Multi-objective optimization method and system for wave energy recovery of container ship built-in heave oscillators

Abstract

The application relates to the technical field of wave energy recovery, and discloses a container ship built-in heaving oscillator wave energy recovery multi-target optimization method and system. The method comprises the following steps: based on a boundary element method, water dynamics of multiple groups of speed and encounter angle combinations is solved to obtain a water dynamic coefficient matrix; additional mass in the water dynamic coefficient matrix is used for iterative solving of oscillator natural frequency and calculation of encounter frequency to obtain a frequency mistuning amount; a speed deviation amount, an encounter angle deviation amount, PTO stiffness and PTO damping constitute a four-dimensional decision vector, three-target collaborative optimization is carried out by taking the water dynamic coefficient matrix and the frequency mistuning amount as input, and a Pareto optimal solution set is obtained; a net positive income solution is screened from the Pareto optimal solution set, and a joint scheduling instruction is output. The application improves the executability of the wave energy recovery multi-target optimization scheme in an actual shipping scheduling scene.

Description

Technical Field

[0001] This application relates to the field of wave energy recovery technology, and in particular to a multi-objective optimization method and system for wave energy recovery using a container ship built-in heave oscillator. Background Technology

[0002] Container ships experience continuous wave excitation during navigation, resulting in heaving motion. Installing heaving oscillators inside the hull and converting the relative motion between the oscillators and the hull into electrical energy through a power output system is a technological approach to wave energy recovery without altering the ship's external geometry. Existing solutions have established frequency-domain mathematical models based on the boundary element method in this field. These models analyze the oscillator response and the damping strategy of the power output system by solving for the ship's hydrodynamic coefficients. A radial basis function surrogate model is used to replace the computationally expensive boundary element method for online solution. Furthermore, a multi-objective optimization algorithm is combined to optimize the stiffness and damping parameters of the power output system, achieving a synergistic balance between maximizing wave energy capture power and minimizing mechanical load.

[0003] However, existing solutions use the statistical parameters of wave conditions along a fixed route as model input when building the surrogate model. This results in the generalization domain of the surrogate model being hard-coded within the distribution range of the training samples. Once the container ship enters a sea area not covered by the training set, the prediction error of the surrogate model will increase sharply, and the optimization results will fail. A more fundamental limitation is that existing solutions always treat the container ship's speed and encounter angle as fixed inputs unilaterally determined by the external wave environment, rather than decision variables that can participate in optimization. This means that the detuning state between the encounter frequency and the oscillator's natural frequency cannot be actively intervened through scheduling. The optimization of the power output system parameters can only passively adapt to a given encounter frequency, and cannot reduce the frequency detuning at the source to expand the energy capture space.

[0004] Because existing schemes do not model frequency detuning as a controllable variable that can be adjusted by speed and encounter angle, the optimization of power output system parameters and ship navigation decisions remain disconnected. In this disconnected state, even if the power output system parameters have reached a local optimum at a given encounter frequency, the oscillator will still operate in an inefficient range that deviates from the resonance point for a long time, and this inefficiency cannot be eliminated by adjusting the power output system parameters alone. Furthermore, since the adjustment of speed and encounter angle also affects the main engine fuel consumption, if the wave energy recovery benefits and the fuel consumption increase introduced by speed adjustment are not included in the same optimization framework for quantitative comparison, it is impossible to determine whether the adjustment of speed and encounter angle has a net positive benefit on a specific route. As a result, existing schemes lack the ability to convert the wave energy recovery optimization results into directly executable shipping scheduling instructions. Summary of the Invention

[0005] This application provides a multi-objective optimization method and system for wave energy recovery using a built-in heave oscillator in container ships. It solves the problems of disconnect between navigation decision-making and power output system parameter optimization in the wave energy recovery optimization of built-in heave oscillators in container ships, and the inability to actively intervene when encountering frequency detuning. It improves the feasibility of the multi-objective optimization scheme for wave energy recovery in actual shipping scheduling scenarios.

[0006] Firstly, this application provides a multi-objective optimization method for wave energy recovery using a container ship's built-in heave oscillator, the multi-objective optimization method for wave energy recovery using a container ship's built-in heave oscillator includes: Step S1: Based on the boundary element method, hydrodynamic solutions are performed on the excitation force transmission relationship, added mass and radiation damping of the container ship under multiple combinations of speed and encounter angle to obtain the hydrodynamic coefficient matrix. Step S2: Using the added mass in the hydrodynamic coefficient matrix as a parameter, iteratively solve the natural frequency of the built-in heave oscillator, and calculate the encounter frequency with the current speed and encounter angle as independent variables. Subtract the encounter frequency from the natural frequency to obtain the frequency detuning. Step S3: Construct a four-dimensional decision vector from the speed deviation, encounter angle deviation, PTO stiffness, and PTO damping. Using the hydrodynamic coefficient matrix and the frequency detuning as inputs, and wave energy capture power, PTO mechanical load, and net fuel consumption as three optimization objectives, under the constraints of the upper limit of speed deviation, the upper limit of encounter angle deviation, and the upper limit of oscillator effective stroke, perform three-objective collaborative optimization on the four-dimensional decision vector using a non-dominated sorting genetic algorithm to obtain the Pareto optimal solution set. Step S4: Select the solution with net positive benefit that is greater than net fuel consumption increase from the Pareto optimal solution set, and output a joint scheduling command including the speed deviation, encounter angle deviation, PTO stiffness and PTO damping.

[0007] Secondly, this application provides a multi-objective optimization system for wave energy recovery using a container ship-integrated heave oscillator, the multi-objective optimization system for wave energy recovery using a container ship-integrated heave oscillator includes: The solution module is used to solve the hydrodynamic relationship of excitation force transmission, added mass and radiation damping of container ships under multiple combinations of speed and encounter angle based on the boundary element method, and obtain the hydrodynamic coefficient matrix. The difference module is used to iteratively solve the natural frequency of the built-in heave oscillator using the added mass in the hydrodynamic coefficient matrix as a parameter, and to calculate the encounter frequency using the current speed and encounter angle as independent variables. The difference between the encounter frequency and the natural frequency is used to obtain the frequency detuning. The input module is used to construct a four-dimensional decision vector from the speed deviation, encounter angle deviation, PTO stiffness, and PTO damping. Taking the hydrodynamic coefficient matrix and the frequency detuning as input, and wave energy capture power, PTO mechanical load, and net fuel consumption as three optimization objectives, under the constraints of the upper limit of speed deviation, the upper limit of encounter angle deviation, and the upper limit of oscillator effective stroke, the four-dimensional decision vector is optimized by a non-dominated sorting genetic algorithm to obtain the Pareto optimal solution set. The output module is used to filter the net positive benefit solutions from the Pareto optimal solution set where the net fuel savings are greater than the net fuel consumption increase, and output a joint scheduling command including the speed deviation, the encounter angle deviation, the PTO stiffness, and the PTO damping.

[0008] Thirdly, a container ship built-in heave oscillator wave energy recovery multi-objective optimization device is provided, comprising: a memory and at least one processor, wherein the memory stores instructions; the at least one processor invokes the instructions in the memory to cause the container ship built-in heave oscillator wave energy recovery multi-objective optimization device to execute the above-described container ship built-in heave oscillator wave energy recovery multi-objective optimization method.

[0009] Fourthly, a computer-readable storage medium is provided, wherein instructions are stored therein, which, when executed on a computer, cause the computer to perform the aforementioned multi-objective optimization method for wave energy recovery using a container ship built-in heave oscillator.

[0010] The technical solution provided in this application applies the boundary element method to solve the hydrodynamic problems of container ships under multiple combinations of speed and encounter angles, obtaining a hydrodynamic coefficient matrix covering all operating conditions. This allows the additional mass, radiation damping, and excitation force transmission relationships under any operating condition to be directly obtained through trilinear interpolation in subsequent calculations, avoiding the problem of repeatedly performing computationally expensive numerical simulations for each operating condition in existing solutions. Based on this, the natural frequency of the oscillator is iteratively solved using the additional mass as a parameter, and the encounter frequency is calculated using speed and encounter angle as independent variables. The difference between the two is defined as the frequency detuning, which quantitatively characterizes the frequency matching degree between the oscillator and wave excitation, providing a clear physical basis for incorporating speed and heading into subsequent optimization decisions.

[0011] This invention constructs a four-dimensional decision vector by combining speed deviation, encounter angle deviation, PTO stiffness, and PTO damping. This overcomes the limitation of existing schemes that only optimize PTO parameters and treat navigation status as a fixed input, making encounter frequency a variable that can be actively intervened through scheduling decisions. This achieves the first systematic coupling between wave energy recovery optimization and container ship shipping scheduling. A non-dominated sorting genetic algorithm collaboratively optimizes among three objectives: wave energy capture power, PTO mechanical load, and net fuel consumption increase, outputting a complete Pareto optimal solution set. This allows decision-makers to weigh energy recovery benefits against shipping efficiency according to actual operational constraints. Finally, using net fuel savings exceeding net fuel consumption increase as the selection criterion, a joint scheduling command including speed deviation, encounter angle deviation, PTO stiffness, and PTO damping is output. This directly transforms the optimization results into executable control parameters, solving the problem in existing schemes where wave energy recovery optimization results are disconnected from the actual shipping scheduling system and cannot directly guide ship control. Attached Figure Description

[0012] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a schematic diagram of an embodiment of the multi-objective optimization method for wave energy recovery using a container ship with an internal heave oscillator, as described in this application. Figure 2 This is a schematic diagram comparing the wave energy capture power at different encounter angles under different speed deviations in the embodiments of this application; Figure 3 This is a schematic diagram showing the distribution of the Pareto optimal solution set in the two-dimensional target space of wave energy capture power and PTO mechanical load in the embodiments of this application. Detailed Implementation

[0014] This application provides a multi-objective optimization method and system for wave energy recovery using a container ship with an integrated heave oscillator. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or device that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or devices.

[0015] For ease of understanding, the specific process of the embodiments of this application is described below. Please refer to [link / reference]. Figure 1 One embodiment of the multi-objective optimization method for wave energy recovery using a container ship with an internal heave oscillator in this application includes: Step S1: Based on the boundary element method, hydrodynamic solutions are performed on the excitation force transmission relationship, added mass and radiation damping of the container ship under multiple combinations of speed and encounter angle to obtain the hydrodynamic coefficient matrix. Specifically, for the hydrodynamic problems of container ships under multiple speed and encounter angle conditions, the boundary element method is used to solve the wave diffraction and radiation problems respectively, obtaining the excitation force transmission relationship, added mass, and radiation damping under each condition. These excitation force transmission relationships, added mass, and radiation damping are then used as elements and arranged according to the combined index of speed and encounter angle to form a hydrodynamic coefficient matrix.

[0016] The speed discrete range was set to 16 to 24 knots with a step size of 2 knots, and the encounter angle discrete range was set to 0° to 180° with a step size of 30°, resulting in 35 sets of operating conditions. The step size was chosen based on the fact that this discrete density covers all typical operating conditions of container ships in actual operation. If the step size is too large, the subsequent trilinear interpolation error will exceed the acceptable range in engineering, while if the step size is too small, the computational workload of the boundary element method will increase significantly. The 35 sets of operating conditions strike a balance between computational accuracy and computational efficiency.

[0017] Step S2: Using the added mass in the hydrodynamic coefficient matrix as a parameter, iteratively solve the natural frequency of the built-in heave oscillator, and calculate the encounter frequency with the current speed and encounter angle as independent variables. Subtract the encounter frequency from the natural frequency to obtain the frequency detuning. Specifically, the oscillator mass refers to the structural mass of the heave oscillator installed inside the container ship's hold, including the total mass of the oscillator body, guide rails, sliders, and auxiliary connecting parts. This value is a known fixed parameter after the oscillator is manufactured, determined during the system design phase, and measured and calibrated during installation and commissioning. The iterative solution for the natural frequency uses the sum of the added mass and the oscillator mass as the equivalent inertial mass, and the sum of the PTO stiffness and the spring stiffness as the equivalent restoring stiffness. The square root of the ratio of the two is used to obtain the initial value of the natural frequency. This initial value is then substituted into the hydrodynamic coefficient matrix to re-query the corresponding added mass and update the equivalent inertial mass. The above square root operation is repeated until the absolute value of the difference between the two natural frequencies is lower than the first convergence threshold of 0.0001 radians per second. The first convergence threshold is set at 0.0001 radians per second because the typical natural frequency range of the built-in heave oscillator in a container ship is 0.5 to 1.5 radians per second, and the first convergence threshold of 0.0001 radians per second is on the order of one ten-thousandth relative to the natural frequency value. Numerical simulations verify that when the difference between two consecutive natural frequencies decreases from 0.001 radians per second to 0.0001 radians per second, the relative change in the calculated wave energy capture power is less than 0.1%, which is lower than the engineering measurement error. Further reducing the threshold does not change the optimization result. This iterative process typically converges within 3 to 5 iterations, with calculation time on the order of milliseconds. The encounter frequency is calculated based on the dominant wave frequency, current speed, and the cosine of the encounter angle. The frequency mistuning is the algebraic difference between the encounter frequency and the converged natural frequency; a positive value indicates undertuning, and a negative value indicates overtuning. This quantity directly characterizes the frequency matching degree between the built-in heave oscillator and the current wave excitation.

[0018] Step S3: Construct a four-dimensional decision vector from the speed deviation, encounter angle deviation, PTO stiffness, and PTO damping. Use the hydrodynamic coefficient matrix and frequency detuning as inputs, and the wave energy capture power, PTO mechanical load, and net fuel consumption as three optimization objectives. Under the constraints of the upper limit of speed deviation, the upper limit of encounter angle deviation, and the upper limit of oscillator effective stroke, use a non-dominated sorting genetic algorithm to perform three-objective collaborative optimization on the four-dimensional decision vector to obtain the Pareto optimal solution set. Specifically, the four-dimensional decision vector consists of speed deviation, encounter angle deviation, PTO stiffness, and PTO damping. The upper limit for speed deviation is set at 2 knots, and the upper limit for encounter angle deviation is set at 20°. Both values ​​are based on the rigid constraints of on-time performance in container liner shipping scheduling. Exceeding these limits will result in arrival time deviations exceeding the contractually permissible range. The upper limit for the effective stroke of the oscillator is determined by the maximum permissible travel of the oscillator guide rail within the ship's hold, and is set at 1.5 meters. The wave energy capture power is obtained by taking half of the product of PTO damping and the variance of the relative velocity of the oscillator and hull. The relative velocity variance is obtained by integrating the product of the JONSWAP wave spectrum and the excitation force transmission relationship over the entire frequency range. The PTO mechanical load is obtained by taking the square root of the sum of the squares of the product of PTO damping and the variance of relative velocity, and the product of PTO stiffness and the variance of relative displacement. The net fuel consumption increase is obtained by multiplying the main engine power increase corresponding to the adjusted speed by the segment duration and then by the unit fuel consumption, subtracting the wave energy capture power multiplied by the segment duration and then dividing by the product of the low calorific value of heavy fuel oil and the thermal efficiency of the main engine. The three-objective collaborative optimization uses a non-dominated sorting genetic algorithm to sequentially perform non-dominated sorting, crowding distance calculation, tournament selection, simulated binary crossover, and polynomial mutation on the initial population until the continuous rate of change of the hypervolume index is lower than the second convergence threshold, thus obtaining the Pareto optimal solution set.

[0019] Step S4: Select the solution with net positive benefit that is greater than net fuel consumption from the Pareto optimal solution set, and output a joint scheduling command that includes speed deviation, encounter angle deviation, PTO stiffness and PTO damping.

[0020] Specifically, the selection criterion for net positive benefit solutions is that the equivalent fuel savings are greater than the net fuel consumption increase. The equivalent fuel savings are obtained by multiplying the wave energy capture power by the segment duration and then dividing by the product of the lower calorific value of heavy fuel and the thermal efficiency of the main engine, in tons. The fuel consumption increase is obtained by multiplying the increase in main engine power corresponding to the adjusted speed by the segment duration and then by the unit fuel consumption, in tons. The equivalent fuel savings are also obtained by multiplying the wave energy capture power by the segment duration and then dividing by the product of the lower calorific value of heavy fuel and the thermal efficiency of the main engine, in tons. The net fuel consumption increase is obtained by subtracting the equivalent fuel savings from the fuel consumption increase. Both are compared in the same unit, and only solutions with equivalent fuel savings greater than net fuel consumption are retained to form the net positive benefit solution set. In the net positive benefit solution set, solutions with PTO mechanical loads exceeding the preset mechanical load safety threshold are further removed. The remaining solutions are sorted from largest to smallest net benefit, and the solution at the top of the sort is used to output a joint scheduling command including speed deviation, encounter angle deviation, PTO stiffness, and PTO damping.

[0021] In one specific embodiment, step S1 includes: The speed of the container ship is discretized within a preset speed range with a preset step size, and the encounter angle is discretized within a range of 0° to 180° with a preset step size to obtain multiple combinations of speed and encounter angle. Based on the boundary element method, the wave diffraction and radiation problems of container ships under multiple combinations of speed and encounter angle are numerically solved to obtain the excitation force transmission relationship, added mass and radiation damping under each working condition. The excitation force transmission relationship, additional mass, and radiation damping under various operating conditions are arranged according to the index of multiple combinations of speed and encounter angle to obtain the hydrodynamic coefficient matrix.

[0022] Specifically, the speed discrete range for container ships is set to 16 to 24 knots with a step size of 2 knots, and the encounter angle discrete range is set to 0° to 180° with a step size of 30°, forming a total of 35 operating condition combinations. The speed range covers all actual operating conditions of container ships from economic speed to design speed. The 2-knot step size is based on the fact that the influence of two adjacent speeds on the hydrodynamic coefficient changes approximately linearly. At a step size of 2 knots, the trilinear interpolation error is within an acceptable range for engineering purposes, while the increased computational load of the boundary element method due to further decreasing the step size is disproportionate to the improvement in interpolation accuracy. The 30° step size for the encounter angle is based on the fact that the influence of the wave encounter angle change on the hydrodynamic coefficient in actual operation of container ships can be accurately restored by interpolation at a step size of 30°. An excessively large step size will lead to distortion of the excitation force transmission relationship near the side wave condition.

[0023] The excitation force transmission relationship refers to the ratio of the wave excitation force amplitude to the wave amplitude experienced by a container ship at a specific encounter frequency under a unit amplitude sinusoidal wave excitation. This quantity is directly obtained by solving the wave diffraction problem using the boundary element method, and its value varies with the encounter frequency, speed, and encounter angle. In the offline pre-calculation stage, the added mass and radiation damping are obtained by solving the radiation problem using the boundary element method and stored in the hydrodynamic coefficient matrix. The added mass represents the equivalent inertial increment generated by the displaced fluid during hull motion, and the radiation damping represents the equivalent damping coefficient corresponding to the energy dissipated by the outward radiation of waves during hull motion; both are functions of the encounter frequency. Arranging the excitation force transmission relationships, added mass, and radiation damping corresponding to each encounter frequency under 35 operating conditions according to the combination index of speed and encounter angle constitutes the hydrodynamic coefficient matrix. This matrix uses speed, encounter angle, and encounter frequency as three-dimensional indices, supporting subsequent trilinear interpolation for any combination of speed and encounter angle.

[0024] In one specific embodiment, step S2 includes: Based on the current speed and encounter angle, trilinear interpolation is performed on the hydrodynamic coefficient matrix to obtain the additional mass under the current operating conditions. The sum of the added mass and the oscillator mass is taken as the equivalent inertial mass, and the sum of the PTO stiffness and the spring stiffness is taken as the equivalent restoring stiffness. The square root of the ratio of the equivalent inertial mass and the equivalent restoring stiffness is performed to obtain the initial value of the natural frequency. The initial value of the natural frequency is substituted into the hydrodynamic coefficient matrix to re-interpolate and obtain the updated added mass. The square root of the ratio is repeated until the absolute value of the difference between the two natural frequencies is lower than the first convergence threshold, and the converged natural frequency is obtained. Based on the current speed and the cosine of the encounter angle, the encounter frequency is calculated from the frequency of the dominant wave. The frequency detuning is obtained by subtracting the encountered frequency from the converged natural frequency.

[0025] Specifically, in the online calculation phase, trilinear interpolation uses the current operating condition's speed, encounter angle, and encounter frequency as three interpolation dimensions. The input value for the third dimension is taken as the initial value of the natural frequency. A weighted average of the additional mass of adjacent nodes in the hydrodynamic coefficient matrix is ​​applied, with the weights determined by the distance ratios between the current interpolation point and each adjacent node in the three dimensions. The interpolation result is the additional mass value at the corresponding natural frequency under the current operating condition. Equivalent inertial mass refers to the total mass actually borne by the built-in heave oscillator during coupled motion, consisting of the oscillator's own mass and the additional mass. The additional mass is the equivalent inertial increment generated by the fluid displaced during the oscillator's motion. Equivalent restoring stiffness refers to the ratio of the restoring force to the displacement after the oscillator experiences heave displacement, consisting of the spring stiffness and the PTO equivalent stiffness. The initial value of the natural frequency is obtained by dividing the equivalent restoring stiffness by the equivalent inertial mass and taking the positive square root. This initial value is then substituted into the hydrodynamic coefficient matrix to re-interpolate and update the added mass, and the above square root operation is performed again. During the iteration process, the first convergence threshold is set to the absolute value of the difference between the two natural frequencies being less than 0.0001 radians per second. The basis for this setting is that when the natural frequency change is below this threshold, the impact of the frequency detuning on the natural frequency change is less than the engineering measurement error.

[0026] The dominant wave frequency refers to the angular frequency corresponding to the point of highest energy concentration in the current sea wave spectrum, provided in real time by the shipborne wave measurement system or weather forecasting system. Encounter frequency calculation uses the dominant wave frequency, current speed, and the cosine of the encounter angle as inputs. It is derived based on the physical relationship between wave encounter frequency and speed / encounter angle during container ship navigation, characterizing the frequency at which the oscillator is actually excited by the waves. Frequency detuning is the algebraic difference between the encounter frequency and the converged natural frequency. A positive value indicates that the encounter frequency is higher than the natural frequency (undertuned state), while a negative value indicates that the encounter frequency is lower than the natural frequency (overtuned state). The absolute value of this quantity directly reflects the degree to which the built-in heave oscillator deviates from the resonant operating point. It serves as input for subsequent four-dimensional decision vector optimization, guiding the direction and amplitude of PTO stiffness adjustment.

[0027] In one specific embodiment, step S3 constructs a four-dimensional decision vector from the speed deviation, encounter angle deviation, PTO stiffness, and PTO damping, including: The container ship's speed deviation is limited to a preset upper limit, the encounter angle deviation is limited to a preset upper limit, the PTO stiffness is limited to a feasible region of PTO stiffness, and the PTO damping is limited to a feasible region of PTO damping, thus obtaining the feasible region of the four-dimensional decision vector. Based on Latin hypercube sampling, the speed deviation, encounter angle deviation, PTO stiffness, and PTO damping are uniformly sampled within the feasible region of the four-dimensional decision vector to obtain the initial population.

[0028] Specifically, the upper limit for speed deviation is set at 2 knots, and the upper limit for encounter angle deviation is set at 20°. Both are based on the rigid constraint of on-time performance in container liner shipping scheduling. A speed deviation exceeding 2 knots will result in an increase in main engine fuel consumption exceeding the wave energy recovery benefit, and an encounter angle deviation exceeding 20° will result in an arrival time deviation exceeding the allowable range of the transportation contract. The lower limit of the feasible region for PTO stiffness is determined by the minimum preload stiffness of the spring, and the upper limit is determined by the structural strength limit corresponding to the maximum allowable load of the oscillator guide rail. The lower limit of the feasible region for PTO damping is determined by the minimum damping coefficient of the PTO mechanical system, and the upper limit is determined by the maximum damping coefficient corresponding to the rated power of the PTO. Both feasible regions are directly constrained by the mechanical structural parameters of the container ship's built-in heave oscillator system.

[0029] Latin hypercube sampling is a hierarchical uniform sampling method. It works by dividing the feasible region of each dimension of the four-dimensional decision vector into a number of sub-intervals equal to the population size. A sampling point is randomly selected within each sub-interval, ensuring that the sampling points in each dimension are uniformly distributed and non-overlapping within the feasible region. Finally, the sampling points from all four dimensions are randomly combined to obtain each individual in the initial population. Compared to pure random sampling, Latin hypercube sampling ensures the uniform distribution of the initial population within the four-dimensional feasible region, preventing multiple individuals from concentrating in local areas and missing the region containing the global optimum. The population size is set at 200 individuals. This setting is based on the following: below 200 individuals, the Pareto front coverage of the non-dominated sorting genetic algorithm is insufficient; above 200 individuals, the computation time per generation increases significantly while the improvement in Pareto front quality is limited. A population size of 200 individuals strikes a balance between convergence quality and computational efficiency.

[0030] In one specific embodiment, step S3 uses the hydrodynamic coefficient matrix and frequency detuning as inputs, and wave energy capture power, PTO mechanical load, and net fuel consumption increase as three optimization objectives, including: Substitute the speed deviation and encounter angle deviation of each individual in the initial population into the hydrodynamic coefficient matrix for trilinear interpolation to obtain the excitation force transmission relationship, added mass and radiation damping under the corresponding working conditions. Based on the excitation force transmission relationship, added mass and radiation damping, frequency domain integration is performed on the relative velocity variance and relative displacement variance between the oscillator and the hull to obtain the wave energy capture power and PTO mechanical load. Based on the relationship between speed deviation and main engine power-speed, the difference between the main engine power increment corresponding to the adjusted speed and the equivalent fuel saving corresponding to wave energy capture power is calculated to obtain the net fuel consumption increase.

[0031] Specifically, the integrand of the frequency domain integral is constituted by the frequency response of the oscillator-hull coupled system, jointly determined by the JONSWAP wave spectral density, the excitation force transmission relationship, the added mass, and the radiation damping. The integration interval covers the entire effective encounter frequency range. The relative velocity variance refers to the statistical variance of the relative velocity between the oscillator and the hull under irregular wave excitation, obtained by integrating the square of the ratio of the JONSWAP wave spectral density to the amplitude of the oscillator's relative velocity with respect to the wave surface displacement over the entire frequency range. The relative displacement variance refers to the statistical variance of the relative displacement between the oscillator and the hull, obtained by integrating the square of the ratio of the JONSWAP wave spectral density to the amplitude of the oscillator's relative displacement with respect to the wave surface displacement over the entire frequency range. The wave energy capture power is obtained by taking half the product of the PTO damping and the relative velocity variance. The PTO mechanical load is obtained by taking the positive square root of the sum of the squares of the products of the PTO damping and the relative velocity variance, and the products of the PTO stiffness and the relative displacement variance, characterizing the root mean square load value borne by the PTO system.

[0032] The main engine power-speed relationship is derived from the standard propulsion curve for container ships. This curve describes the relationship between main engine output power and ship speed. The rated main engine power at the design speed is used as a benchmark, and the increase in main engine power is obtained by the difference between the main engine power at the adjusted speed and the main engine power at the benchmark speed. The equivalent fuel savings are calculated by multiplying the wave energy capture power by the sailing duration to obtain the total power generated, then dividing by the product of the lower calorific value of the heavy fuel oil and the main engine thermal efficiency, converting it into tons equivalent to the mass of fuel saved. The lower calorific value of the heavy fuel oil is taken as 42,700 kJ / kg, and the main engine thermal efficiency as 0.52; both are commonly used engineering parameters for container ship main engines. Net fuel consumption is calculated by multiplying the increase in main engine power by the segment duration and then by the unit fuel consumption of the main engine, and then subtracting the equivalent fuel savings. A positive net fuel consumption indicates that the fuel consumption introduced by speed adjustment is greater than the savings from wave energy recovery, while a negative net fuel consumption indicates that the savings from wave energy recovery are greater than the fuel consumption introduced by speed adjustment. This difference is directly used as the objective function value of the third optimization objective to participate in the subsequent non-dominated sorting genetic algorithm optimization.

[0033] Figure 2This is a schematic diagram comparing the wave energy capture power corresponding to different encounter angles under different speed deviations in the embodiments of this application. The horizontal axis of the figure is the encounter angle, and the vertical axis is the wave energy capture power. The three sets of bars correspond to three cases with speed deviations of 0 knots, +1 knots, and +2 knots, respectively, which are 0 knots, 1 knot, and 2 knots added to the base speed. The corresponding values ​​are marked at the top of each set of bars. The data in the figure shows that the wave energy capture power is the largest when the encounter angle is around 90°, and the larger the speed deviation, the higher the wave energy capture power. This verifies the necessity of incorporating the speed deviation into the four-dimensional decision vector for optimization.

[0034] In one specific embodiment, in step S3, under the constraints of the upper limit of speed deviation, the upper limit of encounter angle deviation, and the upper limit of the effective stroke of the oscillator, a non-dominated sorting genetic algorithm is used to perform three-objective collaborative optimization on the four-dimensional decision vector to obtain the Pareto optimal solution set, including: Wave energy capture power, PTO mechanical load, and net fuel consumption increase are used as three optimization objectives. The individuals in the initial population are non-dominated and ordered, and the crowding distance is calculated for individuals within the same non-dominated level to obtain the non-dominated level and crowding distance of each individual. Based on the non-dominant level and crowding distance, the initial population is subjected to tournament selection, simulated binary crossover and polynomial mutation in sequence. Under the constraint of the upper limit of the effective stroke of the oscillator, individuals exceeding the constraint are penalized to obtain an updated population. Repeatedly perform non-dominated sorting, crowding distance calculation and tournament selection, simulated binary crossover and polynomial mutation on the updated population until the continuous rate of change of the hypervolume index is lower than the second convergence threshold to obtain the Pareto optimal solution set.

[0035] Specifically, the logic for determining non-dominated ranking is as follows: For any two individuals in the initial population, if individual A is not inferior to individual B in all three objectives—wave energy capture power, PTO mechanical load, and net fuel consumption increase—and is superior to individual B in at least one objective, then individual A is said to dominate individual B. All individuals not dominated by any individual constitute the first non-dominated rank. After removing individuals of the first rank from the population, the above judgment is repeated to obtain the second non-dominated rank, and so on until all individuals have completed the rank division. Crowding distance refers to the average target value distance between an individual within the same non-dominated rank and its adjacent individuals in the three target spaces. It is calculated as follows: for each target dimension, individuals of the same rank are ranked according to their target values. The crowding distance of each internal individual in that dimension is the difference between the target values ​​of its two adjacent individuals. The crowding distance of boundary individuals is assigned an infinite value. The total crowding distance of each individual is obtained by summing the crowding distances of the three target dimensions. The tournament selects two individuals randomly from the population, prioritizing those with lower non-dominated ranks. If the ranks are the same, those with larger crowding distances are selected to enter the parent generation. The distribution index for simulated binary crossover is set to 20, the distribution index for polynomial mutation is set to 20, and the mutation probability is set to the reciprocal of the dimension of the four-dimensional decision vector, i.e., 0.25. The above parameter values ​​are based on the following: the distribution index of 20 makes the crossover and mutation results concentrated near the parent generation, ensuring the local search capability of the population, and the mutation probability of 0.25 ensures that on average one of the four decision variables will mutate, maintaining population diversity.

[0036] The upper limit of the effective stroke of the oscillator is set at 1.5 meters, which is determined by the maximum allowable stroke of the oscillator guide rail in the cabin. For individuals that exceed this upper limit of stroke, a penalty is imposed by superimposing the objective function value to place them in the worst category in the non-dominated ranking. The penalty is set to ten times the range of the three objective function values ​​to ensure that individuals that exceed the constraints are completely eliminated during the selection process. The hypervolume index refers to the hypervolume value enclosed by all non-dominated solutions of the Pareto front in the three-dimensional target space relative to a preset reference point. This index comprehensively reflects the convergence and distribution uniformity of the Pareto front. The hypervolume index is calculated as follows: First, a reference point is set, which is composed of the worst values ​​of three objectives in the current population: wave energy capture power, PTO mechanical load, and net fuel consumption increase. Then, the volume of the closed region enclosed by all non-dominated solutions in the current Pareto front and the reference point in the three-dimensional target space is used as the value of the hypervolume index. The larger the value, the farther the Pareto front is from the reference point and the more uniform the distribution of solutions, that is, the better the convergence and diversity of the Pareto front. When the rate of change of the hypervolume index value is lower than the second convergence threshold for twenty consecutive iterations, it indicates that the Pareto front has stabilized and the iteration is terminated.

[0037] The second convergence threshold is set to a rate of change of hypervolume index of less than 0.001 for 20 consecutive generations. The basis for this setting is that when the rate of change is below this threshold, the Pareto front is basically stable. Continuing the iteration will not change the final solution set distribution. At this point, the iteration is terminated and all individuals of the current first non-dominated level are output as the Pareto optimal solution set.

[0038] Figure 3 This is a schematic diagram showing the distribution of the Pareto optimal solution set in the two-dimensional target space of wave energy capture power and PTO mechanical load in the embodiments of this application. In the figure, solid circles represent net positive benefit solutions where the net fuel savings are greater than the net fuel consumption increase, hollow squares represent net negative benefit solutions, and pentagrams mark the optimal scheduling solutions output after screening by the PTO mechanical load safety threshold and sorting by net benefit. The distribution pattern in the figure shows that there is a constraint relationship between wave energy capture power and PTO mechanical load. The non-dominated sorting genetic algorithm provides a complete Pareto tradeoff boundary between the two objectives.

[0039] In one specific embodiment, step S4 includes: The wave energy capture power corresponding to each solution in the Pareto optimal solution set is converted into thermal equivalent based on the low calorific value of heavy fuel oil and the thermal efficiency of the main engine, and the product of wave energy capture power and flight duration is calculated to obtain the equivalent fuel savings corresponding to each solution. Based on the equivalent fuel savings and net fuel consumption increase, the difference operation is performed on each solution in the Pareto optimal solution set to obtain the net benefit corresponding to each solution. Solutions with net profit greater than zero are selected from the Pareto optimal solution set to obtain a solution set with net positive profit; Based on the PTO mechanical load corresponding to each solution in the net positive gain solution set, solutions whose PTO mechanical load exceeds the preset mechanical load safety threshold are eliminated. The remaining solutions are sorted from largest to smallest net gain, and the solution at the top of the sort is used to output a joint scheduling command that includes speed deviation, encounter angle deviation, PTO stiffness, and PTO damping.

[0040] Specifically, the thermal equivalent conversion process is as follows: The wave energy capture power corresponding to each solution in the Pareto optimal solution set is multiplied by the segment duration to obtain the total wave energy recovery power corresponding to that solution. This power is then divided by the product of the lower heating value of the heavy fuel oil and the main engine thermal efficiency to obtain the equivalent fuel savings, in tons. The lower heating value of the heavy fuel oil is taken as 42,700 kJ / kg, which is the standard lower heating value of heavy fuel oil commonly used in container ships; the main engine thermal efficiency is taken as 0.52, which is the typical thermal efficiency of a low-speed two-stroke diesel main engine for container ships under rated operating conditions. The net benefit is obtained by subtracting the net fuel consumption increase from the equivalent fuel savings, in tons. A positive value indicates that the fuel savings converted from wave energy recovery exceed the fuel consumption increase introduced by speed adjustment, while a negative value indicates that the fuel consumption increase introduced by speed adjustment exceeds the fuel savings converted from wave energy recovery. Only solutions with a net benefit greater than zero constitute a net positive benefit solution set.

[0041] The preset mechanical load safety threshold is determined by the structural strength design limit of the container ship's built-in heave oscillator (PTO) system, and is set to 800 kN. Solutions exceeding this threshold will subject the PTO system to loads exceeding the allowable structural range during actual operation and must be removed from the net positive benefit solution set. The remaining solutions are sorted from largest to smallest net benefit, and the solution at the top of the sort is used to output a joint scheduling command. This command contains four components: speed deviation guides the automatic steering system's adjustment of the main engine speed; encounter angle deviation guides the automatic steering system's adjustment of the course; PTO stiffness guides the PTO controller's setting of the spring preload; and PTO damping guides the PTO controller's setting of the damping coefficient. These four components together constitute a complete multi-objective joint optimization scheduling command for wave energy recovery using the container ship's built-in heave oscillator.

[0042] The above describes the multi-objective optimization method for wave energy recovery using a container ship with an internal helical oscillator in this application embodiment. The following describes the multi-objective optimization system for wave energy recovery using a container ship with an internal helical oscillator in this application embodiment. One embodiment of this multi-objective optimization system for wave energy recovery using a container ship with an internal helical oscillator in this application embodiment includes: The solution module is used to solve the hydrodynamic relationship of excitation force transmission, added mass and radiation damping of container ships under multiple combinations of speed and encounter angle based on the boundary element method, and obtain the hydrodynamic coefficient matrix. The difference module is used to iteratively solve the natural frequency of the built-in heave oscillator using the added mass in the hydrodynamic coefficient matrix as a parameter, and to calculate the encounter frequency using the current speed and encounter angle as independent variables. The difference between the encounter frequency and the natural frequency is used to obtain the frequency detuning. The input module is used to construct a four-dimensional decision vector from the speed deviation, encounter angle deviation, PTO stiffness, and PTO damping. Taking the hydrodynamic coefficient matrix and the frequency detuning as input, and wave energy capture power, PTO mechanical load, and net fuel consumption as three optimization objectives, under the constraints of the upper limit of speed deviation, the upper limit of encounter angle deviation, and the upper limit of oscillator effective stroke, the four-dimensional decision vector is optimized by a non-dominated sorting genetic algorithm to obtain the Pareto optimal solution set. The output module is used to filter the net positive benefit solutions from the Pareto optimal solution set where the net fuel savings are greater than the net fuel consumption increase, and output a joint scheduling command including the speed deviation, the encounter angle deviation, the PTO stiffness, and the PTO damping.

[0043] This invention also provides a container ship-integrated heave oscillator wave energy recovery multi-objective optimization device, which can be a server. The device includes a processor, memory, display screen, input device, network interface, and database connected via a system bus. The processor provides computational and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database stores the data corresponding to this embodiment. The network interface communicates with external terminals via a network connection. The computer program is executed by the processor to implement the above-described method.

[0044] The present invention also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when the instructions are executed on a computer, cause the computer to perform the steps of the multi-objective optimization method for wave energy recovery of the container ship's built-in heave oscillator.

[0045] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0046] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the existing solution, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a container ship's built-in helical oscillator wave energy recovery multi-objective optimization device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0047] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-objective optimization method for wave energy recovery using a container ship with an internal heave oscillator, characterized in that, The method includes: Step S1: Based on the boundary element method, hydrodynamic solutions are performed on the excitation force transmission relationship, added mass and radiation damping of the container ship under multiple combinations of speed and encounter angle to obtain the hydrodynamic coefficient matrix. Step S2: Using the added mass in the hydrodynamic coefficient matrix as a parameter, iteratively solve the natural frequency of the built-in heave oscillator, and calculate the encounter frequency with the current speed and encounter angle as independent variables. Subtract the encounter frequency from the natural frequency to obtain the frequency detuning. Step S3: Construct a four-dimensional decision vector from the speed deviation, encounter angle deviation, PTO stiffness, and PTO damping. Using the hydrodynamic coefficient matrix and the frequency detuning as inputs, and wave energy capture power, PTO mechanical load, and net fuel consumption as three optimization objectives, under the constraints of the upper limit of speed deviation, the upper limit of encounter angle deviation, and the upper limit of oscillator effective stroke, perform three-objective collaborative optimization on the four-dimensional decision vector using a non-dominated sorting genetic algorithm to obtain the Pareto optimal solution set. Step S4: Select solutions from the Pareto optimal solution set that have a net positive benefit where the net fuel savings are greater than the net fuel consumption increase, and output a joint scheduling command including the speed deviation, encounter angle deviation, PTO stiffness, and PTO damping. This includes: calculating the equivalent fuel savings for each solution by performing a thermal equivalence conversion on the product of the wave energy capture power and the flight duration, based on the low calorific value of heavy fuel oil and the main engine thermal efficiency; and adjusting the PTO damping of the Pareto optimal solution set based on the equivalent fuel savings and the net fuel consumption increase. The difference operation is performed on each solution in the optimal solution set to obtain the net profit corresponding to each solution; the solutions with net profit greater than zero are selected from the Pareto optimal solution set to obtain a net positive profit solution set; based on the PTO mechanical load corresponding to each solution in the net positive profit solution set, the solutions in the net positive profit solution set whose PTO mechanical load exceeds the preset mechanical load safety threshold are eliminated, and the remaining solutions are sorted in descending order of net profit, and the solution at the top of the sort is used to output a joint scheduling command including the speed deviation, the encounter angle deviation, the PTO stiffness, and the PTO damping.

2. The multi-objective optimization method for wave energy recovery using a container ship with an internal heave oscillator according to claim 1, characterized in that, Step S1 includes: The speed of the container ship is discretized within a preset speed range with a preset step size, and the encounter angle is discretized within a range of 0° to 180° with a preset step size to obtain multiple combinations of speed and encounter angle. Based on the boundary element method, the wave diffraction and radiation problems of container ships under the multiple combinations of speed and encounter angle are numerically solved to obtain the excitation force transmission relationship, added mass and radiation damping under each working condition. The excitation force transmission relationship, the additional mass, and the radiation damping under each working condition are arranged according to the index of the multiple combinations of speed and encounter angle to obtain the hydrodynamic coefficient matrix.

3. The multi-objective optimization method for wave energy recovery using a container ship with an internal heave oscillator according to claim 1, characterized in that, Step S2 includes: Based on the current speed and encounter angle, the hydrodynamic coefficient matrix is ​​trilinearly interpolated to obtain the additional mass under the current operating conditions; The sum of the added mass and the oscillator mass is taken as the equivalent inertial mass, and the sum of the PTO stiffness and the spring stiffness is taken as the equivalent restoring stiffness. The square root of the ratio of the equivalent inertial mass and the equivalent restoring stiffness is performed to obtain the initial value of the natural frequency. The initial value of the natural frequency is substituted into the hydrodynamic coefficient matrix to re-interpolate and obtain the updated added mass. The square root operation is repeated until the absolute value of the difference between the two natural frequencies is lower than the first convergence threshold to obtain the converged natural frequency. Based on the current speed and the cosine of the encounter angle, the encounter frequency is calculated from the frequency of the dominant wave. The frequency detuning is obtained by subtracting the encounter frequency from the converged natural frequency.

4. The multi-objective optimization method for wave energy recovery using a container ship with an internal heave oscillator according to claim 1, characterized in that, In step S3, the speed deviation, encounter angle deviation, PTO stiffness, and PTO damping are used to construct a four-dimensional decision vector, including: The container ship's speed deviation is limited to a preset upper limit, the encounter angle deviation is limited to a preset upper limit, the PTO stiffness is limited to a feasible region of PTO stiffness, and the PTO damping is limited to a feasible region of PTO damping, thus obtaining the feasible region of the four-dimensional decision vector. Based on Latin hypercube sampling, the speed deviation, encounter angle deviation, PTO stiffness, and PTO damping are uniformly sampled within the feasible region of the four-dimensional decision vector to obtain the initial population.

5. The multi-objective optimization method for wave energy recovery using a container ship with an internal heave oscillator according to claim 4, characterized in that, In step S3, the hydrodynamic coefficient matrix and the frequency detuning are used as inputs, and the wave energy capture power, PTO mechanical load, and net fuel consumption increase are used as three optimization objectives, including: Substitute the speed deviation and encounter angle deviation of each individual in the initial population into the hydrodynamic coefficient matrix for trilinear interpolation to obtain the excitation force transmission relationship, added mass and radiation damping under the corresponding working conditions. Based on the excitation force transmission relationship, the added mass and the radiation damping, frequency domain integration is performed on the relative velocity variance and relative displacement variance between the oscillator and the hull to obtain the wave energy capture power and PTO mechanical load. Based on the speed deviation and the relationship between main engine power and speed, the difference between the main engine power increment corresponding to the adjusted speed and the equivalent fuel saving corresponding to the wave energy capture power is calculated to obtain the net fuel consumption increase.

6. The multi-objective optimization method for wave energy recovery using a container ship built-in heave oscillator according to claim 5, characterized in that, In step S3, under the constraints of the upper limit of speed deviation, the upper limit of encounter angle deviation, and the upper limit of the effective stroke of the oscillator, a non-dominated sorting genetic algorithm is used to perform three-objective collaborative optimization on the four-dimensional decision vector to obtain the Pareto optimal solution set, including: The wave energy capture power, the PTO mechanical load, and the net fuel consumption increase are used as three optimization objectives. The individuals in the initial population are sorted into non-dominated categories, and the crowding distance is calculated for individuals within the same non-dominated level to obtain the non-dominated level and crowding distance of each individual. Based on the non-dominant level and the crowding distance, the initial population is subjected to tournament selection, simulated binary crossover and polynomial mutation in sequence. Under the constraint of the upper limit of the effective stroke of the oscillator, individuals exceeding the constraint are penalized to obtain an updated population. Repeat the non-dominated sorting, crowding distance calculation, tournament selection, simulated binary crossover, and polynomial mutation on the updated population until the continuous rate of change of the hypervolume index is lower than the second convergence threshold to obtain the Pareto optimal solution set.

7. A multi-objective optimization system for wave energy recovery using a built-in helical oscillator on a container ship, characterized in that, For implementing the multi-objective optimization method for wave energy recovery of container ship built-in helical oscillator as described in any one of claims 1-6, the multi-objective optimization system for wave energy recovery of container ship built-in helical oscillator includes: The solution module is used to solve the hydrodynamic relationship of excitation force transmission, added mass and radiation damping of container ships under multiple combinations of speed and encounter angle based on the boundary element method, and obtain the hydrodynamic coefficient matrix. The difference module is used to iteratively solve the natural frequency of the built-in heave oscillator using the added mass in the hydrodynamic coefficient matrix as a parameter, and to calculate the encounter frequency using the current speed and encounter angle as independent variables. The difference between the encounter frequency and the natural frequency is used to obtain the frequency detuning. The input module is used to construct a four-dimensional decision vector from the speed deviation, encounter angle deviation, PTO stiffness, and PTO damping. Taking the hydrodynamic coefficient matrix and the frequency detuning as input, and wave energy capture power, PTO mechanical load, and net fuel consumption as three optimization objectives, under the constraints of the upper limit of speed deviation, the upper limit of encounter angle deviation, and the upper limit of oscillator effective stroke, the four-dimensional decision vector is optimized by a non-dominated sorting genetic algorithm to obtain the Pareto optimal solution set. The output module is used to filter solutions from the Pareto optimal solution set where the net fuel savings are greater than the net fuel consumption increase, and output a joint scheduling command including the speed deviation, encounter angle deviation, PTO stiffness, and PTO damping. This includes: converting the wave energy capture power corresponding to each solution in the Pareto optimal solution set into a thermal equivalent based on the low calorific value of heavy fuel oil and the main engine thermal efficiency, and multiplying the wave energy capture power by the segment duration to obtain the equivalent fuel savings for each solution; and based on the equivalent fuel savings and the net fuel consumption increase, adjusting the Pareto optimal solution set accordingly. The difference operation is performed on each solution in the Pareto optimal solution set to obtain the net profit corresponding to each solution; the solutions with net profit greater than zero are selected from the Pareto optimal solution set to obtain a net positive profit solution set; based on the PTO mechanical load corresponding to each solution in the net positive profit solution set, the solutions in the net positive profit solution set whose PTO mechanical load exceeds the preset mechanical load safety threshold are eliminated, and the remaining solutions are sorted from largest to smallest according to the net profit, and the solution at the top of the sort is used to output a joint scheduling command including the speed deviation, the encounter angle deviation, the PTO stiffness, and the PTO damping.

8. A multi-objective optimization device for wave energy recovery with a built-in heave oscillator on a container ship, characterized in that, The system includes a memory and a processor, the memory storing a computer program that can run on the processor, and the processor executing the computer program to implement the multi-objective optimization method for wave energy recovery of a container ship built-in heave oscillator as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is run by the processor, the processor executes the multi-objective optimization method for wave energy recovery of container ship built-in heave oscillator as described in any one of claims 1 to 6.

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