Numerical simulation based floating photovoltaic wave energy protection multi-objective design method and system

Abstract

The application relates to the technical field of simulation optimization, and discloses a floating photovoltaic wave energy protection multi-objective design method and system based on numerical simulation. The method comprises the following steps: performing numerical simulation on a geometric parameter set of an FB-WEC-OFPV integrated system to obtain a transmission coefficient, a capture width ratio and a levelized cost of electricity; calculating a gradient vector negative cosine value of each sampling point according to the transmission coefficient and the capture width ratio to obtain an attenuation-capture conflict intensity field; taking the gradient amplitude of the attenuation-capture conflict intensity field as a priority criterion to cyclically supplement simulation and update a surrogate model to obtain a refined sample database; and screening a Pareto optimal engineering scheme set according to each index in the refined sample database and a frequency integral value of the attenuation-capture conflict intensity field through multi-objective genetic algorithm optimization and high-fidelity simulation verification. The application solves the problem that a sampling strategy of a surrogate model cannot identify the spatial distribution of an attenuation-capture physical conflict, which leads to the mixing of pseudo-Pareto solutions into an optimal solution set.

Description

Technical Field

[0001] This application relates to the field of simulation optimization technology, and in particular to a multi-objective design method and system for floating photovoltaic wave energy protection based on numerical simulation. Background Technology

[0002] When deploying offshore floating photovoltaic (PV) arrays to deep seas, they must withstand wave loads under complex sea conditions. The integrated system of a floating breakwater and an oscillating buoy-type wave energy converter serves as its core protection measure. Through a synergistic mechanism of breakwater attenuating incident wave energy and wave energy converter capturing wave energy, the system reduces the PV array's motion response while enabling the secondary utilization of wave energy. For the design of this integrated system, existing technologies generally employ computational fluid dynamics and linear potential flow theory to numerically simulate wave propagation, structural response, and energy capture processes. Transmission coefficient, capture width ratio, and levelized cost of electricity (LCOE) are extracted as performance evaluation indicators. Furthermore, a surrogate model and multi-objective genetic algorithm are combined to optimize the WEC buoy geometry, breakwater structure, and integrated layout scheme, outputting a Pareto optimal solution set.

[0003] However, existing technologies, in the surrogate model refinement sampling stage, generally use mathematical statistics such as root mean square error and Kriging prediction variance as priority criteria for supplementing simulation points. This mechanism blindly searches for the region with the greatest statistical uncertainty in the parameter space, failing to identify the distribution pattern of the physical opposition between the transmission coefficient and the capture width ratio in the parameter space. Since the wave energy attenuation of the breakwater and the wave energy captured by the wave energy converter are inherently opposed in physical mechanism, the gradient vectors of the two optimization objectives are opposite in direction in a specific region of the parameter space. This region happens to correspond to the location with the maximum curvature of the Pareto front and the highest risk of inaccurate prediction by the surrogate model. Existing sampling strategies are unaware of and do not provide targeted compensation for this physical conflict region, resulting in the surrogate model's accuracy being significantly lower in the conflict activation region than in other regions. Consequently, the multi-objective optimization process misclassifies the parameter combination with the higher prediction of the surrogate model in this region as a non-dominated solution, resulting in the problem of pseudo-Pareto solutions being mixed into the optimal solution set. Summary of the Invention

[0004] This application provides a multi-objective design method and system for floating photovoltaic wave energy protection based on numerical simulation. It solves the problem in the prior art that the surrogate model sampling strategy cannot identify the spatial distribution of attenuation-capture physical conflict, which leads to pseudo Pareto solutions being mixed into the optimal solution set. It improves the physical effectiveness and engineering reliability of the multi-objective optimization design results of the FB-WEC-OFPV integrated system under wide-band sea conditions.

[0005] Firstly, this application provides a multi-objective design method for floating photovoltaic wave energy protection based on numerical simulation, the multi-objective design method for floating photovoltaic wave energy protection based on numerical simulation includes: Step S1: Perform numerical simulation on the geometric parameter set of the FB-WEC-OFPV integrated system to obtain the transmission coefficient, capture width ratio and levelized power cost corresponding to each parameter combination. Step S2: Based on the transmission coefficient and the capture width ratio, calculate the negative cosine value of the gradient vectors of the two at each sampling point in the parameter space to obtain the attenuation-capture conflict intensity field. Step S3: Using the gradient magnitude of the attenuation-capture conflict intensity field as the priority criterion, supplement the parameter combination corresponding to the maximum gradient magnitude in the attenuation-capture conflict intensity field into the numerical simulation, and iteratively update the surrogate model to obtain a refined sample database. Step S4: Based on the transmission coefficient, capture width ratio, levelized power cost, and frequency integral value of the attenuation-capture conflict intensity field in the refined sample database, a Pareto optimal engineering scheme set is obtained through multi-objective genetic algorithm optimization and high-fidelity simulation verification.

[0006] Secondly, this application provides a multi-objective design system for floating photovoltaic wave energy protection based on numerical simulation, the multi-objective design system for floating photovoltaic wave energy protection based on numerical simulation includes: The simulation module is used to perform numerical simulation of the geometric parameter set of the FB-WEC-OFPV integrated system to obtain the transmission coefficient, capture width ratio and levelized cost of electricity corresponding to each parameter combination. The calculation module is used to calculate the negative cosine value of the gradient vector of the transmission coefficient and the capture width ratio at each sampling point in the parameter space, so as to obtain the attenuation-capture conflict intensity field. The update module is used to supplement the parameter combination corresponding to the maximum gradient magnitude in the attenuation-capture conflict intensity field into the numerical simulation, based on the gradient magnitude of the attenuation-capture conflict intensity field as a priority criterion, and iteratively update the surrogate model to obtain a refined sample database. The verification module is used to select a Pareto optimal engineering scheme set based on the transmission coefficient, capture width ratio, levelized power cost and frequency integral value of the attenuation-capture conflict intensity field in the refined sample database, through multi-objective genetic algorithm optimization and high-fidelity simulation verification.

[0007] Thirdly, a floating photovoltaic wave energy protection multi-objective design device based on numerical simulation is provided, comprising: a memory and at least one processor, wherein the memory stores instructions; the at least one processor calls the instructions in the memory to cause the floating photovoltaic wave energy protection multi-objective design device based on numerical simulation to execute the above-described floating photovoltaic wave energy protection multi-objective design method based on numerical simulation.

[0008] Fourthly, a computer-readable storage medium is provided, wherein instructions are stored therein, which, when executed on a computer, cause the computer to execute the above-described multi-objective design method for floating photovoltaic wave energy protection based on numerical simulation.

[0009] The technical solution provided in this application performs numerical simulation on the geometric parameter set of the FB-WEC-OFPV integrated system, using transmission coefficient, capture width ratio, and levelized cost of electricity (LCOE) as three independent performance quantification indicators. This integrates wave protection performance, wave energy capture efficiency, and engineering economics into a unified data description framework, overcoming the limitations of existing technologies where performance indicators are evaluated in a scattered manner and lack systematic correlation. Furthermore, by calculating the negative cosine values ​​of the gradient vectors of the transmission coefficient and capture width ratio in the parameter space, the physical opposition between the two targets at each sampling point is transformed into a continuously distributed attenuation-capture conflict intensity field. This field explicitly transforms the target conflict relationship, originally implicit in the physical mechanism, into a computable spatial scalar, enabling the precise location of the region with the maximum Pareto front curvature and the highest risk of surrogate model prediction inaccuracies in the parameter space. This fundamentally solves the problem in existing technologies where sampling strategies are unaware of the distribution of physical conflict.

[0010] Using the gradient magnitude of the attenuation-capture conflict intensity field as the priority criterion for refining the surrogate model sampling, the conflict intensity gradient magnitude, along with the transmission coefficient and the standard deviation of the surrogate model prediction, are weighted at 0.6, 0.2, and 0.2, respectively, to form the conflict gradient-driven filling priority value. The core contribution of this algorithm lies in placing the physical conflict gradient signal above the statistical uncertainty signal, ensuring that each round of high-fidelity CFD simulation calculation is accurately applied to the conflict activation region. The surrogate model is cyclically updated until the leave-one-out cross-validation error is less than 2%, resulting in a refined sample database. This fundamentally eliminates the physical causes of pseudo-Pareto solutions. Based on the transmission coefficient, capture width ratio, levelized cost of electricity, and frequency integral value of the attenuation-capture conflict intensity field in the refined sample database, a four-objective optimization system is constructed. The broadband integral value of the conflict intensity is incorporated into the Pareto optimization, ensuring that each scheme in the output Pareto optimal engineering scheme set has a quantifiable broadband sea state applicability assessment result. After high-fidelity simulation verification and elimination of pseudo-Pareto solutions, the physical validity and engineering reliability of the final scheme set are doubly guaranteed. Attached Figure Description

[0011] 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.

[0012] Figure 1 This is a schematic diagram of an embodiment of the floating photovoltaic wave energy protection multi-objective design method based on numerical simulation in this application. Detailed Implementation

[0013] This application provides a multi-objective design method and system for floating photovoltaic wave energy protection based on numerical simulation. 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.

[0014] 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 design method for floating photovoltaic wave energy protection based on numerical simulation in this application includes: Step S1: Perform numerical simulation on the geometric parameter set of the FB-WEC-OFPV integrated system to obtain the transmission coefficient, capture width ratio and levelized power cost corresponding to each parameter combination. Specifically, the FB-WEC-OFPV integrated system refers to an integrated nearshore power generation and protection structure consisting of a floating breakwater, an oscillating buoy-type wave energy converter, and an offshore floating photovoltaic array. All three share a mooring foundation and grid connection interface. The geometric parameter set covers seven design variables: WEC buoy draft, buoy outer diameter, buoy mass, breakwater type parameters, breakwater structural width, relative position offset between WEC and breakwater, and power output damping coefficient. Numerical simulation uses CFD methods to calculate at multiple incident wave frequencies. The transmission coefficient is taken as the ratio of the effective wave height on the back wave side of the breakwater to the effective wave height on the front wave side. The capture width ratio is taken as the ratio of the actual captured power of the WEC to the incident wave power per unit wave crest length. The levelized cost of electricity (LCOE) is obtained by discounting the sum of the total life-cycle construction cost and the annual operation and maintenance costs, and then dividing by the sum of the discounted values ​​of the annual power generation. The discount rate is 8%, and the design life is 25 years. These values ​​conform to the industry's generally accepted financial evaluation standards for nearshore renewable energy projects.

[0015] Step S2: Based on the transmission coefficient and the capture width ratio, calculate the negative cosine value of the gradient vectors of the two at each sampling point in the parameter space to obtain the attenuation-capture conflict intensity field. Specifically, the physical meaning of the attenuation-capture conflict intensity field is as follows: In the parameter space, when the gradient vectors of the transmission coefficient and the capture width ratio are in opposite directions along the same geometric parameter variation direction, they are physically opposed. The degree of this opposition is measured by taking the negative value of the dot product of the two gradient vectors divided by the product of their magnitudes. The result falls in the range of -1 to +1, with a larger positive value indicating a more severe conflict between the attenuation and capture performance at that parameter point. After inputting the conflict intensity values ​​at each discrete sampling point into Kriging interpolation, a continuously distributed conflict intensity field, i.e., the attenuation-capture conflict intensity field, is formed in the entire parameter space. The spatial gradient magnitude of this field reflects the direction and location of the most drastic change in conflict intensity in the parameter space.

[0016] Step S3: Using the gradient magnitude of the attenuation-capture conflict intensity field as the priority criterion, supplement the parameter combination corresponding to the maximum gradient magnitude in the attenuation-capture conflict intensity field into the numerical simulation, and iteratively update the surrogate model to obtain the refined sample database. Specifically, in the process of refining the sample database, the gradient magnitude of the attenuation-capture conflict intensity field is used as the priority criterion for supplementing sampling of the surrogate model, which differs from the sampling methods driven by statistical quantities such as root mean square error or Kriging prediction variance in existing technologies. The parameter combination corresponding to the maximum gradient magnitude is the region where the changes in transmission coefficient and capture width ratio of physical conflict are most drastic and the curvature of the Pareto front is the largest. In this region, CFD high-fidelity simulation calculations are supplemented and the surrogate model is updated, so that the accuracy distribution of the surrogate model actively aligns with the parameter region where physical conflict is most concentrated. The loop termination condition is that the leave-one-out cross-validation error of the three surrogate models—transmission coefficient, capture width ratio, and levelized cost of electricity—is all below 2%. This threshold ensures that the prediction accuracy of the surrogate model in the conflict-dominant region meets the reliability requirements of subsequent multi-objective optimization.

[0017] Step S4: Based on the transmission coefficient, capture width ratio, levelized power cost, and frequency integral value of the attenuation-capture conflict intensity field in the refined sample database, the Pareto optimal engineering scheme set is obtained through multi-objective genetic algorithm optimization and high-fidelity simulation verification.

[0018] Specifically, the selection of the Pareto optimal engineering solution set is based on a four-dimensional objective system consisting of transmission coefficient, capture width ratio, levelized cost of electricity, and the frequency integral value of the attenuation-capture conflict intensity field. The frequency integral value is defined as the average integral of the conflict intensity field over the incident wave frequency range for each parameter combination. A smaller value indicates lower conflict intensity in terms of transmission coefficient and capture width ratio under wide-bandgap sea conditions, and more stable engineering applicability. A multi-objective genetic algorithm is used to optimize and obtain a candidate Pareto solution set. High-fidelity simulation is performed on each parameter combination for verification. When the relative error between the surrogate model prediction and the high-fidelity simulation result exceeds 5%, it is considered a pseudo-Pareto solution and is removed. The 5% threshold is set based on the engineering accuracy requirements of nearshore structure hydrodynamic simulation. The remaining solution set after removal is the Pareto optimal engineering solution set.

[0019] In one specific embodiment, step S1 includes: The set of geometric parameters consisting of WEC float draft, float outer diameter, float mass, breakwater type parameters, breakwater structural width, WEC relative position offset to the breakwater, and power output damping coefficient is input into Latin hypercube sampling for initial sampling processing to obtain the initial parameter sample set. Based on the initial parameter sample set, CFD numerical simulations were performed on the FB-WEC-OFPV integrated system at each incident wave frequency point. The transmission coefficient was obtained by the ratio of the effective wave height on the back wave side of the breakwater to the incident effective wave height on the front wave side, and the capture width ratio was obtained by the ratio of the actual capture power of WEC to the incident wave power per unit wave crest length. Based on the construction cost, annual operation and maintenance cost, and annual power generation corresponding to the initial parameter sample set, the ratio is obtained after discounting according to the discount rate to obtain the levelized cost per kilowatt-hour. By combining the initial parameter sample set, transmission coefficient, capture width ratio, and levelized cost of electricity, the transmission coefficient, capture width ratio, and levelized cost of electricity corresponding to each parameter combination are obtained.

[0020] Specifically, in the geometric parameter set, the WEC buoy draft ranges from 0.5m to 3.0m, the buoy outer diameter from 0.5m to 4.0m, and the buoy mass from 500kg to 8000kg. The breakwater type parameters include four discrete configurations: box-type, I-type, L-type, and U-type. The breakwater structural width ranges from 1.0m to 6.0m. The relative position offset between the WEC and the breakwater ranges from 0m to 2.0m. The power output damping coefficient ranges from 1000N·s / m to 50000N·s / m. These ranges are determined based on engineering scale experience and structural stability constraints of the nearshore FB-WEC-OFPV integrated system. The initial sample size for Latin hypercube sampling is five times the number of design variables, i.e., 35 sample points. This value ensures uniformity of parameter spatial coverage while keeping the CFD computation within an acceptable range. The CFD numerical simulation was performed at 25 frequency points at 0.1 rad / s intervals within the incident wave frequency range of 0.2 rad / s to 2.5 rad / s. This frequency range covers the main energy concentration range of typical nearshore wind and wave spectra. The k-ε turbulence model was adopted, the computational domain length was 30 times the wavelength, the grid scale near the free surface was one-hundredth of the wavelength, and the time step satisfied that the CFL number was less than 0.5.

[0021] The transmission coefficient is the ratio of the effective wave height on the back wave side of the breakwater to the incident effective wave height on the front wave side. The smaller this ratio, the better the wave protection effect of the breakwater on the OFPV array. The capture width ratio is the ratio of the actual captured power of the WEC to the incident wave power per unit wave crest length. This ratio reflects the conversion efficiency of the WEC for incident wave energy and is directly related to the buoy geometry parameters and power output damping coefficient. The levelized cost of electricity (LCOE) is calculated by summing the total life-cycle construction cost and the annual operation and maintenance cost at a discount rate of 8%, dividing by the annual power generation at the same discount rate, and summing again. The discount rate of 8% is determined according to the industry financial evaluation standards for near-shore renewable energy projects. The design life is taken as 25 years. The annual power generation is obtained by superimposing the average annual captured power of the WEC and the average annual photovoltaic power generation of the OFPV array. Both are converted from the numerical simulation results of the corresponding parameter combinations.

[0022] In one specific embodiment, step S2 includes: The transmission coefficient and capture width ratio are subjected to finite difference processing along the directions of each geometric parameter to obtain the gradient vector of the transmission coefficient and the gradient vector of the capture width ratio at each sampling point. The collision intensity value at each sampling point is obtained by dividing the dot product of the gradient vector of the transmission coefficient and the gradient vector of the capture width ratio by the product of their magnitudes. Based on the conflict intensity value, the Kriging interpolation is used to perform full parameter space continuity processing to obtain the attenuation-capture conflict intensity field.

[0023] Specifically, in finite difference processing, the difference step size along the k-th geometric parameter direction is taken as 2% of the parameter's value range. This value ensures the accuracy of gradient calculation while avoiding numerical noise amplification caused by excessively small step sizes. The transmission coefficient gradient vector is composed of its partial derivative components in the seven geometric parameter directions, and the capture width ratio gradient vector is similarly calculated; both are 7-dimensional vectors. The negative value obtained by dividing the dot product of the transmission coefficient gradient vector and the capture width ratio gradient vector by the product of their magnitudes is the conflict intensity value at that sampling point. This value falls within the range of -1 to +1. A positive value indicates that the two targets consume each other at that parameter point, while a negative value indicates that they change together at that point. A numerical stability correction term is added to the denominator to prevent division by zero errors when the magnitudes of both gradient vectors simultaneously approach zero. The physical meaning of the conflict intensity value is the degree of opposition between the transmission coefficient and the capture width ratio in the gradient direction in the parameter space. The closer the value is to +1, the more severe the contradiction between reducing the transmission coefficient and increasing the capture width ratio in the direction of geometric parameter change at that parameter combination.

[0024] The collision intensity values ​​at each discrete sampling point are input into Kriging interpolation. The Matérn 5 / 2 kernel is used, and its hyperparameters are determined through maximum likelihood estimation. The field is then made continuous in a joint space consisting of a 7-dimensional geometric parameter space and 25 incident wave frequency points to obtain the attenuation-capture collision intensity field. This field is a continuous scalar field defined in the joint domain of the geometric parameter space and frequency space, with a spatial dimension of 8 dimensions: 7 geometric parameters plus 1 incident wave frequency. The field values ​​at any combination of parameters and frequencies can be predicted by the Kriging model, providing the predicted mean and standard deviation. Compared to the commonly used squared exponential kernel, the Matérn 5 / 2 kernel has a stronger fitting ability for non-smooth functions and is suitable for physical scenarios where the transmission coefficient and capture width ratio exhibit abrupt changes near the resonance frequency. The kernel function was selected based on the non-smooth characteristics of the hydrodynamic response of the FB-WEC-OFPV system in the resonance region.

[0025] In one specific embodiment, step S3, using the gradient magnitude of the attenuation-capture collision intensity field as the priority criterion, includes: Gradient calculations are performed on the attenuation-capture conflict intensity field along the directions of each geometric parameter to obtain the conflict intensity gradient magnitude at each candidate parameter combination. The conflict intensity gradient magnitude, the standard deviation of the transmission coefficient surrogate model prediction, and the standard deviation of the capture width ratio surrogate model prediction are weighted and summed with weights of 0.6, 0.2, and 0.2, respectively, to obtain the conflict gradient-driven filling priority value at each candidate parameter combination.

[0026] Specifically, partial derivatives of the attenuation-capture conflict intensity field are calculated along the directions of the seven geometric parameters. The square root of the sum of the squares of the partial derivatives in the seven directions is taken to obtain the magnitude of the conflict intensity gradient at the candidate parameter combination. This magnitude reflects the severity of the spatial variation of the attenuation-capture conflict intensity field at that point. A larger magnitude indicates a more non-uniform spatial distribution of conflict intensity in the neighborhood of that parameter point, a greater curvature of the Pareto front in that region, and a more significant impact of the surrogate model's prediction bias on the final optimization result. The candidate parameter combination generates 10,000 candidate points in the full parameter space using Latin hypercube sampling, covering the entire range of values ​​for the seven geometric parameters. The standard deviations of the transmission coefficient and capture width ratio predictions of the surrogate model are both obtained by taking the square root of the posterior variance of their respective Kriging surrogate models at that candidate point, reflecting the statistical uncertainty of the surrogate model's prediction results at that point. Before weighted summation, the three terms—conflict intensity gradient magnitude, transmission coefficient surrogate model prediction standard deviation, and capture width ratio surrogate model prediction standard deviation—are normalized by dividing each by its maximum value across all 10,000 candidate points. After normalization, all three terms fall within the range of 0 to 1. They are then linearly superimposed with weights of 0.6, 0.2, and 0.2 to obtain the conflict gradient-driven fill priority value for each candidate parameter combination.

[0027] A weight of 0.6 is assigned to the magnitude of the conflict intensity gradient, and 0.2 is assigned to the prediction standard deviations of the two surrogate models. This weight allocation is based on the core mechanism of this invention, which uses the physical conflict gradient signal to dominate the sampling direction and the statistical uncertainty signal as an auxiliary correction. If the three terms are weighted equally, it degenerates into the hybrid sampling strategy in the prior art, which cannot guarantee that the supplementary simulation points will preferentially fall into the parameter region where the physical conflict changes most drastically. The conflict gradient-driven filling priority value selects the parameter combination corresponding to the maximum value among 10,000 candidate points as the supplementary simulation point for this round. This selection mechanism ensures that the newly added CFD high-fidelity simulation calculations in each iteration are accurately placed in the parameter region where the decay-capture conflict is most severe, rather than the region with the largest statistical error but mild physical conflict. This eliminates the physical cause of the surrogate model producing pseudo Pareto solutions in the conflict activation region due to insufficient accuracy.

[0028] In one specific embodiment, step S3 involves supplementing the numerical simulation with the parameter combination corresponding to the maximum gradient magnitude in the attenuation-capture conflict intensity field, and iteratively updating the surrogate model, including: The parameter combination corresponding to the maximum value of the conflict gradient-driven fill priority is input into CFD numerical simulation for high-fidelity calculation, and the newly added transmission coefficient and capture width ratio at the corresponding parameter combination are obtained. Based on the newly added transmission coefficient and capture width ratio, the transmission coefficient proxy model, capture width ratio proxy model, and attenuation-capture conflict intensity field are updated to obtain the updated proxy model and the updated attenuation-capture conflict intensity field.

[0029] Specifically, when inputting the parameter combination corresponding to the maximum priority value of the conflict gradient into the CFD numerical simulation, the simulation settings are completely consistent with the initial sample generation stage. A k-ε turbulence model is used, and calculations are performed at 25 frequency points in 0.1 rad / s intervals within the range of 0.2 rad / s to 2.5 rad / s. The computational domain length is 30 times the wavelength, the grid scale near the free surface is one-hundredth of the wavelength, and the time step satisfies that the CFL number is less than 0.5. This yields the newly added transmission coefficient and capture width ratio sequences at these 25 frequency points for this parameter combination. After merging the new data with the existing sample data, both the transmission coefficient surrogate model and the capture width ratio surrogate model are retrained using the full sample data with Kriging. The kernel function remains the Matérn5 / 2 kernel, and the hyperparameters are re-determined through maximum likelihood estimation, resulting in updated surrogate models. This retraining method ensures that the impact of each round of new samples on the predicted standard deviation distribution of the surrogate model is fully reflected.

[0030] The updated attenuation-capture conflict intensity field is generated in the same way as the initial construction. It takes the recalculated conflict intensity values ​​at each sampling point in the full sample data as input, and re-executes Kriging interpolation to generate a new continuous scalar field in the joint space consisting of the 7-dimensional geometric parameter space and 25 incident wave frequency points. When recalculating the conflict intensity values, the calculation of the transmission coefficient gradient vector and the capture width ratio gradient vector relies on the finite difference of the predicted values ​​of the updated surrogate model at each sampling point. The difference step size is still 2% of the corresponding parameter value range. After the negative value of the product of the two gradient vectors divided by the product of their magnitudes, a numerical stability correction term of 10⁻⁸ is added to obtain the updated conflict intensity values ​​at each sampling point. These are then input into Kriging interpolation to complete the full parameter space continuity, ultimately forming the updated attenuation-capture conflict intensity field. The gradient magnitude distribution of this field dynamically adjusts with the addition of new sample points, driving the selection position of the next round of fill points to shift accordingly.

[0031] In one specific embodiment, step S3 involves iteratively updating the proxy model to obtain a refined sample database, including: With the termination condition that the cross-validation error of the leave-one-out method for the proxy model of the transmission coefficient, the proxy model of the capture width ratio, and the proxy model of the levelized cost of electricity is less than 2%, the updated proxy model and the updated attenuation-capture conflict intensity field are cyclically subjected to the following steps: conflict intensity gradient magnitude calculation, conflict gradient-driven filling priority value determination, CFD high-fidelity simulation of parameter combination at the maximum priority value, and updating of the proxy model and the attenuation-capture conflict intensity field. By combining the transmission coefficient, capture width ratio, levelized power cost, and updated attenuation-capture conflict intensity corresponding to all parameter combinations at the end of the cycle, a refined sample database is obtained.

[0032] Specifically, the leave-one-out cross-validation error is calculated as follows: Each sample point in the sample database is sequentially removed, and the Kriging surrogate model is retrained with the remaining samples. The target quantity at the removed point is predicted, and the absolute value of the relative error between the predicted value and the actual value in the CFD simulation is calculated. The average of the relative errors of all sample points is then used to obtain the leave-one-out cross-validation error of the surrogate model. The leave-one-out cross-validation errors of the transmission coefficient surrogate model, the capture width ratio surrogate model, and the levelized cost of electricity surrogate model must all be below 2% to trigger termination. If any one of them is above 2%, the next round of fill point selection and CFD simulation continues. The 2% threshold is set based on the accuracy requirements of nearshore hydrodynamic simulation engineering. Under this threshold, the impact of the surrogate model prediction error on the multi-objective optimization results is lower than the engineering allowable deviation range of the Pareto solution set. The training data for the levelized cost of electricity surrogate model comes from the levelized cost of electricity calculated according to the discount rate after each round of CFD simulation. It is fully retrained synchronously with the transmission coefficient surrogate model and the capture width ratio surrogate model, and the kernel function also uses the Matérn 5 / 2 kernel. The maximum number of iterations is set to 140 sample points, which means that a maximum of 105 CFD simulation points are added on the basis of the initial 35 samples. When the total number of samples reaches 140 but the leave-one-out cross-validation error of the three surrogate models is still not lower than 2% at the same time, the maximum number of samples is used as the forced termination condition.

[0033] The refined sample database is composed of data from all sample points at the end of the loop. Each record contains the values ​​of 7 geometric parameters, a transmission coefficient sequence at 25 frequency points, a capture width ratio sequence at 25 frequency points, a levelized cost per kilowatt-hour scalar value, and the field value and gradient magnitude of the updated attenuation-capture conflict intensity field at that parameter combination. The updated attenuation-capture conflict intensity field is stored in the database as Kriging model parameters, rather than storing field values ​​point by point. This storage method allows the corresponding field value to be directly calculated using the Kriging prediction equation at any new parameter combination, ensuring the complete accessibility of the field data in subsequent multi-objective optimization. The number of sample points in the conflict-dominant region of the refined sample database is no less than 55% of the total sample size. This proportion is naturally guaranteed by the weight allocation of the conflict gradient-driven priority values, requiring no additional constraints. The verification method is to statistically analyze the proportion of parameter combinations in the database that satisfy the conflict intensity frequency integral value greater than 0.3.

[0034] In one specific embodiment, step S4 includes: The attenuation-capture collision intensity field in the refined sample database is integrated at the incident wave frequency to obtain the frequency integral value corresponding to each parameter combination. The transmission coefficient, capture width ratio, levelized power cost, and frequency integral value are input into a multi-objective genetic algorithm for four-objective optimization to obtain a candidate Pareto solution set. Based on the parameter combinations in the candidate Pareto solution set, the FB-WEC-OFPV integrated system is subjected to high-fidelity simulation verification. The relative error between the surrogate model prediction and the high-fidelity simulation result exceeds 5% as the elimination criterion. The candidate Pareto solution set is then screened to obtain the Pareto optimal engineering solution set.

[0035] Specifically, the frequency integral value of the attenuation-capture conflict intensity field uses the spectral density value of the JONSWAP spectrum in the target sea area as the frequency weight. The conflict intensity field values ​​at each parameter combination are weighted and summed within the incident wave frequency range of 0.2 rad / s to 2.5 rad / s, and then divided by the number of frequency points (25) to obtain the frequency integral value corresponding to each parameter combination. This value reflects the weighted average level of the transmission coefficient and capture width ratio of the conflict intensity under broadband sea conditions. The smaller the frequency integral value, the lower the degree of antagonism between the two targets under broadband incident wave conditions. The peak frequency of the JONSWAP spectrum is set to 0.8 rad / s, and the peak elevation factor is set to 3.3, based on typical nearshore wind and wave spectrum parameters. The multi-objective genetic algorithm adopted is NSGA-II, with a population size of 200, an iteration number of 500 generations, a crossover probability of 0.9, and a mutation probability of 1 / 7, which is one-seventh of the number of design variables. Before inputting the four objective quantities into the algorithm, they are normalized by dividing them by their respective maximum values ​​in the refined sample database. After normalization, each objective falls within the range of 0 to 1, eliminating the influence of dimensional differences on the determination of dominance relationships. After the optimization is completed, the first-level non-dominated solution set is taken as the candidate Pareto solution set.

[0036] Each parameter combination in the candidate Pareto solution set was validated using high-fidelity boundary element method (BEM) simulation. The simulation frequency points were set consistent with the initial CFD simulation, using 25 frequency points ranging from 0.2 rad / s to 2.5 rad / s. The mesh scale for the wet surface of the structure was set to 1 / 15 of the structural feature size. For each candidate solution, the relative error between the surrogate model predictions of the transmission coefficient and capture width ratio and the BEM simulation results was calculated. When the relative error of any target exceeded 5%, the surrogate model prediction was replaced with the BEM simulation result to reassess whether the solution was still a non-dominated solution. If the solution was dominated by other candidate solutions after replacement, it was removed from the candidate Pareto solution set and identified as a pseudo-Pareto solution. If it was still a non-dominated solution after replacement, it was retained and the corresponding target quantity was updated with the simulation value. The 5% removal criterion was set based on the acceptable accuracy range of nearshore hydrodynamic engineering simulation. Under this threshold, the impact of the surrogate model prediction deviation on the final engineering scheme selection result was lower than the allowable deviation of the engineering decision. The remaining non-dominated solutions after the elimination process constitute the Pareto optimal engineering solution set. Each solution in this set is accompanied by real simulation results of four objective quantities verified by the boundary element method: transmission coefficient, capture width ratio, levelized cost of electricity, and frequency integral value.

[0037] The above describes the multi-objective design method for floating photovoltaic wave protection based on numerical simulation in the embodiments of this application. The following describes the multi-objective design system for floating photovoltaic wave protection based on numerical simulation in the embodiments of this application. One embodiment of the multi-objective design system for floating photovoltaic wave protection based on numerical simulation in the embodiments of this application includes: The simulation module is used to perform numerical simulation of the geometric parameter set of the FB-WEC-OFPV integrated system to obtain the transmission coefficient, capture width ratio and levelized cost of electricity corresponding to each parameter combination. The calculation module is used to calculate the negative cosine value of the gradient vector of the transmission coefficient and the capture width ratio at each sampling point in the parameter space, so as to obtain the attenuation-capture conflict intensity field. The update module is used to supplement the parameter combination corresponding to the maximum gradient magnitude in the attenuation-capture conflict intensity field into the numerical simulation, based on the gradient magnitude of the attenuation-capture conflict intensity field as a priority criterion, and iteratively update the surrogate model to obtain a refined sample database. The verification module is used to select a Pareto optimal engineering scheme set based on the transmission coefficient, capture width ratio, levelized power cost and frequency integral value of the attenuation-capture conflict intensity field in the refined sample database, through multi-objective genetic algorithm optimization and high-fidelity simulation verification.

[0038] This invention also provides a floating photovoltaic (PV) energy protection multi-objective design device based on numerical simulation, which can be a server. This device includes a processor, memory, display screen, input device, network interface, and database connected via a system bus. The processor, designed in computer mode, 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, when executed by the processor, implements the above-described method.

[0039] 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 floating photovoltaic wave energy protection multi-objective design method based on numerical simulation.

[0040] 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.

[0041] 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 prior art, 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 floating photovoltaic wave energy protection multi-target design device based on numerical simulation (which may 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.

[0042] 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 design method for floating photovoltaic wave energy protection based on numerical simulation, characterized in that, The method includes: Step S1: Perform numerical simulation on the geometric parameter set of the FB-WEC-OFPV integrated system to obtain the transmission coefficient, capture width ratio and levelized power cost corresponding to each parameter combination. Step S2: Based on the transmission coefficient and the capture width ratio, calculate the negative cosine value of the gradient vectors of the two at each sampling point in the parameter space to obtain the attenuation-capture conflict intensity field. Step S3: Using the gradient magnitude of the attenuation-capture conflict intensity field as the priority criterion, supplement the parameter combination corresponding to the maximum gradient magnitude in the attenuation-capture conflict intensity field into the numerical simulation, and iteratively update the surrogate model to obtain a refined sample database. Step S4: Based on the transmission coefficient, capture width ratio, levelized power cost, and frequency integral value of the attenuation-capture conflict intensity field in the refined sample database, a Pareto optimal engineering scheme set is obtained through multi-objective genetic algorithm optimization and high-fidelity simulation verification.

2. The multi-objective design method for floating photovoltaic wave energy protection based on numerical simulation according to claim 1, characterized in that, Step S1 includes: The set of geometric parameters consisting of WEC float draft, float outer diameter, float mass, breakwater type parameters, breakwater structural width, WEC relative position offset to the breakwater, and power output damping coefficient is input into Latin hypercube sampling for initial sampling processing to obtain the initial parameter sample set. Based on the initial parameter sample set, CFD numerical simulations were performed on the FB-WEC-OFPV integrated system at each incident wave frequency point. The transmission coefficient was obtained by the ratio of the effective wave height on the back wave side of the breakwater to the incident effective wave height on the front wave side. The capture width ratio was obtained by the ratio of the actual capture power of WEC to the incident wave power per unit wave crest length. Based on the construction cost, annual operation and maintenance cost, and annual power generation corresponding to the initial parameter sample set, the ratio is obtained after discounting at the discount rate to obtain the levelized cost per kilowatt-hour. The initial parameter sample set, the transmission coefficient, the capture width ratio, and the levelized cost of electricity are combined to obtain the transmission coefficient, capture width ratio, and levelized cost of electricity corresponding to each parameter combination.

3. The multi-objective design method for floating photovoltaic wave energy protection based on numerical simulation according to claim 1, characterized in that, Step S2 includes: The transmission coefficient and the capture width ratio are subjected to finite difference processing along each geometric parameter direction to obtain the gradient vector of the transmission coefficient and the gradient vector of the capture width ratio at each sampling point; The negative value is obtained by dividing the dot product of the gradient vector of the transmission coefficient and the gradient vector of the capture width ratio by the product of their magnitudes, thus obtaining the collision intensity value at each sampling point. Based on the conflict intensity value, Kriging interpolation is used to perform full parameter space continuity processing to obtain the attenuation-capture conflict intensity field.

4. The multi-objective design method for floating photovoltaic wave energy protection based on numerical simulation according to claim 1, characterized in that, In step S3, the gradient magnitude of the attenuation-capture collision intensity field is used as the priority criterion, including: The attenuation-capture conflict intensity field is subjected to gradient calculation along the direction of each geometric parameter to obtain the conflict intensity gradient magnitude at each candidate parameter combination; The conflict intensity gradient magnitude, the standard deviation of the transmission coefficient surrogate model prediction, and the standard deviation of the capture width ratio surrogate model prediction are weighted and summed with weights of 0.6, 0.2, and 0.2, respectively, to obtain the conflict gradient-driven fill priority value at each candidate parameter combination.

5. The multi-objective design method for floating photovoltaic wave energy protection based on numerical simulation according to claim 4, characterized in that, In step S3, the parameter combination corresponding to the maximum gradient magnitude in the attenuation-capture conflict intensity field is added to the numerical simulation, and the surrogate model is updated iteratively, including: The parameter combination corresponding to the maximum value of the conflict gradient-driven fill priority is input into CFD numerical simulation for high-fidelity calculation to obtain the newly added transmission coefficient and capture width ratio at the corresponding parameter combination. Based on the newly added transmission coefficient and the capture width ratio, the transmission coefficient proxy model, the capture width ratio proxy model, and the attenuation-capture conflict intensity field are updated to obtain the updated proxy model and the updated attenuation-capture conflict intensity field.

6. The multi-objective design method for floating photovoltaic wave energy protection based on numerical simulation according to claim 5, characterized in that, In step S3, the proxy model is updated cyclically to obtain a refined sample database, including: With the termination condition that the cross-validation error of the leave-one-out method for the proxy model of the transmission coefficient, the proxy model of the capture width ratio, and the proxy model of the levelized cost of electricity is less than 2%, the updated proxy model and the updated attenuation-capture conflict intensity field are cyclically subjected to the following steps: conflict intensity gradient magnitude calculation, conflict gradient-driven filling priority value determination, CFD high-fidelity simulation of parameter combination at the maximum priority value, and updating of the proxy model and the attenuation-capture conflict intensity field. The refined sample database is obtained by combining the transmission coefficient, capture width ratio, levelized cost of electricity, and updated attenuation-capture conflict intensity corresponding to all parameter combinations at the end of the loop.

7. The multi-objective design method for floating photovoltaic wave energy protection based on numerical simulation according to claim 1, characterized in that, Step S4 includes: The attenuation-capture collision intensity field in the refined sample database is integrated at the incident wave frequency to obtain the frequency integral value corresponding to each parameter combination. The transmission coefficient, the capture width ratio, the levelized cost per kilowatt-hour, and the frequency integral value are input into a multi-objective genetic algorithm for four-objective optimization to obtain a candidate Pareto solution set. Based on the parameter combinations in the candidate Pareto solution set, the FB-WEC-OFPV integrated system is subjected to high-fidelity simulation verification. The relative error between the surrogate model prediction value and the high-fidelity simulation result exceeds 5% as the elimination criterion. The candidate Pareto solution set is then screened to obtain the Pareto optimal engineering solution set.

8. A multi-objective design system for floating photovoltaic wave energy protection based on numerical simulation, characterized in that, For implementing the multi-objective design method for floating photovoltaic wave energy protection based on numerical simulation as described in any one of claims 1-7, the multi-objective design system for floating photovoltaic wave energy protection based on numerical simulation comprises: The simulation module is used to perform numerical simulation of the geometric parameter set of the FB-WEC-OFPV integrated system to obtain the transmission coefficient, capture width ratio and levelized cost of electricity corresponding to each parameter combination. The calculation module is used to calculate the negative cosine value of the gradient vector of the transmission coefficient and the capture width ratio at each sampling point in the parameter space, so as to obtain the attenuation-capture conflict intensity field. The update module is used to supplement the parameter combination corresponding to the maximum gradient magnitude in the attenuation-capture conflict intensity field into the numerical simulation, based on the gradient magnitude of the attenuation-capture conflict intensity field as a priority criterion, and iteratively update the surrogate model to obtain a refined sample database. The verification module is used to select the Pareto optimal engineering scheme set based on the transmission coefficient, capture width ratio, levelized power cost and frequency integral value of the attenuation-capture conflict intensity field in the refined sample database, through multi-objective genetic algorithm optimization and high-fidelity simulation verification.

9. A floating photovoltaic wave energy protection multi-target design device based on numerical simulation, characterized in that, It 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 design method for floating photovoltaic wave energy protection based on numerical simulation as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is run by the processor, it causes the processor to execute the multi-objective design method for floating photovoltaic wave energy protection based on numerical simulation as described in any one of claims 1 to 7.

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