A method for predicting the dynamic response of a ship roll system to a sudden change

Abstract

The application provides a prediction method for the chaotic dynamics of a ship roll system, and relates to the field of dynamics analysis. The method comprises the following steps: establishing a nonlinear dynamics model of the ship roll system; solving the critical state of the nonlinear dynamics model by using the continuation shooting method to obtain an analysis result; obtaining a behavior simulation result by combining the nonlinear dynamics model and the analysis result with a numerical simulation technology; performing numerical simulation on the optimized nonlinear dynamics model by using a GPU parallel computing method to obtain a numerical result; and predicting the chaotic dynamic behavior of the ship roll system and identifying potential catastrophic instability phenomena of the system based on the numerical result and the behavior simulation result. The technical solution has high calculation efficiency and accuracy, can be widely applied to the fields of ship roll instability risk prediction and ship design optimization, and has important engineering application value.

Description

Technical Field

[0001] This application relates to the field of dynamic analysis, and in particular to a method for predicting the abrupt changes in the dynamics of a ship's rolling system. Background Technology

[0002] Ship rolling motion refers to the periodic motion of a ship around its longitudinal axis under the influence of shear waves. Due to the nonlinear nature and complexity of waves in the marine environment, ship rolling motion under shear waves often exhibits strong nonlinear characteristics. The amplitude and frequency of rolling are affected by multiple factors, including wave intensity, hull geometry, and damping effects. Especially in extreme sea states, wave excitation can cause ship rolling motion to enter an unstable state, or even trigger abrupt changes, manifesting as the system transitioning from a stable periodic motion to an unstable state, producing violent oscillations or capsizing, which can lead to ship damage or sinking in severe cases, endangering ship safety. Therefore, accurately predicting the abrupt changes in the ship's rolling system is of great significance for ensuring safe navigation.

[0003] Traditional ship roll studies primarily rely on numerical simulations and theoretical analysis. These methods establish mathematical models and analyze the system's stability and oscillatory behavior by combining wave excitation with the ship's dynamic characteristics. However, the nonlinear nature of ship roll systems renders these methods computationally inefficient and lacking in simulation accuracy. Existing numerical methods typically analyze dynamic responses through simplified assumptions, but they exhibit significant limitations under complex wave conditions or nonlinear ship characteristics. Especially when system parameters approach critical points, abrupt changes often result in bifurcation phenomena, and traditional methods are inefficient in large-scale parameter scanning and critical point determination, making accurate predictions difficult within a reasonable timeframe. Although some research has begun to apply nonlinear dynamics and complex systems theory to ship roll studies, abrupt change prediction methods are still not widely used in practice, particularly in predicting abrupt changes in ship roll. Therefore, a new method is urgently needed to efficiently and accurately predict the abrupt behavior of ship roll systems, helping engineers and designers identify potential instability risks in advance and ensuring the safe operation of ships in complex sea conditions. This patent addresses the shortcomings of existing technologies by providing a new prediction method. By combining extended target shooting method and GPU parallel computing, it can efficiently and accurately predict the abrupt changes in the rolling behavior of a ship, providing a theoretical basis for ship design and operation. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the abrupt changes in the dynamics of a ship's roll system, in order to solve the technical problem that the existing ship roll nonlinear dynamics model is insufficient for predicting catastrophic instability.

[0005] The above-mentioned objective of this application is achieved through the following technical solution:

[0006] S1: Establish a nonlinear dynamic model of the ship's rolling system;

[0007] S2: The critical state of the nonlinear dynamic model is solved by using the extended target shooting method, and the analysis results are obtained;

[0008] S3: Based on the nonlinear dynamics model and analysis results, combined with numerical simulation technology, the behavioral simulation results are obtained;

[0009] S4: Using GPU parallel computing, numerical simulations are performed on the optimized nonlinear dynamics model to obtain numerical results;

[0010] S5: Based on numerical results and behavioral simulation results, predict the abrupt dynamic behavior of the ship's roll system and identify potential catastrophic instability phenomena of the system.

[0011] Optionally, step S1 includes:

[0012] Based on the restoring torque, damping torque, and wave excitation torque, a nonlinear dynamic model of the ship's rolling system is constructed as follows:

[0013]

[0014] in, For the total moment of inertia, The moment of inertia related to the ship's mass, This is the disturbance term of the moment of inertia, representing the change in the moment of inertia of the ship due to structural changes or load changes during actual operation. This indicates the acceleration of a ship's roll. To restore torque, Indicates the roll angle; For damping torque, This refers to the roll angular velocity; For wave excitation torque, This indicates the amplitude of the wave excitation. Indicates the frequency of the wave.

[0015] Optionally, step S1 may further include:

[0016] ;

[0017] in and These are the coefficients of the third and fifth nonlinear restoring moment; This indicates the change in the ship's center of buoyancy height.

[0018] Optionally, step S1 may further include:

[0019]

[0020] in Linear damping coefficient It is the nonlinear cubic damping coefficient.

[0021] Optionally, step S1 may further include:

[0022] Substitute the expressions for the restoring torque and the damping torque into the general equation of motion, and divide by... After normalization, we obtain the nonlinear differential equation describing the ship under the action of shear waves:

[0023]

[0024] in, Indicates the natural rolling frequency of a ship. and It is the nonlinear restoring moment coefficient; It is a linear damping coefficient. It is the third damping coefficient; It is wave excitation force;

[0025] The nonlinear differential equation is transformed into the following state equation form:

[0026]

[0027] in, Indicates the roll angular velocity; It indicates the roll acceleration.

[0028] Optionally, step S2 includes:

[0029] By using the extended target method, the search for periodic solutions to the nonlinear dynamic model is transformed into solving the fixed-point problem of the following Poincaré mapping:

[0030]

[0031] in For state variables; For parameter vectors; The residual function of the Poincaré map is used to measure the difference between the current state of the system and the periodic solution. For the corresponding periodic Poincaré mapping;

[0032] The fixed-point problem is solved using the Newton-Raphson iterative method, as follows:

[0033]

[0034] in For the first The state variable vector at the next iteration; The Jacobi matrix is ​​the Poincaré mapping; It is the identity matrix; In the current state The Poincaré mapping below;

[0035] The calculation satisfies the following initial value problem:

[0036]

[0037]

[0038] in, The system's dynamic equations; It is a time variable; This is the state sensitivity vector, representing the direction and magnitude of the system state change; This is the sensitivity vector of the initial state;

[0039] Through iterative calculation, the state variables are continuously adjusted during the iteration process. This causes the residual to gradually decrease, resulting in a fixed point and a periodic solution. The periodic solution is the critical point of the abrupt change.

[0040] By analyzing the distribution of the Floquet multiplier through the periodic solution, the instability of the ship's rolling system can be determined. When the Floquet multiplier crosses the unit circle, the ship's rolling system undergoes bifurcation or abrupt change, and the bifurcation point is obtained. The analysis results are the critical point of abrupt change and the bifurcation point of the bifurcation phenomenon.

[0041] Optionally, step S3 includes:

[0042] S31: Conduct multi-condition experiments on the target ship or model ship to obtain measured data; the measured data includes: time-domain response data of ship roll angle, angular velocity, angular acceleration and wave excitation torque;

[0043] S32: Based on the analysis results, numerical simulation technology was used to simulate the ship's roll system under different working conditions, and simulation results were obtained. The simulation results include: free decay curve and static restoring moment experimental data.

[0044] S33: Compare the measured data with the simulation results to optimize the damping coefficient, stiffness coefficient, and excitation torque of the nonlinear dynamic model;

[0045] S34: Using the optimized nonlinear dynamic model, dynamic behavior simulations are performed under different parameter combinations to obtain the behavior simulation results.

[0046] Optionally, step S4 includes:

[0047] Divide the state space into There are several small regions, each containing a preset number of initial conditions, as follows:

[0048]

[0049] in Indicates the first The first in the region Initial conditions;

[0050] The state space represents the set of all possible states of a ship's roll system, and the initial conditions represent the initial states selected within each small region; the initial conditions include: roll angle. and roll rate Different initial values;

[0051] All initial conditions for a small region are processed by a single GPU core, specifically including:

[0052] On each GPU core, numerical integration is used to calculate the integral for each initial condition, and the Runge-Kutta method is used to solve the system's state equations.

[0053]

[0054] in, For time step, For time The state at any given moment, The equation of state;

[0055] By performing integral calculations over a preset time, the state equation of the ship's rolling system will tend to a steady-state solution, which is the attractor.

[0056] Stability analysis is performed by calculating the Lyapunov exponent of the ship's rolling system or determining whether the ship's rolling system converges to a periodic solution, thereby obtaining the attractor type and attraction domain range of each small region.

[0057] Based on the attractor type and the range of the attraction domain, determine whether the sub-region belongs to a stable region, a rapidly changing region, or a transition region, and obtain numerical results.

[0058] An electronic device includes a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to enable the electronic device to perform a method for predicting the dynamics of a ship's roll system.

[0059] A computer-readable storage medium storing instructions that, when executed, perform a method for predicting abrupt changes in the dynamics of a ship's roll system.

[0060] The beneficial effects of the technical solution provided in this application are:

[0061] This invention combines nonlinear dynamics modeling and numerical computation techniques to accurately capture the complex dynamic behavior of ship roll systems, with significant advantages, particularly in predicting catastrophic instability phenomena. By employing an extended target method, this invention can effectively track the system's periodic solutions and bifurcation points, thus providing an efficient tool for bifurcation analysis. Furthermore, utilizing GPU parallel computing technology, this invention significantly improves the computational efficiency of attraction domain analysis, meeting the demands for high-efficiency computation in practical applications. This prediction method not only provides theoretical support for ship design but also offers a scientific basis for navigation safety, possessing significant engineering application value. Attached Figure Description

[0062] The present application will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0063] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0064] Figure 2 This is a schematic diagram of ship rolling in an embodiment of the present invention;

[0065] Figure 3 This is a bifurcation diagram of the ship roll system in an embodiment of the present invention;

[0066] Figure 4 This is the attraction field of the ship roll system in the embodiments of the present invention;

[0067] Figure 5 This is the attractor phase diagram of the ship roll system in this embodiment of the invention before the agitation point;

[0068] Figure 6 This is the attractor phase diagram of the ship roll system in this embodiment of the invention after the agitation point;

[0069] Figure 7 This is a Lyapunov index diagram of the ship roll system before and after the agitation point in an embodiment of the present invention.

[0070] Figure 8 This is a schematic diagram of the electronic device structure in the embodiments of this application. Detailed Implementation

[0071] To provide a clearer understanding of the technical features, objectives, and effects of this application, the specific embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0072] The embodiments of this application provide a method for predicting the abrupt changes in the dynamics of a ship's roll system.

[0073] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating the steps of a method for predicting abrupt changes in the dynamics of a ship's roll system, as described in an embodiment of this application, including:

[0074] S1: Establish a nonlinear dynamic model of the ship's rolling system;

[0075] S2: The critical state of the nonlinear dynamic model is solved by using the extended target shooting method, and the analysis results are obtained;

[0076] As one example, the extended target method is used to calculate the nonlinear dynamic model, in which the critical state of the system is gradually approximated by setting initial values ​​and scanning parameters, and the critical point and bifurcation phenomenon of the abrupt change are determined according to the changes in the system response.

[0077] S3: Based on the nonlinear dynamics model and analysis results, combined with numerical simulation technology, the behavioral simulation results are obtained;

[0078] S4: Using GPU parallel computing, numerical simulations are performed on the optimized nonlinear dynamics model to obtain numerical results;

[0079] S5: Based on numerical results and behavioral simulation results, predict the abrupt dynamic behavior of the ship's roll system and identify potential catastrophic instability phenomena of the system.

[0080] This application employs the aforementioned technical solution, constructing a nonlinear dynamic model and combining it with the extended target method to analyze the periodic solutions and bifurcation behavior of a ship's rolling system. GPU parallel computing is used to improve computational efficiency, rapidly identifying the system's abrupt change critical points and stability boundaries. Numerical simulations verify the model parameters, and experimental data are used to conduct a comprehensive analysis of the ship's rolling motion. Finally, by combining attraction domain evolution and Lyapunov exponent analysis, this invention can effectively predict the abrupt change behavior of a ship's rolling system in complex wave environments, providing a theoretical basis for ship design and navigation safety. This method has high computational efficiency and accuracy, and can be widely applied in fields such as ship rolling instability risk prediction and ship design optimization, possessing significant engineering application value.

[0081] This application addresses the potential for abrupt changes and instability in ship roll systems under complex wave conditions by employing the aforementioned technical solution. Currently, traditional ship roll prediction methods suffer from low computational efficiency and cannot accurately predict abrupt changes near critical states, leaving a significant technological gap, particularly in ship design and navigation safety assurance. By combining extended target acquisition and GPU parallel computing, this invention can efficiently and accurately identify the abrupt change critical point of the system, overcoming the limitations of traditional methods in large-scale parameter scanning and nonlinear system analysis. This novel prediction method demonstrates significant innovation in improving computational efficiency and optimizing prediction accuracy, providing a scientific basis for ship design, navigation safety, and marine engineering, and possessing important theoretical research value and practical application prospects. Furthermore, this invention fills a technological gap in this field, offering a complete technical solution with a clearly defined scope of protection, exhibiting significant potential for licensing and engineering application value.

[0082] Step S1 includes:

[0083] Based on the restoring torque, damping torque, and wave excitation torque, a nonlinear dynamic model of the ship's rolling system is constructed as follows:

[0084]

[0085] in, For the total moment of inertia, The moment of inertia related to the ship's mass, This is the disturbance term of the moment of inertia, representing the change in the moment of inertia of the ship due to structural changes or load changes during actual operation. This indicates the acceleration of a ship's roll. To restore torque, Indicates the roll angle; For damping torque, This refers to the roll angular velocity; For wave excitation torque, This indicates the amplitude of the wave excitation. Indicates the frequency of the wave.

[0086] Step S1 also includes:

[0087] ;

[0088] in and These are the coefficients of the third and fifth nonlinear restoring moment; This indicates the change in the ship's center of buoyancy height.

[0089] As one example, for small roll angles Thus, the restoring torque is linear. However, as the roll angle increases, the relationship between the restoring torque and the roll angle becomes nonlinear. To account for this, the restoring torque is usually expressed as a polynomial function of the roll angle, including both linear and nonlinear terms: and These are the third and fifth order nonlinear restoring moment coefficients, which are usually determined by fitting the static stability curve of the ship.

[0090] Step S1 also includes:

[0091]

[0092] in Linear damping coefficient It is a nonlinear cubic damping coefficient;

[0093] As an example, the linear plus cubic damping model reflects the damping effect of the ship's side more accurately than other models because it captures nonlinear damping behavior without requiring an absolute value term.

[0094] Step S1 also includes:

[0095] Substitute the expressions for the restoring torque and the damping torque into the general equation of motion, and divide by... After normalization, we obtain the nonlinear differential equation describing the ship under the action of shear waves:

[0096]

[0097] in, Indicates the natural rolling frequency of a ship. and It is the nonlinear restoring moment coefficient; It is a linear damping coefficient. It is the third damping coefficient; It is wave excitation force;

[0098] The nonlinear differential equation is transformed into the following state equation form:

[0099]

[0100] in, Indicates the roll angular velocity; It indicates the roll acceleration.

[0101] Step S2 includes:

[0102] By using the extended target method, the search for periodic solutions to the nonlinear dynamic model is transformed into solving the fixed-point problem of the following Poincaré mapping:

[0103]

[0104] in For state variables; For parameter vectors; The residual function of the Poincaré map is used to measure the difference between the current state of the system and the periodic solution. For the corresponding periodic Poincaré mapping;

[0105] The fixed-point problem is solved using the Newton-Raphson iterative method, as follows:

[0106]

[0107] in For the first The state variable vector at the next iteration; The Jacobi matrix is ​​the Poincaré mapping; It is the identity matrix; In the current state The Poincaré mapping below;

[0108] The calculation satisfies the following initial value problem:

[0109]

[0110]

[0111] in, The system's dynamic equations; It is a time variable; This is the state sensitivity vector, representing the direction and magnitude of the system state change; This is the sensitivity vector of the initial state;

[0112] Through iterative calculation, the state variables are continuously adjusted during the iteration process. This causes the residual to gradually decrease, resulting in a fixed point and a periodic solution. The periodic solution is the critical point of the abrupt change.

[0113] As one example, the iterative process continuously adjusts the state variables, causing the residual to gradually decrease, and eventually finding a fixed point.

[0114] By analyzing the distribution of the Floquet multiplier through the periodic solution, the instability of the ship's rolling system can be determined. When the Floquet multiplier crosses the unit circle, the ship's rolling system undergoes bifurcation or abrupt change, and the bifurcation point is obtained. The analysis results are the critical point of abrupt change and the bifurcation point of the bifurcation phenomenon.

[0115] In one embodiment, the stability of the system is determined by analyzing the distribution of the Floquet multipliers. When the Floquet multipliers cross the unit circle, the system undergoes bifurcation or abrupt changes; the system's stability varies with the amplitude of the external excitation under different initial values. A changing bifurcation diagram, such as Figure 3 As shown. Among them. The point is a fork bifurcation point. Point and The point is the saddle-node bifurcation point, and the system is accompanied by the occurrence of hysteresis bifurcation; its jump point is... and Lag cycle It consists of a stable red period 1 attractor, a stable black period 1 attractor with a period multiplication sequence, and an unstable sky blue period 1 attractor.

[0116] As one example, the target shooting method selects a series of discrete points in the state space, constructs an objective function that is calculated multiple times to approximate the critical point of the roll system, and optimizes the initial conditions and parameter settings through sensitivity analysis of the system's bifurcation points and related parameters.

[0117] Step S3 includes:

[0118] S31: Conduct multi-condition experiments on the target ship or model ship to obtain measured data; the measured data includes: time-domain response data of ship roll angle, angular velocity, angular acceleration and wave excitation torque;

[0119] As one example, based on a nonlinear dynamic model, numerical simulation technology is used to comprehensively verify and optimize the dynamic behavior of the ship's rolling system under different operating conditions. First, measured data is acquired by conducting multi-condition experiments on the target ship or model ship, collecting time-domain response data for the ship's rolling angle, angular velocity, angular acceleration, and wave excitation torque. This ensures that the measured data covers the transition region from steady state to abrupt change, providing a complete verification range.

[0120] S32: Based on the analysis results, numerical simulation technology was used to simulate the ship's roll system under different working conditions, and simulation results were obtained. The simulation results include: free decay curve and static restoring moment experimental data.

[0121] S33: Compare the measured data with the simulation results to optimize the damping coefficient, stiffness coefficient, and excitation torque of the nonlinear dynamic model;

[0122] As one example, the relevant parameters are optimized by comparing the measured data with the simulation results. The following parameters are adjusted in particular: damping coefficient, which is fitted to the damping component by the free decay curve obtained from the simulation experiment; stiffness coefficient, which is fitted to a polynomial form by the static restoring torque experimental data; and excitation torque, which is determined by the excitation frequency and amplitude through experimental data.

[0123] S34: Using the optimized nonlinear dynamic model, dynamic behavior simulations are performed under different parameter combinations to obtain the behavior simulation results.

[0124] As one embodiment, different parameter combinations include: nonlinear restoring torque coefficient and Damping moment coefficient and .

[0125] As one implementation example, based on the optimized model, dynamic behavior simulations under different parameter combinations are further conducted, with particular attention to the following key characteristics: 1. The amplitude and frequency of periodic solutions, ensuring that the optimized model can accurately reflect the periodic behavior of the system in a steady state; 2. The occurrence and characteristics of chaotic trajectories, such as the matching of Lyapunov exponents and bifurcation diagrams. Furthermore, the model's predictive ability for periodic doubling bifurcation, saddle-node bifurcation, and chaotic attractor transitions is verified by combining bifurcation phenomena observed in experiments. The effectiveness and accuracy of the model and algorithm are further verified by comparing phase diagrams with measured data one by one.

[0126] As one example, by introducing changes in physical quantities such as external wave excitation and ship structural stiffness, the complex nonlinear characteristics of the ship's rolling system are further considered, thereby improving prediction accuracy.

[0127] As one example, simulations under different operating conditions are conducted using measured ship data, including roll angle, angular velocity, and wave excitation, to verify the model's predictive ability for different types of bifurcation phenomena and the effectiveness of the extended target method in identifying agitation points. Attention is paid to the amplitude and frequency of periodic solutions to ensure the model accurately reflects the ship's roll behavior under normal operating conditions. It is also necessary to note the presence of chaotic trajectories in the system, especially when the system approaches an agitation point, and to analyze the system's behavior using methods such as phase diagrams and Lyapunov exponents.

[0128] Step S4 includes:

[0129] As one example, GPU parallelization enables the integration of a large number of initial conditions in a short time, and quickly determines the attractor type and attraction domain boundary of each region, thereby predicting the conditions and probability of abrupt changes. In GPU parallel computing, each small region of the state space can be regarded as an independent task, and each task is assigned to a different GPU core.

[0130] Divide the state space into There are several small regions, each containing a preset number of initial conditions, as follows:

[0131]

[0132] in Indicates the first The first in the region Initial conditions;

[0133] The state space represents the set of all possible states of a ship's roll system, and the initial conditions represent the initial states selected within each small region, such as the roll angle. and roll rate Different initial values;

[0134] All initial conditions for a small region are processed by a single GPU core, specifically including:

[0135] On each GPU core, numerical integration is used to calculate the integral for each initial condition, and the Runge-Kutta method is used to solve the system's state equations.

[0136]

[0137] in, For time step, For time The state at any given moment, The equation of state;

[0138] By performing integral calculations over a preset time, the state equation of the ship's rolling system will tend to a steady-state solution, which is the attractor.

[0139] In one embodiment of this application, if the system state converges to a specific periodic solution or chaotic attractor over a sufficiently long period of time, then the initial condition is considered to belong to that attractor.

[0140] Stability analysis is performed by calculating the Lyapunov exponent of the ship's rolling system or determining whether the ship's rolling system converges to a periodic solution, thereby obtaining the attractor type and attraction domain range of each small region.

[0141] Based on the attractor type and the range of the attraction domain, determine whether the sub-region belongs to a stable region, a rapidly changing region, or a transition region, and obtain numerical results.

[0142] As one implementation, stability determination is typically achieved by calculating the Lyapunov exponent or determining whether the system converges to a periodic solution. Through long-term integration and stability analysis, the attractor type for each small region is determined. Each GPU core outputs the attractor type for that region, along with its corresponding attraction domain range. Figure 4 It is the attraction region corresponding to the coexistence of two periodic three-attractors and one periodic one-attractor. Depending on the type of attractor, it can be further determined whether the region belongs to a stable region, a volatile region, or a transition region.

[0143] As one example, the abrupt change behavior prediction identifies the critical parameter range of the system by performing evolutionary analysis on the attraction domain, and further confirms the possible abrupt change regions using bifurcation diagrams and phase diagrams.

[0144] As one example, by combining numerical results and behavioral simulation results, the present invention can accurately predict the abrupt changes in the rolling behavior of a ship's rolling system in a complex wave environment and identify the stability boundary of the system. Figure 5 and Figure 6 The diagrams show the phases before and after the abrupt change. Figure 7 Analysis of the Lyapunov exponent diagrams before and after the agitation reveals that as the ship's rolling system approaches the agitation point, the attractor transforms from a stable periodic solution into a chaotic attractor. Therefore, by combining meteorological and oceanographic data, ship rolling models and agitation dynamics can be used to predict the arrival of severe sea conditions in advance, plan safe routes, avoid potential agitation and instability zones, and ensure safe navigation.

[0145] As one example, by comparing the changes in the system's attraction domain at different times and under different operating conditions, the critical moment of the system can be determined, providing a theoretical basis for ship roll control and potential instability.

[0146] This application also discloses an electronic device. (See reference...) Figure 8 , Figure 8 This is a schematic diagram of the structure of an electronic device disclosed in an embodiment of this application. The electronic device 500 may include: at least one processor 501, at least one network interface 504, a user interface 503, a memory 505, and at least one communication bus 502.

[0147] The communication bus 502 is used to enable communication between these components.

[0148] The user interface 503 may include a display screen, and optionally, the user interface 503 may also include a standard wired interface or a wireless interface.

[0149] The network interface 504 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface).

[0150] This application also discloses a computer-readable storage medium storing multiple instructions adapted for loading by a processor to execute the above-described method for predicting the dynamic changes in a ship roll system.

[0151] The above are merely exemplary embodiments of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure.

[0152] This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure. The specification and embodiments are to be considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

Claims

1. A method for predicting the abrupt changes in the dynamics of a ship's roll system, characterized in that, The method includes the following steps: S1: Establish a nonlinear dynamic model of the ship's rolling system; S2: The critical state of the nonlinear dynamic model is solved by using the extended target shooting method, and the analysis results are obtained; Step S2 includes: By using the extended target method, the search for periodic solutions to the nonlinear dynamic model is transformed into solving the fixed-point problem of the following Poincaré mapping: in It is a state vector; For parameter vectors; The residual function of the Poincaré map is used to measure the difference between the current state of the system and the periodic solution. For the corresponding periodic Poincaré mapping; The fixed-point problem is solved using the Newton-Raphson iterative method, as follows: in For the first The state variable vector at the next iteration; The Jacobi matrix is ​​the Poincaré mapping; It is the identity matrix; In the current state The Poincaré mapping below; The calculation satisfies the following initial value problem: in, The system's dynamic equations; It is a time variable; This is the state sensitivity vector, representing the direction and magnitude of the system state change; This is the sensitivity vector of the initial state; Through iterative calculation, the state vector is continuously adjusted during the iteration process. This causes the residual to gradually decrease, resulting in a fixed point and a periodic solution. The periodic solution is the critical point of the abrupt change. By analyzing the distribution of the Floquet multiplier through the periodic solution, the instability of the ship's rolling system can be determined. When the Floquet multiplier crosses the unit circle, the ship's rolling system undergoes bifurcation or abrupt change, and the bifurcation point is obtained. The analysis results are the critical point of abrupt change and the bifurcation point of the bifurcation phenomenon. S3: Based on the nonlinear dynamics model and analysis results, combined with numerical simulation technology, the behavioral simulation results are obtained; Step S3 includes: S31: Conduct multi-condition experiments on the target ship or model ship to obtain measured data; the measured data includes: time-domain response data of ship roll angle, angular velocity, angular acceleration and wave excitation torque; S32: Based on the analysis results, numerical simulation technology was used to simulate the ship's roll system under different working conditions, and simulation results were obtained. The simulation results include: free decay curve and static restoring moment experimental data. S33: Compare the measured data with the simulation results to optimize the damping coefficient, stiffness coefficient, and excitation torque of the nonlinear dynamic model; S34: Using the optimized nonlinear dynamic model, dynamic behavior simulations are performed under different parameter combinations to obtain the behavior simulation results; S4: Using GPU parallel computing, numerical simulations are performed on the optimized nonlinear dynamics model to obtain numerical results; Step S4 includes: Divide the state space into There are several small regions, each containing a preset number of initial conditions, as follows: in Indicates the first The first in the region Initial conditions; The state space represents the set of all possible states of a ship's roll system, and the initial conditions represent the initial states selected within each small region; the initial conditions include: roll angle. and roll rate Different initial values; All initial conditions for a small region are processed by a single GPU core, specifically including: On each GPU core, numerical integration is used to calculate the integral for each initial condition, and the Runge-Kutta method is used to solve the system's state equations. in, For time step, For time The state at any given moment, The equation of state; By performing integral calculations over a preset time, the state equation of the ship's rolling system will tend to a steady-state solution, which is the attractor. It is a state vector; For parameter vectors; Stability analysis is performed by calculating the Lyapunov exponent of the ship's rolling system or determining whether the ship's rolling system converges to a periodic solution, thereby obtaining the attractor type and attraction domain range of each small region. Based on the attractor type and the range of the attraction domain, determine whether the small region belongs to the stable region, the abrupt change region, or the transition region, and obtain the numerical results; S5: Based on numerical results and behavioral simulation results, predict the abrupt dynamic behavior of the ship's roll system and identify potential catastrophic instability phenomena of the system.

2. The method for predicting the abrupt changes in the dynamics of a ship's roll system as described in claim 1, characterized in that, Step S1 includes: Based on the restoring torque, damping torque, and wave excitation torque, a nonlinear dynamic model of the ship's rolling system is constructed as follows: in, For the total moment of inertia, The moment of inertia related to the ship's mass, This is the disturbance term of the moment of inertia, representing the change in the moment of inertia of the ship due to structural changes or load changes during actual operation. This indicates the acceleration of a ship's roll. To restore torque, Indicates the roll angle; For damping torque, This refers to the roll angular velocity; For wave excitation torque, This indicates the amplitude of the wave excitation. Indicates the frequency of the wave.

3. The method for predicting the abrupt changes in the dynamics of a ship's roll system as described in claim 2, characterized in that, Step S1 also includes: ； in and These are the coefficients of the third and fifth nonlinear restoring moment; This indicates the change in the ship's center of buoyancy height.

4. The method for predicting the abrupt changes in the dynamics of a ship's roll system as described in claim 3, characterized in that, Step S1 also includes: in Linear damping coefficient It is the nonlinear cubic damping coefficient.

5. The method for predicting the abrupt changes in the dynamics of a ship's roll system as described in claim 4, characterized in that, Step S1 also includes: Substitute the expressions for the restoring torque and the damping torque into the general equation of motion, and divide by... After normalization, we obtain the nonlinear differential equation describing the ship under the action of shear waves: in, Indicates the natural rolling frequency of a ship. and It is the nonlinear restoring moment coefficient; It is a linear damping coefficient. It is the third damping coefficient; ; The nonlinear differential equation is transformed into the following state equation form: in, Indicates the roll angular velocity; It indicates the roll acceleration.

6. An electronic device, characterized in that, The device includes a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to cause the electronic device to perform the method as described in any one of claims 1-5.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores instructions that, when executed by a computer, perform the method as described in any one of claims 1-5.

Images