S401: Establish a dynamic equation of the ship's rolling motion, and the dynamic equation of the ship's rolling motion includes: a dynamic equation of the ship's rolling motion, a dynamic equation of the ship's pitching motion, and a dynamic equation of the ship's heaving motion.

[0053] Step S402: Determine the damping moment through experiments, and the damping moment includes: a rolling motion damping moment, a pitching motion damping moment, and a heaving motion damping moment.

[0054] Step S403: Determine the inertia moment using a regression equation, and the inertia moment includes: a rolling motion inertia moment, a pitching motion inertia moment, and a heaving motion inertia moment.

[0055] Step S404: Determine the restoring moment according to the ship's basic parameters, and the restoring moment includes: a rolling motion restoring moment, a pitching motion restoring moment, and a heaving motion restoring moment.

[0056] Step S405: According to the Froude theory, introduce the encounter frequency and correction coefficient to obtain the disturbing moment, and the disturbing moment includes: a rolling motion disturbing moment, a pitching motion disturbing moment, and a heaving motion disturbing moment.

[0057] Step S406: Determine the amplitude-frequency response operator of the rolling motion according to each coefficient, and obtain the power spectral density function of the ship's rolling motion. The amplitude-frequency response operator of the rolling motion includes: the amplitude-frequency response operator of the rolling motion, the amplitude-frequency response operator of the pitching motion, and the amplitude-frequency response operator of the heaving motion. The power spectral density function of the ship's rolling motion includes: the power spectral density function of the ship's rolling motion, the power spectral density function of the ship's pitching motion, and the power spectral density function of the ship's heaving motion.

[0058] As an example, in step S401, the dynamic equation of the ship's rolling motion is established as follows: Among them, is the rolling motion inertia moment, is the inertia moment about the rolling axis, The added inertia moment about the roll axis, The damping moment of the roll motion, The restoring moment of the roll motion, The disturbing moment of the roll motion, The roll acceleration, The roll velocity, The roll angle, The inertia moment of the pitch motion, The inertia moment about the pitch axis, The added inertia moment about the pitch axis, The damping moment of the pitch motion, The restoring moment of the pitch motion, The disturbing moment of the pitch motion, The pitch acceleration, The pitch velocity, The pitch angle, The inertia moment of the heave motion, The mass, The added mass, The damping moment of the heave motion, The restoring moment of the heave motion, The disturbing moment of the heave motion, The heave acceleration, The heave velocity, The heave value. Further, solve the coefficients of the dynamic equation of the ship rolling motion. The coefficients of the dynamic equation of the ship rolling motion include: damping moment, inertia moment, and restoring moment.

[0059] Taking the roll motion as an example, the steps S402 to S407 are specifically introduced below.

[0060] Further, in step S402, the roll motion damping moment has many influencing factors, including the viscous resistance of water, wave-making resistance, and the structural damping of the ship itself, etc. Due to the complexity of these factors, it is difficult to directly and accurately calculate through theoretical formulas and needs to be determined through experiments.

[0061] As an example, the parameter identification method can be used to determine the roll motion damping moment , by using the motion amplitude and period statistically obtained during the actual navigation of the ship under different sea conditions to determine the coefficients of the dynamic equation of the ship rolling motion, the extended Kalman filter (EKF) algorithm can be used for parameter identification, and finally the roll motion damping moment is determined. At the same time, the coefficients in the inertia moment, restoring moment, and disturbing moment can also be corrected.

[0062] Further, in step S403, the roll motion inertia moment The moment of inertia about the roll axis and the additional moment of inertia about the roll axis of the hull generated by the waves are combined and can be obtained by the following regression formula: where, is the moment of inertia of the roll motion, is the moment of inertia about the roll axis, is the additional moment of inertia about the roll axis, d is the draft, B is the beam, L is the length of the ship, g is the acceleration due to gravity, m is the mass.

[0063] As an example, the additional moment of inertia about the pitch axis of the moment of inertia of the pitch motion can be obtained by the following regression formula: where, is the additional moment of inertia about the pitch axis, is the prismatic coefficient of the ship, B is the beam, L is the length of the ship, m is the mass, T is the draft.

[0064] As an example, the moment of inertia about the pitch axis of the moment of inertia of the pitch motion is: where, is the moment of inertia about the pitch axis, m is the mass, L is the length of the ship.

[0065] As an example, the added mass of the moment of inertia of the heave motion can be obtained by the following regression formula: where, is the added mass, is the coefficient of the waterplane area, T is the draft, B is the beam, m is the mass.

[0066] As an example, the mass m can be achieved by the following formula: wherein is the fluid density, is the displaced volume.

[0067] Furthermore, in step S404, when the roll angle is a roll motion restoring moment that approximately linearly varies will be generated , then the roll motion restoring moment is expressed by the following formula: wherein, is the displacement of the ship, is the metacentric height, is the roll angle. The positions of the center of buoyancy and the center of gravity of the ship under different draft conditions can be calculated using the ship's lines plan and hydrostatic principles, and then the metacentric height is determined.

[0068] Furthermore, in step S405, according to Froude's theory, the roll motion restoring moment can be further expressed as: wherein, is the wave surface angle of the sea wave, is the displacement of the ship, is the metacentric height, is the moment of inertia about the roll axis, is the roll acceleration, is the roll angle. The encounter frequency is introduced, then the wave surface angle can be expressed by the following formula: wherein, is the finite draft correction coefficient; is the finite beam correction coefficient; is the encounter frequency at the wave surface angle; is the acceleration due to gravity; is the encounter frequency; is the encounter angle; is the encounter frequency at the i th sea wave power spectral density function, is the sea wave direction; is the increment of the encounter frequency, , is the maximum value of the encounter frequency, is the minimum value of the encounter frequency; is a random phase uniformly distributed between 0 and 2π; t is the time;n is the number of discrete points of the frequency density spectrum; is the i th angular frequency, ; is the i th encounter frequency.

[0069] As an example, the finite draft correction coefficient can be expressed by the following formula: where d is the draft, k is the wave number.

[0070] Furthermore, the wave number k can be expressed by the following formula: where λ is the wavelength, ω i is the i th angular frequency, g is the acceleration due to gravity.

[0071] As an example, the finite beam correction coefficient can be expressed by the following formula: where λ is the wavelength, is the waterplane area coefficient, B is the beam.

[0072] Furthermore, by introducing the roll motion correction coefficient , the roll motion disturbing moment is: where is the displacement of the ship, is the metacentric height, is the encounter frequency at the wave surface angle, is the encounter frequency, t is the time.

[0073] Furthermore, in step S406, according to the obtained damping moment, inertia moment, restoring moment, and disturbing moment, the dynamic equation of the ship's roll motion can be further expressed by the following formula: where is the roll motion decay coefficient, is the roll acceleration, is the rolling speed, is the rolling angle, is the rolling decay coefficient, is the rolling motion correction coefficient, is the encounter frequency of the wave surface angle under, is the angular frequency, is the natural frequency of the free rolling motion, t is the time.

[0074] As an example, the rolling motion decay coefficient can be expressed as: where, is the rolling motion damping moment, is the rolling motion inertia moment, is the rolling axis inertia moment, is the rolling axis added inertia moment.

[0075] As an example, the natural frequency of the free rolling motion is expressed as: where, is the ship's displacement, is the metacentric height, is the rolling motion inertia moment, is the rolling axis inertia moment, is the rolling axis added inertia moment.

[0076] Furthermore, the encounter frequency of the rolling angle under is: where, is the relative frequency of the wave and the ship's rolling motion, is the dimensionless rolling motion decay coefficient, is the encounter frequency of the wave surface angle under, is the correction coefficient. The relative frequency of the wave and the ship's rolling motion can be expressed as: where, is the angular frequency, is the ship's displacement, is the metacentric height, is the rolling motion inertia moment, is the rolling axis inertia moment, Additional inertia moment for the roll axis.

[0077] As an example, the non-dimensional decay coefficient of the roll motion can be expressed as: where is the roll decay coefficient, is the decay coefficient of the roll motion.

[0078] Furthermore, the i th amplitude-frequency response operator of the roll motion is: where is the encounter angle, is the encounter frequency, is the gravitational acceleration, is the relative frequency of the sea wave and the roll motion of the ship, is the non-dimensional decay coefficient of the roll motion.

[0079] Furthermore, the power spectral density function of the ship's roll motion is: where is the encounter angle, is the encounter frequency, is the gravitational acceleration, is the relative frequency of the sea wave and the roll motion of the ship, is the non-dimensional decay coefficient of the roll motion, V is the ship speed, is the angular frequency, is the power spectral density function of the sea wave, is the sea wave direction.

[0080] As an example, the power spectral density function of the ship's pitch motion is: where is the non-dimensional decay coefficient of the pitch motion, is the encounter angle, is the encounter frequency, is the gravitational acceleration, is the relative frequency of the sea wave and the pitch motion of the ship, V is the ship speed, is the angular frequency, is the power spectral density function of the sea wave, is the sea wave direction. Obtain the power spectral density function of the ship's pitch motion The specific method can refer to the method of obtaining the power spectral density function of the ship's rolling motion in step S40 The specific method will not be elaborated here

[0081] As an example, the relative frequency of the sea wave and the pitching motion of the ship can be expressed as: wherein, is the angular frequency, is the displacement of the ship, is the longitudinal metacentric height, is the pitching motion inertia moment, is the inertia moment about the pitching axis, is the additional inertia moment about the pitching axis

[0082] As an example, the power spectral density function of the ship's heaving motion can be obtained is: wherein, is the non-dimensional decay coefficient of the heaving motion, is the encounter angle, is the encounter frequency, is the gravitational acceleration, is the relative frequency of the sea wave and the heaving motion of the ship, V is the ship speed, is the angular frequency, is the sea wave power spectral density function, is the sea wave direction. The specific method of obtaining the power spectral density function of the ship's heaving motion can refer to the method of obtaining the power spectral density function of the ship's rolling motion in step S40 The specific method will not be elaborated here

[0083] As an example, the relative frequency of the sea wave and the heaving motion of the ship can be: wherein, is the angular frequency, is the displacement of the ship, is the vertical metacentric height, is the heaving motion inertia moment, is the mass, that is , is the added mass

[0084] As an example, the mass m is: wherein, m is the mass, is the fluid density, is the displaced volume.

[0085] In step S50, refer to Figure 1 step S50 therein, and solve the dynamic equation of the ship's rolling motion based on the coefficients of the dynamic equation of the ship's rolling motion, and obtain the time history data of the ship's three-degree-of-freedom rolling motion through inverse Fourier transform.

[0086] As an example, substitute the coefficients of the damping moment, inertia moment, restoring moment, disturbing moment and other coefficients of the obtained dynamic equation of the ship's rolling motion into the dynamic equation of the ship's rolling motion to solve the equation. Further, based on the solution result, perform inverse Fourier transform on the power spectral density function of the ship's rolling motion, which can convert the frequency domain information into time domain information, and obtain the three-degree-of-freedom rolling motion of the ship under any sea conditions. Finally, simulate and calculate the three-degree-of-freedom rolling motion of the ship under different sea conditions to obtain the time history data of the three-degree-of-freedom rolling motion of the ship under any sea conditions.

[0087] As an example, the time history data can be curve-fitted by professional mathematical software or programming tools to intuitively present the motion change process of the ship on the time axis, providing an important basis for ship motion analysis and performance evaluation.

[0088] In one example, refer to Figures 3 to 5 , Figure 3 is the time history data of the rolling motion of a certain large ship when sailing against the waves at a sea state of five and a speed of 12 kn, Figure 4 is the time history data of the pitching motion of a certain large ship when sailing against the waves at a sea state of five and a speed of 12 kn, Figure 5 is the time history data of the heaving motion of a certain large ship when sailing against the waves at a sea state of five and a speed of 12 kn. By reasonably designing the ship structure, or by optimizing the installation and fixing methods of exploration equipment according to the time history data, and further analyzing the time history data of the ship's three-degree-of-freedom rolling motion, the motion stability of the ship under different sea conditions can be deeply understood, the influence of ship motion on equipment can be reduced, and the smooth progress of exploration operations can be ensured.

[0089] It should be understood that although the steps in the flowchart of the accompanying drawings are shown in sequence according to the indication of the arrows, these steps are not necessarily executed in the sequence indicated by the arrows. Unless there is a clear description in this article, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, at least a part of the steps in the accompanying drawings may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed alternately or in turn with at least a part of other steps or sub-steps or stages of other steps.

[0090] In the three-degree-of-freedom real-time motion simulation method of a ship in waves based on power spectrum analysis of the present application, by establishing a wave simulation model based on the frequency density spectrum, the characteristics of waves under real sea conditions can be accurately simulated, providing a reliable environmental basis for ship motion analysis; by establishing the relationship between the rolling motion of the ship and the wave spectrum, the internal connection between the rolling motion of the ship and the waves can be systematically quantified, and the motion law of the ship in waves can be deeply revealed; by establishing and solving the dynamic equation of the ship's rolling motion, the influence of the ship's own characteristics and wave forces on the ship's motion can be comprehensively considered, and the motion state of the ship under any sea conditions can be accurately predicted. In the case of lacking a large amount of real data, the method of the present application can still obtain accurate ship motion results through reasonable theoretical derivation and calculation, overcoming the limitations of traditional measured data-dependent methods, effectively saving manpower, material resources and financial resources, while improving the simulation efficiency and accuracy, providing strong support for ship design, navigation safety guarantee, ocean engineering operations, etc., and strongly promoting the development of related research and practice in the field of ship engineering.

[0091] In another embodiment, please refer to Figure 6 , the present application also provides a three-degree-of-freedom real-time motion simulation system of a ship in waves based on power spectrum analysis, which may include: a data acquisition module 10, a wave simulation module 20, a dynamic equation construction module 30, and a fitting analysis module 40. Among them, the data acquisition module 10 is used to acquire wave data and ship basic parameters; the wave simulation module 20 is used to establish a wave simulation model based on the frequency density spectrum according to the wave data and ship basic parameters, and construct the power spectral density function of the ship's rolling motion; the dynamic equation construction module 30 is used to establish the dynamic equation of the ship's rolling motion, determine the coefficients, and solve the dynamic equation of the ship's rolling motion; the fitting analysis module 40 is used to obtain the time history data of the ship's three-degree-of-freedom rolling motion according to the solution result of the dynamic equation of the ship's rolling motion and the power spectral density function of the ship's rolling motion, and perform curve fitting and analysis.

[0092] In the above three-degree-of-freedom real-time motion simulation system of a ship in waves based on power spectrum analysis, the data acquisition module 10 collects the wave and ship basic data to provide a reliable basis for subsequent calculations; the wave simulation module 20 establishes a wave simulation model based on the frequency density spectrum and the power spectral density function of the ship's rolling motion to effectively quantify the relationship between the ship and the waves; the dynamic equation construction module 30 constructs and solves the dynamic equation of the ship's rolling motion to accurately describe the ship's motion law; the fitting analysis module 40 uses the solution results of the dynamic equation of the ship's rolling motion and the power spectral density function of the ship's rolling motion to obtain the time history data of the three-degree-of-freedom rolling motion of the ship and perform fitting analysis, so as to be able to efficiently and accurately realize the real-time three-degree-of-freedom motion simulation of arbitrary ship types in arbitrary sea conditions, provide strong support for the research, design, navigation safety guarantee, etc. in the field of ship engineering, and strongly promote the development of related industries.

[0093] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0094] Although this application has been disclosed above with embodiments, it is not intended to limit this application. Any person with ordinary knowledge in the technical field to which this application pertains can make some changes and modifications without departing from the spirit and scope of this application. Therefore, the protection scope of this application shall be subject to that defined by the appended patent application scope.

Claims

1. A three-degree-of-freedom real-time motion simulation method for a ship in waves based on power spectrum analysis, characterized in that: The following steps are involved: Obtain wave data and basic ship parameters; According to the ocean wave data, a wave simulation model based on a frequency density spectrum is established to obtain an ocean wave spectrum; Based on the wave spectrum and the basic parameters of the ship, a power spectrum density function of the ship's swaying motion is established to obtain the relationship between the ship's swaying motion and the wave spectrum; Establishing a dynamic equation of the ship's swaying motion, and solving the coefficients of the dynamic equation of the ship's swaying motion and the power spectral density function of the ship's swaying motion according to the wave data and the basic parameters of the ship; Based on the coefficients of the dynamic equation of the ship's swaying motion, the dynamic equation of the ship's swaying motion is solved, and the time history data of the ship's three-degree-of-freedom swaying motion is obtained through inverse Fourier transformation.

2. The three-degree-of-freedom real-time motion simulation method of a ship in waves based on power spectrum analysis according to claim 1 is characterized in that: According to the wave data, a wave simulation model based on the frequency density spectrum is established to obtain the wave spectrum, including: According to the wave data, establishing a wave spectrum of irregular waves using a frequency density spectrum; The parameters of the wave spectrum of the irregular waves are input into the wave model, the wave simulation model based on the frequency density spectrum is constructed, and the final wave spectrum is obtained.

3. The three-degree-of-freedom real-time motion simulation method of a ship in waves based on power spectrum analysis according to claim 2 is characterized in that: The formula of the wave spectrum of the irregular waves is as follows: Where ω is the wave frequency, is the direction of the waves, is the frequency density spectrum, is the direction distribution function.

4. The three-degree-of-freedom real-time motion simulation method of a ship in waves based on power spectrum analysis according to claim 2 is characterized in that: The ocean wave model is the Gerstner model.

5. The three-degree-of-freedom real-time motion simulation method of a ship in waves based on power spectrum analysis according to claim 2, characterized in that: The frequency density spectrum includes PM spectrum and trinity wave height.

6. The three-degree-of-freedom real-time motion simulation method of a ship in waves based on power spectrum analysis according to claim 1, characterized in that: The formula of the power spectral density function of the ship's swaying motion is as follows: in, is the power spectral density function of the waves, that is, the final wave spectrum; is the direction of the waves; For the swing movement i Amplitude-frequency response operator; is the angular frequency.

7. The three-degree-of-freedom real-time motion simulation method of a ship in waves based on power spectrum analysis according to claim 1, characterized in that: The coefficients of the dynamic equation of the ship's swaying motion include: damping moment, inertia moment, and restoring moment.

8. The three-degree-of-freedom real-time motion simulation method of a ship in waves based on power spectrum analysis according to claim 1, characterized in that: Establishing a dynamic equation of the ship's swaying motion, and solving the coefficients of the dynamic equation of the ship's swaying motion and the power spectrum density function of the ship's swaying motion according to the wave data and the basic parameters of the ship, including: Establishing a dynamic equation of the ship's swaying motion, wherein the dynamic equation of the ship's swaying motion includes: a dynamic equation of the ship's rolling motion, a dynamic equation of the ship's pitching motion, and a dynamic equation of the ship's heaving motion; Determine the damping moment through experiments, wherein the damping moment includes: rolling motion damping moment, pitching motion damping moment, and heaving motion damping moment; Determine the inertia moment by using the regression equation, wherein the inertia moment includes: the inertia moment of the rolling motion, the inertia moment of the pitching motion, and the inertia moment of the heaving motion; Determine the restoring moment according to the basic parameters of the ship, the restoring moment includes: the restoring moment of rolling motion, the restoring moment of pitching motion, and the restoring moment of heaving motion; According to Froude theory, encounter frequency and correction coefficient are introduced to obtain disturbance moment, and the disturbance moment includes: disturbance moment of rolling motion, disturbance moment of pitching motion and disturbance moment of heaving motion; the amplitude-frequency response operator of the rolling motion is determined according to each coefficient, and the power spectrum density function of the ship's rolling motion is obtained, and the amplitude-frequency response operator of the rolling motion includes: the amplitude-frequency response operator of the rolling motion, the amplitude-frequency response operator of the pitching motion and the amplitude-frequency response operator of the heaving motion; the power spectrum density function of the ship's rolling motion includes: the power spectrum density function of the ship's rolling motion, the power spectrum density function of the ship's pitching motion and the power spectrum density function of the ship's heaving motion.

9. The three-degree-of-freedom real-time motion simulation method of a ship in waves based on power spectrum analysis according to claim 8, characterized in that: The formula of the dynamic equation of the ship's swaying motion is as follows: in, is the inertia moment of rolling motion, is the inertia moment of the roll axis, Add the inertia moment of the roll axis, is the rolling motion damping moment, is the restoring moment of the rolling motion, is the rolling motion disturbance moment, is the roll acceleration, is the rolling speed, is the roll angle, is the inertia moment of pitch motion, is the pitch axis inertia moment, Add the inertia moment of the pitch axis, is the pitch motion damping moment, is the restoring moment of pitch motion, is the pitch motion disturbance moment, Pitch acceleration, is the pitch speed, is the pitch angle, is the inertia moment of the heaving motion, For quality, For the additional mass, is the heave motion damping torque, is the restoring torque of the heave motion, is the disturbance torque of the heave motion, is the heave acceleration, is the heave speed, is the heave value.

10. A three-degree-of-freedom real-time motion simulation system for ships in waves based on power spectrum analysis, characterized in that: The three-degree-of-freedom real-time motion simulation system of a ship in waves based on power spectrum analysis comprises: Data acquisition module, used to obtain wave data and basic ship parameters; A wave simulation module, used to establish a wave simulation model based on a frequency density spectrum according to the wave data and the basic parameters of the ship, and to construct a power spectrum density function of the ship's swaying motion; A dynamic equation building module is used to establish a dynamic equation of the ship's swaying motion, determine coefficients, and solve the dynamic equation of the ship's swaying motion; The fitting analysis module is used to obtain the time history data of the three-degree-of-freedom swaying motion of the ship according to the solution results of the dynamic equation of the swaying motion of the ship and the power spectrum density function of the swaying motion of the ship, and to perform curve fitting and analysis.

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