Fast Laplace Domain Calculation Method for Hydrodynamic Response of Deep-Sea Mining Vessels

Abstract

This invention belongs to the field of marine engineering technology and provides a fast Laplace domain calculation method for the hydrodynamic response of deep-sea mining vessels. The method involves segmenting a continuous external wave excitation load signal; constructing the coupled motion control equations of the deep-sea mining vessel; solving for the displacement response, velocity response, and dynamic positioning system thrust in the Laplace domain; and further iteratively solving for the natural and forced responses of the deep-sea mining vessel in each segment of the time history to obtain the dynamic response, including displacement response, velocity response, and dynamic positioning system thrust; repeating this process until the dynamic response of the deep-sea mining vessel under all segmented time histories of external loads is obtained. This method solves for the response of the dynamically positioned deep-sea mining vessel through pole-residue algebraic operations in the Laplace domain, accurately simulating the coupling effect caused by external loads and the dynamic positioning system.

Description

Technical Field

[0001] This invention relates to the field of marine engineering technology, specifically to a fast Laplace domain calculation method for the hydrodynamic response of deep-sea mining vessels. Background Technology

[0002] With the continuous development of deep-sea mining technology, the demand for dynamic positioning (DP) systems for marine structures such as offshore platforms and deep-sea mining vessels is increasing. Deep-sea mining operations typically face ultra-deep water depths of 6,000 meters and complex marine environmental loads, making traditional anchoring methods inadequate for the high-precision positioning requirements in such deep water. In this context, dynamic positioning systems, through high-precision sensors, thrusters, and control algorithms, enable platforms and vessels to maintain stability under the influence of environmental factors such as wind, waves, and currents, thereby ensuring the safety and stability of deep-sea mining operations.

[0003] Traditional dynamic response analysis of deep-sea mining vessels typically employs time-domain (TD) analysis methods. This approach, by solving the governing equations at each discrete time point, can accurately calculate the vessel's dynamic response. However, TD analysis methods are computationally expensive, especially in complex marine environments, resulting in lengthy computation times and low efficiency. Therefore, improving computational efficiency and reducing computation time has become a crucial issue in the study of dynamic positioning of deep-sea mining vessels.

[0004] In recent years, novel methods, such as the pole-residue method based on the Laplace domain, have been proposed and applied to the dynamic response analysis of floating structures. This method transforms the dynamic response of the system into poles and residuals through the Laplace transform, thereby significantly improving computational efficiency. Compared with traditional time-domain methods, the pole-residue method can significantly reduce computation time while maintaining high accuracy. However, existing pole-residue methods cannot achieve coupled computation between the floating body and the dynamic positioning system, and in the analysis of multi-degree-of-freedom systems, how to effectively calculate the system's poles and residuals and overcome the problem of numerical singularity remains a challenge. Summary of the Invention

[0005] The purpose of this invention is to solve the above-mentioned technical problems and provide a fast Laplace domain calculation method for the hydrodynamic response of deep-sea mining vessels.

[0006] To achieve the above objectives, some embodiments of the present invention provide the following technical solutions:

[0007] A fast Laplace domain method for calculating the hydrodynamic response of deep-sea mining vessels includes the following steps:

[0008] S1: Signal of continuous external wave excitation load on a deep-sea mining vessel Perform segmentation processing to obtain External wave excitation load in segmented time history , ;

[0009] S2: Calculate the added mass of the hydrodynamic system of a deep-sea mining vessel and radiation damping Based on the aforementioned radiation damping Calculate the time delay function of the hydrodynamic system of a deep-sea mining vessel. Based on the time delay function and the added mass Calculate the added mass at infinite frequency of the hydrodynamic system of a deep-sea mining vessel. ; for the time delay function Performing a Laplace transform yields the time delay function in pole-residue form. The time delay function based on the pole-residue form Additional mass at infinite frequency Calculate the transfer function and its pole-residue form for the hydrodynamic system of a deep-sea mining vessel in the Laplace domain. .

[0010] S3: Based on the aforementioned time delay function, the added mass at the infinite frequency of the deep-sea mining vessel's hydrodynamic system. A coupled motion control equation for a deep-sea mining vessel is constructed, and a dynamic positioning system model is built based on PID theory. Then, using the Laplace domain pole-residue method, the equation is solved. Segmented time history external wave excitation load Thrust of the dynamic positioning system under action and the motion response of a deep-sea mining vessel, the motion response including displacement response and speed response ;

[0011] S4: According to the... Displacement response of segmented time history and speed response Iteratively solve the first... The natural and forced responses of a deep-sea mining vessel under external hydrodynamic loads are obtained in segmented time histories. Based on the natural and forced responses, the first... The dynamic response of a segmented time-history deep-sea mining vessel, including displacement response. Speed ​​response and dynamic positioning system thrust ;

[0012] S5: Repeat step S4 until the dynamic response of the deep-sea mining vessel under all segmented time-history out-of-history loads is obtained.

[0013] In some embodiments of this application, step S1 includes:

[0014] At fixed time intervals Continuous external wave excitation load signal for deep-sea mining vessels The duration is discretized to obtain discrete sampling time points. :

[0015] ;

[0016] in, For sampling sequence number, This represents the total number of sampling points;

[0017] The entire external wave excitation load time history is divided into... There are several intervals, each interval includes... Each sampling point is used to combine the external wave excitation loads at each sampling point to form a wave excitation load subsequence for each interval. ,Will Combining wave excitation load subsequences, we obtain a piecewise time sequence:

[0018] .

[0019] In some embodiments of this application, based on the radiation damping Calculate the time delay function of the hydrodynamic system of a deep-sea mining vessel. The methods include:

[0020] ;

[0021] in, It is the angular frequency. The cutoff time coefficient, It is the Euler number.

[0022] In some embodiments of this application, based on the time delay function and the added mass Calculate the added mass at infinite frequency of the hydrodynamic system of a deep-sea mining vessel. The methods include:

[0023]

[0024] in: For discrete frequencies, for Added mass at frequency, This represents the total number of frequencies.

[0025] In some embodiments of this application, the time delay function is based on the pole-residue form. Additional mass at infinite frequency Calculate the transfer function of the hydrodynamic system of a deep-sea mining vessel The methods include:

[0026]

[0027] in: For the quality matrix, This is the still water restoring stiffness matrix calculated using ship statics methods. For complex variables in the Laplace field, The equivalent stiffness matrix, , To add artificial stiffness.

[0028] In some embodiments of this application, based on the transfer function The pole-residue model of the transfer function of the hydrodynamic system of a deep-sea mining vessel was obtained. The methods include:

[0029] The transfer function In Replace with To obtain discrete frequencies Discrete frequency response function of the floating hydrodynamic system :

[0030] Discrete frequency response function Perform an inverse Fourier transform to obtain the impulse response function of the floating hydrodynamic system. :

[0031]

[0032] in, It is pi. It is the discrete frequency of the frequency response function. It is time. It is an imaginary number. It is the Euler number. It is a complex exponential function. The number of discrete frequencies of the frequency response function, for the impulse response function By performing a Laplace transform, the pole-residue form model of the transfer function of the hydrodynamic system of a deep-sea mining vessel is obtained. :

[0033]

[0034] in for The First-order poles, yes The The residues corresponding to the first-order poles. For transfer function The number of poles and residues is the same, since the order of the poles and residues is the same. .

[0035] In some embodiments of this application, step S3 includes:

[0036] Constructing the coupled motion control equations for a deep-sea mining vessel:

[0037]

[0038] in, For the mass matrix of deep-sea mining vessels, For virtual time variables, Let be the time delay function of the mining vessel. For the still water recovery stiffness matrix, The equivalent stiffness matrix, For the displacement of deep-sea mining vessels, For the speed of deep-sea mining ships, The acceleration of the deep-sea mining vessel; For wave loads, For the load of the dynamic positioning system, The load on the system under artificial stiffness;

[0039] A dynamic positioning system model is constructed based on PID theory:

[0040]

[0041] in, For the thrust of the dynamic positioning system, This represents the offset of the deep-sea mining vessel from its current position to its initial position. ,in This represents the current position of the mining vessel. This represents the initial position of the mining ship. , , These represent proportional, integral, and differential gains, respectively.

[0042] In the first time segment, assuming the deep-sea mining vessel is displaced... =0, If it is 0, then Substituting into the dynamic system model, we can obtain and If the value is 0, then for the first segment of the time history, only wave loads are considered as external loads. , for:

[0043]

[0044] in: For discrete frequencies, for The corresponding complex coefficients, Represents the total number of discrete frequencies;

[0045] right Performing a Laplace transform, we obtain its pole-residue form:

[0046]

[0047] based on ,as well as The displacement response of a deep-sea mining vessel in the Laplace domain under the first segment of the time history external wave excitation load is expressed as:

[0048]

[0049] Will Rewritten in pole-residue form in the complex plane:

[0050]

[0051] in: , for Residue:

[0052]

[0053]

[0054] right Performing the inverse Laplace transform yields the first piecewise time-history external wave excitation load. Time-domain displacement response of deep-sea mining vessel under action :

[0055]

[0056] right Differentiating, we obtain the first piecewise time-history external load. Speed ​​response of deep-sea mining vessels under action ;

[0057] Calculated , Substituting the values ​​into the dynamic positioning system model, the thrust value of the dynamic positioning system is obtained by solving the problem. The solution obtained Substituting the coupled motion control equations of the deep-sea mining vessel, the system loads under artificial stiffness are obtained by solving the equations. ;

[0058] Based on the solution , Update the first external load. :

[0059]

[0060] Based on the updated first external load Iteratively solve for the external load of the first segmented time history. The time-domain displacement and velocity responses of the deep-sea mining vessel under the action of external loads were calculated until the first segmented time-history external load was obtained. The displacement and velocity responses of the deep-sea mining vessel under the action of the load satisfy the convergence condition; the first time-history external load that satisfies the convergence condition is applied. The displacement and velocity responses of the deep-sea mining vessel under the action are used as the final displacement response of the first piecewise time history. and final speed response ;

[0061] Based on the final displacement response and final speed response , The deep-sea mining vessel's coupled motion control equations and dynamic positioning system model are used to iteratively solve the displacement response of the deep-sea mining vessel under the action of the time history in each segment. Speed ​​response Thrust of dynamic positioning system .

[0062] In some embodiments of this application, step S4 includes:

[0063] Initial displacement and speed Under the influence of the Laplace domain structure, the governing equations for the natural vibration motion of the hydrodynamic system of a deep-sea mining vessel are expressed as follows:

[0064]

[0065] Based on the aforementioned self-vibration motion control equations and the pole-residue model of the transfer function of the deep-sea mining vessel's hydrodynamic system. Displacement in the Laplace domain of the hydrodynamic system of a deep-sea mining vessel The representation of:

[0066] ;

[0067] in:

[0068]

[0069] make We can obtain:

[0070]

[0071] right Perform the inverse Laplace transform and simplify to obtain the first... Natural vibration response of a dynamically positioned deep-sea mining vessel under external loads:

[0072]

[0073] The first The Laplace domain form of the radiation damping load caused by the fluid memory effect in the external load segment is expressed as:

[0074] ;

[0075] in, , The time delay function and velocity are in Laplace domain form:

[0076]

[0077]

[0078] in, and yes The Pole and residue of order, and yes The First-order poles and residues;

[0079] right Performing the inverse Laplace transform yields the first... Segmented Radiation Damping Load:

[0080]

[0081] in, and They are respectively The The poles and residues of the order, the hydrodynamic system of a deep-sea mining vessel in the first order. The external excitation load of the segment can be written as:

[0082]

[0083] right Performing the inverse Laplace transform yields the pole-residue characterization of the external excitation load:

[0084]

[0085] in and yes The Pole and residue of order, Let be the number of poles and residues of the external excitation load, then the th The Laplace domain characterization of forced motion under segmental load can be written as:

[0086]

[0087] in and yes The Pole and residue.

[0088] right Performing the inverse Laplace transform, we obtain the... The time-domain form of forced motion under segmental load is:

[0089] .

[0090] In some embodiments of this application, the method of obtaining the first [response] based on the natural vibration response and the forced response is described. The dynamic response of a segmented time-history deep-sea mining vessel, including displacement response. Dynamic response The methods include:

[0091] Will , Superimpose to obtain the first Displacement response of deep-sea mining vessel under hydrodynamic load Repeat the iteration until the calculations are repeated twice. If the convergence threshold is less than the specified threshold, the first convergence threshold is obtained. Final response results of a deep-sea mining vessel under hydrodynamic load. , and dynamic positioning system thrust .

[0092] Compared with the prior art, the beneficial effects of the technical solution of this application are as follows:

[0093] This invention proposes a rapid calculation method for the hydrodynamic response of a dynamically positioned deep-sea mining vessel based on pole-residue operations. The response of the dynamically positioned deep-sea mining vessel is solved by pole-residue algebraic operations in the Laplace domain. The stability of the numerical solution is increased by introducing artificial stiffness. The corrective coupling effect caused by external loads and the dynamic positioning system is accurately simulated by the time-domain iterative method. This method provides a powerful tool for the dynamic response analysis of deep-sea mining vessels, and is particularly suitable for the dynamic analysis of DP system vessels. Attached Figure Description

[0094] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0095] Figure 1 Flowchart of a frequency domain calculation method for the transient dynamic response of floating marine structures;

[0096] Figure 2 Numerical model diagram of the MT6027 dynamically positioned deep-sea mining vessel disclosed in an embodiment of the present invention;

[0097] Figure 3 The impulse response function of the deep-sea mining vessel system disclosed in the embodiments of the present invention;

[0098] Figure 4a The irregular wave JONSWAP spectrum time history used in the embodiments of the present invention;

[0099] Figure 4b The irregular wave time history used in the embodiments of the present invention;

[0100] Figure 5 This is a comparison diagram of the first stage displacement response of a deep-sea mining vessel under irregular action obtained by the method of the present invention;

[0101] Figure 6 This is a comparison diagram of the first stage velocity response of a deep-sea mining vessel under irregular action obtained by the method of the present invention;

[0102] Figure 7 A comparison diagram of the thrust of the first stage dynamic positioning system of a deep-sea mining vessel under irregular action, obtained by the method of the present invention;

[0103] Figure 8 A comparison diagram of the displacement response of the second segment of the natural vibration motion of a deep-sea mining vessel under irregular action, obtained by the method of the present invention;

[0104] Figure 9A comparison diagram of the velocity response of the second segment of the natural vibration motion of a deep-sea mining vessel under irregular action, obtained by the method of the present invention;

[0105] Figure 10 A comparison diagram of the second-stage radiation damping load of a deep-sea mining vessel under irregular action, obtained by the method of the present invention.

[0106] Figure 11 This is a comparison diagram of the second-stage displacement response of a deep-sea mining vessel under irregular action, obtained by the method of this invention.

[0107] Figure 12 This is a comparison diagram of the second-stage velocity response of a deep-sea mining vessel under irregular action, obtained by the method of this invention.

[0108] Figure 13 A comparison diagram of the thrust of the second stage dynamic positioning system of a deep-sea mining vessel under irregular action, obtained by the method of the present invention;

[0109] Figure 14a This is a comparison diagram of the complete displacement response of a deep-sea mining vessel under irregular action obtained by the method of the present invention;

[0110] Figure 14b for Figure 14a Enlarged view of the displacement response comparison during the 950s-1000s time period;

[0111] Figure 15a This is a comparison chart of the complete velocity response of a deep-sea mining vessel under irregular action obtained by the method of the present invention;

[0112] Figure 15b for Figure 15a Enlarged view of the complete velocity response comparison in the 950s-1000s time period;

[0113] Figure 16a This is a comparison diagram of the thrust of the complete dynamic positioning system of a deep-sea mining vessel under irregular action obtained by the method of the present invention;

[0114] Figure 16b for Figure 16a A magnified view of the system thrust comparison during the 950s-1000s period. Detailed Implementation

[0115] To make the technical problems to be solved, the technical solutions, and the beneficial effects of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0116] The prefixes such as "first" and "second" used in this application embodiment are merely for distinguishing different descriptive objects and do not limit the position, order, priority, quantity, or content of the described objects. The use of ordinal numbers and other prefixes used to distinguish descriptive objects in this application embodiment does not constitute a limitation on the described objects. The description of the described objects is given in the claims or the context of the embodiments, and should not constitute unnecessary restrictions due to the use of such prefixes. Furthermore, in the description of this embodiment, unless otherwise stated, "multiple" means two or more.

[0117] The technical solutions of the embodiments of this application will be described below with reference to the accompanying drawings. In the description of the embodiments of this application, unless otherwise stated, " / " means "or," for example, A / B can mean A or B; the term "and / or" in this document is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone.

[0118] In the embodiments provided in this application, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0119] This application proposes a fast Laplace domain calculation method for the hydrodynamic response of deep-sea mining vessels, including the following steps:

[0120] S1: Signal of continuous external wave excitation load on a deep-sea mining vessel Perform segmentation processing to obtain External wave excitation load in segmented time history , ;

[0121] Step S1 includes:

[0122] At fixed time intervals Continuous external wave excitation load signal for deep-sea mining vessels The duration is discretized to obtain discrete sampling time points. :

[0123] ;

[0124] in, For sampling sequence number, This represents the total number of sampling points;

[0125] The entire external wave excitation load time history is divided into... There are several intervals, each interval includes... Each sampling point is used to combine the external wave excitation loads at each sampling point to form a wave excitation load subsequence for each interval. ,Will Combining wave excitation load subsequences, we obtain a piecewise time sequence:

[0126] .

[0127] S2: Calculate the added mass of the hydrodynamic system of a deep-sea mining vessel and radiation damping Based on the aforementioned radiation damping Calculate the time delay function of the hydrodynamic system of a deep-sea mining vessel. Based on the time delay function and the added mass Calculate the added mass at infinite frequency of the hydrodynamic system of a deep-sea mining vessel. ; for the time delay function Performing a Laplace transform yields the time delay function in pole-residue form. The time delay function based on the pole-residue form Additional mass at infinite frequency Calculate the transfer function and its pole-residue form for the hydrodynamic system of a deep-sea mining vessel in the Laplace domain. .

[0128] The added mass of the floating hydrodynamic system is calculated using the frequency domain three-dimensional potential flow theory. and radiation damping .

[0129] In some embodiments of this application, based on radiation damping Calculate the time delay function of the hydrodynamic system of a deep-sea mining vessel. The methods include:

[0130]

[0131] in, It is the angular frequency. This is the truncation time coefficient, which has no special physical meaning. It is the Euler number.

[0132] In some embodiments of this application, based on a time delay function and added mass Calculate the added mass at infinite frequency of the hydrodynamic system of a deep-sea mining vessel. The methods include:

[0133]

[0134] in: For discrete frequencies, for Added mass at frequency, Let be the total number of discrete frequencies.

[0135] In some embodiments of this application, the time delay function is based on the pole-residue form. Additional mass at infinite frequency Calculate the transfer function of the hydrodynamic system of a deep-sea mining vessel The methods include:

[0136] ;

[0137] in: For the quality matrix, The still water restoring stiffness matrix, calculated using ship statics methods, can be obtained using methods in the prior art. For complex variables in the Laplace field, The equivalent stiffness matrix, , To add artificial stiffness.

[0138] In some embodiments of this application, based on transfer functions The pole-residue model of the transfer function of the hydrodynamic system of a deep-sea mining vessel was obtained. The methods include:

[0139] The transfer function In Replace with To obtain discrete frequencies Discrete frequency response function of the floating hydrodynamic system :

[0140] Discrete frequency response function Perform an inverse Fourier transform to obtain the impulse response function of the floating hydrodynamic system. :

[0141]

[0142] in, It is pi. It is the discrete frequency of the frequency response function. It is time. It is an imaginary number. It is the Euler number. It is a complex exponential function. The number of discrete frequencies of the frequency response function, for the impulse response function By performing a Laplace transform, the pole-residue form model of the transfer function of the hydrodynamic system of a deep-sea mining vessel is obtained. :

[0143]

[0144] in for The First-order poles, yes The The residues corresponding to the first-order poles. For transfer function The number of poles and residues is the same, both being [missing information]. .

[0145] S3: Construct a dynamic positioning system model based on PID theory. Based on the coupled motion control equations and the dynamic positioning system model, construct the coupled motion control equations for the deep-sea mining vessel. Then, based on the PID theory, construct the dynamic positioning system model and, using the Laplace domain pole-residue method, solve for the... Segmented time history external hydrodynamic loads Thrust of the dynamic positioning system under action The motion response of deep-sea mining vessels, including displacement response. and speed response .

[0146] In some embodiments of this application, step S3 includes:

[0147] Based on the Cummins method, the coupled motion control equations for a deep-sea mining vessel are constructed:

[0148]

[0149] in, For the mass matrix of deep-sea mining vessels, For virtual time variables, Let be the time delay function of the mining vessel. For the still water recovery stiffness matrix, The equivalent stiffness matrix, For the displacement of deep-sea mining vessels, For the speed of deep-sea mining ships, The acceleration of the deep-sea mining vessel; For wave loads, For the load of the dynamic positioning system, The load is the system load under artificial stiffness; among them, the dynamic positioning system refers to the position control system mounted on the ship, which uses its own thruster to resist environmental interference such as wind, waves and currents in order to maintain the preset position of the mining vessel.

[0150] A dynamic positioning system model is constructed based on PID theory:

[0151]

[0152] in, For the thrust of the dynamic positioning system, This represents the offset of the deep-sea mining vessel from its current position to its initial position. ,in This represents the current position of the mining vessel. This represents the initial position of the mining ship. , , These represent proportional, integral, and differential gains, respectively.

[0153] In the first time segment, assuming the deep-sea mining vessel is displaced... =0, If it is 0, then Substituting the dynamic positioning system model, we can obtain and If the value is 0, then for the first segment of the time history, only wave loads are considered as external loads. , for:

[0154]

[0155] in: For discrete frequencies, for The corresponding complex coefficients, Represents the total number of discrete frequencies;

[0156] right Performing a Laplace transform, we obtain its pole-residue form:

[0157]

[0158] based on ,as well as The displacement response of a deep-sea mining vessel in the Laplace domain under the first segment of the time history external wave excitation load is expressed as:

[0159]

[0160] Will Rewritten in pole-residue form in the complex plane:

[0161]

[0162] in: , for Residue:

[0163]

[0164]

[0165] right Performing the inverse Laplace transform yields the first piecewise time-history external wave excitation load. Time-domain displacement response of deep-sea mining vessel under action :

[0166]

[0167] right Differentiating, we obtain the first piecewise time-history external load. Speed ​​response of deep-sea mining vessels under action ;

[0168] Calculated , Substituting the values ​​into the dynamic positioning system model, the thrust value of the dynamic positioning system is obtained by solving the problem. The solution obtained Substituting the coupled motion control equations of the deep-sea mining vessel, the system load under artificial stiffness is obtained by solving the equations. ;

[0169] Based on the solution , Update the first external load. :

[0170]

[0171] Based on the updated first external load Iteratively solve for the external load of the first segmented time history. The time-domain displacement and velocity responses of the deep-sea mining vessel under the action of external loads were calculated until the first segmented time-history external load was obtained. The displacement and velocity responses of the deep-sea mining vessel under the action of the load satisfy the convergence condition; the first time-history external load that satisfies the convergence condition is applied. The displacement and velocity responses of the deep-sea mining vessel under the action are used as the final displacement response of the first piecewise time history. and final speed response ;

[0172] Based on the final displacement response and final speed response , The deep-sea mining vessel's coupled motion control equations and dynamic positioning system model are used to iteratively solve the displacement response of the deep-sea mining vessel under the action of the time history in each segment. Speed ​​response Thrust of dynamic positioning system .

[0173] For example, during the iterative calculation, the calculation is performed twice. absolute error between calculated values , until Less than the preset convergence threshold The calculation then stops, and the hydrodynamic response of the dynamically positioned deep-sea mining vessel under the first external load is obtained. , and the thrust results of the dynamic positioning system Based on the response calculation results under the first external load. , The hydrodynamic response under each subsequent segment of load is solved iteratively. , , .

[0174] S4: According to the... Displacement response of segmented time history and speed response Iteratively solve the first... The natural and forced responses of a deep-sea mining vessel under external hydrodynamic loads are obtained in segmented time histories. Based on the natural and forced responses, the first... The dynamic response of a segmented time-history deep-sea mining vessel, including displacement response. Speed ​​response and dynamic positioning system thrust .

[0175] Based on the principle of linear superposition, the first The hydrodynamic response of a dynamically positioned deep-sea mining vessel under external loads can be linearly decomposed into two parts: the natural motion of the floating body caused by the initial displacement and velocity, and the forced motion caused by the external loads. The radiation damping load caused by the fluid memory effect should be considered in the calculation of the forced motion.

[0176] In some embodiments of this application, step S4 includes:

[0177] Initial displacement and speed Under the influence of the Laplace domain structure, the governing equations for the natural vibration motion of the hydrodynamic system of a deep-sea mining vessel are expressed as follows:

[0178]

[0179] Based on the aforementioned self-vibration motion control equations and the pole-residue model of the transfer function of the deep-sea mining vessel's hydrodynamic system. Displacement in the Laplace domain of the hydrodynamic system of a deep-sea mining vessel The representation of:

[0180]

[0181] in:

[0182] make We can obtain:

[0183]

[0184] right Perform the inverse Laplace transform and simplify to obtain the first... Natural vibration response of a dynamically positioned deep-sea mining vessel under external loads:

[0185]

[0186] The first The Laplace domain form of the radiation damping load caused by the fluid memory effect in the external load segment is expressed as:

[0187] ;

[0188] in, , The time delay function and velocity are in Laplace domain form:

[0189]

[0190]

[0191] in, and yes The Pole and residue of order, and yes The First-order poles and residues;

[0192] right Performing the inverse Laplace transform yields the first... Segmented Radiation Damping Load:

[0193]

[0194] in, and They are respectively The The poles and residues of the order, the hydrodynamic system of a deep-sea mining vessel in the first order. The external excitation load of the segment can be written as:

[0195]

[0196] right Performing the inverse Laplace transform yields the pole-residue characterization of the external excitation load:

[0197]

[0198] in and yes The Pole and residue of order, Let be the number of poles and residues for the external excitation load. The number of poles and residues is the same, which is 1 / 2. Then the first The Laplace domain characterization of forced motion under segmental load can be written as:

[0199]

[0200] in and They are The Pole and residue.

[0201] right Performing the inverse Laplace transform, we obtain the... The time-domain form of forced motion under segmental load is:

[0202]

[0203] In some embodiments of this application, the method of obtaining the first [response] based on the natural vibration response and the forced response is described. The dynamic response of a segmented time-history deep-sea mining vessel, including displacement response. Dynamic response The methods include:

[0204] Will , Superimpose to obtain the first Displacement response of deep-sea mining vessel under hydrodynamic load Repeat the iteration until the calculations are repeated twice. If the convergence threshold is less than the specified threshold, the first convergence threshold is obtained. Final response results of a deep-sea mining vessel under hydrodynamic load. , and dynamic positioning system thrust .

[0205] During the calculation process, based on the motion response calculation results of the first segment, the natural motion and forced motion of the second segment under the segmented load are iteratively solved to obtain the motion response of the dynamically positioned deep-sea mining vessel under the external load of the second segment. and and the thrust of the dynamic positioning system And so on, to complete the calculation of each data segment.

[0206] S5: Repeat step S4 until the dynamic response of the deep-sea mining vessel under all segmented time-history out-of-history loads is obtained.

[0207] The following example, using the motion of a dynamically positioned deep-sea mining vessel in the sway degree of freedom, illustrates the specific implementation effect of the method provided by this invention.

[0208] The embodiments of the present invention select a 20,000-ton multi-functional deep-sea mining vessel MT6027 as a numerical example, see... Figure 2 The mining vessel is equipped with a DP3 dynamic positioning system. It is 142.9 m long, 27 m wide, and has a draft of 8 m; its weight is 2.1095 × 10⁷ kg; and its roll, pitch, and bow radii of inertia are 11.66 m, 35.82 m, and 35.82 m, respectively. Its center of gravity coordinates are (0 m, 0 m, 3.6 m), where the coordinate system is... The plane is located on the still water surface. The axis is positive and pointing upwards. This embodiment will calculate along... The six-degree-of-freedom motion response of a dynamically positioned deep-sea mining vessel under the excitation of an irregular wave incident at a 45-degree angle.

[0209] The frequency domain added mass of the mining vessel was calculated using SESAM software. and radiation damping Parameters (frequency range 0.05-2.5 rad / s, frequency interval is...) rad / s, further adding artificial stiffness to the sway, pitch, and yaw degrees of freedom. , , Perform inverse Fourier transform and Laplace transform to obtain the impulse response function. Its pole residue form characterization ,See Figure 3 .

[0210] The irregular wave input in this embodiment is generated by the JONSWAPO wave spectrum:

[0211]

[0212] in , It is the gravitational acceleration constant, the wave direction is incident at 45 degrees, and the spectral peak period is... =0.8135rad / s, significant wave height Irregular waves It will be composed of a series of superimposed waves, and the calculation formula is as follows:

[0213]

[0214] The JONSWAP spectrum of the irregular wave and the corresponding time history of the generated irregular wave are shown in [reference needed]. Figure 4a , Figure 4b .

[0215] The dynamic positioning system of the mining vessel is modeled based on a PID controller. The PID control parameters are determined through iterative debugging. The specific parameter values ​​are shown in Table 1.

[0216] Table 1 PID Controller Parameters

[0217]

[0218] Figure 5 , Figure 6 , Figure 7 The demonstration shows the motion response of the deep-sea mining vessel and the output thrust of the dynamic positioning system under the first segment of external load lasting 50 seconds, and the two are in good agreement. Figure 8 , Figure 9 , Figure 10 This diagram illustrates the natural vibration response and radiation damping load of the mining vessel under the second segment of external loads. The kinematic response and output thrust of the dynamic positioning system of the mining vessel under the first two segments of external loads, obtained through iterative solutions, are shown below. Figure 11 , Figure 12 , Figure 13 Furthermore, by performing subsequent segmented calculations one by one, the response time of the mining vessel and the output thrust time of the dynamic positioning system under the complete external load can be obtained, see... Figure 14a , Figure 14b , Figure 15a , Figure 15b , Figure 16a , Figure 16b .

[0219] This invention proposes a rapid calculation method for the hydrodynamic response of a dynamically positioned deep-sea mining vessel based on pole-residue operations. The response of the dynamically positioned deep-sea mining vessel is solved by pole-residue algebraic operations in the Laplace domain. The stability of the numerical solution is increased by introducing artificial stiffness. The corrective coupling effect caused by external loads and the dynamic positioning system is accurately simulated by the time-domain iterative method. This method provides a powerful tool for the dynamic response analysis of deep-sea mining vessels, and is particularly suitable for the dynamic analysis of DP system vessels.

[0220] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

[0221] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. It should be noted that any modifications, equivalent substitutions, and improvements made by those skilled in the art within the spirit and principles of the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of this patent application should be determined by the scope of the appended claims.

Claims

1. A fast Laplace domain calculation method for hydrodynamic response of a deep sea mining vessel, characterized in that, The method comprises the following steps: S1 : a continuous external wave excitation load signal received by a deep sea mining ship is processed in segments to obtain external wave excitation loads for each segment , ; S2: calculating an added mass of the water dynamic system of the deep-sea mining ship and a radiation damping ; based on the radiation damping , calculating a time delay function of the water dynamic system of the deep-sea mining ship , based on the time delay function and the added mass , calculating an added mass at an infinite frequency of the water dynamic system of the deep-sea mining ship ; performing a Laplace transform on the time delay function , to obtain a time delay function in a pole-residue form ; a time delay function in pole-residue form , additional mass at infinity calculating the transfer function of the hydrodynamic system of a deep sea mining vessel in laplace domain and its pole-residue form representation ; a time delay function in pole-residue form , additional mass at infinite frequency computing laplace domain transfer functions for a hydrodynamic system of a deep sea mining vessel the method comprises: wherein: is a mass matrix, is a hydrostatic restoring stiffness matrix calculated according to the ship statics method, is a complex variable in Laplace domain, is an equivalent stiffness matrix, , is an additional artificial stiffness; S3: an added mass at an infinite frequency of the deep-sea mining ship hydrodynamic system based on the time delay function constructing a deep-sea mining ship coupled motion control equation, constructing a dynamic positioning system model based on a PID theory, according to the coupled motion control equation and the dynamic positioning system model, solving a first-order transfer function of the deep-sea mining ship coupled motion control equation in the Laplace domain by using a pole-residue method under a segmental time history external wave excitation load of a dynamic positioning system thrust and a deep-sea mining ship motion response, the motion response including a displacement response and a velocity response ; S4: according to the first segmented time history of the displacement response , and the velocity response , iteratively solve the natural response and forced response of the deep-sea mining ship under the external hydrodynamic load of the segmented time history of the first segment, based on the natural response and forced response, obtain the dynamic response of the deep-sea mining ship of the first segmented time history, the dynamic response includes the displacement response , the velocity response and the thrust of the dynamic positioning system ; S5: repeating step S4 until the dynamic response of the deep-sea mining ship under all segmented time-varying external loads is obtained.

2. The method according to claim 1, wherein, Step S1 comprises: At fixed time intervals The duration of the continuous external wave excitation load signal of the deep sea mining ship is discretely processed to obtain discrete sampling time points :​ ； wherein is a sample number, is the total number of sample points; The whole external wave excitation load time history is divided into intervals, each interval includes sampling points, the external wave excitation load of each sampling point is combined to form a wave excitation load sub-sequence of each interval , and wave excitation load sub-sequences are combined to obtain a segmented time sequence 。 3. The quick Laplace domain calculation method of the hydrodynamic response of a deep sea mining vessel according to claim 1, characterized in that: A method of calculating a time delay function of a hydrodynamic system of a deep sea mining vessel based on said radiation damping comprises:​ wherein is the circular frequency, is the cut-off time coefficient, is Euler's number.

4. The method according to claim 1 or 3, characterized in that: based on the time delay function and the added mass , a method for calculating the added mass of a hydrodynamic system of a deep-sea mining vessel at infinite frequency comprises: where: is the number of discrete frequencies, is the number of discrete frequencies, is the additional mass at frequency, is the total number of discrete frequencies.

5. The quick Laplace domain calculation method of the hydrodynamic response of a deep sea mining vessel according to claim 1, characterized in that: based on the transfer function a method of obtaining a pole-residue form model of a transfer function of a hydrodynamic system of a deep sea mining vessel comprises: replacing in the transfer function with , resulting in a discrete frequency response function of the floating hydrodynamic system at discrete frequencies : : Discrete frequency response function performing an inverse Fourier transform to obtain an impulse response function of the floating hydrodynamic system : where is the ratio of a circle's circumference to its diameter, is the discrete frequency of the frequency response function, is time, is the imaginary unit, is the Euler number, is the complex exponential function, is the number of discrete frequencies of the frequency response function, and is the Laplace transform of the impulse response function : wherein is the pole of order is the residue corresponding to the pole of order is the number of poles and residues of the transfer function G(s).

6. The quick Laplace domain calculation method of the hydrodynamic response of a deep sea mining vessel according to claim 5, characterized in that: Step S3 comprises: The coupled motion control equation of the deep-sea mining ship is constructed: wherein, is the mass matrix of the deep-sea mining vessel, is a virtual time variable, is a time delay function of the mining vessel, is the hydrostatic restoring stiffness matrix, is the equivalent stiffness matrix, is the displacement of the deep-sea mining vessel, is the velocity of the deep-sea mining vessel, is the acceleration of the deep-sea mining vessel; is the wave load, is the dynamic positioning system load, is the system load under the action of artificial stiffness; The dynamic positioning system model is constructed based on the PID theory: wherein, is a force of the dynamic positioning system, is an offset value of the deep sea mining vessel from the initial position to the current position, wherein represents the current position of the mining vessel, represents the initial position of the mining vessel, , , represent proportional, integral, derivative gains, respectively; In the first sub-period, the displacement of the deep-sea mining vessel is assumed to be 0, 0, and Substituting these into the model of the dynamic positioning system, we have and 0; then in the first sub-period, the external load only considers the wave load , is: wherein: is a discrete frequency, is corresponding complex coefficients, represents the total number of discrete frequencies; For Taking Laplace transform, the pole-residue form is obtained: Based on and The displacement response of the first segment in the Laplace domain under the external wave excitation load is represented as Rewrite into polar-exponential form in the complex plane: Rewrite into polar-exponential form in the complex plane: wherein: , is the residue of To perform an inverse Laplace transform, the first time history of external wave excitation loads under the action of the time domain displacement response of the deep sea mining ship : For derivation, the first segment time history external load under the action of the deep-sea mining ship speed response ; The calculated , is substituted into the dynamic positioning system model to obtain the thrust value of the dynamic positioning system The calculated is substituted into the deep-sea mining ship coupled motion control equation to obtain the system load under the action of artificial stiffness ; Based on the solving obtained , , update the first segment external load : based on the updated first segment external load , iteratively solve the first segment time history external load under the time domain displacement response and velocity response of the deep-sea mining ship until the first segment time history external load is obtained by calculation under the displacement response and velocity response of the deep-sea mining ship that meet the convergence condition; the first segment time history external load under the displacement response and velocity response of the deep-sea mining ship that meet the convergence condition as the first segment time history final displacement response and final velocity response ; based on the final displacement response and final velocity response , deep-sea mining ship coupled motion control equation, dynamic positioning system model, iteration solving each subsection time history under the action of deep-sea mining ship displacement response , velocity response , dynamic positioning system thrust .

7. The quick Laplace domain calculation method of the hydrodynamic response of a deep sea mining vessel according to claim 6, characterized in that: Step S4 comprises: The initial displacement and velocity under the action of the Laplace domain structure of deep-sea mining ship hydrodynamic system of motion equation is expressed as: Based on the self-oscillation motion control equation and the pole-residue model of the transfer function of the deep-sea mining ship hydrodynamic system characterization of the displacement in the laplace domain of the deep-sea mining ship hydrodynamic system ​ Wherein: Let It follows that: For Taking inverse Laplace transform and simplifying, the first The natural vibration response of the dynamically positioned deep-sea mining ship under the action of external load: The first The Laplace domain expression of the radiation damping load due to the fluid memory effect in the external load of the segment is given by ； wherein , is the Laplace domain form of the delay function and velocity: wherein and are respectively the poles and residues of order of and are respectively the poles and residues of order of right Performing the inverse Laplace transform yields the first... Segmented Radiation Damping Load: in, and They are respectively The The poles and residues of the order, the hydrodynamic system of a deep-sea mining vessel in the first order. The external excitation load of the segment can be written as: right Performing the inverse Laplace transform yields the pole-residue characterization of the external excitation load: in and They are The Pole and residue of order, Let be the number of poles and residues of the external excitation load, then the th The Laplace domain characterization of forced motion under segmental load can be written as: wherein and are respectively the first order residue; For Doing inverse Laplace transform, the time domain form of forced motion under segment load is: segment load is: 。 8. The quick Laplace domain calculation method of the hydrodynamic response of a deep sea mining vessel according to claim 7, characterized in that: The method for obtaining the dynamic response of the segmented time-phased deep sea mining ship based on the self-vibration response and the forced response comprises the steps of: obtaining the dynamic response of the segmented time-phased deep sea mining ship, the dynamic response including displacement response , dynamic response of the ship Will , Superimpose to obtain the first Displacement response of deep-sea mining vessel under hydrodynamic load Repeat the iteration until the calculations are repeated twice. If the convergence threshold is less than the specified threshold, the first convergence threshold is obtained. Final response results of a deep-sea mining vessel under hydrodynamic load. , and dynamic positioning system thrust .

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