CN117556623A - Digital twinning-based large ship navigation kinematic model construction method - Google Patents
Digital twinning-based large ship navigation kinematic model construction method Download PDFInfo
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Abstract
The invention discloses a digital twinning-based large ship navigation kinematic model construction method, which comprises the following steps: establishing a digital twin model of ship navigation, and analyzing a ship swinging energy spectrum under the condition that the isomerism factors influence the action; analyzing ship swing energy spectrums at natural frequency and encountered frequency by a spectrum analysis method; superposing the ship swinging energy spectrum under the action condition of the influence of the heterogeneous elements on the ship swinging energy spectrum under the encountered frequency to obtain a motion equation of the influence of the regular wave on the ship swinging; superposing motion equations of influence of a plurality of regular waves on ship swaying, and calculating a ship swaying energy spectrum function under irregular waves; converting the ship swinging motion coordinate into a geodetic coordinate system, solving a ship navigation motion equation, adjusting the position and the posture of the ship in real time, and performing motion simulation based on a digital twin model.
Description
Technical Field
The invention belongs to the technical field of digital twinning, and particularly relates to a large ship navigation kinematic model construction method based on digital twinning.
Background
The ship is a complex system integrating multiple subjects such as machinery, electricity, fluid, control, information and the like, for a large ship, the navigation operation of the large ship needs the cooperation of all systems in the ship, the information in the cabin of the large ship is relatively closed, the environment outside the cabin is complex and changeable, the monitoring is difficult during navigation, and the digital unified management and control is lacking in the whole system scheduling at present.
At present, ship motion decisions based on physical models are mainly performed in fixed modes, such as gyratory and Z-line steering, and prediction researches under free steering and host control commands are rarely performed due to lack of real ship data. Meanwhile, the environment in existing predictions is typically based on constant assumptions or single effects. Such as constant winds, currents and waves, do not reflect the true sea conditions and the coupled effects of various environmental factors. On the other hand, when the ship is sailing at sea, the roll angle and the water area required for turning around due to the influence of wind waves are relatively large, and accidents of ship overturning and collision due to improper steering occur.
Along with the intelligent continuous propulsion of ships, the demands for real-time monitoring and prediction of ship navigation states are becoming urgent. Because the marine environment is complex and changeable, the state monitoring and decision making of the ship need multidisciplinary knowledge fusion, and the digital twin technology is a powerful tool for realizing the function. However, the application of the existing digital twin technology on ships is mainly focused on the aspects of equipment model modeling, visual monitoring and the like. For example, the invention patent with publication number CN116309732a discloses a ship motion visualization method based on digital twinning, which obtains real ship information from a plurality of data sources, updates the motion state of the digital twinning ship through kalman filtering, dynamically adjusts the update frequency of the motion state of the twinning ship, and ensures the stable transition of the motion state of the twinning ship during the update of the motion state. The important point is that the visual effect of digital twinning is guaranteed, visual monitoring is facilitated, but effective assistance cannot be provided for ship motion decisions in real time, and early warning cannot be provided for a potential dangerous situation in the ship navigation process.
Disclosure of Invention
In view of the above, the invention provides a digital twinning-based large-scale ship navigation kinematic model construction method, which is used for solving the problem that the prior art cannot provide effective assistance for ship motion decision in real time.
The invention provides a digital twinning-based large ship navigation kinematic model construction method, which comprises the following steps:
establishing a digital twin model of the ship, and analyzing the ship swing energy spectrum under the condition that the heterogeneous elements influence the action;
analyzing ship swing energy spectrums at natural frequency and encountered frequency by a spectrum analysis method;
superposing the ship swinging energy spectrum under the action condition of the influence of the heterogeneous elements on the ship swinging energy spectrum under the encountered frequency to obtain a motion equation of the influence of the regular wave on the ship swinging;
superposing motion equations of influence of a plurality of regular waves on ship swaying, and calculating a ship swaying energy spectrum function under irregular waves;
converting the ship swinging motion coordinate into a geodetic coordinate system, solving a ship navigation motion equation, adjusting the position and the posture of the ship in real time, and performing motion simulation based on a digital twin model.
On the basis of the technical scheme, preferably, the heterogeneous element influence condition comprises the influence of course, navigational speed, wave speed and external acting force on the disturbance frequency of the ship.
On the basis of the above technical solution, preferably, the ship swing energy spectrum under the encountered frequency is:
wherein s is r′ (w e ) To be a ship rocking energy spectrum density function of pitch angle under encountered frequency s θ′ (w e ) To be a ship rocking energy spectrum density function of roll angle under encountered frequency s z (w e ) To meet the ship's roll energy spectrum density function of the head-shake angle under frequency, s (w 0 ) Is the ship swaying energy spectrum under the natural frequency, s (w e ) To meet the ship swaying energy spectrum density function under the frequency, r' a Is the pitch angle, θ' a Roll angle, z a Head rocking angle, ζ a Is the swing angle, w 0 Is of natural frequency, w e To encounter frequency, v is the linear velocity of the wobble and μ is the wave angle.
On the basis of the above technical solution, preferably, before the motion equation for superimposing the influence of the plurality of regular waves on the ship swaying further includes:
based on an empirical formula of sea wave spectrum, the swing of the ship body caused by the unit regular wave is analyzed, and the unit wave amplitude and the ship running factor are calculated by adopting the following formula:
ξ n ＝a n cos(w n t+ε n )
Y n ＝Y y ξ(w n )cos(ω n t+ε n )
wherein a is n For unit regular wave amplitude, w n For the frequency of the unit regular wave epsilon n The phase angle of the unit regular wave is randomly changed between 0 pi and 2 pi, and xi n A unit rule amplitude function; y is Y n As an amplitude function of the vessel sway under the influence of unit regular waves, Y yξ (w n ) Is a ship navigation factor.
On the basis of the above technical solution, preferably, the formula for calculating the ship rocking energy spectrum function under the irregular wave is:
wherein S is yξ (w) is a ship swaying energy spectrum function under irregular waves, w is the wave frequency, deltaw is the derivative of the wave frequency of a certain section, y n Is a function value of the irregular wave amplitude function.
On the basis of the above technical solution, preferably, the converting the ship swaying motion coordinate to the geodetic coordinate system, and adjusting the position and the posture of the ship specifically includes:
tracking the swing angle of the ship according to the ship swing energy spectrum function under the irregular wave;
converting the swing angle of the ship from a dynamic coordinate to a ship-following coordinate system, and then converting the ship-following coordinate system to a geodetic coordinate system;
calculating the centroid coordinates of the ship swing, and calculating the restoring moment of the ship and the incident force of the received waves according to the centroid coordinates and the gravity center;
solving a roll, pitch, yaw, roll, heave and heave motion differential equation in a time domain by adopting a Dragon library tower method;
and respectively judging whether the real-time rolling, pitching, swaying or swaying movement amplitude is larger than a corresponding set threshold value, and if so, adjusting the ship movement position and posture to reduce the ship swaying amplitude.
On the basis of the above technical solution, preferably, the calculation formula of the restoring moment is:
F＝ρVg*X
wherein ρ is the sea water density, g is the gravitational acceleration, V is the ship's drain volume, and X is the abscissa of the centroid;
the wave incident force has the following calculation formula:
wherein, (x, y, z) is the center coordinate of the ship and water contact surface, S is the ship and water contact area, A is the amplitude, w is the wave frequency, t is the time, k is the wave number, h is the water depth, and ψ is the course angle.
On the basis of the above technical solution, preferably, the performing motion simulation based on the digital twin model specifically includes:
and updating a digital twin model of ship navigation based on the real-time navigation data of the ship, and performing real-time ship motion simulation and three-dimensional visual display based on the position and posture adjustment operation of the ship.
Compared with the prior art, the invention has the following beneficial effects:
1) The invention is based on a digital twin technology, in a virtual ship digital twin model, external interference factors such as stroke, wave and the like in the actual navigation environment of a ship are considered, a ship swinging energy spectrum function under irregular waves is analyzed and calculated, a mathematical model of ship navigation motion is established, the swinging motion of the ship in the wave is combined with the ship maneuvering motion, and the position and the posture of the ship are adjusted in real time, so that the ship swinging amplitude is reduced, and effective assistance is provided for ship motion decision while digital simulation is carried out.
2) According to the invention, the ship swaying energy spectrum function under the irregular wave is established by analyzing the swaying of the regular wave of the unit, and the rolling, pitching, head-shaking, swaying and heave motion differential equations are solved by combining the restoring force and the wave incidence force, so that the accuracy of monitoring the ship motion state can be improved.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for constructing a large ship navigation kinematic model based on digital twinning;
fig. 2 is a schematic diagram of a ship motion simulation.
Detailed Description
The following description of the embodiments of the present invention will clearly and fully describe the technical aspects of the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, are intended to fall within the scope of the present invention.
Referring to fig. 1, the invention provides a digital twinning-based large ship navigation kinematic model construction method, which comprises the following steps:
s1, establishing a digital twin model of ship navigation, and analyzing the ship swing energy spectrum under the action condition of the influence of the isomerism elements.
For large-scale marine vessels, the actual sailing state is greatly influenced by wind waves and external acting forces (such as reef impact and the like), so that the influence of regular waves on the disturbance frequency of heterogeneous elements such as heading, navigational speed, wave speed and external acting forces is considered when the sailing kinematic model is carried out, and the ship swinging energy spectrum under the condition that the heterogeneous elements influence is analyzed.
To analyze the effect of the isomerism elements on the rocking spectrum, the individual spectral functions of the isomerism elements are first analyzed. Based on real-time heading, navigational speed, wave speed of sea waves and external acting force, the method analyzes each energy spectrum function of the heterogeneous elements under the comprehensive actions of encountering frequency, encountering wave speed and encountering period.
S2, analyzing the ship swing energy spectrum under the natural frequency and the encountered frequency by a spectrum analysis method.
S21, taking the ship swaying energy spectrum under the natural frequency into consideration, wherein the calculation formulas are respectively as follows:
wherein w is 0 Is natural frequency s r′ (w 0 ) Is a ship swaying energy spectrum density function of pitching angle under natural frequency, s θ′ (w 0 ) Ship rocking energy spectrum density function s being roll angle under natural frequency z (w 0 ) Is a ship swaying energy spectrum density function of the head shaking angle under the natural frequency, s (w 0 ) Is the ship swaying energy spectrum under the natural frequency; r's' a Is the pitch angle, θ' a Roll angle, z a Head rocking angle, ζ a Is the swing angle.
S22, considering the conversion of natural frequency and encountered frequency, the calculation formulas are respectively as follows:
s(w e )dw e ＝s(w 0 )dw 0 (4)
wherein v is the linear velocity of swing, μ is the wave angle
S23, ship swaying energy spectrum under encountering frequency is as follows:
wherein s is r′ (w e ) To be a ship rocking energy spectrum density function of pitch angle under encountered frequency s θ′ (w e ) To be a ship rocking energy spectrum density function of roll angle under encountered frequency s z (w e ) To meet the ship's roll energy spectrum density function of the head-shake angle under frequency, s (w 0 ) Is the ship swaying energy spectrum under the natural frequency, s (w e ) To meet the ship swaying energy spectrum density function under the frequency, r a ' is pitch angle, θ a ' roll angle, z a Head rocking angle, ζ a Is the swing angle, w e To encounter frequencies.
S3, superposing the ship swing energy spectrum under the condition that the heterogeneous elements influence the ship swing energy spectrum under the encountered frequency, and analyzing a motion equation of influence of the regular wave on the ship swing.
Aiming at course and speed, combining with sea wave speed and external acting force, under the comprehensive actions of encountering frequency, encountering wave speed and encountering period, analyzing the influence of regular wave on disturbance frequency of the isomerism elements by superposing each energy spectrum function of the isomerism elements on the ship swaying energy spectrum, and obtaining a motion equation of the influence of the regular wave on the ship swaying.
S4, superposing motion equations of influence of a plurality of regular waves on ship swaying, and calculating a ship swaying energy spectrum function under the irregular waves.
And analyzing the unit swing and the overall swing of the ship by adopting an ocean wave spectrum empirical formula, wherein the unit swing refers to the swing of the ship body caused by unit regular waves.
The Pierson-Moscow spectrum (P-M spectrum) and the wave spectrum empirical formula:
wherein S is ξ (w) is the wave energy spectrum function, ω is the wave frequency, g is the gravitational acceleration, v ωd Is the wind speed on the sea surface.
On the basis, the unit wave amplitude and the ship travel factor are calculated by adopting the following formula:
ξ n ＝a n cos(w n t+ε n ) (11)
Y n ＝Y yξ (w n )cos(ω n t+ε n ) (12)
wherein a is n For unit regular wave amplitude, w n For the frequency of the unit regular wave epsilon n The phase angle of the unit regular wave is randomly changed between 0 pi and 2 pi, and xi n A unit rule amplitude function; y is Y n As an amplitude function of the vessel sway under the influence of unit regular waves, Y yξ (w n ) Is a ship navigation factor.
Since the irregular wave is superimposed by the unit regular wave, the expression Y (t) of the irregular wave is:
n represents the number of superimposed regular waves, s n Is the phase angle of the irregular wave.
Therefore, the invention analyzes the whole swing motion characteristics of the ship in the irregular wave through the motion equation of the superimposed unit regular wave, and calculates the ship swing energy spectrum function under the irregular wave
The formula for calculating the ship swaying energy spectrum function under the irregular wave is as follows:
wherein S is yξ (w) is a ship swaying energy spectrum function under irregular waves, w is the wave frequency, deltaw is the derivative of the wave frequency of a certain section, y n Is a function value of the irregular wave amplitude function.
S5, converting the ship swinging motion coordinate into a geodetic coordinate system, solving a ship navigation motion equation, adjusting the position and the posture of the ship in real time, and performing motion simulation based on a digital twin model.
The ship body point coordinates of a movable coordinate system are obtained from the ship in the motion equation (13), the movable coordinate system takes the center of gravity of the ship as an origin to construct a right-hand coordinate system, and the movable coordinate is firstly converted into a ship-following coordinate system and then into a geodetic coordinate system.
S51, tracking the swing angle of the ship according to the ship swing energy spectrum function under the irregular wave, such as theta' a ，z a ，ξ a 。
S52, converting the swing angle of the ship from a dynamic coordinate to a ship-following coordinate system, and then converting the ship-following coordinate system to a ground coordinate system.
And S53, calculating the centroid coordinates of the ship swing, and calculating the restoring moment of the ship and the incident force of the received waves according to the centroid coordinates and the gravity center.
Swing angle theta' a ，z a ，ξ a After coordinate system conversion, centroid coordinates (X, Y, Z) are calculated.
And calculating according to the centroid coordinates and the gravity center to obtain the recovery moment of the ship, wherein the calculation formula of the recovery moment F is as follows:
F＝ρVg*X
wherein ρ is the sea water density, g is the gravitational acceleration, V is the ship's drain volume, and X is the abscissa of the centroid.
Let (x, y, z) be the center coordinate of the ship and water contact surface, and the contact area of the ship and water be S, the wave incident force F on the surface d The method comprises the following steps:
wherein A is amplitude, w is wave frequency, t is time, k is wave number, h is water depth, and ψ is course angle.
S54, solving roll, pitch, yaw, roll, pitch and heave motion differential equations in a time domain by adopting a Dragon library tower method.
According to the Dalangbeil principle, a method for calculating restoring force and wave incident force is adopted, a Longbean tower method is adopted to solve rolling, pitching, yawing, pitching and heaving coupling motion differential equations in a time domain, and the differential equations are used as a ship kinematic model.
And S55, respectively judging whether the real-time rolling, pitching and yawing movement amplitude is larger than a corresponding set threshold value, and if so, adjusting the ship movement position and posture to reduce the ship swaying amplitude.
For example, if the roll angle is larger than the water inlet angle set by the ship, the navigation state of the ship is adjusted to make the roll angle smaller than the water inlet angle, the ship roll probability is reduced, and the navigation of the ship is driven by changing the coordinates of the ship in the geodetic coordinate system.
And S6, updating a digital twin model of ship navigation based on the ship real-time navigation data, and carrying out real-time ship motion simulation and three-dimensional visual display based on the position and posture adjustment operation of the ship.
As shown in fig. 2, which is a schematic diagram of ship motion simulation, the invention establishes a virtual ship corresponding to a real ship based on a twin data service platform, serves as a digital twin model for ship navigation, and establishes a live model for propagation operation based on navigation data of the real ship, thereby updating the digital twin model for ship navigation in real time, and carrying out three-dimensional visual display on the twin data service platform. In the simulation process, if the ship swinging amplitude of a certain angle is larger than a corresponding set threshold, adjusting the ship movement position and posture to reduce the ship swinging amplitude, and updating the ship state in the three-dimensional visual display process.
The effectiveness of the method is verified through simulation experiments.
According to the standard operability experiment of the ship, the most common application is selected and the most representative rotation experiment is used for simulation calculation, and the characteristic change condition of the ship rotation motion in the stormy waves is considered. The gyratory test can be used for evaluating the rapidness of the gyratory motion of the ship and the size of the required water area, and is one of the most common tests.
Take a certain ocean-going practice ship as an example. The main parameters are as follows: the total length of the ship is 139.80 meters, the water discharge amount is 14680.08 tons, the design waterline length is 130.55 meters, the rudder area is 18.80m square meters, the design draft is 8 meters, and the diameter of the propeller is 4.6 meters.
In calm water without wind and waves, the initial state values of the ship when the ship is subjected to a gyratory real ship test are shown in the following table 1:
TABLE 1 initial State principal parameters for the rotation experiments
On the basis, the heterogeneous elements such as heading, navigational speed, wave speed and external acting force are considered, real-time ship motion simulation and three-dimensional visual display are carried out, real-ship experiments are carried out, errors are within an acceptable range when simulation calculation results are compared with real-ship experiment results, and therefore the mathematical model established by the invention can meet the engineering precision requirement.
In summary, the mathematical model of the ship sailing motion considers the influence of regular waves on the disturbance frequency of heterogeneous elements, the spectrum analysis method is used for analyzing the overall swing of the ship, 6 basic motion modes such as rolling, pitching, swaying and heaving are coupled, enough model precision can be realized, simulation is easy to carry out, and the provided digital twin-based large ship sailing kinematic model construction method can combine the swing motion of the ship in waves with the ship maneuvering motion, adjust the position and the posture of the ship in real time, thereby reducing the swing amplitude of the ship, and providing effective assistance for ship motion decision while carrying out digital simulation.
The invention also discloses an electronic device, comprising: at least one processor, at least one memory, a communication interface, and a bus; the processor, the memory and the communication interface complete communication with each other through the bus; the memory stores program instructions executable by the processor that the processor invokes to implement the aforementioned methods of the present invention.
The invention also discloses a computer readable storage medium storing computer instructions for causing a computer to implement all or part of the steps of the methods of the embodiments of the invention. The storage medium includes: a usb disk, a removable hard disk, a ROM, a RAM, a magnetic disk, or an optical disk, or other various media capable of storing program codes.
The system embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, i.e., may be distributed over a plurality of network elements. One of ordinary skill in the art may select some or all of the modules according to actual needs without performing any inventive effort to achieve the objectives of the present embodiment.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
Claims (8)
1. A method for constructing a model of large vessel navigation kinematics based on digital twinning, the method comprising:
establishing a digital twin model of ship navigation, and analyzing a ship swinging energy spectrum under the condition that the isomerism factors influence the action;
analyzing ship swing energy spectrums at natural frequency and encountered frequency by a spectrum analysis method;
superposing the ship swinging energy spectrum under the action condition of the influence of the heterogeneous elements on the ship swinging energy spectrum under the encountered frequency to obtain a motion equation of the influence of the regular wave on the ship swinging;
superposing motion equations of influence of a plurality of regular waves on ship swaying, and calculating a ship swaying energy spectrum function under irregular waves;
converting the ship swinging motion coordinate into a geodetic coordinate system, solving a ship navigation motion equation, adjusting the position and the posture of the ship in real time, and performing motion simulation based on a digital twin model.
2. The method for constructing the digital twin-based large ship navigation kinematic model according to claim 1, wherein the heterogeneous element influence conditions comprise the influence of heading, navigational speed, wave speed and external acting force on the disturbance frequency of the ship.
3. The method for constructing a digital twin based large ship navigation kinematic model according to claim 2, wherein the ship rocking energy spectrum under the encountered frequency is:
wherein s is r′ (w e ) To be a ship rocking energy spectrum density function of pitch angle under encountered frequency s θ′ (w e ) To be a ship rocking energy spectrum density function of roll angle under encountered frequency s z (w e ) To meet the ship's roll energy spectrum density function of the head-shake angle under frequency, s (w 0 ) Is the ship swaying energy spectrum under the natural frequency, s (w e ) To meet the ship swaying energy spectrum density function under the frequency, r' a Is the pitch angle, θ' a Roll angle, z a Head rocking angle, ζ a Is the swing angle, w 0 Is of natural frequency, w e To encounter frequency, v is the linear velocity of the wobble and μ is the wave angle.
4. The method for constructing a digital twin-based large ship navigation kinematic model according to claim 1, wherein before the motion equation for the influence of the superimposed plurality of regular waves on the ship swing, the method further comprises:
based on an empirical formula of sea wave spectrum, the swing of the ship body caused by the unit regular wave is analyzed, and the unit wave amplitude and the ship running factor are calculated by adopting the following formula:
ξ n ＝a n cos(w n t+ε n )
Y n ＝Y yξ (w n )cos(ω n t+ε n )
wherein a is n For unit regular wave amplitude, w n For the frequency of the unit regular wave epsilon n Phase angle of unit regular wave, inRandom variation between 0 and 2 pi, xi n A unit rule amplitude function; y is Y n As an amplitude function of the vessel sway under the influence of unit regular waves, Y yξ (w n ) Is a ship navigation factor.
5. The method for constructing a digital twin based large ship navigation kinematic model according to claim 4, wherein the formula for calculating the ship rocking energy spectrum function under irregular waves is as follows:
wherein S is yξ (w) is a ship swaying energy spectrum function under irregular waves, w is the wave frequency, deltaw is the derivative of the wave frequency of a certain section, y n Is a function value of the irregular wave amplitude function.
6. The method for constructing a digital twin based large-scale ship navigation kinematic model according to claim 5, wherein the transforming the ship swinging motion coordinate to the geodetic coordinate system, solving the ship navigation motion equation, and adjusting the position and the posture of the ship in real time specifically comprises:
tracking the swing angle of the ship according to the ship swing energy spectrum function under the irregular wave;
converting the swing angle of the ship from a dynamic coordinate to a ship-following coordinate system, and then converting the ship-following coordinate system to a geodetic coordinate system;
calculating the centroid coordinates of the ship swing, and calculating the restoring moment of the ship and the incident force of the received waves according to the centroid coordinates and the gravity center;
solving a roll, pitch, yaw, roll, heave and heave motion differential equation in a time domain by adopting a Dragon library tower method;
and respectively judging whether the real-time rolling, pitching, yawing, swaying, pitching or swaying movement amplitude is larger than a corresponding set threshold value, and if so, adjusting the ship movement position and posture to reduce the ship swaying amplitude.
7. The method for constructing a model of large vessel navigation kinematics based on digital twinning as claimed in claim 6, wherein the calculation formula of the restoring moment F is:
F＝ρVg*X
wherein ρ is the sea water density, g is the gravitational acceleration, V is the ship's drain volume, and X is the abscissa of the centroid;
wave incident force F d The calculation formula of (2) is as follows:
wherein, (x, y, z) is the center coordinate of the ship and water contact surface, S is the ship and water contact area, A is the amplitude, w is the wave frequency, t is the time, k is the wave number, h is the water depth, and ψ is the course angle.
8. The method for constructing a digital twin-based large ship navigation kinematic model according to claim 1, wherein the digital twin-based kinematic model specifically comprises:
and updating a digital twin model of ship navigation based on the real-time navigation data of the ship, and performing real-time ship motion simulation and three-dimensional visual display based on the position and posture adjustment operation of the ship.
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| CN116415463A (en) * | 2023-04-17 | 2023-07-11 | 中船智能科技(上海)有限公司 | Ship simulation state data analysis method |
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