Joint calculation method for wave energy converter platform motion response and energy capture efficiency

Abstract

The present application relates to the field of ocean engineering and hydrodynamic calculation technology, and discloses a wave-fish integrated platform motion response and energy capture efficiency joint calculation method, comprising the following steps: S1: based on three-dimensional potential flow theory, establishing a frequency domain motion equation of a wave-fish integrated platform composed of multiple floating body modules; S2: converting the frequency domain motion equation into a time domain state space model, and establishing a gas dynamics equation of an oscillating water column device, combining the time domain motion equation corresponding to the frequency domain motion equation with the gas dynamics equation to construct a unified time domain state space model; S3: solving the time domain state space model by using a double-layer optimization algorithm containing outer optimization and inner solution to obtain optimal power extraction parameters; S4: under the optimal power extraction parameters, outputting platform frequency domain motion response and energy capture efficiency evaluation results. The present application realizes integrated and accurate evaluation of platform motion response, wave surface distribution and wave energy capture efficiency.

Description

Technical Field

[0001] This invention belongs to the field of marine engineering and hydrodynamic calculation technology, specifically relating to a method for jointly calculating the motion response and energy capture efficiency of a wave-fishing integrated platform. Background Technology

[0002] With the integration of deep-sea aquaculture and marine renewable energy development technologies, integrating wave energy converters (WECs) into large floating aquaculture platforms has become an important development direction. Such platforms are typically composed of multiple floating modules connected by hinges (such as elastic connections and ball joints) and integrate wave energy capture systems such as oscillating water columns (OWCs).

[0003] Currently, the mainstream method for hydrodynamic analysis of such complex structures is based on the frequency domain boundary element method (BEM). This method can effectively solve the diffraction and radiation problems of multi-buoy systems, obtaining the added mass, radiation damping, and hydrodynamic coefficients. However, existing technologies have the following technical limitations when dealing with such "wave-fishery fusion" platforms: (1) Separation of motion response and energy harvesting efficiency calculation: Traditional methods usually solve the frequency domain motion response of the platform first, and then perform energy assessment of the OWC device afterward. This fails to dynamically couple the changes in aerodynamic pressure in the air chamber with the motion of each module of the platform in the same solution system. This separated method cannot accurately reflect the reaction of the energy harvesting process of the OWC device on the platform motion (especially pitch and heave), resulting in biases in the assessment of the platform's hydrodynamic characteristics and energy output characteristics.

[0004] (2) Lack of joint solution capability for the influence of articulation constraints: Although existing technologies can handle simple articulation or spring connections, they are mostly limited to kinematic constraints. They fail to provide a unified mathematical solution for the connector stiffness, energy output damping (PTO damping), and motion response of each module of the platform in the dynamic equations of complex coupled systems containing OWC devices. It is difficult to quantify the synergistic influence of different articulation methods (such as elastic connection and ball joint connection) on the overall dynamic behavior and energy capture efficiency of the platform.

[0005] (3) Nonlinear PTO damping leads to difficulties in frequency domain iterative convergence: The aerodynamic damping introduced by the air turbine in actual OWC devices often has nonlinear characteristics (such as being proportional to the square of the flow velocity). If the traditional frequency domain method handles this nonlinearity through equivalent linearization, it is necessary to iteratively solve for each frequency point and update the linearization coefficients in each iteration. Under strongly nonlinear conditions, this iterative process is prone to divergence or slow convergence, and the initial value of the linearization coefficients is sensitive. Existing technologies do not provide algorithmic improvements that guarantee convergence. Summary of the Invention

[0006] The purpose of this invention is to provide a joint calculation method for the motion response of a wave-fishery integrated platform considering articulated constraints and the energy harvesting efficiency of an oscillating water column wave energy device. This method aims to overcome the shortcomings of existing technologies that separate motion analysis from energy harvesting assessment, and the difficulty of iterative convergence under nonlinear PTO damping. By introducing state enhancement and bi-level optimization techniques, the aerodynamic model of the OWC device and the articulated multibody dynamics model of the platform are jointly solved within a unified mathematical framework. This achieves an integrated and accurate assessment of the platform's motion response, wave surface distribution, and wave energy harvesting efficiency, providing theoretical support for the selection of connection methods and energy system design of wave-fishery integrated platforms. This invention is applicable to the hydrodynamic performance analysis and evaluation of deep-sea aquaculture-power generation integrated platforms composed of multiple articulated modules and wave energy devices. This method has been validated in a scaled numerical simulation model; actual scale engineering applications require parameter optimization and model correction.

[0007] To achieve the above objectives, the following technical solution is adopted: This invention provides a method for jointly calculating the motion response and energy capture efficiency of a wave-fishing fusion platform, comprising the following steps: S1: Based on the three-dimensional potential flow theory, the frequency domain motion equation of the wave fishing fusion platform composed of multiple floating body modules is established. The frequency domain motion equation contains mathematical expressions for describing the hinge constraints between modules. S2: Convert the frequency domain motion equation established in step S1 into a time domain state space model, and add the air chamber pressure of the oscillating water column device as an augmented state variable to the time domain state space model. Establish the gas dynamics equation of the oscillating water column device, and combine the time domain motion equation corresponding to the frequency domain motion equation with the gas dynamics equation to construct a unified time domain state space model. S3: A two-layer optimization algorithm, including outer-layer optimization and inner-layer solution, is used to solve the time-domain state-space model to obtain the optimal power extraction parameters. The outer-layer optimization uses an evolutionary algorithm to globally optimize the power extraction parameters of the oscillating water column device. For each set of candidate power extraction parameters generated by the outer-layer optimization, the inner-layer solution directly constructs a linearized system equation in the frequency domain and solves the steady-state frequency domain response to obtain the platform motion response and the energy capture efficiency of the oscillating water column device. S4: Under the optimal power extraction parameters, output the frequency domain motion response and energy capture efficiency evaluation results of the platform.

[0008] Furthermore, in step S1, the hinge constraint includes two connection methods: ideal ball joint connection and elastic connection. For ideal ball joint connections, the Lagrange multiplier method is used to handle the constraints. By constructing a displacement constraint matrix and introducing Lagrange multiplier vectors, the constraints are integrated into the frequency domain motion equations. For elastic connections, the connection stiffness matrix is ​​introduced and directly superimposed onto the corresponding degrees of freedom of the frequency domain dynamic coefficient matrix in the frequency domain motion equations.

[0009] Furthermore, in step S2, the Cummins equation method based on rational function approximation is used to perform the frequency domain to time domain conversion. Specifically, this includes: using the least squares frequency domain fitting method to fit the delay function with a rational function to obtain the time domain motion equation: ; in, For the quality matrix, Add a mass matrix to infinite frequencies; The delay function matrix; , , These are the displacement vector, velocity vector, and acceleration vector in the time domain, respectively. The restoring force matrix in still water. This represents the time-domain wave excitation force vector; To extract the reaction force vector for power, For time.

[0010] Furthermore, in step S3, the evolutionary algorithm used for the outer layer optimization is the covariance matrix adaptive evolutionary strategy. Its optimization objective is to maximize the average energy capture efficiency of the oscillating water column device under the specified sea state and to impose constraints on the platform motion response. When the platform motion response exceeds the safety threshold, a penalty term is introduced into the objective function. The iteration termination condition of the evolutionary algorithm is that the change in the objective function is less than a preset threshold or the preset maximum number of iterations is reached.

[0011] Furthermore, in step S3, the inner layer solution includes: transforming the gas chamber dynamics equation of the oscillating water column device to the frequency domain to obtain the gas chamber pressure. With water column volume flow rate Frequency domain aerodynamic impedance relationship between them: ,in, The frequency-domain aerodynamic impedance of the air chamber of the oscillating water column device is given; this impedance relationship is then embedded as an additional impedance term into the frequency-domain dynamic coefficient matrix of the frequency-domain motion equation in step S1, resulting in the corrected frequency-domain dynamic coefficient matrix. .

[0012] Furthermore, the frequency domain aerodynamic impedance The expression is: ; in, Let c be the air density and c be the speed of sound. Where ω is the volume of the air chamber and ω is the wave angular frequency. The turbine admittance coefficient is the power extraction parameter.

[0013] Furthermore, in step S3, for an oscillating water column device with two air chambers (front and rear), the total energy capture efficiency is defined as the ratio of the sum of the energy capture power of the front air chamber and the energy capture power of the rear air chamber to the incident wave power: ; in, The energy harvesting power of the fore-chamber. The energy harvesting power of the rear chamber; The energy-harvesting power of a single gas chamber is calculated using the following formula: ;in, This refers to the air chamber pressure of the oscillating water column device; Incident wave power Calculate using the following formula: ;in, The density of seawater, It is the acceleration due to gravity. For wave height, For wave cycles, Let be the total width of the wave-facing opening of the oscillating water column device, for a device with two air chambers, front and rear. It is the sum of the widths of the two air chambers.

[0014] Furthermore, in step S3, the constructed linearized system equations are a system of linear equations containing hinged constraints, and their matrix form is as follows: ; in, This is the corrected frequency domain dynamic coefficient matrix. The displacement constraint matrix is... It is the transpose of the displacement constraint matrix. It is a generalized displacement vector. Let Lagrange multiplier vectors be used. This is the corrected wave excitation force vector. It is a zero vector; The linear equations are solved using a direct solver to obtain the platform motion response amplitude operator and the air chamber pressure at each frequency point.

[0015] Furthermore, the calculation method was first verified in a scaled numerical simulation model, in which the aerodynamic similarity treatment of the scaled model adopted Froude similarity correction to scale the equivalent sound speed; when applied to full-scale engineering, parameter optimization and model correction need to be combined.

[0016] Furthermore, in step S4, the comparative analysis of different articulation methods is conducted by assigning different motion constraint weights to the objective function to obtain the trade-off between motion suppression effect and energy capture efficiency, and output in the form of Pareto front.

[0017] Compared with existing technologies, the main beneficial effects of this invention are as follows: (1) This invention achieves a complete joint solution for platform motion and wave energy capture: by using state enhancement, the air chamber pressure of the OWC device is used as an augmented state variable, and the frequency domain hydrodynamic coefficients are converted into a time domain state-space model using the Cummins equation, providing a unified mathematical framework for bi-level optimization. This method overcomes the technical bias of traditional methods that calculate the two separately and ignore aerodynamic reaction.

[0018] (2) This invention improves robustness under nonlinear PTO damping while ensuring the feasibility of the solution: For the nonlinear aerodynamic damping problem of the OWC device, this invention adopts a two-layer optimization architecture of outer CMA-ES global search + inner frequency domain linear system direct solution. The inner layer does not perform time-consuming time step advancement, but constructs a linearized system for each set of candidate parameters and solves the steady-state frequency domain response at once, controlling the computational load of each candidate parameter to the level of a single linear solution (20 frequency points). In the numerical comparison of 15 irregular wave conditions, the method of this invention converges stably in all the above test conditions; while the traditional equivalent linearized iterative method diverges in 3 of the strongly nonlinear conditions, and the convergence speed of the remaining conditions is about 2-3 times slower than the method of this invention.

[0019] (3) This invention provides a unified evaluation capability for articulated constraints and energy output characteristics: by using the Lagrange multiplier method (spherical hinge) and the stiffness superposition method (elastic connection) to handle different articulation methods respectively, and combined with the optimization of PTO damping, the trade-off between motion suppression and energy capture efficiency under different connection methods can be quantitatively revealed. By adjusting the penalty weight in the objective function or multi-objective optimization, the Pareto front can be generated, providing an intuitive basis for decision-making in engineering design.

[0020] (4) The direct solution method in the inner frequency domain adopted in this invention only requires one linear system solution for each of the 20 frequency points for each candidate parameter, with a computational load of 20 linear solutions. In contrast, the traditional equivalent linearization iterative method requires 7-8 iterations, each iteration including reanalysis of 20 frequency points, with a computational load of approximately 140-160 linear solutions, and there is a risk of divergence. This proves that the solution of this invention has innovativeness and practical value.

[0021] It should be understood that the description in the Summary of the Invention is not intended to limit the key or essential features of the embodiments of the present invention, nor is it intended to restrict the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0022] The above and other features, advantages, and aspects of the various embodiments of the present invention will become more apparent from the accompanying drawings and the following detailed description. The drawings are provided for a better understanding of the invention and are not intended to limit the invention. In the drawings, the same or similar reference numerals denote the same or similar elements, wherein: Figure 1 This is a flowchart of the method for jointly calculating the motion response and energy capture efficiency of the wave-fishing fusion platform according to an embodiment of the present invention; Figure 2 This is a detailed flowchart of the two-layer optimization algorithm of the present invention (outer layer CMA-ES iteration and inner layer frequency domain linear solution). Figure 3 This is a schematic diagram of the heave response curve of the modular floating platform with ball joint connection according to Embodiment 2 of the present invention; Figure 4 This is a schematic diagram of the pitch response curve of the modular floating platform with ball joint connection according to Embodiment 2 of the present invention; Figure 5 This is a comparison chart of the energy capture efficiency of the dual-chamber OWC wave energy device in Embodiment 2 of the present invention (single-chamber vs. dual-chamber). Figure 6 This is a breakdown diagram of the energy capture efficiency of the dual-chamber OWC before and after embodiment two of the present invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] Furthermore, the term "and / or" in this article 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, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0025] Example 1: Figure 1 This is a flowchart illustrating the method for jointly calculating the motion response and energy capture efficiency of the wave-fishing fusion platform according to an embodiment of the present invention. Figure 1As shown, this method transforms the platform's dynamic response problem into a two-layer optimization problem: the outer layer uses an evolutionary algorithm to optimize the PTO parameters, while the inner layer constructs and solves linearized frequency domain system equations for the given parameters. Its core lies in establishing a joint solution framework capable of handling both articulated displacement continuity conditions and OWC aerodynamic boundary conditions through state enhancement and constraint linearization techniques. This method includes the following steps: S1: Based on the three-dimensional potential flow theory, the frequency domain motion equation of the wave fishing fusion platform composed of multiple floating body modules is established. The frequency domain motion equation contains mathematical expressions for describing the hinge constraints between modules. Step S1 is used to establish a multibody hydrodynamic model (frequency domain) of the platform considering articulated constraints.

[0026] Based on the three-dimensional potential flow theory, a system is established... The frequency domain motion equations of the wave-fishing fusion platform composed of floating modules. Each module is considered a rigid body, and its wetted surface satisfies impenetrable boundary conditions. In the linear frequency domain framework, the matrix form of the system's motion equations is: ; in, The generalized displacement vector contains the displacement magnitudes of all modules in six degrees of freedom, with dimensions of . ; : The number of floating modules, a dimensionless integer; Wave angular frequency, unit: ; The wave excitation force vector is the generalized force amplitude generated by the incident wave acting on each module; This is the frequency domain dynamic coefficient matrix, used to describe the system at frequencies. The impedance characteristic under the given conditions is defined as follows: ; In the formula, This is the mass matrix, which contains the mass and moment of inertia of all modules; An additional mass matrix is ​​added to reflect the effect of fluid inertia on the module motion, which varies with frequency; The radiation damping matrix reflects the energy dissipation caused by wave radiation generated by the module's motion, and varies with frequency. It is the still water restoring force matrix, composed of buoyancy and gravity, providing restoring torque / force. The equivalent linear PTO damping matrix introduced for the OWC device is set as follows in the baseline calculation of this step: The matrix is ​​used to simulate energy extraction, specifically for extracting the pure water dynamic coefficients. Nonlinear PTO damping will be handled by the outer optimization framework in step S3.

[0027] The PTO damping matrix, in the inner-layer solution in the frequency domain, has elements derived from the turbine admittance coefficients. The geometric parameters of the air chamber are determined and can be directly introduced through the additional impedance term in the boundary element method, without the need to explicitly construct the transformation matrix related to the air chamber pressure-module motion coupling coefficient. .

[0028] The articulation constraints in this invention include two typical connection methods: ideal ball joint connection and elastic connection. (1) For an ideal ball joint connection: only the translational degree of freedom is constrained to be continuous, while the rotational degree of freedom is free, and no stiffness parameter is introduced. The Lagrange multiplier method is used to handle the constraint conditions. By constructing the displacement constraint matrix and introducing the Lagrange multiplier vector, the constraint conditions are integrated into the frequency domain motion equation.

[0029] (2) Elastic connection: The relative motion between modules is constrained by spring connectors, and a connection stiffness matrix is ​​introduced. The frequency domain dynamic coefficient matrix is ​​directly superimposed on the frequency domain motion equations. On the corresponding degrees of freedom, that is No Lagrange multipliers are needed. Under flexible connections, the displacement constraint matrix... If empty, the constraint is manifested in the form of elastic force.

[0030] in, : The connection stiffness matrix of the elastic connection, which describes the stiffness characteristics of the spring connector; : Frequency domain dynamic coefficient matrix under flexible connection; : Displacement constraint matrix, used to describe displacement continuity constraints in ball joint connections; it is an empty matrix in elastic connections.

[0031] The following uses an ideal ball joint connection as an example to illustrate the displacement constraint matrix. The construction method is as follows: Define the coordinate system: Use a right-handed coordinate system, with the origin located at the projection point of the platform's center of gravity on the still water surface. The positive axis points towards the bow (facing the waves). The axis is pointing positively to the port side. The axis is vertically upward. The positive direction of rotation is determined by the right-hand rule (vertical rotation). Around The axis, with its positive direction causing the bow to rise. In this coordinate system, any point on the rigid body... Translational displacement and module generalized displacement The relationship is: ; ; ; Any point on a rigid body Translational displacement components in the direction; The six degrees of freedom displacement of a single module correspond to sway, roll, heave, roll, pitch, and sway in sequence. : The coordinates of the hinge point in the global coordinate system.

[0032] For a ball joint connection between two modules (module I and module J), ​​the coordinates of the hinge point are ( The continuity condition for translation at point () is: ; Among them, superscript They respectively represent vertical swaying, horizontal swaying, vertical swaying, horizontal rocking, vertical rocking, and vertical rocking; The six degrees of freedom displacement of module I; The six degrees of freedom displacement of module J; The displacement constraint submatrix corresponding to a single hinge point organizes the displacement continuity conditions of the two modules at that point into matrix form.

[0033] For adjacent modules I and J, the coordinates of the hinge point are taken as the global coordinates of the same point on the connection surface of the two modules. This point has the same spatial position in the local coordinate systems of modules I and J.

[0034] Rearrange the above three equations into matrix form. Then the overall displacement constraint matrix By all hinge points The equations are stacked row by row. Using the Lagrange multiplier method, constraints are introduced into the equations of motion, resulting in: ; : Lagrange multiplier vector, used to apply hinge constraints, its physical meaning is the constraint reaction force at the hinge point.

[0035] Solving this equation yields the motion response RAO of each module in six degrees of freedom. RAO is the amplitude response operator, describing the change in amplitude of the motion response of each module of the platform with frequency at unit amplitude.

[0036] The output of step S1 ( , (etc.) will be used as input for the subsequent time-domain transformation in step S2.

[0037] S2: Convert the frequency domain motion equation established in step S1 into a time domain state space model, and add the air chamber pressure of the oscillating water column device as an augmented state variable to the time domain state space model. Establish the gas dynamics equation of the oscillating water column device, and combine the time domain motion equation corresponding to the frequency domain motion equation with the gas dynamics equation to construct a unified time domain state space model. Step S2 is used to realize the conversion from the frequency domain to the time domain and the joint state-space model of the OWC device.

[0038] To handle nonlinear PTO damping and achieve joint solution with the OWC device, the frequency domain model needs to be converted into a time-domain state-space model. The Cummins equation method based on rational function approximation is used for the frequency-to-time domain conversion, approximating the delay function in the frequency-domain radiation force using a state-space representation. This embodiment employs a least-squares frequency-domain fitting method to approximate the delay function. Perform a 6th-order rational function fitting, with the fitting frequency range consistent with the frequency sweep range in step S1. ).

[0039] Rational function fitting takes the following form: Where s is the Laplace variable, and p, q, and r are the coefficients to be fitted. During fitting, the initial poles and residues can be determined automatically using a logarithmic distribution or through least squares optimization. Those skilled in the art can achieve this using conventional state-space identification methods.

[0040] Furthermore, the delay function is fitted with a rational function using the least squares frequency domain fitting method to obtain the time-domain equation of motion: ; in, : Time-domain acceleration vector; : Time-domain velocity vector; : Time-domain displacement vector; The delay function matrix in the Cummins equation describes the fluid memory effect and is approximated by rational functions. : The mass matrix with infinite frequency, representing the asymptotic value of the mass as the frequency approaches infinity; : Time-domain wave excitation force vector; Power Extraction Tolerance (PTO) reaction force vector, generated by energy extraction from wave energy devices; For time.

[0041] Wherein, the delay function matrix By analyzing the frequency domain radiation damping matrix and additional mass matrix By performing a rational function approximation, the following frequency-to-time domain transformation relationship is obtained: Corresponding to the radiative force term in the frequency domain .

[0042] PTO reaction force vector in the time domain With the PTO damping matrix in the frequency domain Satisfies the Fourier transform relation: In the two-level optimization framework, nonlinear PTO damping is achieved through the time-domain model. The expression is used, while the inner frequency domain solution is transformed into an equivalent linearization. .

[0043] For the OWC device, the gas chamber pressure is introduced. As an augmented state variable, the gas dynamics within the chamber can be approximated as a linearized isentropic process: ; In the formula, The instantaneous pressure inside the OWC chamber is introduced as an augmented state variable. Air density, unit: ; Speed ​​of sound, unit: ; OWC chamber volume, in units of ; The volumetric flow rate caused by the motion of the water column is defined as the surface integral of the normal derivative of the velocity potential at the free surface in the gas chamber. The unit is ; Velocity potential is a fundamental unknown in hydrodynamic analysis, and its time derivative is used to calculate volumetric flow rate.

[0044] The PTO characteristics of a turbine are typically nonlinear; to handle this within an optimization framework, they are represented in a linearized form. .in, Volumetric flow rate through an air turbine, expressed in m³ / s. 3 / s; Turbine admittance coefficient: A coefficient that linearly correlates pressure and flow rate, measured in units of... .

[0045] By combining the above OWC dynamic equations with the platform motion equations, we define the augmented state vector. This allows us to obtain a unified time-domain state-space model: ; in, Excited by the incident wave, For the PTO parameters (turbine admittance coefficients) to be optimized ). : The augmented state vector is composed of displacement, velocity, and air chamber pressure. : Nonlinear state transition function, describing the time evolution of the augmented state vector; Incident wave excitation serves as the system input; : The PTO parameter vector to be optimized in the outer layer optimization, which is the turbine admittance coefficient here.

[0046] for Each module, displacement vector and velocity vector Each for Dimension, air chamber pressure Since it is 2-dimensional (front and rear air chambers), the total dimension of the augmented state vector is 36+36+2=74.

[0047] Explanation of the logical relationship between S2 and S3: The time-domain state-space model established in step S2 has two functions: (1) Provides a state-space implementation of the delay function for the inner frequency domain linearization solution in step S3, so as to accurately transform the Cummins equation back to the frequency domain form at each frequency point (i.e., Ogilvie relation: frequency domain representation of radiative force). ); The frequency domain radiative force vector is given by the Ogilvie relation and is associated with the added mass and radiative damping.

[0048] (2) When time-domain verification is required (such as checking transient response), the time-domain model can be directly called for numerical integration. Therefore, S2 is not redundant, but a bridge connecting the frequency domain coefficients and the inner frequency domain solution.

[0049] S3: A two-layer optimization algorithm, including outer-layer optimization and inner-layer solution, is used to solve the time-domain state-space model to obtain the optimal power extraction parameters. The outer-layer optimization uses an evolutionary algorithm to globally optimize the power extraction parameters of the oscillating water column device. For each set of candidate power extraction parameters generated by the outer-layer optimization, the inner-layer solution directly constructs a linearized system equation in the frequency domain and solves the steady-state frequency domain response to obtain the platform motion response and the energy capture efficiency of the oscillating water column device. Step S3 is a joint response solving algorithm based on two-layer optimization.

[0050] To address the challenges of joint state-space models incorporating nonlinear PTO damping and ensure solution convergence and computational feasibility, this invention proposes a two-layer optimization algorithm. The core idea is: the outer layer performs a global search for PTO parameters, while the inner layer constructs a linearized system for each set of candidate parameters and directly solves the steady-state frequency domain response, avoiding time-consuming time-step progression. The outer layer optimization employs a covariance matrix adaptive evolution strategy, aiming to maximize the average energy capture efficiency of the oscillating water column device under specified sea conditions, while imposing constraints on the platform's motion response. A penalty term is introduced into the objective function when the platform's motion response exceeds a safety threshold. The iteration termination condition of the evolutionary algorithm is that the change in the objective function is less than a preset threshold or the preset maximum number of iterations is reached. The inner layer solution includes: transforming the air chamber dynamic equations of the oscillating water column device to the frequency domain to obtain the frequency domain aerodynamic impedance relationship between the air chamber pressure and the water column volumetric flow rate; and embedding this impedance relationship as an additional impedance term into the frequency domain dynamic coefficient matrix of the frequency domain motion equations in step S1, obtaining the corrected frequency domain dynamic coefficient matrix. Figure 2 The diagram shown is a detailed flowchart of the two-layer optimization algorithm of this invention (outer layer CMA-ES iteration and inner layer frequency domain linear solution). Specifically: (1) Outer layer optimization (non-convex parameter search): The covariance matrix adaptive evolution strategy (CMA-ES) is used to optimize the PTO parameters. (i.e., turbine admittance coefficient) Global optimization is performed. CMA-ES does not rely on gradient information and is suitable for situations where the objective function may be non-convex or discontinuous. The goal of the outer optimization is to maximize the average energy harvesting efficiency of the OWC device under specified sea conditions, while constraining the platform motion response within safe limits.

[0051] (2) Inner layer solution (linearized frequency domain response calculation): For each set of candidate parameters generated by CMA-ES The linearized system equations are directly constructed in the frequency domain and the steady-state response is solved.

[0052] a. Frequency domain embedding of the OWC aerodynamic model: Transforming the OWC chamber dynamic equations to the frequency domain, including chamber pressure. With water column volume flow rate The relationship is: ; The frequency domain aerodynamic impedance of the OWC chamber describes the transfer function between the chamber pressure and the volumetric flow rate of the water column, with units of . .

[0053] The linearized kinetic boundary conditions for the free liquid surface inside the gas chamber are: .in, Vertical displacement of the free liquid surface inside the gas chamber, in units of ; Seawater density, compared to air density Distinguish, unit is .

[0054] Substituting this condition into the free surface influence matrix of the boundary element method is equivalent to adding a frequency-dependent additional impedance term to the free surface degree of freedom within the air chamber. Specifically, for the water surface element inside the OWC air chamber, the free surface term in the original boundary element equation... Revised to . : The outward normal direction of the object surface, used in the boundary element method to express the impenetrable condition. This correction term can be equivalently represented as the increments of mass, damping, and stiffness added to the corresponding degree of freedom, thus changing the original dynamic coefficient matrix. Revised to At the same time, the excitation force vector Revised to (Including the response of the pressure gradient inside the chamber to the incident wave).

[0055] b. Solving the system equations: In step S3, the constructed linearized system equations are a set of linear equations containing hinge constraints. The matrix form is as follows: the block matrix is ​​composed of the modified frequency domain dynamic coefficient matrix, displacement constraint matrix and its transpose matrix, multiplied by the unknown vector composed of the generalized displacement vector and the Lagrange multiplier vector, which is equal to the right-hand side composed of the modified wave excitation force vector and the zero vector. The linear equations are solved by the direct solver to obtain the platform motion response amplitude operator and the air chamber pressure at each frequency point.

[0056] Specifically, the system of linear equations containing hinge constraints is as follows: ; This system of equations is a linear system, and each frequency point and each candidate... Only one linear solution is required (e.g., LU decomposition or calling the SOCP solver to handle inequality constraints), without time stepping. The solution yields the frequency domain displacement. Then, the oscillation velocity amplitude of the water column inside the OWC is recovered through velocity potential. or air chamber pressure Amplitude of the water column oscillation velocity within the OWC Obtained from velocity potential recovery, unit is .

[0057] c. Energy capture efficiency calculation: A single oscillating water column (OWC) device at a frequency The energy-harvesting power is calculated using the following formula: ; in, OWC device at frequency The energy capture power is expressed in W. Take the real part of the complex number; Air volume flow rate . From step a and It can be solved Alternatively, it can be obtained through motion response post-processing.

[0058] For an oscillating water column device with two air chambers (front and rear), the total energy capture efficiency is defined as the ratio of the sum of the energy capture power of the front air chamber and the energy capture power of the rear air chamber to the incident wave power: ; frequency The incident wave power Calculate using the following formula: ; in, The energy harvesting power of the fore-chamber. The energy harvesting power of the rear chamber; Total energy capture efficiency, dimensionless; The average power of the incident wave per unit crest width, expressed in units of... ; The wave height of a regular wave, measured in meters (m). Wave period, measured in seconds; OWC wave-facing opening total width, which is the sum of the widths of the two air chambers, in meters.

[0059] (3) Objective function and convergence judgment: The objective function of the outer CMA-ES is the total energy capture efficiency under the specified sea state (weighted integral over the frequency band), while applying a linear penalty to the platform motion response (such as heave RAO peak value and pitch RAO peak value), and reducing the target value when it exceeds the safety threshold.

[0060] CMA-ES iterates until the change in the objective function is less than a preset threshold (e.g., ...). (or reaches the maximum number of iterations (e.g., 50 generations). The population size is set to 20, and each candidate parameter...) The linear system needs to be solved for approximately 20 discrete frequency points, so the computational cost of a single outer iteration is 20 × 20 = 400 linear system solutions. The total computational cost is approximately 50 × 400 = 20,000 linear solutions, which is acceptable in offline design scenarios.

[0061] (4) Output: The final output solution also gives the optimal PTO parameters. And the platform's frequency domain motion response and energy capture efficiency under these parameters.

[0062] S4: Under the optimal power extraction parameters, output the frequency domain motion response and energy capture efficiency evaluation results of the platform.

[0063] Step S4 is used to perform performance evaluation and output results.

[0064] After optimizing the PTO parameters, the evaluation results are output according to the RAO and energy capture efficiency curves obtained in step S3.

[0065] In step S4, the comparative analysis of different articulation methods, by assigning different motion constraint weights (adjusting the penalty coefficient) to the objective function, yields the trade-off between motion suppression effect and energy capture efficiency, which is output as a Pareto front (the horizontal axis represents motion indicators, such as peak heave RAO; the vertical axis represents total energy capture efficiency). This Pareto front can be obtained by running CMA-ES multiple times (each time with different penalty weights) or by using a multi-objective CMA-ES (MO-CMA-ES) variant in one go.

[0066] Example 2: The following example uses a scaled numerical simulation model (scale ratio 1:20) of a wave-fishing fusion platform containing 6 modules to illustrate the specific implementation of the method of this invention.

[0067] Furthermore, this calculation method was first validated in a scaled numerical simulation model, where the aerodynamic similarity treatment of the scaled model employed Froude similarity correction to scale the equivalent sound velocity. When applied to full-scale engineering, parameter optimization and model correction are required. Full-scale engineering applications need to consider Reynolds number differences, changes in the proportion of viscous effects, and scaling of the gas dynamics time constant, combined with parameter optimization and model correction. The calculation results of this invention can be directly used to guide the selection of connection methods for full-scale wave-fishing fusion platforms, the design of PTO system parameters, and the prediction and optimization of platform motion performance.

[0068] (a) System Definition: The platform consists of six identical square modules. Each module has an outer side length of 40m (full scale, 2.0m in scaled-down model), an inner side length of 30m (1.5m in scaled-down model), a draft of 5m (0.25m in scaled-down model), and a spacing of 5m between adjacent modules (0.25m in scaled-down model). The modules are connected by ideal spherical hinges (only constrained for translation, not rotation). The hinge points are located at the center of the module's side (2.5m above the baseline, 0.125m in scaled-down model). The horizontal coordinates of the hinge points of adjacent modules coincide. Two hinge points are arranged along the width of the module, with a spacing equal to 50% of the module's width (i.e., 20m, 1.0m in scaled-down model).

[0069] The platform integrates a dual-chamber OWC wave energy device. To ensure that the OWC device has a non-negligible impact on the platform's motion (meeting the technical premise of this invention), the chamber dimensions are adapted to the module dimensions: each chamber is 10m long (full scale, scaled down 0.5m), 8m wide (scaled down 0.4m), and 6.8m high (scaled down 0.34m), with a horizontal perforated plate opening ratio. and The operating sea state is 30m deep (1.5m scale), and the wave frequency range is [missing information]. , wave angle (Upstream) and 45°. The scaled-down model physical model test was conducted in a water tank, which was 33m long, 0.8m wide and 1.0m high, with wave height of 0.05~0.075m and period of 1.0~2.0s.

[0070] (ii) Aerodynamic similarity treatment of scaled-down models In scaled numerical simulations, to achieve aerodynamic similarity, the equivalent sound velocity needs to be corrected for Froude similarity. Maintaining the same Froude number requires a velocity ratio that is proportional to the scale. The speed of sound, as a physical constant, cannot be changed in the model, but the elastic stiffness coefficient of the air chamber... The dimensions are To ensure time scale matching, an equivalent speed of sound can be used in the numerical model. This ensures that the characteristic frequencies of the air chamber pressure response and the wave characteristic frequencies satisfy Froude similarity. In this embodiment, the numerical simulation uses... The speed of sound in air across the entire scale is taken as 340. (Typical values ​​under standard atmospheric pressure and 15°C).

[0071] (III) Implementation of the two-level optimization algorithm 1. Frequency domain modeling (step S1): Based on the frequency domain boundary element method, the wetted surface of a single module is meshed (approximately 360 surface elements per module), and the boundary integral equations of each module are established.

[0072] Calculate the added mass of each module Radiation damping and wave excitation force .

[0073] Based on the coordinates of the ball joint connection point, establish the displacement constraint matrix using the aforementioned method. An ideal spherical joint constraint does not introduce a stiffness parameter.

[0074] set up The platform motion RAO without PTO damping is used as a reference.

[0075] 2. Time-domain model transformation and OWC augmentation (step S2): The least squares frequency domain fitting method (6th order rational function) is used to transform the frequency domain radiation force into a time domain delay function, and a state-space model in the form of the Cummins equation is established.

[0076] Introducing pressure variables in dual-chamber OWC The dynamic equations for the air chamber are established. The air chamber volume is calculated on a full-scale basis: (Scaled-down model correspondence) In numerical simulation, the parameters are set according to the scaled-down model.

[0077] Forming augmented state vectors The total dimensions are 36+36+2=74.

[0078] 3. Two-level optimization solution (step S3): Outer CMA-ES settings: Variables to be optimized are (Turbine admittance coefficients of the two chambers). Population size is set to 20, and maximum number of iterations is 50.

[0079] Inner frequency domain solution: For each candidate First, correct it according to step S3-a. get and Linear systems are constructed at 20 discrete frequency points. A direct solver (LU decomposition) is used to solve the problem in one step, obtaining the RAO and RAO at each frequency point. .

[0080] Objective function: Calculate the overall energy capture efficiency (Sum over the frequency band), where Calculated according to the aforementioned formula, For platforms with a peak heave RAO exceeding 1.5 m or a peak pitch RAO exceeding [a certain value], [the following conditions apply]. Apply a linear penalty (with a penalty coefficient of 0.1).

[0081] Convergence: After approximately 30 iterations, the objective function of CMA-ES tends to stabilize, and the output becomes optimal. .

[0082] Results output: Under optimal PTO parameters, the heave and pitch responses of each module of the computational platform, as well as the energy capture efficiency at different frequencies, are calculated. Through multiple runs with different penalty coefficients, the Pareto front between motion suppression and energy capture efficiency can be obtained.

[0083] Figure 3The heave response of each module of a modular floating platform under ball joint connection conditions is demonstrated. Compared with the elastic connection system, the ball joint connection has a significant suppression effect on the peak heave response, and the suppression effect exhibits frequency-dependent and wave angle-dependent characteristics. Figure 3 In (a) of the diagram, under the condition of wave angle β=0° (facing the waves), the ball joint connection can effectively reduce the peak value of the heave response in the mid-frequency range (1.0<ω<1.5 rad / s). This frequency range is originally the resonance range where the heave response of the hingeless system is relatively significant. The introduction of the ball joint changes the vertical constraint characteristics between modules, weakens the excitation intensity of the heave mode, and thus plays a role in peak reduction. Figure 3 In (b), under the condition of wave angle β=45° (oblique wave), the ball joint connection mainly suppresses the peak value of the heave response in the low-frequency range (ω<1.0 rad / s). Under the action of oblique waves, low-frequency excitation easily induces the overall swaying motion between modules, while the ball joint connection allows a certain relative rotation but limits the vertical displacement difference, thus effectively suppressing the amplitude of the low-frequency heave response.

[0084] Figure 4 The pitch response of a modular floating platform under ball-joint connection conditions is demonstrated. (Comparison with heave response...) Figure 3 Consistent with this, the ball joint connection also has a significant peak suppression effect on the pitch response, and the suppression effect shows a clear frequency and wave direction dependence. For example... Figure 4 In (a) of the diagram, under the condition of wave angle β=0° (facing the waves), the ball joint connection can effectively reduce the peak value of the pitch response in the mid-frequency range (1.0<ω<1.5 rad / s). This frequency range is originally a region where pitch resonance of articulated systems is relatively concentrated. The introduction of the ball joint, by allowing limited relative rotation between modules, changes the overall stiffness and damping characteristics of the system, thereby weakening the resonance intensity of the pitch mode and achieving peak reduction. Figure 4 In (b), under the action of oblique waves (β=45°), the pitch response is also significantly suppressed. Unlike the wave-facing condition, the pitch suppression effect of the ball joint connection under oblique waves covers a wider frequency range, and the response amplitude is significantly lower than that of the system without a joint. This is mainly because the ball joint connection effectively restricts the roll-pitch coupling motion between modules, reducing the energy transfer efficiency of the oblique excitation to the pitch mode.

[0085] like Figure 5 The image shows a comparison of the energy capture efficiency of the dual-chamber OWC wave energy capture device (single-chamber vs. dual-chamber), demonstrating the energy capture efficiency comparison between single-chamber and dual-chamber OWCs. The energy capture efficiency of both structures peaks near the dimensionless parameter kh = 1.78 corresponding to the resonant frequency. Specifically, the energy capture efficiency is 9% higher than that of the single-chamber structure at kh = 1.78, and the efficiency improvement reaches 13.6% at kh = 1.56. Overall, near the resonant period, the dual-chamber structure has a more significant synergistic effect on wave energy capture.

[0086] Figure 6 The diagram shows the energy harvesting efficiency decomposition of the front and rear chambers in a dual-chamber OWC system. The energy contribution of the front and rear chambers is further decomposed. The energy harvesting efficiency of the front chamber is generally higher than that of the rear chamber, and it is the main contributing unit to the overall efficiency of the dual-chamber structure. In the range of kh=1.26~2.06, the contribution of the front chamber is always greater than 60%. The front and rear chambers achieve the overall energy harvesting efficiency improvement through synergistic effect.

[0087] Comparison with traditional methods: The method of this invention is compared with the conventional frequency domain equivalent linearization iterative method (linearization coefficients are determined by the initial RAO ​​calculation, the iteration step size is fixed at 0.5, and the maximum number of iterations is 10). Under regular wave conditions, the results of the two methods are basically in agreement (difference <5%). In numerical simulations of 15 conditions for irregular waves (JONSWAP spectrum, significant wave height 0.05–0.075 m, spectral peak period 1.2–1.8 s), the method of this invention converges stably within the above test conditions; while the conventional iterative method diverges in 3 of these conditions (strong nonlinear conditions such as spectral peak period 1.2 s and significant wave height 0.075 m) (iteration sequence oscillation, residuals cannot decrease). In the remaining convergence conditions, the convergence speed of some conditions is about 2-3 times slower than that of the method of this invention (averaging 7-8 iterations, while this invention is a single linear solution). This shows that the method of this invention has better robustness while maintaining computational accuracy.

[0088] Through the above technical means, this invention provides a more accurate, robust, and insightful innovative solution for the design, analysis, and performance evaluation of complex fishing fusion platforms.

[0089] It should also be noted that, in the embodiments of this application, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0090] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined in the embodiments of this application may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown in this application, but is to be accorded the widest scope consistent with the principles and novel features disclosed in the embodiments of this application.

Claims

1. A method for jointly calculating the motion response and energy capture efficiency of a wave-fishing fusion platform, characterized in that, Includes the following steps: S1: Based on the three-dimensional potential flow theory, the frequency domain motion equation of the wave fishing fusion platform composed of multiple floating body modules is established. The frequency domain motion equation contains mathematical expressions for describing the hinge constraints between modules. S2: Convert the frequency domain motion equation established in step S1 into a time domain state space model, and add the air chamber pressure of the oscillating water column device as an augmented state variable to the time domain state space model. Establish the gas dynamics equation of the oscillating water column device, and combine the time domain motion equation corresponding to the frequency domain motion equation with the gas dynamics equation to construct a unified time domain state space model. S3: A two-layer optimization algorithm, including outer-layer optimization and inner-layer solution, is used to solve the time-domain state-space model to obtain the optimal power extraction parameters. The outer-layer optimization uses an evolutionary algorithm to globally optimize the power extraction parameters of the oscillating water column device. For each set of candidate power extraction parameters generated by the outer-layer optimization, the inner-layer solution directly constructs a linearized system equation in the frequency domain and solves the steady-state frequency domain response to obtain the platform motion response and the energy capture efficiency of the oscillating water column device. S4: Under the optimal power extraction parameters, output the frequency domain motion response and energy capture efficiency evaluation results of the platform.

2. The method for jointly calculating the motion response and energy capture efficiency of the wave-fishing fusion platform according to claim 1, characterized in that, In step S1, the hinge constraint includes two connection methods: ideal ball joint connection and elastic connection; For ideal ball joint connections, the Lagrange multiplier method is used to handle the constraints. By constructing a displacement constraint matrix and introducing Lagrange multiplier vectors, the constraints are integrated into the frequency domain motion equations. For elastic connections, the connection stiffness matrix is ​​introduced and directly superimposed onto the corresponding degrees of freedom of the frequency domain dynamic coefficient matrix in the frequency domain motion equation described in step S1.

3. The method for jointly calculating the motion response and energy capture efficiency of the wave-fishing fusion platform according to claim 1, characterized in that, Step S2 employs the Cummins equation method based on rational function approximation to perform the frequency domain to time domain transformation. Specifically, this includes: using the least squares frequency domain fitting method to fit the delay function with a rational function, obtaining the time-domain motion equation: ； in, For the quality matrix, Add a mass matrix to infinite frequencies; The delay function matrix; , , These are the displacement vector, velocity vector, and acceleration vector in the time domain, respectively. The restoring force matrix in still water. This represents the time-domain wave excitation force vector; To extract the reaction force vector for power, For time.

4. The method for jointly calculating the motion response and energy capture efficiency of the wave-fishing fusion platform according to claim 1, characterized in that, In step S3, the evolutionary algorithm used for the outer layer optimization is the covariance matrix adaptive evolutionary strategy. Its optimization objective is to maximize the average energy capture efficiency of the oscillating water column device under the specified sea state and to impose constraints on the platform motion response. When the platform motion response exceeds the safety threshold, a penalty term is introduced into the objective function. The iteration termination condition of the evolutionary algorithm is that the change in the objective function is less than a preset threshold or the preset maximum number of iterations is reached.

5. The method for jointly calculating the motion response and energy capture efficiency of the wave-fishing fusion platform according to claim 1, characterized in that, In step S3, the inner layer solution includes: transforming the gas chamber dynamic equation of the oscillating water column device to the frequency domain to obtain the gas chamber pressure. With water column volume flow rate Frequency domain aerodynamic impedance relationship between them: ,in, The frequency-domain aerodynamic impedance of the air chamber of the oscillating water column device is given; this impedance relationship is then embedded as an additional impedance term into the frequency-domain dynamic coefficient matrix of the frequency-domain motion equation in step S1, resulting in the corrected frequency-domain dynamic coefficient matrix. .

6. The method for jointly calculating the motion response and energy capture efficiency of the wave-fishing fusion platform according to claim 5, characterized in that, The frequency domain aerodynamic impedance The expression is: ； in, where c is the air density and c is the speed of sound. Where ω is the volume of the air chamber and ω is the wave angular frequency. The turbine admittance coefficient is the power extraction parameter.

7. The method for jointly calculating the motion response and energy capture efficiency of the wave-fishing fusion platform according to claim 6, characterized in that, In step S3, for an oscillating water column device with two air chambers (front and rear), the total energy capture efficiency is defined as the ratio of the sum of the energy capture power of the front air chamber and the energy capture power of the rear air chamber to the incident wave power: ； in, The energy harvesting power of the fore-chamber. This represents the energy harvesting power of the rear chamber; The energy-harvesting power of a single gas chamber is calculated using the following formula: ;in, This refers to the air chamber pressure of the oscillating water column device; Incident wave power Calculate using the following formula: ;in, The density of seawater, It is the acceleration due to gravity. For wave height, For wave cycles, The total width of the wave-facing opening of the oscillating water column device is given for devices with two air chambers, one at the front and one at the back. It is the sum of the widths of the two air chambers.

8. The method for jointly calculating the motion response and energy capture efficiency of the wave-fishing fusion platform according to claim 5, characterized in that, In step S3, the constructed linearized system equations are a system of linear equations containing hinged constraints, and their matrix form is as follows: ； in, This is the corrected frequency domain dynamic coefficient matrix. The displacement constraint matrix is... It is the transpose of the displacement constraint matrix. It is a generalized displacement vector. Let Lagrange multiplier vectors be used. This is the corrected wave excitation force vector. It is a zero vector; The linear equations are solved using a direct solver to obtain the platform motion response amplitude operator and the air chamber pressure at each frequency point.

9. The method for jointly calculating the motion response and energy capture efficiency of the wave-fishing fusion platform according to claim 1, characterized in that, The calculation method was first verified in a scaled numerical simulation model, in which the aerodynamic similarity treatment of the scaled model adopted Froude similarity correction to scale the equivalent sound speed; when applied to real-scale engineering, it is necessary to combine parameter optimization and model correction.

10. The method for jointly calculating the motion response and energy capture efficiency of the wave-fishing fusion platform according to claim 1, characterized in that, In step S4, the comparative analysis of different articulation methods is conducted by assigning different motion constraint weights to the objective function to obtain the trade-off between motion suppression effect and energy capture efficiency, and output in the form of Pareto front.

Images