Parameter design optimization method for gravity type submerging net cage

Abstract

The invention discloses a gravity type submerging net cage parameter design optimization method, and relates to the field of mariculture equipment structure optimization, and the method comprises the steps: collecting the multi-period marine environment data of a target sea area, and constructing an environment load sequence with a time-varying characteristic; establishing a three-dimensional coupling finite element model, performing disturbance analysis on a plurality of structure control parameters, and identifying a key design parameter set based on a response sensitivity function; and constructing a multi-objective optimization model including floating and sinking time control, maximum stress minimization and attitude offset constraint, performing global optimization by adopting an adaptive genetic algorithm, obtaining an optimal parameter solution, substituting the optimal parameter solution into the simulation model for dynamic response verification, and if a response index is converged to a target interval, outputting the optimal parameter solution as final design configuration. According to the method, systematic optimization of structural parameters of the submerging and surfacing net cage can be achieved, the stability and safety of the submerging and surfacing net cage under complex sea conditions are improved, and the method has high engineering applicability.

Description

Technical Field

[0001] This invention relates to the field of marine aquaculture equipment structure optimization, specifically to a method for optimizing the design parameters of a gravity-type submersible cage. Background Technology

[0002] Gravity-type floating cages are a type of aquaculture facility commonly used in deep-water aquaculture. They combine advantages such as high stability, strong resistance to wind and waves, and adjustable water depth, and are widely used in marine aquaculture engineering. Their structure mainly includes a float, gravity anchor, lifting system, and netting system. By adjusting the combination of buoyancy and gravity, the cage can operate stably at different water depths.

[0003] However, due to the dynamic loads of waves, tides, and currents in the marine environment, different structural parameters have a significant impact on the overall stress performance, stability, and durability of floating and submersible cages. For example, parameters such as the arrangement of the floats, buoyancy layout, anchor configuration, and hoisting point location all affect the cage's attitude response, stress distribution, and structural safety under extreme conditions during the floating and sinking process.

[0004] Existing design methods for gravity-type submersible cages mostly rely on empirical design or finite element analysis based on a single static condition, lacking a systematic parameter optimization mechanism. In particular, it is difficult to comprehensively consider the nonlinear relationship between different sea states, load conditions, and structural responses, resulting in deviations in design results and making it difficult to meet the actual operational requirements in complex marine environments.

[0005] Therefore, there is an urgent need to propose a parameter design optimization method for gravity-type submersible cages based on a combination of numerical simulation and parameter sensitivity analysis, so as to achieve systematic and scientific optimization of cage structural parameters and improve its structural performance and operational reliability under varying marine conditions. Summary of the Invention

[0006] The purpose of this invention is to provide a method for optimizing the design parameters of gravity-fed submersible cages to address the shortcomings in the prior art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for designing and optimizing parameters of a gravity-type submersible cage, comprising:

[0008] Collect marine environmental data of the target sea area at multiple time periods during the design service life, including changes in wave height, period, current velocity and current direction, and construct an environmental load sequence with time-varying characteristics;

[0009] A three-dimensional coupled finite element model including the floating body, anchorage, lifting points and netting was constructed, and the environmental load sequence was used as the input boundary conditions to simulate the floating and sinking response and force transmission.

[0010] Perturbation analysis was performed on multiple structural control parameters in the model. Based on the response sensitivity function, the set of parameters that have a significant impact on buoyancy stability, attitude response and stress peak under extreme loads was identified and denoted as the key design parameter set P.

[0011] A multi-objective optimization model is constructed based on a set of objective functions, including a floating and sinking time control function, a maximum stress minimization function, and an attitude offset constraint function. An adaptive genetic algorithm is then used to globally optimize the parameter set P to obtain the optimal parameter solution P_opt.

[0012] Substitute P_opt back into the three-dimensional coupled finite element model, perform dynamic simulation iteration, and compare whether the response characteristics before and after optimization converge to the target interval. If they do not converge, adjust the optimization weights according to the sensitivity matrix until the optimization convergence condition is met.

[0013] The optimal parameter P_opt is output as the final design parameter configuration for the gravity-fed submersible cage.

[0014] Preferably, the construction of a three-dimensional coupled finite element model including a floating body, anchorage, sling points, and netting, and the use of the environmental load sequence as input boundary conditions for buoyancy response and force transmission simulation, includes:

[0015] A three-dimensional coupled finite element model covering four structural units—floating body, anchorage, hoisting point, and netting—was constructed. The three-dimensional coupled finite element model is based on the principle of fluid-structure interaction and simulates the nonlinear mechanical relationship between the floating body and the anchorage by setting flexible connection boundaries.

[0016] Using the environmental loads with time-series characteristics collected from the target sea area as time-varying boundary inputs, wave height, wave period, flow velocity and flow direction are mapped into dynamic pressure fields and shear flow fields acting on the surface of the floating body and the mesh nodes.

[0017] Nonlinear dynamic response simulation was performed to obtain the attitude change, anchor tension and net deformation response of the structure during the floating and sinking process, and the contact stiffness and coupling damping parameters at the connection between the float and the suspension point were updated in real time during the simulation.

[0018] Preferably, perturbation analysis is performed on multiple structural control parameters in the model, and the set of parameters that have a significant impact on buoyancy stability, attitude response, and stress peak under extreme loads is identified based on the response sensitivity function. This set is denoted as the key design parameter set P, specifically:

[0019] Multiple structural control parameters were selected, including the volume of the floating body, the height of the buoyancy center, the preload of the anchorage, the position of the lifting point, and the initial value of the netting tension. Positive and negative perturbations were applied within their respective design ranges to construct a sample set of perturbation parameters.

[0020] For the disturbance parameter sample set, a three-dimensional coupled finite element model is called to perform simulations in sequence under floating and sinking conditions, attitude adjustment conditions and extreme wave conditions, and to extract floating and sinking stability index, attitude deviation angle and maximum stress response value.

[0021] The relationship between each input parameter and the response variable is quantified by a normalized response sensitivity function. The global sensitivity weight of each parameter is calculated, and parameters with an impact value lower than a specified limit are removed based on a set threshold. The parameters with significant impact are retained to form the key design parameter set P.

[0022] Preferably, the step of using a normalized response sensitivity function to quantify the relationship between each input parameter and the response variable, and calculating the global sensitivity weight of each parameter, specifically involves:

[0023] Based on the constructed disturbance sample set, the difference calculation is performed on the change of response variable caused by each input parameter before and after the disturbance to obtain the initial sensitivity value of each parameter relative to the floating and sinking stability, attitude response and extreme stress response.

[0024] All initial sensitivity values ​​are normalized and mapped to a dimensionless numerical range using a uniform scale.

[0025] For the normalized sensitivity values, a weighted average method is used to calculate the global sensitivity weight of each input parameter under multiple operating conditions and response variables.

[0026] Preferably, a multi-objective optimization model is constructed based on a set of objective functions, specifically as follows:

[0027] For the key design parameter set P, a floating and sinking time control function, a maximum stress minimization function, and an attitude deviation constraint function are constructed respectively. The floating and sinking time control function uses the time required for the float to complete the ascent or descent to the target depth and the preset process time difference as the evaluation index. The maximum stress minimization function uses the maximum structural stress of the mesh or connecting parts under extreme wave conditions as the optimization objective. The attitude deviation constraint function uses the maximum lateral and longitudinal tilt angle deviation of the float under disturbance conditions as the boundary control condition.

[0028] The objective function is normalized and a penalty factor mechanism is introduced, in which the attitude offset constraint function is transformed into a constraint penalty term and embedded into the objective function, forming a unified and solvable composite optimization objective expression.

[0029] A multi-objective optimization model is formed by constructing a weighted summation model based on weight coefficients or a non-dominated sorting method for Pareto optimal solution sets.

[0030] Preferably, an adaptive genetic algorithm is used to globally optimize the parameter set P to obtain the optimal parameter solution P_opt, specifically as follows:

[0031] Based on a multi-objective optimization model, the genetic population is initialized and population codes are generated using the key design parameter set P as the variable dimension, while a multi-objective fitness evaluation function is set.

[0032] Based on the population evolution generation and the current individual fitness distribution characteristics, the selection probability, crossover probability and mutation probability are dynamically adjusted. The mutation probability is automatically increased when the population fitness tends to converge, so as to escape the local optimum trap.

[0033] In each generation, selection, crossover, and mutation operations are performed based on the multi-objective weighted fitness value of the individual. The current best individual is retained in combination with the elite retention strategy. After the iteration satisfies the termination criterion or convergence condition, the parameter combination corresponding to the best fitness individual is output, which is denoted as the optimal parameter solution P_opt.

[0034] Preferably, P_opt is substituted back into the three-dimensional coupled finite element model, and dynamic simulation iteration is performed, specifically as follows:

[0035] Substitute the optimized parameter solution P_opt into the constructed three-dimensional coupled finite element model and redefine the floating body, anchor system, lifting point and netting.

[0036] Dynamic simulations were performed under floating and sinking conditions, attitude disturbance conditions, and extreme wave conditions. The floating and sinking time, attitude angle change curves, and maximum stress values ​​of the structure were extracted, and the simulation outputs were compared and analyzed with the response values ​​under the corresponding conditions before optimization.

[0037] Set a convergence criterion interval. If all target response indicators converge within the target interval or threshold range, then P_opt is confirmed as a valid solution; otherwise, automatically adjust the optimization weight parameters or penalty function coefficients based on the degree of response deviation, and restart the optimization iteration.

[0038] Preferably, the weight parameters or penalty function coefficients are automatically adjusted and optimized based on the degree of response deviation, specifically as follows:

[0039] By comparing the simulation output results of the optimal parameter solution P_opt under various typical working conditions with the corresponding target response interval, the deviation rate of each optimized objective function is calculated. The deviation rate is defined as the ratio obtained by dividing the absolute value of the difference between the actual response value and the target value by the target value.

[0040] The target weight parameters are dynamically adjusted according to the deviation rate of each objective function. If the deviation rate of a certain response is higher than the preset threshold, the optimization weight of the objective function corresponding to that response is increased. If the attitude offset constraint is violated, its penalty function coefficient is increased simultaneously.

[0041] The updated weight parameters and penalty function coefficients are re-introduced into the optimization model to construct the corrected set of optimization objective functions, triggering the next round of adaptive genetic algorithm iteration.

[0042] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0043] 1. This invention constructs a system optimization framework for core performance indicators such as buoyancy efficiency, structural stress, and attitude stability by introducing multi-objective optimization modeling, response sensitivity analysis, and adaptive genetic algorithms, breaking through the limitations of traditional experience-based design or single-objective optimization methods. By combining a three-dimensional coupled finite element simulation model with a dynamic response feedback mechanism, precise coupling between structural control parameters and environmental loads is achieved, making the optimization results closer to actual working conditions and significantly improving the structural reliability and operational safety of the submersible cage.

[0044] 2. This invention introduces a response deviation-driven weight adjustment and constraint penalty self-correction mechanism to construct a closed-loop iterative intelligent optimization system, effectively avoiding optimization getting trapped in local optima or target deviation problems. This method possesses good convergence, robustness, and engineering adaptability, and is suitable for the design of various types of submersible aquaculture equipment. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0046] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] For examples, please refer to Figure 1 As shown in this embodiment, a method for designing and optimizing parameters of a gravity-type submersible cage includes:

[0049] Collect marine environmental data of the target sea area at multiple time periods during the design service life, including changes in wave height, period, current velocity and current direction, and construct an environmental load sequence with time-varying characteristics;

[0050] A three-dimensional coupled finite element model including the floating body, anchorage, lifting points and netting was constructed, and the environmental load sequence was used as the input boundary conditions to simulate the floating and sinking response and force transmission.

[0051] Perturbation analysis was performed on multiple structural control parameters in the model. Based on the response sensitivity function, the set of parameters that have a significant impact on buoyancy stability, attitude response and stress peak under extreme loads was identified and denoted as the key design parameter set P.

[0052] A multi-objective optimization model is constructed based on a set of objective functions, including a floating and sinking time control function, a maximum stress minimization function, and an attitude offset constraint function. An adaptive genetic algorithm is then used to globally optimize the parameter set P to obtain the optimal parameter solution P_opt.

[0053] Substitute P_opt back into the three-dimensional coupled finite element model, perform dynamic simulation iteration, and compare whether the response characteristics before and after optimization converge to the target interval. If they do not converge, adjust the optimization weights according to the sensitivity matrix until the optimization convergence condition is met.

[0054] The optimal parameter P_opt is output as the final design parameter configuration for the gravity-fed submersible cage.

[0055] In the gravity-type submersible cage parameter design optimization method provided by this invention, the first key step is to collect multi-period marine environmental data of the target sea area during the design service life, and construct a time-varying environmental load sequence based on this data. The purpose of this step is to provide realistic and dynamic boundary input conditions for subsequent numerical simulation and parameter optimization, so as to ensure a high degree of consistency between the optimization process and actual marine conditions.

[0056] The "target sea area" mentioned in this invention refers to the actual sea area where the floating cages are to be deployed, and its marine environmental conditions will directly affect the stress behavior and structural response of the cages during service. The "design service period" refers to the time span during which the cages are expected to operate continuously in that sea area, typically including multiple seasonal cycles, and even covering sea state characteristics throughout the year. To comprehensively reflect the dynamic evolution of the marine environment, segmented sampling is required for representative time periods within this period.

[0057] In terms of data acquisition, the following four types of marine environmental data are mainly obtained: wave height, wave period, current velocity, and current direction. Wave height represents the vertical distance between wave crests and troughs, and is an important parameter reflecting wave intensity; wave period describes the time required for adjacent wave crests to pass the same point, characterizing wave frequency; current velocity refers to the speed of water flow, and current direction indicates the direction of flow. Both of these factors jointly affect the force distribution and stability of the buoy and mooring. The above data can be obtained through long-term deployed marine observation buoys, historical oceanographic databases, or numerical oceanographic forecasting systems, and the data format can be discrete time series or periodic sampling data.

[0058] To construct a dynamic load sequence that accurately reflects sea state variations, the collected data needs to be cleaned and interpolated chronologically to remove missing and outlier values, and then divided according to the design period. For example, for a one-year service period, the time can be divided into multiple typical months, ten-day periods, or representative operating days. For each time period, the corresponding wave height, period, current velocity, and current direction parameters are jointly analyzed to form a subsequence of environmental loads for that period. Multiple subsequences are arranged chronologically to form a complete master sequence of time-varying environmental loads.

[0059] To describe the evolution of environmental loads over time, this invention introduces a time-domain weighting function when constructing the load sequence to reflect the representativeness and extremes of each time period. For example, a weighted moving average method can be used to smooth extreme waves, or high-occurrence conditions can be assigned higher weights based on their frequency. The resulting time-varying environmental load sequence not only includes wave and flow field information from multiple time periods but also dynamically reflects the continuous effect of sea state disturbances on the submersible cages.

[0060] The load sequence is used as a boundary condition input into the subsequent numerical simulation model, so that the simulation process is no longer limited to static conditions or single design wave parameters, but can simulate the complex and variable dynamic load conditions faced by the submersible cage in actual operation, thereby significantly improving the accuracy of structural response prediction and the reliability of parameter optimization.

[0061] In the gravity-type submerged cage parameter design optimization method provided by this invention, the construction of a three-dimensional coupled finite element model and its application in the simulation of floating and sinking response and force transmission are one of the core links. The purpose is to accurately predict the dynamic response behavior of the submerged cage under different working conditions through the linkage modeling of multiple structural units, thereby providing a real and reliable mechanical basis for parameter optimization.

[0062] The modeling process begins with the identification and integration of structural units. Gravity-type submersible gabions mainly consist of floating body units, anchoring units, hoisting point connection units, and a netting system, with complex structural coupling relationships between these units. This invention establishes a unified finite element coordinate system to perform integrated modeling of each structural unit, and on this basis, introduces fluid-solid-flexible multi-field coupling theory to predict the dynamic behavior of the overall model under time-varying sea conditions.

[0063] Specifically, the floating body element model uses three-dimensional solid elements, considering its six-degree-of-freedom response behavior under wave excitation. To simulate realistic hydrodynamic effects, time-varying wave loads and flow field disturbances derived from marine environmental data are applied to the floating body surface. These disturbances include dynamic pressure and shear terms, which are corrected using hydrodynamic coefficients. The floating body model considers its material properties to be a homogeneous and isotropic structure, which can be obtained by importing measured material data or fitting empirical models.

[0064] The anchor system is simulated using a multi-segment flexible chain cable model, exhibiting strong nonlinear tensile characteristics. The connection between the anchor system and the floating body is modeled using flexible connection boundary conditions, which can reflect the response and transient behavior of the anchor cable during tensioning and relaxation. To further improve simulation accuracy, nonlinear contact stiffness and damping terms are applied to the anchor system nodes. This stiffness adjusts with displacement to simulate the pre-tensioning and deformation process of the anchor cable under hydrodynamic disturbance.

[0065] The suspension point connection unit, as the structural transition between the float and the netting system, is modeled using a hybrid rigid-flexible connection method. Specifically, a spring-damping component model is set at the float end, and a flexible node is set at the netting end. By setting the spring stiffness coefficient and damping coefficient, the suspension point can adaptively adjust the connection strength during the simulation, thereby capturing the characteristics of the netting's pulling or buffering response in actual operation.

[0066] The netting system is modeled using shell elements or cable-membrane elements, depending on the specific netting form (such as flexible fishing nets or rigid netting covers). This invention preferably uses a tensioned flexible netting structure, which exhibits large deformation behavior under the influence of flow. Therefore, nonlinear geometric control equations are introduced into the model, coupled with hydrodynamic added mass terms and netting drag coefficient terms, to more realistically simulate the shaking, deformation, and force transmission path changes of the netting under the combined influence of waves and flow velocity.

[0067] Based on the above structural model, environmental load sequences need to be input into the model as boundary conditions. This invention uses a data mapping method to convert parameters such as wave height, period, current velocity, and current direction collected from historical marine environmental data into nodal pressure, volume force, or velocity boundary conditions. Specifically:

[0068] Wave height and period are converted into periodic variable amplitude dynamic pressure loads, which are applied to the surface of the float and the netting;

[0069] The flow velocity is converted into a constant or varying shear flow field, which acts on the mesh nodes;

[0070] The flow direction, as a vector direction input, affects the load distribution characteristics.

[0071] The additional mass term is estimated according to the water disturbance model and applied to the floating mass matrix.

[0072] To improve simulation stability, this invention performs static initial equilibrium calculations on the model before simulation. That is, static loads such as self-weight, buoyancy, and hydrostatic pressure are applied first to bring the model to a force equilibrium state, and then time-varying dynamic loads are gradually added to solve the response.

[0073] A nonlinear dynamic explicit integration method, combined with an adaptive time step control strategy, is employed in the response solution to ensure response capture accuracy under high-frequency disturbances. The following output variables are recorded in real-time during the simulation:

[0074] The six-degree-of-freedom motion response of a floating body (including heave, pitch, roll, etc.);

[0075] Anchor tension over time curve and identification of the location of maximum tension;

[0076] The evolution of force and displacement at the suspension point connection;

[0077] Maximum deformation, additional tension distribution and stable morphological evolution of netting under different sea conditions.

[0078] Meanwhile, the simulation system has a feedback mechanism that can dynamically adjust the local contact stiffness and damping parameters according to the changes in structural response during model operation, making the model closer to the actual physical state and avoiding rigid instability or abnormal tensile stress.

[0079] Furthermore, the response analysis pays special attention to the extreme response capability of the cage system under typical extreme sea conditions (such as strong winds and waves, and reverse current fields). This invention establishes a three-dimensional mapping relationship of "structure-operating condition-response". Based on evaluation indicators such as the maximum offset of the floating body, the maximum tension value of the anchorage, and the maximum deformation rate of the netting, the modeling parameters and structural morphology are retrospectively analyzed to provide a reliable response benchmark for the optimization algorithm.

[0080] In the gravity-type submersible cage parameter design optimization method provided by this invention, to effectively identify key structural parameters and improve the focus and efficiency of parameter optimization calculations, a key design parameter screening mechanism based on a combination of disturbance analysis and normalized response sensitivity function is proposed. This mechanism quantifies the influence of structural parameters on buoyancy performance, attitude stability, and extreme load response capabilities through multi-parameter disturbance experiments, three-dimensional coupled finite element simulation, and multi-condition response extraction, thereby constructing a parameter set with the highest engineering control value.

[0081] This method first selects several structural control parameters that are closely related to the response of the floating net cage structure, including but not limited to the following five types of parameters: (1) the volume of the float, which directly determines the buoyancy and floating behavior of the system; (2) the height of the buoyancy center, which affects the overall stability and restoring moment; (3) the preload of the anchor, which determines the structure's resistance to displacement under the action of ocean currents; (4) the location of the hoisting point, which affects the force distribution path of the float and the net system; and (5) the initial value of the net tension, which determines the deformation behavior and tension state of the net under wave load.

[0082] For the aforementioned structural control parameters, limited-amplitude positive and negative disturbances are applied within their preset design parameter range. For example, the floating body volume parameter can fluctuate by 5% to 10% above and below its nominal value, forming upper and lower limit disturbance comparison samples. By changing each parameter one by one while keeping other parameters constant, a set of parameter disturbance sample sets is formed. Each set of disturbance samples represents a structural configuration scheme and is used to evaluate the corresponding structural response in subsequent simulations.

[0083] Next, the three-dimensional coupled finite element model constructed in this invention is used to perform simulation analysis on each set of parameter perturbation samples under three typical working conditions. The three working conditions include:

[0084] Floating and sinking conditions: Simulate the entire process of a floating body sinking from the water surface to the target depth, or rising from underwater to the working water layer, and extract response variables such as floating and sinking time, maximum pitch angle, and maximum roll angle;

[0085] Attitude adjustment condition: Simulate the attitude response capability of the floating body and the net under external disturbance conditions (such as wave direction deviation, increase in unidirectional flow velocity), and extract the response variables as attitude stabilization time and maximum deflection angle;

[0086] Extreme wave conditions: Simulate the stress behavior of the system under large-cycle, large-wave, and high-wave conditions, and extract the response variables as the peak stress at the suspension point, the maximum tension of the anchor cable, and the maximum stress at the mesh node.

[0087] After completing the simulation analysis of all perturbation samples, a sample database containing input parameter perturbation information and output response indicators is formed.

[0088] Subsequently, the sensitivity analysis phase begins. This invention employs a normalized response sensitivity function to process the aforementioned sample data, thereby quantifying the influence of parameters on the response. First, for each input parameter, its sensitivity value is defined as the degree of change in the response variable caused by a small change in that parameter. To avoid interference from absolute dimensions, the sensitivity value is expressed as a relative rate of change, i.e.:

[0089] For a given input parameter A, the change ΔR of a response variable R caused by its disturbance is divided by the baseline value of R to obtain the percentage change in response; then, this percentage change in response is divided by the percentage of the disturbance amplitude of parameter A to obtain the relative sensitivity value of A to R.

[0090] This process can be achieved through a differential method, that is, by calculating the response variables in the simulation results before and after the disturbance, and obtaining the ratio of the changes.

[0091] To facilitate comparative analysis across response dimensions, this invention normalizes all response sensitivity values. The normalization method employs a linear mapping strategy, mapping all sensitivity values ​​to the [0,1] interval. The mapping formula is: subtract the minimum value from a given sensitivity value, then divide by the difference between the maximum and minimum values. This operation eliminates the order-of-magnitude differences between various response indicators, improving the comparability of sensitivity functions.

[0092] After obtaining the normalized sensitivity matrix, this invention further calculates the global sensitivity weight of each input parameter across multiple response dimensions. Specifically, the method involves: defining the importance of each response variable (such as buoyancy time, attitude angle, and maximum stress) in the engineering objective, assigning corresponding weight coefficients (e.g., buoyancy stability 30%, attitude response 40%, extreme stress 30%), and using a weighted averaging strategy to comprehensively calculate the normalized sensitivity values ​​of each parameter across each response dimension, thereby obtaining the global sensitivity weight value of that parameter.

[0093] For example, if the normalized sensitivity values ​​of the floating body volume in the three response indicators are 0.8, 0.6, and 0.7, and the response weights are 0.3, 0.4, and 0.3, then the global sensitivity weight of the floating body volume is: (0.8×0.3)+(0.6×0.4)+(0.7×0.3)=0.24+0.24+0.21=0.69.

[0094] This invention sorts and filters the global sensitivity weights of each parameter by setting a reasonable response contribution threshold, eliminating parameters with an impact below a specified limit (e.g., those with a weight less than 0.2), and retaining the parameters with significant impact to form the final key design parameter set P. This parameter set serves as the target variable set in subsequent optimization steps, not only reducing the dimensionality of the design space but also significantly improving the convergence speed and result controllability of the optimization algorithm.

[0095] The multi-objective optimization model proposed in this invention uses the parameters in the key design parameter set P as input dimensions for design variables, including but not limited to the floating body volume, buoyancy center height, anchor preload, hoisting point position, and initial netting tension, comprehensively covering the controllable parameter space of the core structural subsystem of the submersible gabion. The model integrates three core optimization objective functions, described as follows:

[0096] The buoyancy-sinking time control function uses the difference between the actual time required for the floating body to complete its ascent or descent from its initial position to the target depth and the design-allowed time as the evaluation index. Its physical meaning is to optimize the structural response speed, enabling the system to complete attitude transitions within a set time range as much as possible while satisfying buoyancy-sinking stability. This function is in the form of an objective function, and its expression can be described as:

[0097] The floating and sinking time control function is F1 = |T_actual - T_design|; where T_actual is the floating and sinking time obtained in the simulation, and T_design is the preset process control time.

[0098] The maximum stress minimization function optimizes the maximum stress generated by the mesh system or its connections (such as suspension points and anchor cable connections) under extreme wave conditions. The goal is to control the stress peak within the material strength margin to improve the structural safety of the system. The objective function is in the form of:

[0099] The maximum stress function is F2 = Max(σ_max); where σ_max represents the maximum equivalent stress of the structural element under extreme wave excitation.

[0100] The attitude deviation constraint function considers the attitude deflection effect of the floating body under disturbances in different flow directions. Especially under the superposition of high current velocity and oblique waves, the system may experience excessive roll or pitch. Therefore, it is necessary to constrain the maximum tilt angle deviation. This function is transformed into an inequality constraint expression, expressed as:

[0101] The attitude offset constraint G1 = Max(θ_pitch, θ_roll) ≤ θ_limit; where θ_pitch and θ_roll are the pitch and roll angles, respectively, and θ_limit is the maximum allowable offset angle in the design.

[0102] To achieve a unified solution, all objective functions F1, F2, and constraint functions G1 must be normalized when constructing the optimization model. Specifically, extreme value normalization is used to map each function value to the [0,1] interval to unify the objective dimensions. The constraint function G1 is converted into an embeddable expression through a penalty factor mechanism. When a constraint is violated, its value is converted into a penalty term and added to the comprehensive objective function, thus automatically avoiding infeasible solutions during the optimization process.

[0103] Ultimately, the comprehensive optimization objective can be constructed into one of the following two models:

[0104] Weighted summation model (WSM): F_total=w1·F1_norm+w2·F2_norm+w3·Penalty(G1); where w1, w2, and w3 are preset target weight coefficients, and Penalty(G1) is a penalty function constructed based on the degree of constraint offset.

[0105] A non-dominated sorting method is used to obtain the optimal Pareto solution set in the three objective function space, which is suitable for adaptive optimization scenarios without weights.

[0106] To solve the above multi-objective optimization model, this invention adopts an improved adaptive genetic algorithm (AGA), which achieves a balance between global search and local convergence under high-dimensional nonlinear and multi-constraint conditions by dynamically adjusting the control parameters of the genetic operators.

[0107] The algorithm includes the following main steps:

[0108] After determining the design parameter set P, the parameter dimension n is first set, and a feasible range is defined for each parameter. An initial population is then generated using floating-point real-number encoding, where each individual is an n-dimensional vector representing a candidate solution. Compared to traditional binary encoding, floating-point encoding can handle continuous variables more accurately, improving the algorithm's convergence quality and resolution.

[0109] Initialize the population size to N (e.g., 100 individuals), and set the maximum number of generations G_max (e.g., 200 generations) and the termination criterion.

[0110] For each generation of the population, the weighted fitness or Pareto rank of individuals is calculated based on the normalized values ​​of the objective functions F1, F2, and G1. Based on this, the following adaptive genetic control strategy is introduced:

[0111] Crossover probability Pc: Dynamically adjusted based on the current fitness variance of the population. When the fitness difference is large (strong population diversity), Pc is appropriately reduced; when the fitness tends to be concentrated (population convergence), Pc is appropriately increased to enhance gene mixing.

[0112] Mutation probability Pm: When the fitness of individuals in the population is concentrated but the solution quality does not improve significantly, the Pm value is automatically increased to help escape the local optimum trap. A typical control function can be: Pm = Pm_min + (1 - σ_fit / σ_max)·(Pm_max - Pm_min); where σ_fit is the current standard deviation of the population fitness, σ_max is the historical maximum standard deviation, Pm_min is the minimum mutation probability, and Pm_max is the maximum mutation probability.

[0113] The selection operation employs tournament selection or roulette wheel selection to ensure that individuals with high fitness are preferentially retained; the crossover uses the simulated binary crossover (SBX) algorithm under real number encoding to maintain numerical continuity; and the mutation uses Gaussian perturbation to slightly perturb the individual genes, increasing the search space coverage.

[0114] An elitist strategy is employed to retain the individual with the best fitness in each generation, ensuring that excellent solutions are not replaced. Iteration termination criteria include: reaching the maximum number of generations G_max, the optimal fitness changing less than a preset threshold ε over several consecutive generations, or the Pareto boundary solution becoming stable.

[0115] The final output is the combination of design parameters corresponding to the individual with the best fitness, which is taken as the optimal parameter solution P_opt. This solution simultaneously satisfies the multidimensional performance balance of buoyancy efficiency, structural safety, and attitude stability, and has high engineering adaptability and environmental robustness.

[0116] In the gravity-type submerged cage parameter design optimization method proposed in this invention, after solving the optimal parameter solution P_opt based on the multi-objective optimization model, it is not immediately used as the final design conclusion. Instead, through back-substitution verification and response reanalysis mechanisms, the performance of P_opt in the actual application scenario is fully and dynamically simulated to ensure that the obtained parameter solution meets the engineering design requirements in multiple dimensions such as buoyancy efficiency, attitude stability and structural stress response.

[0117] First, the structural parameters in the optimal parameter solution P_opt are assigned to the three-dimensional coupled finite element model to complete the model structure reconstruction. The variables included in P_opt include, but are not limited to, the volume of the floating body, the height of the buoyancy center, the preload of the anchorage, the spatial position of the lifting point, and the initial tension value of the netting.

[0118] After updating the model parameters, dynamic simulations of the submersible cage system were performed under three typical operating conditions, including:

[0119] Floating and sinking conditions: Simulates the floating and sinking process of the floating body from the working depth to the mooring depth. The simulation cycle covers the entire floating process. The extracted output variables include the actual floating and sinking time, the floating body's trajectory, and the acceleration curves of rising or falling.

[0120] Attitude disturbance conditions: Simulates the attitude adjustment process of the floating body under disturbance conditions such as wave direction deviation and sudden change in flow velocity. Output variables include roll angle, pitch angle, attitude adjustment time, and angle fluctuation amplitude after stabilization.

[0121] Extreme wave conditions: Simulates the instantaneous structural response under the historical maximum wave height or design extreme sea state. The main output variables are the maximum tension of the anchor cable, the stress concentration at the suspension point, and the maximum stress point of the netting system.

[0122] The simulation employs a nonlinear dynamic explicit integration method, taking into account buoyancy, water resistance, drag force, added mass, and flexible coupling response to ensure that the simulation process closely approximates the actual operating environment.

[0123] To determine the performance improvement effect of the optimal parameter solution P_opt, the simulation output results are compared item by item with the response indices under the corresponding working conditions before optimization (i.e., initial structural parameter configuration). To quantify the degree of improvement or deviation of each objective function, this invention introduces a response deviation rate calculation model.

[0124] For any objective function (such as the buoyancy-sinking time function F1), the deviation rate δ1 is defined as follows:

[0125] Deviation rate δ1 = |T_actual - T_target| ÷ T_target; where T_actual is the floating and sinking time under the simulation of the optimal parameter solution, and T_target is the design target time.

[0126] For the maximum stress function F2 and the attitude deviation constraint G1, the deviation rates δ2 and δ3 are defined in the same way as follows:

[0127] Deviation rate δ2=|σ_max_actual-σ_target|÷σ_target;

[0128] Deviation rate δ3=Max(|θ_pitch_actual-θ_limit|,|θ_roll_actual-θ_limit|)÷θ_limit.

[0129] Where σ_max_actual is the peak value of the simulation stress, θ_pitch_actual and θ_roll_actual are the maximum tilt angles of the simulation output, and θ_limit is the attitude allowable threshold.

[0130] The physical meaning of the above deviation rate is that the closer the value is to 0, the closer it is to the design target. If the deviation rate exceeds the preset tolerance range, it indicates that although the current P_opt is the optimal solution, its actual response has not yet met the convergence requirements.

[0131] To improve the convergence and practicality of the optimization model, this invention automatically activates the weight parameter and penalty coefficient adjustment mechanism when it detects that the target response has not completely fallen into the preset target interval, thus forming the self-correction and iterative update capability of the optimization model.

[0132] The specific mechanism is as follows:

[0133] For each objective function, its initial optimization weights are set as w1, w2, w3, etc. When the deviation rate δ of a certain function is significantly greater than that of other functions (e.g., δ2 >> δ1, δ3), the system judges that the response of that function is insufficient, that is, its optimization weight needs to be increased. The adjustment strategy is as follows: w_i_new = w_i_original × (1 + α × δ_i / δ_avg); where α is the adjustment coefficient (empirical value is generally 0.5 to 1.0), δ_avg is the average deviation rate of all objective functions, w_i_new is the adjusted weight, and w_i_original is the initial weight;

[0134] This formula ensures that the greater the deviation rate of the objective function, the higher its optimization priority, thereby driving the adaptive genetic algorithm to explore more fully in that direction.

[0135] When the attitude deviation exceeds θ_limit, the constraint function G1 is considered to have violated the constraint. The original penalty function Penalty(G1) is part of the objective function and activates the penalty term when the constraint is violated. To strengthen the control over constraint violations, the penalty term coefficient β needs to be adjusted according to the deviation magnitude, and the update formula is as follows: β_new=β_original×(1+γ×δ3); where γ is the constraint penalty sensitivity coefficient and δ3 is the deviation rate of the attitude deviation constraint.

[0136] After updating the weights and penalty coefficients, the system automatically generates a revised set of optimization objective functions and reconstructs the fitness function with the updated objective expression, driving the next round of adaptive genetic algorithm iteration. Specifically, this includes:

[0137] The updated set of objective functions was re-embedded into the optimization model;

[0138] Initialize a new population, partially inheriting from the elite individuals of the previous generation;

[0139] Reassess population fitness according to the new fitness criteria;

[0140] Repeated selection, crossover, and mutation operations continue to evolve until a new convergence condition is met.

[0141] This response-driven closed-loop mechanism of optimization-verification-re-optimization overcomes the shortcomings of traditional optimization, which only "solves once" without posterior response feedback, and realizes an intelligent self-correcting optimization system centered on performance response.

[0142] After completing multi-objective optimization, dynamic simulation verification, and response convergence determination, this invention uses the final optimal parameter solution P_opt as the final design parameter configuration for gravity-type submersible gabions. P_opt encompasses key structural control parameters such as float volume, buoyancy center height, anchor preload, hoisting point location, and initial netting tension, achieving a performance balance in terms of buoyancy efficiency, attitude stability, and stress response under extreme conditions. Through systematic modeling and simulation feedback closed-loop optimization, P_opt ensures stable operation and safety redundancy of the structure under complex sea conditions, providing a reliable parametric design basis for gabion engineering applications and achieving a precise mapping from multi-dimensional performance objectives to optimal structural parameters.

[0143] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for optimizing the design parameters of a gravity-fed submersible cage, characterized in that: include: Collect marine environmental data of the target sea area at multiple time periods during the design service life, including changes in wave height, period, current velocity and current direction, and construct an environmental load sequence with time-varying characteristics; A three-dimensional coupled finite element model including the floating body, anchorage, lifting points and netting was constructed, and the environmental load sequence was used as the input boundary conditions to simulate the floating and sinking response and force transmission. Perturbation analysis was performed on multiple structural control parameters in the model. Based on the response sensitivity function, the set of parameters that have a significant impact on buoyancy stability, attitude response and stress peak under extreme loads was identified and denoted as the key design parameter set P. A multi-objective optimization model is constructed based on a set of objective functions, including a floating and sinking time control function, a maximum stress minimization function, and an attitude offset constraint function. An adaptive genetic algorithm is then used to globally optimize the parameter set P to obtain the optimal parameter solution P_opt. Substitute P_opt back into the three-dimensional coupled finite element model, perform dynamic simulation iteration, and compare whether the response characteristics before and after optimization converge to the target interval. If they do not converge, adjust the optimization weights according to the sensitivity matrix until the optimization convergence condition is met. The optimal parameter P_opt is output as the final design parameter configuration for the gravity-fed submersible cage.

2. The method for parameter design and optimization of a gravity-type submersible cage according to claim 1, characterized in that: The construction of a three-dimensional coupled finite element model including the floating body, anchorage, sling points, and netting, and the use of the environmental load sequence as input boundary conditions, includes simulations of buoyancy response and force transmission, including: A three-dimensional coupled finite element model covering four structural units—floating body, anchorage, hoisting point, and netting—was constructed. The three-dimensional coupled finite element model is based on the principle of fluid-structure interaction and simulates the nonlinear mechanical relationship between the floating body and the anchorage by setting flexible connection boundaries. Using the environmental loads with time-series characteristics collected from the target sea area as time-varying boundary inputs, wave height, wave period, flow velocity and flow direction are mapped into dynamic pressure fields and shear flow fields acting on the surface of the floating body and the mesh nodes. Nonlinear dynamic response simulation was performed to obtain the attitude change, anchor tension and net deformation response of the structure during the floating and sinking process, and the contact stiffness and coupling damping parameters at the connection between the float and the suspension point were updated in real time during the simulation.

3. The method for parameter design and optimization of a gravity-type submersible cage according to claim 1, characterized in that: Perturbation analysis was performed on multiple structural control parameters in the model. Based on the response sensitivity function, the set of parameters that significantly affect buoyancy stability, attitude response, and stress peak under extreme loads was identified and denoted as the key design parameter set P, specifically: Multiple structural control parameters were selected, including the volume of the floating body, the height of the buoyancy center, the preload of the anchorage, the position of the lifting point, and the initial value of the netting tension. Positive and negative perturbations were applied within their respective design ranges to construct a sample set of perturbation parameters. For the disturbance parameter sample set, a three-dimensional coupled finite element model is called to perform simulations in sequence under floating and sinking conditions, attitude adjustment conditions and extreme wave conditions, and to extract floating and sinking stability index, attitude deviation angle and maximum stress response value. The relationship between each input parameter and the response variable is quantified by a normalized response sensitivity function. The global sensitivity weight of each parameter is calculated, and parameters with an impact value lower than a specified limit are removed based on a set threshold. The parameters with significant impact are retained to form the key design parameter set P.

4. The method for parameter design and optimization of a gravity-type submersible cage according to claim 3, characterized in that: The normalized response sensitivity function is used to quantify the relationship between each input parameter and the response variable, and the global sensitivity weight of each parameter is calculated, specifically as follows: Based on the constructed disturbance sample set, the difference calculation is performed on the change of response variable caused by each input parameter before and after the disturbance to obtain the initial sensitivity value of each parameter relative to the floating and sinking stability, attitude response and extreme stress response. All initial sensitivity values ​​are normalized and mapped to a dimensionless numerical range using a uniform scale. For the normalized sensitivity values, a weighted average method is used to calculate the global sensitivity weight of each input parameter under multiple operating conditions and response variables.

5. The method for parameter design and optimization of a gravity-type submersible cage according to claim 1, characterized in that: A multi-objective optimization model is constructed based on a set of objective functions, specifically as follows: For the key design parameter set P, a floating and sinking time control function, a maximum stress minimization function, and an attitude deviation constraint function are constructed respectively. The floating and sinking time control function uses the time required for the float to complete the ascent or descent to the target depth and the preset process time difference as the evaluation index. The maximum stress minimization function uses the maximum structural stress of the mesh or connecting parts under extreme wave conditions as the optimization objective. The attitude deviation constraint function uses the maximum lateral and longitudinal tilt angle deviation of the float under disturbance conditions as the boundary control condition. The objective function is normalized and a penalty factor mechanism is introduced, in which the attitude offset constraint function is transformed into a constraint penalty term and embedded into the objective function, forming a unified and solvable composite optimization objective expression. A multi-objective optimization model is formed by constructing a weighted summation model based on weight coefficients or a non-dominated sorting method for Pareto optimal solution sets.

6. The method for parameter design and optimization of a gravity-type submersible cage according to claim 5, characterized in that: An adaptive genetic algorithm is used to globally optimize the parameter set P to obtain the optimal parameter solution P_opt, specifically: Based on a multi-objective optimization model, the genetic population is initialized and population codes are generated using the key design parameter set P as the variable dimension, while a multi-objective fitness evaluation function is set. Based on the population evolution generation and the current individual fitness distribution characteristics, the selection probability, crossover probability and mutation probability are dynamically adjusted. The mutation probability is automatically increased when the population fitness tends to converge, so as to escape the local optimum trap. In each generation, selection, crossover, and mutation operations are performed based on the multi-objective weighted fitness value of the individual. The current best individual is retained in combination with the elite retention strategy. After the iteration satisfies the termination criterion or convergence condition, the parameter combination corresponding to the best fitness individual is output, which is denoted as the optimal parameter solution P_opt.

7. The method for parameter design optimization of a gravity-type submersible cage according to claim 1, characterized in that: Substitute P_opt back into the three-dimensional coupled finite element model and perform dynamic simulation iteration, specifically as follows: Substitute the optimized parameter solution P_opt into the constructed three-dimensional coupled finite element model and redefine the floating body, anchor system, lifting point and netting. Dynamic simulations were performed under floating and sinking conditions, attitude disturbance conditions, and extreme wave conditions. The floating and sinking time, attitude angle change curves, and maximum stress values ​​of the structure were extracted, and the simulation outputs were compared and analyzed with the response values ​​under the corresponding conditions before optimization. Set a convergence criterion interval. If all target response indicators converge within the target interval or threshold range, then P_opt is confirmed as a valid solution; otherwise, automatically adjust the optimization weight parameters or penalty function coefficients based on the degree of response deviation, and restart the optimization iteration.

8. The method for parameter design and optimization of a gravity-type submersible cage according to claim 7, characterized in that: The weight parameters or penalty function coefficients are automatically adjusted and optimized based on the degree of response deviation, specifically as follows: By comparing the simulation output results of the optimal parameter solution P_opt under various typical working conditions with the corresponding target response interval, the deviation rate of each optimized objective function is calculated. The deviation rate is defined as the ratio obtained by dividing the absolute value of the difference between the actual response value and the target value by the target value. The target weight parameters are dynamically adjusted according to the deviation rate of each objective function. If the deviation rate of a certain response is higher than the preset threshold, the optimization weight of the objective function corresponding to that response is increased. If the attitude offset constraint is violated, its penalty function coefficient is increased simultaneously. The updated weight parameters and penalty function coefficients are re-introduced into the optimization model to construct the corrected set of optimization objective functions, triggering the next round of adaptive genetic algorithm iteration.

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