Method for evaluating ship parameter roll motion probability in irregular wave based on AIS data

Abstract

The application discloses a kind of non-regular wave ship parameter roll motion probability evaluation method based on AIS data, comprising: establishing the probability density model of ship density, solving the probability density function to obtain ship density map;According to ship density map, from representative route area, equidistantly select test point, calculate the non-regular wave occurrence probability P1 of target sea area at specific test point;Establish parameter roll motion differential equation, calculate the probability P2 of ship in non-regular wave that parameter roll motion occurs;According to P1, P2, the probability P of ship in non-regular wave that parameter roll motion occurs at specific test point is calculated, and then the total probability of ship parameter roll motion on representative route is obtained.The application can improve ship design, reduce the parameter roll of ship, and provide reasonable suggestions for how to avoid parameter roll in actual navigation of ship, improve the safety of ship navigation in wind and wave.

Description

Technical Field

[0001] This invention belongs to the field of ship nonlinear motion analysis, and in particular relates to a method for evaluating the probability of ship rolling motion parameters in irregular waves based on AIS data. Background Technology

[0002] Parametric roll is one of the five failure modes in second-generation ship integrity stability, and it is currently the most extensively studied stability failure mode both domestically and internationally. As a relatively unique roll phenomenon, parametric roll is based on the principle that when a ship navigates in longitudinal or diagonal waves, the shape of the wave surface and the area of ​​the waterline change over time, causing periodic changes in the ship's restorative characteristics. The wetted surface area differs when the wave crest is amidships versus when the wave trough is amidships, and the waterline area also changes significantly. Essentially, it is a strongly nonlinear phenomenon caused by the time-history variation of ship motion parameters, not directly generated by external excitation, and it poses a significant threat to ship navigation and transportation at sea.

[0003] Early studies have shown that parametric rolling motion of ships requires certain triggering conditions: the ship is sailing head-on or with the waves; the frequency of the waves encountered is approximately twice the ship's natural rolling frequency; the wavelength of the waves encountered is approximately equal to the ship's length; the wave height encountered is greater than a critical value; and the ship's own rolling damping is relatively small. Current research on parametric rolling motion in irregular waves mainly employs three methods: nonlinear dynamics, direct numerical simulation, and model testing. Among these, nonlinear dynamics, with its low computational cost, high efficiency, and low cost, plays an irreplaceable role in the study of parametric rolling motion and can be used as the primary research method for investigating the mechanism of parametric rolling.

[0004] Currently, most research on ship navigation safety is based on a single point on an existing route. However, from a ship operation perspective, wave angle and sea state distribution along the ship's trajectory have a significant impact on the ship's nonlinear motion. Therefore, it is necessary to fully assess and analyze the impact of the route and random sea state distribution on the ship's parametric roll motion, and to comprehensively consider the impact of these factors on the ship's stability and seakeeping under complex sea conditions. Summary of the Invention

[0005] Purpose of the Invention: The purpose of this invention is to provide a method for assessing the probability of parametric roll motion of ships in irregular waves based on AIS data. A ship density calculation model is established based on AIS data and a standard ship. The probability density function of ship density is estimated using a nonparametric kernel density method. The ship density map obtained from the probability density function is used to find representative routes in a certain sea area. The probability of parametric roll motion occurring on these representative routes is studied. To overcome the limitations of numerical methods in nonlinear parametric roll motion of ships in irregular waves, a nonlinear dynamic probability analysis method for parametric roll motion of ships in irregular waves is proposed. This method uses nonlinear dynamic analysis to analyze the probability of parametric roll motion of ships in irregular waves, providing an analytical method and a basis for safe navigation.

[0006] Technical solution: The present invention provides a method for evaluating the probability of ship roll motion in irregular waves based on AIS data, comprising the following steps:

[0007] Step 1: Select AIS data for the target sea area within the target time period, establish a probability density model of ship density, and solve the probability density function of ship density based on the nonparametric kernel density estimation method to obtain the ship density map;

[0008] Step 2: Based on the vessel density map, preset the critical vessel density threshold and define areas with high traffic volume. Identify and characterize representative shipping routes within these areas. Then, select several test points at equal intervals from these representative shipping routes. Based on wave dispersion data from the sea area near each test point, calculate the probability of irregular waves appearing in the target sea area at a specific test point. ;

[0009] Step 3: Establish the ship's motion coordinate system and the differential equation of the ship's parametric roll motion in irregular waves, determine the ship's restoring moment, and solve the probability density function of the parametric roll motion response in irregular waves using the path integral method to obtain the probability of the ship experiencing parametric roll motion in irregular waves. ;

[0010] Step 4: Based on the probability of irregular waves occurring at a specific test point in the target sea area... The probability of a ship rolling motion in irregular waves. The probability of a ship experiencing parametric rolling motion in irregular waves at a specific test point was calculated. ;

[0011] Step 5: Repeat steps 2-4 to calculate the probability of the ship experiencing parametric rolling motion in irregular waves at each test point, and obtain the total probability of the ship experiencing parametric rolling motion on the representative route.

[0012] Furthermore, step 1 specifically includes the following steps:

[0013] Step 1-1: Assumption , … For random variables The sample, random variable The probability density function is The probability density function of the ship's density is shown in the following equation:

[0014]

[0015] in, It is a random variable. Indicates ship density, Indicates the first One ship density sample, Indicates bandwidth length. For the sample size, Represents the kernel function;

[0016] Step 1-2: Select the Gaussian kernel function as the kernel function in the nonparametric kernel density estimation method. The formula for the Gaussian kernel function is as follows:

[0017]

[0018] Steps 1-3: Select as As bandwidth;

[0019] Steps 1-4: The probability density function of the ship density obtained by the nonparametric kernel density estimation method is shown below:

[0020]

[0021] The ship density map was obtained.

[0022] Furthermore, in step 2, 6-8 test points are selected at equal intervals from representative route areas.

[0023] Furthermore, in step 2, based on the wave dispersion data of the sea area near each test point, the probability distribution map of irregular waves appearing in the wave height-period joint probability density data is obtained by using the ratio of the number of occurrences of irregular waves with different specific combinations of meaningful wave heights and characteristic periods to the total number of observations in the wave dispersion data. This yields the probability of irregular waves appearing in the target sea area at a specific test point. ,in:

[0024] =Number of occurrences of irregular waves with a specific combination of meaningful wave height and characteristic period / Total number of observations of wave scattering data.

[0025] Furthermore, step 3 specifically includes the following steps:

[0026] Step 3-1: Assuming the ship's motion in the waves is quasi-static, based on the principle of force balance, establish the differential equation for the ship's parametric roll motion, as shown below:

[0027]

[0028] in, For the moment of inertia of the roll, To add roll moment of inertia, The ship's roll angle, The angular velocity of the roll is... This is the roll acceleration. Represents the damping force experienced by the ship. and These are the linear damping coefficient and the cubic nonlinear damping coefficient, respectively. Represents the roll restoring torque. Represents the wave force experienced by the ship;

[0029] Step 3-2: Determine the ship's restoring moment:

[0030] Determining the ship's restoring moment is crucial for solving the aforementioned equations and studying the ship's parametric roll motion. There are two main methods: one is the direct solution method, which divides the initial metacentric height in waves into two parts: the initial metacentric height in still water and the variation in the wave height. Through detailed derivation, the ship's initial metacentric height in waves can be obtained, and the change in initial metacentric height with respect to wave rise can be directly derived. The second method is the indirect roll damping method. Based on Dostal's research, the ship's restoring moment can be expressed as a function of heel angle, wave rise, wave phase angle, and time, as follows:

[0031]

[0032] in, Represents the ship's displacement. Represents wavefront rise, Represents the phase angle, with a range of After obtaining the restoring moment function of the ship in the numerical model, it is then fitted into a function of the roll angle;

[0033] In this invention, the effects of heave and pitch motion on the recovery arm are not considered. Based on the indirect calculation of roll damping, the recovery arm of the ship is obtained through numerical solution using slice theory, and then the roll arm function is simulated.

[0034] Based on the Froude-Krylov hypothesis, wave force and wave moment are obtained by integrating underwater pressure over the underwater wetted surface area:

[0035]

[0036]

[0037] in, Represents the underwater wetted surface area of ​​the ship's hull. It is a position vector. The unit normal vector representing the wetted surface of the hull, underwater pressure. It consists of two parts, namely the hydrostatic pressure and the dynamic water pressure generated by the rise of the wave surface, as shown in the following formula:

[0038]

[0039] in, It is the density of seawater. It is gravitational acceleration. It's the water depth. It's the amplitude. It is the wave number. It is wave speed;

[0040] Pair Integrating, we obtain the restoring torque acting on the ship:

[0041]

[0042] in, For heading angle, The area of ​​each submerged cross section. and Centroid of each submerged cross section Coordinates in the reference coordinate system The pressure gradient coefficient for each cross section is calculated using the following formula:

[0043]

[0044] in, This represents the draft of the ship in various cross sections when it is upright in still water. It represents the waterline width of each cross section when the ship is in an upright position in still water;

[0045] To determine the ship's restoring moment, it is necessary to obtain... The approximate analytical expression will Expanding on the roll angle The combined form of the polynomial and Fourier series is shown in the following equation:

[0046]

[0047] in, Represents the numerical fitting process The highest power taken is ; The number of terms in the polynomial expansion; , The number of terms in the Fourier series expansion; the values ​​of the above variables are determined by the least squares method; , , , The coefficients representing the expansion terms are determined by the results of numerical fitting.

[0048] The expansion and numerical simulation results The difference needs to be minimized, even if the following formula To reach the minimum:

[0049]

[0050] After comprehensively considering the accuracy of numerical fitting and the complexity of subsequent calculations, the final decision was made. , , , and order , , , , , ,So, The expansion of is expressed as:

[0051]

[0052] Due to the random process obtained from irregular wave decomposition , Written as:

[0053]

[0054] in, The coefficients representing the expansion terms are obtained through... and The results of the numerical fitting are determined;

[0055] Step 3-3: Solve for the steady-state probability density function:

[0056] In this invention, to simplify calculations, the colored properties of waves are temporarily disregarded; that is, the waves are assumed to be white noise. Based on the path integral method, the corresponding Fokker-Planck equations are solved in the time domain to obtain the transition probability density of the ship's roll motion evolving over time. Then, the steady-state probability density function of the ship's parametric roll motion response in irregular waves is solved. This invention uses a two-dimensional example, and the specific steps are as follows:

[0057] Considering the effect of random wave external excitation under oblique waves, the equation is... Substitution The differential equations of motion for the ship's degrees of freedom, considering the parametric roll motion, are obtained as follows:

[0058]

[0059] Divide both sides of the above equation by :

[0060]

[0061] In the formula, , , , , , , ;

[0062] Then the formula Transformed into the following expression:

[0063]

[0064] make , , , , Then we have:

[0065]

[0066] make stochastic differential equations This can be transformed into the following system of state equations:

[0067]

[0068] Parametric excitation and wave load As a colored noise sequence, the outputs after passing through linear filters are as shown in the equation. As shown:

[0069]

[0070] in, For the Wiener function; and the formula The following equations are combined to form a six-dimensional random motion differential equation:

[0071]

[0072] The above system of equations can be written as the following Ito stochastic differential equations:

[0073]

[0074] in: and These are the offset coefficient moments and the diffusion coefficient matrix, respectively;

[0075] When the external stimulus is white noise, the response of the dynamic system is a Markov process, and the transition probability density of this process satisfies the initial conditions: Boundary conditions: The solution to the Fokker-Planck equation; the Fokker-Planck equation is shown in the following equation:

[0076]

[0077] Simultaneous transition probability density Satisfy the normalization condition:

[0078]

[0079] in, This is the initial time. The initial roll angle and roll angular velocity matrix; for The roll angle and roll velocity matrix at each moment; For a moment The roll angle; For a moment The roll angular velocity;

[0080] The transition probability density of the ship's roll motion in the time domain is obtained by solving the Fokker-Planck equations using the path integral method, and then the steady-state probability density function of the ship's parametric roll motion is obtained. The probability of roll motion, a parameter of the ship occurring in irregular waves, is obtained. ,in:

[0081]

[0082] The reference angle for the ship's parametric rolling motion.

[0083] Furthermore, in step 3-3, this invention uses the path integral method (PIS) to solve the Fokker-Planck equations to obtain the evolution of the probability distribution of the ship's rolling motion in the time domain. The basic idea of ​​the path integral method is to discretize the system in both space and time, replacing the integration with paths; that is, by connecting short-time probability densities to form a global transition probability density, the joint probability density of the state vector is obtained. The system operates over a short time period... The transition probability density function on is written as:

[0084]

[0085] In the formula: It is the Dirac function; To determine the drift coefficient using the Longokuta method ; The diffusion coefficient is denoted as . for The roll angle at any given moment; for The roll angular velocity at time t, formula Accurate to After obtaining a short period of time After applying the transition probability density function, the system's transition probability density function can be expressed as:

[0086]

[0087] In the formula, ; Initial time time The number of time intervals; Denotes the degree of integration, with a given initial distribution. After that, the time was obtained. The probability density function is:

[0088]

[0089] The path integral method can be used to find the steady-state probability density function of a ship's rolling motion and obtain the probability of rolling motion in irregular waves. .

[0090] Furthermore, step 4 specifically involves: based on the probability of irregular waves occurring in the target sea area. And the parameter of the ship's roll probability in irregular waves The probability of a ship experiencing parametric rolling motion under specific irregular waves in a test point area representing the route is calculated. As shown in the following formula:

[0091] .

[0092] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0093] 1. The present invention provides a nonlinear dynamic probability calculation and analysis method based on AIS data to evaluate the navigation of a ship under the excitation of irregular waves, which can predict the probability of a ship experiencing parametric roll motion while navigating in irregular waves.

[0094] 2. Based on modern nonlinear dynamics theory and methods, this invention considers the effects of irregular waves and uses the path integral method to calculate the probability density function of the ship's rolling motion parameters. The calculation is relatively small, with high accuracy, high efficiency, and low cost.

[0095] 3. The nonlinear dynamics calculation and analysis method of a ship under irregular wave excitation is applicable to various ship types and has strong versatility.

[0096] 4. This invention relates to the analysis theory and method of ship motion in waves, which can be applied to both ship design and ship navigation. Based on this method, ship design can be improved, the parametric roll of the ship can be reduced, and reasonable suggestions can be made on how to avoid parametric roll in actual ship navigation, thereby improving the safety of ship navigation in wind and waves.

[0097] 5. This invention, based on ship and marine engineering hydrodynamics, fundamental conditions for ship navigation, and nonlinear dynamics theory, presents a nonlinear dynamic probabilistic analysis method for parametric roll of ships in irregular waves. According to the characteristics of parametric roll motion of ships in irregular waves, a physical-mathematical model is established by combining ship motion theory, probability theory, and nonlinear dynamics theory. Based on the path integral method, the corresponding Fokker-Planck equations are solved in the time domain to obtain the transition probability density function. According to the boundary and initial conditions of the differential equations, the steady-state probability density function of the ship's parametric roll motion response is obtained, thereby determining the parametric roll motion law of the ship in irregular waves. This allows for the prediction of potential roll instability risks of the ship. Attached Figure Description

[0098] Figure 1 Ship's motion coordinate system;

[0099] Figure 2 Wave dispersion data at one point along the flight path;

[0100] Figure 3 A schematic diagram illustrating the stability of a ship in water;

[0101] Figure 4 The flowchart of the present invention provides a method for assessing the probability of ship roll motion based on AIS data in irregular waves. Detailed Implementation

[0102] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0103] This invention combines ship motion theory with nonlinear dynamics theory, proposes new indicators and concepts for measuring ship motion instability, and establishes an analysis method and process for nonlinear dynamics.

[0104] Nonlinear dynamics calculation and analysis method for ships under irregular wave excitation, the ship's motion coordinate system is as follows: Figure 1 As shown. Figure 1 middle, For the geodetic fixed coordinate system, For the ship's coordinate system, For wave coordinate system, This represents the position of the ship's center of gravity in the geodetic coordinate system. This represents the position of the ship's center of gravity in the wave coordinate system.

[0105] This invention is a nonlinear dynamic calculation and analysis method for evaluating the roll probability of ship parameters based on AIS data under irregular wave excitation. The specific description of the method for analyzing the roll motion of ship parameters is as follows:

[0106] Step 1: Select AIS data for any time period in a certain sea area, such as ship AIS data from January 23 to March 1, 2022, establish a probability density model of ship density, and use the nonparametric kernel density estimation method to solve the probability density function of ship density.

[0107] Assumption , … For random variables The sample, random variable The probability density function is The probability density function of the ship's density is shown in the following equation:

[0108]

[0109] in, It is a random variable. Indicates ship density, Indicates the first One ship density sample, Indicates bandwidth length. For the sample size, Represents the kernel function.

[0110] The Gaussian kernel function is chosen as the kernel function in the nonparametric kernel density estimation method. The formula for the Gaussian kernel function is as follows:

[0111]

[0112] Bandwidth selection: In this article, the bandwidth is directly taken as [bandwidth value]. ;

[0113] Finally, the probability density function of the ship density obtained by the nonparametric kernel density estimation method is shown below:

[0114]

[0115] The probability density function of ship density is calculated using a nonparametric kernel density estimation method, resulting in a ship density map.

[0116] Step 2: Based on the ship density map, select the critical ship density threshold and define areas with high traffic volume. Identify and characterize representative route areas from these areas, and then select seven test points (A, B, C, D, E, F, and G) at equal intervals within the selected representative route areas.

[0117] Based on wave scattering data from the sea areas near seven locations (A, B, C, D, E, F, and G) within the area covered by the route, the probability distribution map of irregular waves in the wave scattering map is obtained by using the ratio of the number of occurrences of irregular waves with different specific combinations of meaningful wave heights and characteristic periods to the total number of observations in the wave height-period joint probability density data. For example, the wave scattering data around one point is shown below. Figure 2 As shown, the probability of irregular waves appearing in the target sea area at a specific test point is thus obtained as follows: ,in:

[0118] =Number of occurrences of irregular waves with a specific combination of meaningful wave height and characteristic period / Total number of observations of wave scattering data.

[0119] Step 3: A nonlinear dynamic analysis method for parametric roll motion of a ship in irregular waves is shown below:

[0120] Assuming the ship's motion in the waves is quasi-static, and based on the principle of force balance, the differential equation for the ship's parametric roll motion is established as follows:

[0121]

[0122] in, For the moment of inertia of the roll, To add roll moment of inertia, The ship's roll angle, The angular velocity of the roll is... This is the roll acceleration. Represents the damping force experienced by the ship. and These are the linear damping coefficient and the cubic nonlinear damping coefficient, respectively. Represents the roll restoring torque, such as Figure 4 As shown, This represents the wave force experienced by the ship.

[0123] Determined restoring moment of the ship

[0124] Determining the ship's restoring moment is crucial for solving the aforementioned equations and studying the ship's parametric roll motion. There are two main methods: one is the direct solution method, which divides the initial metacentric height in waves into two parts: the initial metacentric height in still water and the variation in the wave height. Through detailed derivation, the ship's initial metacentric height in waves can be obtained, and the change in initial metacentric height with respect to wave rise can be directly derived. The second method is the indirect roll damping method. Based on Dostal's research, the ship's restoring moment can be expressed as a function of heel angle, wave rise, wave phase angle, and time, as follows:

[0125]

[0126] in, Represents the ship's displacement. Represents wavefront rise, Represents the phase angle, with a range of After obtaining the restoring moment function of the ship in the numerical model, it is then fitted into a function of the roll angle.

[0127] In this invention, the effects of heave and pitch motion on the recovery arm are not considered. Based on the indirect calculation of roll damping, the recovery arm of the ship is obtained through numerical solution using slice theory, and then the roll arm function is simulated.

[0128] According to the Froude-Krylov hypothesis, the Froude-Krylov force is the main component of wave action, and wave force and wave moment can be obtained by integrating underwater pressure over the underwater wetted surface area:

[0129]

[0130]

[0131] in, Represents the underwater wetted surface area of ​​the ship's hull. It is a position vector. The unit normal vector representing the wetted surface of the hull, underwater pressure. It consists of two parts, namely the hydrostatic pressure and the dynamic water pressure generated by the rise of the wave surface, as shown in the following formula:

[0132]

[0133] in, It is the density of seawater. It is gravitational acceleration. It's the water depth. It's the amplitude. It is the wave number. It's wave speed.

[0134] Pair Integrating, we can obtain the restoring torque acting on the ship:

[0135]

[0136] in, For heading angle, The area of ​​each submerged cross section. and Centroid of each submerged cross section Coordinates in the reference coordinate system The pressure gradient coefficient for each cross section is calculated using the following formula:

[0137]

[0138] in, This represents the draft of the ship in its upright position in still water at various cross sections. It represents the waterline width of each cross section when the ship is upright in still water.

[0139] To determine the ship's restoring moment, it is necessary to obtain... The approximate analytical expression will Expanding on the roll angle The combined form of the polynomial and Fourier series is shown in the following equation:

[0140]

[0141] in, Represents the numerical fitting process The highest power taken is ; The number of terms in the polynomial expansion; , The number of terms in the Fourier series expansion; the values ​​of the above variables are determined by the least squares method. , , , The coefficients representing the expansion terms are determined by the results of numerical fitting.

[0142] The expansion and numerical simulation results The difference needs to be minimized, even if the following formula To reach the minimum:

[0143]

[0144] After comprehensively considering the accuracy of numerical fitting and the complexity of subsequent calculations, the final decision was made. , , , and order , , , , , ,So, The expansion can be expressed as:

[0145]

[0146] Due to the random process obtained from irregular wave decomposition , It can be further written as:

[0147]

[0148] in, The coefficients representing the expansion terms can be obtained through... and The results of the numerical fitting were determined.

[0149] Solve for the steady-state probability density function

[0150] In this invention, to simplify calculations, the colored properties of waves are temporarily disregarded; that is, the waves are assumed to be white noise. Based on the path integral method, the corresponding Fokker-Planck equations are solved in the time domain to obtain the transition probability density of the ship's roll motion evolving over time. Then, the steady-state probability density function of the ship's parametric roll motion response in irregular waves is solved. This invention uses a two-dimensional example, and the specific steps are as follows:

[0151] Considering the effect of random wave external excitation under oblique waves, the equation is... Substitution The differential equation of motion for a ship with one degree of freedom considering the parameterized roll motion is obtained as follows:

[0152]

[0153] Divide both sides of the above equation by :

[0154]

[0155] In the formula, , , , , , , .

[0156] Then the formula It can be transformed into the following expression:

[0157]

[0158] make , , , , Then we have:

[0159]

[0160] make stochastic differential equations This can be transformed into the following system of state equations:

[0161]

[0162] Parametric excitation and wave load As a colored noise sequence, the outputs after passing through linear filters are as shown in the equation. As shown:

[0163]

[0164] in, For the Wiener function. (and the formula) The following equations are combined to form a six-dimensional random motion differential equation:

[0165]

[0166] The above system of equations can be written as the following Ito stochastic differential equations:

[0167]

[0168] in: and These are the offset coefficient moment and the diffusion coefficient matrix, respectively.

[0169] When the external stimulus is white noise, the response of the dynamic system is a Markov process, and the transition probability density of this process satisfies the initial conditions: Boundary conditions: The solution to the Fokker-Planck equation. The Fokker-Planck equation is shown below:

[0170]

[0171] Simultaneous transition probability density Satisfy the normalization condition:

[0172]

[0173] in, This is the initial time. The initial roll angle and roll angular velocity matrix; for The roll angle and roll velocity matrix at each moment; For a moment The roll angle; For a moment The roll angular velocity.

[0174] This invention uses the path integral method (PIS) to solve the Fokker-Planck equations to obtain the transition probability density of the ship's roll motion in the time domain, and then obtains the steady-state probability density function of the ship's parametric roll motion. The probability of roll motion, a parameter of the ship occurring in irregular waves, is obtained. ,in:

[0175]

[0176] The reference angle for the ship's parametric rolling motion.

[0177] The basic idea of ​​the path integral method is to discretize the system in both space and time, replacing the integral with the path itself. That is, by connecting short-time probability densities to form a global transition probability density, the joint probability density of the state vector is obtained. The system operates over a short time interval... The transition probability density function on can be written as:

[0178]

[0179] In the formula: It is the Dirac function; To determine the drift coefficient using the Longokuta method ; The diffusion coefficient is denoted as . for The roll angle at any given moment; for The roll rate at any given moment. (Formula) Accurate to After obtaining a short period of time After applying the transition probability density function to the given information, the system's transition probability density function can be expressed as:

[0180]

[0181] In the formula, ; Initial time time The number of time intervals; Indicates the degree of integration. Given a fixed initial distribution. After that, the time can be obtained. The probability density function is:

[0182]

[0183] Therefore, the steady-state probability density function of the ship's parametric roll motion can be obtained by applying the path integral method, and the probability of the ship experiencing parametric roll motion in irregular waves can be obtained. .

[0184] Step 4: Based on the probability of irregular waves occurring in the target sea area And the probability of rolling of a ship in irregular waves The probability of a ship experiencing parametric rolling motion under specific irregular waves in a test point area representing the route is calculated. As shown in the following formula:

[0185]

[0186] By analogy, based on the wave scattering map of the area covered by the ideal route, the probability of a ship's rolling motion under each random sea state at the test point is calculated.

[0187] Step 5: Repeat steps 2-4 to calculate the probability of the ship experiencing parametric rolling motion in different irregular waves at other test points, and solve for the total probability of the ship experiencing parametric rolling motion on the representative route.

[0188] In summary, the flowchart of the method for evaluating the probability of ship roll motion based on AIS data in irregular waves according to this invention is as follows: Figure 4 As shown.

Claims

1. A method for evaluating the probability of ship roll motion in irregular waves based on AIS data, characterized in that, The probability density function of ship density is solved by selecting AIS data of the target sea area within the target time period to obtain the ship density map. Based on the ship density map, by executing steps 2-5, the total probability of the occurrence of parameter rolling motion of ships on representative routes in the ship density map is obtained. Step 1: Select AIS data for the target sea area within the target time period, establish the probability density function of ship density, and solve the probability density function of ship density based on the nonparametric kernel density estimation method to obtain the ship density map; Step 2: Based on the ship density map, preset the critical ship density threshold and define the high traffic flow area. Identify and characterize the representative route area from this area, and then select several test points at equal intervals from the representative route area. Based on the wave dispersion data of the sea area near each test point, calculate the probability of irregular waves appearing in the target sea area at a specific test point as P1. Step 3: Establish the ship's motion coordinate system and the differential equation of the ship's parametric roll motion in irregular waves, determine the ship's restoring moment, and solve the probability density function of the parametric roll motion response in irregular waves by means of the path integral method to obtain the probability P2 of the ship's parametric roll motion in irregular waves. Step 4: Based on the probability of irregular waves occurring at a specific test point in the target sea area, P1, and the probability of the ship undergoing parametric rolling motion in irregular waves, P2, calculate the probability P of the ship undergoing parametric rolling motion in irregular waves at the specific test point. Step 5: Repeat steps 2-4 to calculate the probability of the ship experiencing parametric rolling motion in irregular waves at each test point, thereby obtaining the total probability of the ship experiencing parametric rolling motion on the representative route.

2. The method for evaluating the probability of ship roll motion in irregular waves based on AIS data according to claim 1, characterized in that, Step 1 specifically includes the following steps: Step 1-1: Assume x1, x2…x n Let x be a sample of random variable x, and let x be the probability density function of random variable x. The probability density function of the ship's density is shown in the following equation: Where x is a random variable, Indicates ship density, x i Let h represent the i-th ship density sample, h represent the bandwidth length, n represent the number of samples, and K represent the kernel function. Step 1-2: Select the Gaussian kernel function as the kernel function in the nonparametric kernel density estimation method. The formula for the Gaussian kernel function is as follows: Steps 1-3: Select h as the bandwidth; Steps 1-4: The probability density function of the ship density obtained by the nonparametric kernel density estimation method is shown below: The ship density map was obtained.

3. The method for evaluating the probability of ship roll motion in irregular waves based on AIS data according to claim 1, characterized in that, In step 2, select 6-8 test points at equal intervals from representative route areas.

4. The method for evaluating the probability of ship roll motion in irregular waves based on AIS data according to claim 1, characterized in that, In step 2, based on the wave dispersion data of the sea area near each test point, the probability distribution map of irregular waves in the wave height-period joint probability density data is obtained by using the ratio of the number of occurrences of irregular waves with different specific combinations of meaningful wave heights and characteristic periods to the total number of observations in the wave dispersion data. This yields the probability of irregular waves occurring in the target sea area at a specific test point, P1, where: P1 = Number of occurrences of irregular waves with a specific combination of meaningful wave height and characteristic period / Total number of observations of wave scattering data.

5. The method for evaluating the probability of ship roll motion in irregular waves based on AIS data according to claim 1, characterized in that, Step 3 specifically includes the following steps: Step 3-1: Assuming the ship's motion in the waves is quasi-static, based on the principle of force balance, establish the differential equation for the ship's parametric roll motion, as shown below: Among them, I φφ Let δI be the moment of inertia of the roll. φφ To add the rolling moment of inertia, φ is the ship's rolling angle. The angular velocity of the roll is... This is the roll acceleration. B1 and B3 represent the damping force experienced by the ship, respectively, and are the linear damping coefficient and the cubic nonlinear damping coefficient. F represents the roll restoring torque. wave Represents the wave force experienced by the ship; Step 3-2: Determine the ship's restoring moment: The restoring moment of a ship can be expressed as a function of heel angle, wave rise, wave phase angle, and time, as follows: Where Δ represents the ship's displacement, η represents the wave rise, and ψ represents the phase angle, ranging from [0-2π]. The numerical model of the ship's restoring moment function is then fitted into a function of the roll angle. Based on the Froude-Krylov hypothesis, wave force and wave moment are obtained by integrating underwater pressure over the underwater wetted surface area: F=-∫∫ Ω pndΩ (6) Where Ω represents the underwater wetted surface area of ​​the hull. It is a position vector. The unit normal vector represents the wetted surface of the hull. The underwater pressure p consists of two parts: hydrostatic pressure and hydrodynamic pressure generated by the rise of the wave surface, as shown in the following formula: Where ρ is the density of seawater, g is the acceleration due to gravity, and z is the water depth. Where k is wave amplitude, c is wave number, and c is wave speed. Integrating equation (8), we obtain the restoring torque acting on the ship: Where β is the heading angle, and S(x′) is the area of ​​each submerged cross section. and Let B0 be the coordinates of the centroid B0 of each submerged cross section in the reference coordinate system, and F(x′) be the pressure gradient coefficient of each cross section, calculated according to the following formula: Wherein, d(x′) represents the draft of the ship in each cross section when it is upright in still water. It represents the waterline width of each cross section when the ship is in an upright position in still water; To determine the ship's restoring moment, an approximate analytical expression for GZ(φ,η,Ψ) is needed. GZ(φ,η,Ψ) can be expanded into a combination of a polynomial and a Fourier series with respect to the roll angle φ, as shown in the following equation: Where, N φ This represents the highest power that φ takes during the numerical fitting process, which is 2N. φ +1; N k N is the number of terms in the polynomial expansion; S N C The number of terms in the Fourier series expansion; the values ​​of the above variables are determined by the least squares method; Q, Q S Q C , The coefficients representing the expansion terms are determined by the results of numerical fitting. GZ app The difference between the expansion of (φ,η,ψ) and the numerical simulation result GZ(φ,η,ψ) needs to be minimized, that is, the following equation E is minimized: After comprehensively considering the accuracy of numerical fitting and the complexity of subsequent calculations, N was finally determined. φ =2, N k =0, N S =1, N C =1, and let So, GZ app The expansion of (φ,η,ψ) is expressed as: Due to the random process η obtained from irregular wave decomposition c =ηcos(ψ), GZ app (φ,η,ψ) can be written as: GZ app (φ,η,ψ)=q1φ+q2φ 3 +q3φ 5 +q4h c f (14) Where, q i (i = 1, 2, 3, 4) represent the coefficients of the expansion term, obtained through GZ. app The results of the numerical fitting between (φ,η,ψ) and GZ(φ,η,ψ) are determined; Step 3-3: Solve for the steady-state probability density function: Considering the effect of random wave external excitation under oblique waves, substituting equation (14) into equation (4), we obtain the differential equation of motion of the ship's degrees of freedom considering parametric roll motion: Divide both sides of the above equation by I. φφ +δI φφ : In the formula, Equation (16) is then transformed into the following expression: make ξ1(t)=p(t), ξ2(t)=f wave (t), then we have: Let x1 = φ; The stochastic differential equation (18) is transformed into the following system of state equations: Parametric excitation and wave load ξ k (t) is a colored noise sequence, which is output after passing through a linear filter, as shown in equation (20): Among them, W k (t) is the Wiener function; combined with equation (19), it forms a six-dimensional random motion differential equation: The above system of equations can be written as the following Ito stochastic differential equations: dX=m(X,t)dt+Q(X,t)dW(t) (22) Where m(X,t) and Q(X,t) are the offset coefficient moment and the diffusion coefficient matrix, respectively; When the external excitation is white noise, the response of the dynamic system is a Markov process, and the transition probability density of this process satisfies the initial condition: P(X,t′|X′,t′)=δ(XX′) and the boundary conditions: The solution to the Fokker-Planck equation P(-∞,t∣X′,t′)=P(+∞,t∣X′,t′)=0; the Fokker-Planck equation is shown below: Meanwhile, the transition probability density P(X,t|X′,t′) satisfies the normalization condition: ∫∫P(X,t∣X′,t′)dx1dx2dx3dx4dx5dx6=1 (24) Where t′ is the initial time; X′ is the roll angle and roll velocity matrix at the initial time; X is the roll angle and roll velocity matrix at time t; x1 is the roll angle at time t; x2 is the roll velocity at time t1; The transition probability density of the ship's roll motion in the time domain is obtained by solving the Fokker-Planck equation using the path integral method. This leads to the steady-state probability density function p(x1) of the ship's parametric roll motion, and finally the probability P2 of the ship experiencing parametric roll motion in irregular waves. φ0 is the reference angle for the ship to undergo parametric rolling motion.

6. The method for evaluating the probability of ship roll motion in irregular waves based on AIS data according to claim 5, characterized in that, In step 3-3, the path integral method discretizes the system in both space and time, replacing the integral with the path. That is, it connects short-time probability densities to form a global transition probability density, thus obtaining the joint probability density of the state vector. The transition probability density function of the system over a small time interval τ (τ = tt′) is written as: In the formula: δ is the Dirac function; r i (x′) represents the drift coefficient m obtained using the Longokuta method. i (x′); γ 2 x is the diffusion coefficient; x1′ is the roll angle at time t′; x2′ is the roll angular velocity at time t′, and equation (26) is accurate to τ. 2 After obtaining the transition probability density over a short time interval τ, the system's transition probability density function is expressed as: In the formula, t k =t′+kτ; t=t S ;X=X (S) ;X′=X (0) S represents the initial time t' and the time t = t. s The number of time intervals; R n (S-1) Let ω(X) represent the degree of integration, given a fixed initial distribution. (0) After that, the probability density function at time t is obtained as follows: The path integral method can be used to find the steady-state probability density function of the ship's parametric roll motion and obtain the probability P2 of the ship's parametric roll motion in irregular waves.

7. The method for evaluating the probability of ship roll motion in irregular waves based on AIS data according to claim 1, characterized in that, Step 4 specifically involves calculating the probability P of a ship undergoing parametric rolling motion in a specific irregular wave in the test point area representing the route, based on the probability P1 of irregular waves occurring in the target sea area and the parametric rolling probability P2 of the ship in the irregular waves, as shown in the following formula: P = P1P2 (29).

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