An optimization method and structure of a deep-sea semi-submersible net cage mooring system

Abstract

The present application relates to the technical field of ocean engineering equipment, and more particularly to a deep-sea semi-submersible net cage mooring system optimization method and structure, which comprises multi-dimensional design space initialization based on low-bias sequence, construction of a high-fidelity data set of the semi-submersible net cage mooring system in combination with a parameterized physical simulation template; construction of a proxy model fused with physical constraints of the mooring system with the high-fidelity data set as input, training of the proxy model with a composite physical constraint loss function, and verification of prediction accuracy and physical fidelity; establishment of a multi-objective optimization framework, embedding of the proxy model into the multi-objective optimization framework, collaborative evolution optimization based on the proxy model, and output of a Pareto optimal solution set; and output of a final mooring system optimization design scheme, which realizes high-fidelity prediction of the hydrodynamic response of the mooring system and effectively solves the defect of non-physical prediction values produced by traditional pure data-driven models when extrapolated in complex sea conditions.

Description

Technical Field

[0001] This invention relates to the field of marine engineering equipment technology, and in particular to an optimization method and structure for a deep-sea semi-submersible cage mooring system. Background Technology

[0002] Deep-sea aquaculture is an important development direction for alleviating near-shore ecological pressure and ensuring the supply of high-quality protein. Semi-submersible cages have become core equipment for deep-sea aquaculture due to their advantages such as strong resistance to wind and waves and large aquaculture space. As a key support structure for semi-submersible cages in complex marine environments, the design quality of the mooring system directly determines the safety and construction cost of the cages. Currently, the optimization design of semi-submersible cage mooring systems mainly relies on empirical trial-and-error methods based on hydrodynamic simulation software, or directly couples traditional heuristic algorithms with time-consuming nonlinear time-domain physical simulations for parameter optimization. Some studies introduce low-order surrogate models such as response surface methodology to replace some simulation calculations.

[0003] However, the aforementioned existing technologies generally have significant shortcomings. On the one hand, the empirical trial-and-error method relies on the subjective judgment of designers, often blindly increasing the diameter or length of the anchor chain to ensure safety under extreme sea conditions, resulting in excessively high safety factors and serious material redundancy, making it difficult to fundamentally balance construction costs and structural safety. On the other hand, when traditional heuristic algorithms seek optimization in a multi-dimensional continuous parameter space, they need to repeatedly couple the population individuals with physical simulation software for calculation, with a single optimization taking several days or even longer, and are prone to getting trapped in local optima. In addition, existing optimization techniques mostly use simple empirical coefficients for single-objective weighted compromise, without establishing a rigorous cost mathematical model, and cannot simultaneously take into account the economy and safety of the mooring system, making it difficult to adapt to the core goal of cost reduction and efficiency improvement in deep-sea aquaculture. Finally, existing proxy models are mostly pure data-driven black-box models, lacking an embedding mechanism of mooring dynamics physical theorems, and are prone to producing non-physical prediction values ​​that violate engineering physics common sense when extrapolating in complex sea conditions. At present, there is a need for an optimization method and structure for deep-sea semi-submersible cage mooring systems. Summary of the Invention

[0004] To address the problems of long computation time, excessive design, and inability to balance economy and safety in the optimization design of existing deep-sea semi-submersible cage mooring systems, this invention provides an optimization method and structure for deep-sea semi-submersible cage mooring systems.

[0005] Firstly, the present invention provides an optimization method for a deep-sea semi-submersible cage mooring system, which adopts the following technical solution: An optimization method for a deep-sea semi-submersible cage mooring system includes: Multidimensional design space initialization is performed based on low-bias sequences, and a high-fidelity dataset for a semi-submersible cage mooring system is constructed by combining a parametric physical simulation template. Using a high-fidelity dataset as input, a PINN proxy model that integrates the physical constraints of the mooring system is constructed to establish the network topology and physical information flow. A composite physical constraint loss function was constructed to train the PINN surrogate model, and the prediction accuracy and physical fidelity were verified. A multi-objective optimization framework is established, and the PINN surrogate model is embedded in the multi-objective optimization framework. The multi-objective optimization framework includes defining design variables, objective function vectors, and hard constraints of engineering specifications. The NSGA-III multi-objective optimization algorithm is invoked, and co-evolutionary optimization is performed based on the PINN surrogate model to output the Pareto optimal solution set. Based on the Pareto optimal solution set, the final optimized design scheme of the mooring system is output.

[0006] Furthermore, the high-fidelity dataset for constructing the semi-submersible cage mooring system includes using mooring cable diameter, adjustable length, total mooring cable length, and horizontal span of anchor points as design variables, determining the coupling relationship between each design variable, and setting the physical value range of each design variable. A parameterized model template is constructed, design variables are defined as variable parameters, a cross-software time-domain solution mapping mechanism coupled with three-dimensional potential flow theory and Morrison equations is constructed, and hydrodynamic response characteristics are extracted. Halton's low-bias sequence is introduced to perform deterministic sampling of the multidimensional design space. The standard spatial coordinates are mapped to the physical parameter space based on the mirror inversion mapping function to generate the mooring system parameter matrix. The adjustable length is used instead of the total length of the mooring cable as an independent design variable, and the spatial parameterization mechanism of the mooring system is reconstructed based on the absolute straight-line distance constraint between the anchor point and the guide hole. Perform time-domain physical simulations on all samples to extract the static water pretension of the cable, the maximum tension over time, the sway value, heave value, and pitch value of the net cage, and construct a high-fidelity dataset.

[0007] Furthermore, the construction of the PINN proxy model that integrates the physical constraints of the mooring system includes setting the input layer to receive a preprocessed normalized geometric feature vector, wherein the geometric feature vector includes the mooring cable diameter, adjustable length, horizontal span of the anchor point, and total length of the mooring cable; A deep network topology containing multiple hidden layers is constructed. Each hidden layer performs batch normalization and nonlinear activation operations in sequence, and performs nonlinear forward propagation to map low-dimensional mooring parameters to a high-dimensional feature space. An inverse normalization and physical truncation mapping mechanism is introduced at the output layer. Based on the statistics of the training dataset and a preset physical rigid boundary, the normalized output of the network is mapped to a physically meaningful predicted value. The expression for the physical truncation mapping mechanism is as follows: , in, This is the normalized output for the k-th target feature. and Let be the mean and standard deviation of the k-th physical feature in the training dataset, respectively. and These are rigid upper and lower boundaries set based on actual physical constraints and preset operating conditions.

[0008] Furthermore, the construction of the PINN proxy model for integrating the physical constraints of the mooring system also includes: The nonlinear activation operation is performed using a modified linear unit activation function; During the network initialization phase, the He initialization strategy is adopted for the modified linear unit activation function, and the variance of the initial weights is dynamically adjusted according to the number of neurons in the previous layer. A random deactivation mechanism based on Bernoulli distribution is embedded between each hidden layer. During the training phase, a mask matrix is ​​generated with a preset retention probability. Element-wise multiplication is performed on the feature output. During the inference and prediction phase, the expected value scaling operation is performed on the feature output.

[0009] Furthermore, the construction of the composite physical constraint loss function to train the PINN surrogate model includes performing gradient tracking and backpropagation on the mean square error between the surrogate model's predicted value and the actual value of the physical simulation, and constructing a data-driven loss term; The physical control equations of mooring dynamics are extracted, and the dynamic extreme boundary conditions, static monotonicity conditions and extreme dynamic equilibrium conditions are transformed into residual operators and embedded with physical constraint penalty terms. Construct a composite total loss function consisting of a weighted superposition of a data-driven loss term, a physical constraint penalty term, and a weight decay regularization term; The adaptive moment estimator optimizer is invoked to dynamically and adaptively update the network weights and bias vectors based on the first-order and second-order moment estimates of the loss function gradient. A coefficient of determination is introduced to perform quantitative acceptance of the prediction accuracy of the surrogate model. When the coefficient of determination on the validation set reaches a preset threshold and the loss curve converges, the surrogate model is deemed to have completed training and the fixed network weight topology file is exported.

[0010] Furthermore, the physical constraint penalty term includes performing a modified linear unit activation operation on the dynamic extreme boundary conditions, extracting the positive residual between the predicted value of the static pretension and the predicted value of the maximum tension, and constructing the first physical constraint sub-term. For the static monotonicity condition, perform high-order gradient tracking, calculate the partial derivative of the predicted static pretension value with respect to the adjustable length input parameter, and extract the positive residual through the activation of the modified linear unit to construct the second physical constraint sub-term; Based on the still water stiffness of the swaying system, the horizontal component of the mooring system and the extreme values ​​of the environmental load, a quasi-static equilibrium residual equation is constructed, and the square integral operation is performed on the residual equation as the third physical constraint term. The first physical constraint sub-item, the second physical constraint sub-item, and the third physical constraint sub-item are superimposed to form a physical constraint penalty item.

[0011] Furthermore, the establishment of the multi-objective optimization framework includes using the mooring cable diameter, adjustable length, and horizontal span of the anchor point as decision variables to construct a continuous multi-dimensional optimization space; A multidimensional objective function vector is constructed, which includes the total cost of the mooring system, the sway value of the cage, and the maximum tension of the mooring cable. A Pareto non-dominated sorting rule is established to preserve the non-dominated attributes among the objectives. A mathematical constraint function is established, including a safety factor, maximum heave displacement, and static prestress range. The trained surrogate model is embedded into a multi-objective optimization framework to predict the objective function response value. The multi-dimensional objective function vector satisfies: , in, The total cost of the mooring system. This is the cage sway value. This represents the maximum tension experienced by the mooring cable.

[0012] Furthermore, the co-evolutionary optimization based on the PINN surrogate model includes generating reference points in the three-dimensional target space based on simplex lattice design to guide the direction of population evolution. Perform ideal point translation normalization on individuals in the population, calculate the vertical distance from the normalized target vector to the direction vector of the preset reference point, and perform a niche preservation operation based on the vertical distance; The trained surrogate model is invoked to predict the objective function response value, driving the NSGA-III algorithm to perform co-evolutionary optimization and output a Pareto optimal solution set. The formula for calculating the vertical distance is: , in, Let x be the vertical distance from the j-th reference point. The target vector is a normalized translation of the ideal point. Let be the direction vector of the j-th reference point.

[0013] Furthermore, the output Pareto optimal solution set also includes a dynamic adaptive constraint violation penalty mechanism based on evolutionary algebra, which uses the ratio of the power function of the current iteration algebra to the maximum evolutionary algebra as a pre-multiplier to perform exponential accumulation operation on the violation amount of each engineering specification constraint function; Based on the nonlinear increasing characteristics of the pre-multipliers in the evolutionary generations, the intensity of the constraint violation penalty is dynamically adjusted, and the cooperative feasibility rule outputs the Pareto optimal solution set. The expression for the dynamic adaptive constraint violation penalty mechanism is: , in, Let x be the violation function of individual x in the t-th generation population. For the maximum number of generations, Let the current iteration algebra be... For algebraic scaling factor, To constrain the depth penalty index, Let be the constraint function for the k-th engineering specification.

[0014] Secondly, an optimized structure for a deep-sea semi-submersible cage mooring system includes a semi-submersible cage, a cable guide hole, mooring cables, and anchor points. The semi-submersible cage is a floating aquaculture platform with a watertight compartment structure. The semi-submersible operation draft is achieved by adjusting the ballast water, and multiple cable guide holes are fixedly installed on the edge of the lower structure of the semi-submersible cage. The cable guide hole is configured to fix and guide the upper end of the mooring cable and to transmit the mooring restoring force to the semi-submersible cage. The number of mooring lines corresponds to the number of guide holes. The upper end of each mooring line is connected to the corresponding guide hole, and the lower end extends outward and connects to the anchor point fixed to the seabed.

[0015] The mooring cable has a mooring cable diameter and an adjustable length. The horizontal straight-line distance between the vertical projection point of the guide hole on the seabed and the corresponding anchor point is defined as the horizontal span of the anchor point. The actual total length of the mooring cable is determined by the absolute spatial straight-line distance from the anchor point to the guide hole and the adjustable length of the mooring cable.

[0016] In summary, the present invention has the following beneficial technical effects: 1. This invention constructs a physical information neural network proxy model that integrates the physical constraints of mooring dynamics. It transforms the dynamic extreme boundary, static monotonicity, and extreme dynamic equilibrium constraints into residual penalty terms embedded in the network loss function, thereby achieving high-fidelity prediction of the hydrodynamic response of the mooring system. This effectively overcomes the defect of traditional pure data-driven models that produce non-physical prediction values ​​when extrapolating in complex sea states, and improves the engineering rationality and safety of the prediction results.

[0017] 2. This invention introduces Haldane low-bias sequences to perform deterministic sampling of the multidimensional design space and replaces traditional nonlinear time-domain physical simulation with a physical information neural network surrogate model, thereby achieving efficient and intelligent optimization of mooring system design. This avoids the problems of insufficient computing power, easy getting trapped in local optima, and excessively long single optimization time caused by the direct coupling of traditional heuristic algorithms and physical simulation software, thus shortening the optimization cycle.

[0018] 3. This invention establishes a multi-objective optimization framework with the total cost of the mooring system, the sway value of the cage, and the maximum tension of the cable as parallel optimization objectives, and incorporates a dynamic adaptive constraint violation penalty mechanism based on evolutionary algebra. This achieves Pareto optimal solution output that balances safety and economy, and solves the limitation of traditional single-objective weighted compromise design in balancing material cost and structural safety.

[0019] 4. This invention uses an adjustable length instead of the total length of the mooring cable as an independent design variable, and reconstructs the spatial parameterization mechanism of the mooring system based on the absolute straight-line distance constraint between the anchor point and the guide hole. This effectively avoids non-physical sample combinations and improves the construction quality of high-fidelity datasets and the reliability of the optimization process. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the overall process of an optimization method for a deep-sea semi-submersible cage mooring system according to an embodiment of the present invention.

[0021] Figure 2 This is a schematic diagram of the overall structure of the PINN proxy model according to an embodiment of the present invention.

[0022] Figure 3 This is a side view of the deep-sea semi-submersible cage mooring system according to an embodiment of the present invention.

[0023] Figure 4 This is an embodiment of the present invention. Figure 3 A partial enlarged view of region A in the middle.

[0024] Figure 5 This is a top view of the deep-sea semi-submersible cage mooring system according to an embodiment of the present invention.

[0025] Among them, 1. semi-submersible cage; 2. cable guide hole; 3. mooring cable diameter; 4. mooring cable; 5. adjustable length of mooring cable; 6. anchor point; 7. seabed; 8. horizontal span of anchor point. Detailed Implementation

[0026] The present invention will be further described in detail below with reference to the accompanying drawings.

[0027] Example 1 Reference Figure 1An optimization method for a deep-sea semi-submersible cage mooring system according to this embodiment includes: S1. Initialize the multidimensional design space based on low-bias sequences, and construct a high-fidelity dataset for the semi-submersible cage mooring system by combining a parametric physical simulation template. S2. Using a high-fidelity dataset as input, construct a PINN proxy model that integrates the physical constraints of the mooring system to establish the network topology and physical information flow. S3. Construct a composite physical constraint loss function to train the PINN proxy model and verify the prediction accuracy and physical fidelity. S4. Establish a multi-objective optimization framework and embed the surrogate model into the multi-objective optimization framework. The multi-objective optimization framework includes defining design variables, objective function vectors, and hard constraints of engineering specifications. S5. Call the NSGA-III multi-objective optimization algorithm, perform co-evolutionary optimization based on the surrogate model, and output the Pareto optimal solution set; S6. Based on the Pareto optimal solution set, output the final mooring system optimization design scheme.

[0028] Specifically, an optimization method for a deep-sea semi-submersible cage mooring system includes the following steps: like Figure 1 As shown, S1, first determine the mooring cable diameter d and adjustable length. Total length L of mooring cables and horizontal span of anchor points As optimization design variables, and based on the catenary static equilibrium theory to determine the coupling relationship between the variables, the spatial shape of the mooring cable under static pretension follows the following differential control equations: , in, The buoyancy of the mooring cable per unit length in seawater. Let z be the horizontal tension component of the mooring cable at the guide hole, z be the vertical coordinate of the mooring cable, and x be the horizontal coordinate of the mooring cable.

[0029] By analytically solving this physical equation, the horizontal span of the anchor point can be derived. Relative depth of anchor point The higher-order coupling relationship between the total cable length L and the cable total length L, where the total cable length L satisfies: , in, This is the horizontal straight-line distance between the vertical projection point of the cable guide hole on the seabed and the corresponding anchor point, i.e., the horizontal span of the anchor point. This is the vertical distance from the cable guide hole to the seabed, i.e., the relative depth of the anchor point. The mooring cable is adjustable in length.

[0030] To achieve efficient driving and dynamic updating of the underlying physical model, this embodiment constructs a parametric model template and a data interaction mapping layer. Specifically, a standard model file (.dat or .yml format) generated by OrcaFlex software is pre-set as the parametric reference template, and the mooring cable diameter d, adjustable length ΔL, and horizontal span of the anchor point in the template are included. And the calculated total length L Defined as a variable parameter.

[0031] When constructing the instantiated hydrodynamic simulation benchmark template, given that deep-sea semi-submersible cages are typical composite structures of "large-volume floating bodies + permeable flexible netting," a single hydrodynamic solver cannot accurately capture their physical response. Therefore, this embodiment innovatively constructs a cross-software time-domain solution mapping mechanism based on the coupling of three-dimensional potential flow theory and the Morrison Equation.

[0032] First, for the large-volume diffraction units such as the pontoons and columns of the cage, the three-dimensional potential flow theory is used in frequency domain hydrodynamic software (such as AQWA) to solve the problem, extract the additional mass matrix, radiation damping matrix and first-order wave excitation force, and import it as a hydrodynamic database into the OrcaFlex environment.

[0033] Secondly, in the OrcaFlex time-domain analysis model, for each cross brace, strut, and the high-porosity flexible mesh model, since the frequency domain calculation does not consider its viscous effect, this embodiment defines them as Morison Elements. Under wave-current coupling, the transient normal hydrodynamic load on a unit length of mesh member is... Strictly follow Morrison's control equations: , in, Let D be the density of seawater, and D be the equivalent hydrodynamic diameter of the rod / net. The instantaneous velocity of the water particles. The instantaneous acceleration of a water particle. and These are the nonlinear drag force coefficient and inertial force coefficient, respectively, set based on the mesh density and Reynolds number.

[0034] Ultimately, in the baseline template, the overall time-domain rigid body dynamics response of the net cage is governed by the Cummins integral equation: , Where M is the mass matrix of the wire mesh cage structure. For the added mass at infinite frequency, Let C be the delay function matrix, representing the radiation wave memory effect generated by the buoyancy motion, and let C be the still water restoring force stiffness matrix. Let be the acceleration vector of the rigid body of the wire mesh cage. Let V be the velocity vector of the rigid body of the wire mesh cage. Let be the displacement vector of the rigid body of the wire mesh cage. The first-order wave force introduced into potential flow theory The viscous drag is obtained by real-time integration of the Morrison equations described above. For the tension of the mooring system.

[0035] To overcome the local spatial clustering problem caused by pseudo-randomness in traditional Latin hypercube sampling (LHS) and avoid the additional computational overhead of introducing secondary distance filtering (such as the minimax distance criterion), this invention innovatively introduces the Halton Sequence for initializing the multidimensional design space. This sequence generates a uniform spatial distribution through deterministic number theory methods, providing physical feature data for the subsequent construction of a high-quality Physical Information Neural Network (PINN) surrogate model.

[0036] For any dimension in the design space, assuming the cardinality is a prime number b, in this embodiment, different design variables are considered. Adjustable length ΔL, mooring cable length L, and horizontal span of anchor points Select consecutive prime numbers without repetition. , … As the cardinality, where To design the variable dimensions. Any decimal integer sample index i can be uniquely expanded into base b form: , in, For sample index, It is a prime base. The coefficients in base b For power index, It is the highest power.

[0037] Furthermore, the core of the Halton sequence lies in the introduction of a mirror-reversal mapping function. By mirroring the integer indices along the decimal point, uniform coordinate points with extremely low spatial deviation are generated in the interval [0,1]. , in, This is a mirror image reversal mapping function. Using a prime number base, the design variable dimension is... For the i-th sampling combination scheme, its coordinate vector in the multidimensional standard space is defined as Then, through the inverse function of the cumulative distribution function the standard spatial points are mapped to the real physical parameter space of the mooring system, the m -th physical design variable's actual value is calculated as follows: , wherein, is the actual value of the m-th physical design variable of the i-th sample, is the inverse function of the cumulative distribution function of the m-th design variable, is the mirror inversion mapping value based on prime number as the base in the m-th dimension. The above deterministic sampling mechanism based on multi-dimensional prime base ensures efficient traversal and uniformity of the generated mooring system parameter matrix in a large design space, avoids the hidden danger of invalid "physical blank areas" caused by traditional pseudo-random sampling, and greatly improves the completeness of the underlying data.

[0038] To avoid the problem of hydrodynamic time-domain simulation divergence caused by random combination of mooring variables in traditional modeling, in this embodiment, adjustable length replaces the total length L of the mooring cable as an independent design variable, and the spatial parameterization mechanism of the mooring system is reconstructed based on the absolute straight-line distance constraint between the anchor point and the fairlead. The absolute straight-line distance S between the anchor point and the fairlead satisfies: ， wherein, is the absolute straight-line distance between the anchor point and the fairlead.

[0039] If the total length L of the mooring cable and the horizontal span between the anchor point and the are both used as independent free variables for the evolution of genetic algorithm, unreasonable physical samples with L < S (that is, the total length of the cable is shorter than the straight-line distance between the two points) are easily generated. Such non-physical combinations will cause the subsequent dynamic simulation to fail to find the static equilibrium position and diverge. Therefore, when constructing the design space of multi-objective optimization and deep learning surrogate model, this embodiment introduces to replace L as an independent design variable, which avoids the generation of wrong samples from the data source, thereby ensuring the stable convergence of the model training and joint optimization process.

[0040] After a single simulation converges, the Python script automatically intercepts the required 5 key objective features from the background result file, including the hydrostatic pretension of the cable , the maximum time-history tension ( The dataset includes the cage's surge, heave, and pitch values. After iterating through all samples, it automatically outputs a high-fidelity dataset file containing four-dimensional input features and a five-dimensional output target. The four-dimensional input feature vector... With the five-dimensional output target vector They are respectively: , , in, For the input feature vector, For hydrostatic pretensioning of the cable, The maximum tension over time is represented by Surge, which is the cage sway value, Heave, which is the cage heave value, and Pitch, which is the cage pitch value.

[0041] In traditional dynamic simulations, hydrostatic pretension is typically used as an artificially set input variable. However, in the parametric design framework of this embodiment, the design variables are limited to pure geometric and dimensional parameters, including cable diameter, adjustable length, and anchor span. When these geometric parameters are randomly combined in the subsequent genetic algorithm to generate a new mooring system, the corresponding hydrostatic pretension, uniquely determined by the geometric configuration, transforms into a geometrically constrained output response value. In the multi-objective optimization stage, the hydrostatic pretension... The constraints included in the optimization are that the optimal solution selected by the algorithm must satisfy the minimization of maximum tension and cost, while its static pretension is within a reasonable physical range, so as to ensure that the optimized mooring system solution has mechanical rationality in static water conditions.

[0042] S2. This embodiment relies on a deep learning framework to construct a physical information neural network surrogate model, namely the PINN surrogate model, which integrates time-domain hydrodynamic data and the physical theorems of mooring systems, targeting the highly nonlinear and multi-physical quantity coupling characteristics of the dynamic response of deep-sea semi-submersible cages under wave-current coupling. The PINN surrogate model consists of an input layer, a deep hidden layer, and an output layer. The input layer has four neuron nodes that receive the preprocessed normalized geometric feature vector. , Where X is the input feature vector, and d is the diameter of the mooring cable. The mooring cable is adjustable in length. L represents the horizontal span of the anchor point, and L represents the total length of the mooring cable.

[0043] like Figure 2As shown, the hidden layer adopts a five-layer deep network structure, with the number of neurons exhibiting a feature extraction structure of increasing dimensionality, high-dimensional mapping, and decreasing dimensionality. This aims to map low-dimensional mooring parameters to a high-dimensional feature space, thereby fully decoupling the implicit physical relationship between the parameters and the dynamic response of the mooring cage. Each hidden layer sequentially performs batch normalization and modified linear unit activation operations to complete nonlinear forward propagation. Specifically, the first... The output feature matrix of the layer is determined by the following forward propagation equation: , in, For the first l The output feature matrix of the layer, This is the weight matrix for the current layer. This is the bias vector for the current layer. To correct the linear unit activation function and address the gradient vanishing problem in multilayer networks when propagating physical field feature gradients, For batch normalization layer.

[0044] Given the inherent physical scale differences in input physical quantities, such as millimeter-level wire diameter and hundred-meter-level span, the batch normalization layer performs a standard normal distribution mapping transformation on the feature matrix of a small batch of samples to forcibly smooth out the distribution differences of physical features between layers. The batch normalization operation includes: calculating the mean and variance of the feature dimensions of the small batch of samples, performing a standardization transformation on the feature matrix, and then performing a linear transformation through learnable scaling and translation parameters. The specific operation logic is as follows: , , , , in, For small batch sample size, The mean of the feature dimension. The variance of the feature dimension. For the k-th sample in the th... The feature output of the layer, To prevent extremely small constants with a denominator of zero, These are the scaling parameters that the network adaptively learns through backpropagation gradients. These are the translation parameters that the network adaptively learns through backpropagation gradients. This is the standardized feature matrix.

[0045] In the output layer, to overcome the shortcomings of traditional black-box neural networks in complex multi-objective regression tasks, which tend to output predictions that violate ocean physics norms, this embodiment abandons the conventional purely linear fully connected mapping and introduces an inverse normalization and physical truncation mapping mechanism. This mechanism, based on training dataset statistics and a preset physical rigid boundary, restores the network's normalized output to a physically meaningful prediction value. Let the network's original normalized output for the k-th target feature be... Its final mapping is to a predicted value with physical meaning. The nonlinear mapping equation is as follows: , in, This is the normalized output for the k-th target feature. Let be the mean of the k-th physical feature in the training dataset. Let be the standard deviation of the k-th physical feature in the training dataset. and As a rigid upper and lower boundary set based on actual physical constraints and preset operating conditions, this physical truncation mapping mechanism forcibly truncates non-physical gradients at the end of the network forward propagation, ensuring that all prediction schemes passed to the subsequent NSGA-III algorithm have engineering rationality.

[0046] Regarding network weight initialization, to address the complexity of the physical response data distribution, this embodiment abandons the conventional random initialization method and specifically adopts the He initialization strategy for the modified linear unit activation layer. This strategy dynamically adjusts the variance of the initial weights based on the number of neurons in the previous layer, ensuring that the variance of physical features remains consistent during network forward propagation, avoiding the attenuation of physical signals, and accelerating the model's optimization convergence in complex physical spaces.

[0047] To prevent the model from overfitting to a finite number of discrete physical samples, this embodiment embeds a random deactivation mechanism based on Bernoulli distribution between each hidden layer. Let the... The retention probability of the layer is In the forward propagation process of this layer, a mask matrix following a Bernoulli distribution is first generated. Then, element-wise multiplication of the feature outputs is performed to randomly inactivate neurons. During the inference and prediction phase, the expected value is scaled by multiplying by the retention rate to ensure the physical magnitude of the output signal is conserved. Specifically, the mask matrix during the training phase... and the characteristic output after deactivation The definition is as follows: , , , in: Given a vector of binomial random variables that follows a Bernoulli distribution, determine the first... Is the j-th neuron in the layer activated in the current training batch? To preserve probability, For the first The original feature output of the layer, This is the feature output after inactivation during the training phase. This is the feature output scaled by the expected value during the inference and prediction stage. As a representation of element-wise multiplication of matrices, this random deactivation mechanism forces the network to learn more generalizable essential mooring physics, rather than local noise features.

[0048] S3. To ensure the accuracy of the PINN surrogate model in predicting hydrodynamic response and to force the network to follow the objective physical laws of the mooring system, this embodiment constructs a PINN composite total loss function that includes a data-driven loss term, a physical constraint penalty term, and a weight decay regularization term. An adaptive moment estimation optimizer is used to perform backpropagation training. Simultaneously, an early stopping mechanism based on the validation set's generalization ability and a determination coefficient acceptance criterion are introduced. The specific implementation process is as follows: First, construct the data-driven loss term. Using the automatic differentiation technique of a deep learning framework, gradient tracking and backpropagation are performed on the mean square error between the surrogate model's predictions and the actual values ​​in the physical simulation to measure the deviation between the surrogate model's predictions and the actual values ​​in the high-fidelity physical simulation. The mathematical expression for this is: , in, Where K is the batch size and K is the target output dimension. This represents the predicted output value of the surrogate model for the k-th target feature of the i-th sample. This represents the true response value of the k-th target feature of the i-th sample extracted through high-fidelity physical simulation.

[0049] Secondly, the physical governing equations of mooring dynamics are extracted, and the dynamic extreme boundary conditions, static monotonicity conditions, and extreme dynamic equilibrium conditions are transformed into residual operators and embedded with physical constraint penalty terms. The physical constraint penalty term is composed of three physical constraint sub-terms superimposed. For dynamic extreme boundary conditions, the maximum dynamic tension of the cable under wave and current action must be greater than or equal to the still water pretension. In this embodiment, a modified linear unit activation function is used to extract the violation residual and construct the first physical constraint sub-term. : , in, This represents the predicted static prestress value for the i-th sample. For the i-th sample, the predicted maximum tension over time is given. When the predicted value violates the dynamic extreme boundary condition, i.e., the static pretension is greater than the maximum tension, the positive residual is extracted by the modified linear unit activation function and the loss is included.

[0050] For the static monotonicity condition, it is required that, with other geometric and environmental parameters remaining constant, the static pretension must monotonically decrease with the increase of the mooring cable slack (i.e., the adjustable length). In this embodiment, the partial derivative of the predicted static pretension with respect to the adjustable length input parameter is directly calculated through high-order gradient tracing, and the positive residual is extracted by activating the modified linear unit to construct the second physical constraint term. : , in, For the first i The predicted static prestress values ​​for each sample are relevant to the adjustable length. When the partial derivative is greater than zero, which violates the monotonically decreasing law, the activation function of the modified linear unit is used to extract the positive residual and include it in the loss.

[0051] For the extreme dynamic equilibrium condition, considering the physical characteristic that the velocity of a semi-submersible cage is zero at the instant of reaching its maximum sway displacement, this embodiment reduces the Cummins equation of motion to a quasi-static equilibrium residual equation. This equation is used to constrain the mechanical compatibility between the network's output motion response and tension response, and an extreme dynamic equilibrium residual operator is defined. : , in, To pre-calculate the heave static stiffness using hydrodynamic software, This is the cage sway value. This refers to the horizontal component of the force acting on the mooring system under maximum tension. The transient extreme values ​​of environmental loads under the target sea state are given. The maximum tension of the mooring cable during operation. Let be the horizontal span of the anchor point. Based on the above residual operator, this embodiment performs square integration on the residual equation to construct the third physical constraint term. , in, Let be the extreme value dynamic equilibrium residual operator for the i-th sample. The three physical constraint sub-terms are superimposed to form the physical constraint penalty term: + , When the model's predictions violate any of the above physical laws, the modified linear unit activation function will extract the positive residuals and significantly increase the total loss, forcing the neural network weights to revert to the feasible region that conforms to the physical theorems during backpropagation.

[0052] Construct a composite total loss function consisting of a data-driven loss term, a physical constraint penalty term, and a weight decay regularization term, weighted summation: , in, For data-driven loss terms, As a penalty term constrained by physical laws, This is the weight decay regularization term. and These are dynamic weighting coefficients used to balance the orders of magnitude of the various loss terms.

[0053] Subsequently, an adaptive moment estimation optimizer with momentum adjustment capabilities is invoked to perform backpropagation. The initial learning rate is set to 0.01. This optimizer dynamically adjusts the learning rate of each weight by calculating the first and second moment estimates of the loss function gradient. Its core iterative equation is as follows: , , , in, Let be the partial derivative of the loss function with respect to the weights. and These are the first-order moment estimates and second-order moment estimates of the gradient of the loss function, respectively. and These are the attenuation coefficients of the first and second moments, respectively. Step size, and These are the first-order moment estimates and second-order moment estimates after bias correction, respectively. To prevent extremely small constants with a denominator of zero, this mechanism allows the model to accelerate the search in flat regions of the physical response space, while automatically reducing the step size at points of drastically fluctuating nonlinear gradients, thus ensuring a weighted topology file with high physical fidelity.

[0054] To address the underfitting or overfitting risks inherent in conventional models that rely on a fixed number of iterations, this embodiment constructs an early stopping mechanism based on the generalization ability of the validation set. During the training cycle, the mean squared error loss of the validation set is monitored in real time, and a patience threshold is set. If the validation set loss is continuous If no significant decrease occurs within a certain number of iterations, it is determined that the network has fully grasped the parameter mapping boundary. The algorithm then forcibly triggers an early termination instruction and automatically backtracks and solidifies the network weight state with the lowest validation set error, thereby maximizing the saving of computing power costs while ensuring the accuracy of physical response prediction.

[0055] Furthermore, the coefficient of determination is introduced. As the ultimate criterion for evaluating the accuracy of the surrogate model, it quantifies the extent to which the network's predictions explain the variance of the real physical response. For any output physical feature, the coefficient of determination is calculated using the following formula: , in, The total number of samples in the validation set, Let be the true response value extracted from the i-th sample through high-fidelity physical simulation. The predicted output value of the PINN proxy model. The value is the arithmetic mean of the true response values ​​of all samples in the validation set. During the training period, the determination coefficients of the network's predicted values ​​for the five output physical features are monitored in real time. When the early stopping criterion is triggered, and the determination coefficients of all indicators stably reach 0.99 or higher, and the validation set loss curve achieves smooth convergence, the customized PINN surrogate model is considered to have completed training. Subsequently, the network weight topology file with high physical fidelity at this point is exported and archived, serving as the surrogate model for the subsequent NSGA-III multi-objective genetic optimization algorithm.

[0056] S4. Deeply couple the physical information neural network surrogate model trained in step 3 with economic evaluation and engineering specification constraints to construct and solve the multi-objective optimization problem of the mooring system. First, establish the three core continuous variables participating in the joint optimization and their physical value boundaries to form a decision optimization space. Using the mooring cable diameter... Adjustable length and anchor point horizontal span As a decision variable, the total length L of the mooring cables is determined by the aforementioned geometric constraints, and the decision variable vector... satisfy: , Secondly, three mutually restraining optimization objective vectors that need to be minimized simultaneously are constructed, establishing a multidimensional objective function matrix. The multidimensional objective function vectors... Total cost including mooring system cage sway value and maximum tension of mooring cables Its mathematical expression is: , in, The total cost of the mooring system. This is the cage sway value. The maximum tension of the mooring cable over time is taken as the economic objective, and the total cost of the mooring system is calculated based on the material consumption. , in, Let d be a cost constant and d be the diameter of the mooring cable. This refers to the total length of the mooring cables. The total number of mooring lines, and the span of the cage. Surge and maximum tension of mooring cables T `max` is the predicted output of the PINN surrogate model trained in step 3. Unlike traditional techniques that simply add multiple objectives together using subjective experience weights to create a single fitness function, this embodiment constructs a strict Pareto non-dominated ranking rule within the optimization space. For any two mooring design schemes in the population space... and Determination scheme Domination Plan The mathematical criteria for determining it are: , in, and The respective schemes and The algorithm only determines the solution when the objective function value in the i-th objective dimension is strictly satisfied, provided that the above condition is met. Superior This mechanism avoids the risk of losing excellent solutions due to improper manual weight allocation.

[0057] Strict industry boundary constraints are established in the multi-objective optimization space. The trained PINN surrogate model is embedded into the multi-objective optimization framework to predict the objective function response value. The engineering specification hard constraints include safety factor constraints, maximum sway displacement constraints, and static water prestressing interval constraints, the original mathematical expression of which is: , in, This represents the actual minimum safety factor for the mooring cable in the dynamic simulation. As the baseline value for the safety factor, This represents the maximum sway value of the cage during the dynamic simulation process. This is the actual water depth. This represents the lower limit of the hydrostatic prestressing value. This is the upper limit of the static water prestressing.

[0058] To adapt to the standard constraint handling format of the NSGA-III algorithm, the above industry boundary constraints are transformed into four mathematical constraint functions, when the constraint conditions are met. The solution is determined to be a valid and feasible solution under the following specific constraints: Constraint 1 is a safety factor constraint. The breaking force of the mooring cable is dynamically calculated based on the proportional formula of cross-sectional area, requiring that the minimum safety factor value be greater than the specified benchmark value. , , in, For the breaking force of the mooring cable, These are empirical constants related to the material properties and structural type of mooring cables. As the baseline value for the safety factor, This represents the predicted maximum tension value of the mooring cable over time.

[0059] Constraint 2 is the maximum wave displacement constraint. Referring to the guiding principles for determining displacement boundaries based on mooring lines and platform operations in marine engineering mooring design specifications, and considering the actual operational needs and collision avoidance requirements of deep-sea semi-submersible cages, the maximum wave displacement of the cage is limited to 15% of the water depth H: , in, H represents the maximum sway value of the cage during the dynamic simulation process, and H represents the actual water depth.

[0060] Constraints 3 and 4 are constraints on the still water pretension range. If the pretension is too large, the mooring cable will bear a large dynamic tension, which is detrimental to the safety of the mooring cable; if the pretension is too small, the dynamic response of the platform will increase significantly and it will be difficult to meet the normal operation requirements. Therefore, the still water pretension is limited to a reasonable range. , , in, This is the predicted value for static water prestress. This represents the lower limit of the hydrostatic prestressing value. This represents the upper limit of the static water prestress. Through the joint establishment of the above multi-dimensional objective function vector and the four mandatory constraints of the engineering specifications, a complete multi-objective optimization mathematical model for the semi-submersible cage mooring system is formed. The PINN surrogate model is then embedded into this framework to replace time-consuming physical simulations.

[0061] S5. The NSGA-III multi-objective optimization algorithm is invoked, employing a system reference point generation strategy based on simplex lattice design. Pre-defined reference points are established within the three-dimensional target space to guide the population's evolutionary direction. Let the target dimension be... The number of partitions is Then the total number of reference points Determined by the combination formula: , in, The total number of reference points. For the target dimension, The number of segments. Adjust the number of segments. This enables precise control over the Pareto front cover density. Each generated reference point serves as a data point to guide population evolution, ensuring that the algorithm outputs a set of mooring system design schemes with high convergence and uniform spatial distribution while meeting engineering constraints.

[0062] In the optimization process of the three-dimensional target space, in order to maintain the diversity of Pareto non-dominated solution sets, the NSGA-III algorithm preserves niches by calculating the vertical distance from individual populations to a preset hyperplane reference point during the adaptive environment selection phase. Let the ideal point of an individual be the translated and normalized target vector. , to the Direction vectors of each reference point vertical distance The calculation is as follows: , in, Let x be the vertical distance from the j-th reference point. The target vector is a normalized translation of the ideal point. Direction vector The length of the mold, This is the dot product of the normalized target vector and the direction vector. Using this vertical distance metric, the algorithm prioritizes retaining individuals that are close to the reference point and evenly distributed during the environment selection phase, thus maintaining the diversity of the non-dominated solution set in the 3D target space.

[0063] In handling the engineering hard boundary constraints established in step 4 To avoid premature loss of population diversity due to overly strict hard boundary constraints in the early stages of optimization, a dynamic adaptive constraint violation penalty mechanism based on evolutionary generations is constructed. For the ... t Any individual in the population x Its violation function evolves dynamically with algebra The structure is as follows: , in, Let x be the violation function of individual x in the t-th generation population. Here, t represents the maximum number of generations to evolve, and t represents the current iteration generation. It is the algebraic scaling factor and is usually taken as The nonlinear increasing coefficient, To constrain the depth penalty index, The first one defined in step 4 k The project specification constraint function. This dynamic adaptive constraint violation penalty mechanism endows the algorithm with extremely strong exploratory adaptability: in the early stages of evolution when t is small, the pre-multiplier... The algorithm tolerates a small number of slightly violating individuals to maintain genetic diversity and expand the search boundary; as evolution enters the middle and late stages... The pre-multipliers grow exponentially, imposing extremely severe mathematical penalties to eliminate non-compliant solutions from the feasible region. Combined with the feasibility rules of NSGA-III, this ultimately outputs a Pareto front solution set with a high safety margin.

[0064] Based on the aforementioned reference point guidance, niche preservation, and dynamic constraint penalty mechanism, the PINN surrogate model trained in step 3 is invoked to predict the objective function response value, driving the NSGA-III algorithm to perform co-evolutionary optimization. Under the premise of meeting the hard constraints of engineering specifications, the Pareto optimal solution set that takes into account the total cost of the mooring system, the sway value of the cage, and the maximum tension of the cable is output.

[0065] S6. Extract a set of non-dominated design schemes from the Pareto optimal solution set. This set consists of combinations of mooring system parameters that are mutually independent across the three objective dimensions: total cost of the mooring system, cage sway value, and maximum tension of the mooring cables. Perform post-processing on this set of non-dominated design schemes, removing extreme boundary solutions that exceed the feasible range of the project, and retaining a subset of candidate design schemes located in the middle of the Pareto front.

[0066] Decision interpretation is performed on the subset of candidate design schemes. A preference strategy is set based on the actual needs of deep-sea aquaculture projects, and the relative closeness of each candidate scheme to the ideal and negative ideal solutions is calculated. Alternatively, the knee region with the largest rate of change of curvature on the Pareto front is selected as the optimal compromise region, and the final recommended scheme is determined from this optimal compromise region. The decision interpretation process comprehensively considers the construction cost of the mooring system, the structural safety redundancy under extreme sea conditions, and the motion response performance of the cages, and ranks the candidate schemes accordingly.

[0067] Based on the decision interpretation results, a final optimized design scheme for the mooring system is output. This final scheme includes the mooring cable diameter *d* and adjustable length. and anchor point horizontal span The optimal parameter combination is determined, and the corresponding total length L of the mooring cable is calculated based on the geometric coupling relationship.

[0068] Example 2 The difference between this embodiment and Embodiment 1 is that this embodiment provides a structure for a deep-sea semi-submersible cage catenary mooring system; like Figure 3 , Figure 4 As shown, this embodiment provides a deep-sea semi-submersible cage catenary mooring system structure, including a semi-submersible cage 1, a cable guide hole 2, a mooring cable 4, and an anchor point 6.

[0069] The semi-submersible cage 1 is a floating aquaculture platform made of steel or high-strength composite materials, with a box-shaped or cylindrical watertight compartment structure. The semi-submersible draft is adjusted by ballast water to balance aquaculture space and wave resistance. Multiple cable guide holes 2 are fixedly installed along the edges of the lower structure of the semi-submersible cage 1, arranged according to the spatial layout of the four corners. These cable guide holes 2 serve as restraint devices, used to fix and guide the upper end of the mooring cable 4, and are responsible for transmitting the mooring restoring force to the main structure of the semi-submersible cage 1.

[0070] The upper end of the mooring cable 4 is connected to the corresponding guide hole 2, and its lower end extends outward and connects to the anchor point 6 fixed on the seabed 7. Figure 3 As shown, under the combined action of its own weight and the environmental load of the sea surface, the mooring cable 4 exhibits a naturally drooping catenary shape between the guide hole 2 and the anchor point 6. The horizontal straight-line distance between the vertical projection point of the guide hole 2 on the seabed 7 and the corresponding anchor point 6 is defined as the horizontal span of the anchor point. .

[0071] like Figure 4 As shown, the microscopic geometric and physical characteristic variables of the mooring cable 4 are defined, specifically including the mooring cable diameter 3 and the adjustable length 5. In this embodiment, the actual total length of the mooring cable 4 is not arbitrarily set, but is determined by the absolute spatial straight-line distance from the anchor point 6 to the guide hole 2 and the adjustable length. The absolute spatial straight-line distance between anchor point 6 and cable guide hole 2 was calculated together. S The horizontal span 8 of the anchor point and the relative depth of the anchor point It is determined that the actual total length L of the mooring cable 4 is determined by the absolute spatial straight-line distance S and the adjustable length of the mooring cable. Determined by superposition.

[0072] The anchor point 6 is fixedly set on the seabed 7 and is configured to anchor the lower end of the corresponding mooring cable 4 to bear the tensile load transmitted by the mooring cable and provide the position holding force of the cage.

[0073] like Figure 5As shown, the mooring system in this embodiment adopts a multi-point radial layout. Multiple mooring cables 4 extend and anchor from the semi-submersible cage 1 to the surrounding seabed 7 in a divergent pattern, forming a symmetrical multi-point mooring topology. This provides the semi-submersible cage 1 with all-round resistance to wind, waves, and currents in three-dimensional space, ensuring the position and attitude stability of the deep-sea semi-submersible cage under harsh sea conditions. The mooring cable diameter 3, the adjustable length 5, and the horizontal span 8 of the anchor points are used as decision variables in a multi-objective optimization algorithm. After optimization, the optimal parameter combination is determined, and the corresponding total length L of the mooring cables is calculated based on the above geometric relationships, forming a mooring system structural design scheme that takes into account both economy and safety.

[0074] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. An optimization method for a deep-sea semi-submersible cage mooring system, characterized in that, include: Multidimensional design space initialization is performed based on low-bias sequences, and a high-fidelity dataset for a semi-submersible cage mooring system is constructed by combining a parametric physical simulation template. Using a high-fidelity dataset as input, a PINN proxy model that integrates the physical constraints of the mooring system is constructed to establish the network topology and physical information flow. A composite physical constraint loss function was constructed to train the PINN surrogate model, and the prediction accuracy and physical fidelity were verified. The construction of a composite physical constraint loss function to train the PINN surrogate model includes performing gradient tracking and backpropagation on the mean square error between the surrogate model's predicted values ​​and the actual physical simulation values, and constructing a data-driven loss term. Extract the physical control equations of mooring dynamics, and transform the dynamic extreme boundary conditions, static monotonicity conditions, and extreme dynamic equilibrium conditions into residual operators, embedding physical constraint penalty terms; Construct a composite total loss function consisting of a weighted superposition of a data-driven loss term, a physical constraint penalty term, and a weight decay regularization term; The adaptive moment estimator optimizer is invoked to dynamically and adaptively update the network weights and bias vectors based on the first-order and second-order moment estimates of the loss function gradient. A coefficient of determination is introduced to perform quantitative acceptance of the prediction accuracy of the surrogate model. When the coefficient of determination on the validation set reaches a preset threshold and the loss curve converges, the surrogate model is deemed to have completed training and the fixed network weight topology file is exported. The physical constraint penalty term includes performing a modified linear unit activation operation on the dynamic extreme boundary conditions, extracting the positive residual between the predicted value of static pretension and the predicted value of maximum tension, and constructing the first physical constraint sub-term. For the static monotonicity condition, perform high-order gradient tracking, calculate the partial derivative of the predicted static pretension value with respect to the adjustable length input parameter, and extract the positive residual through the activation of the modified linear unit to construct the second physical constraint sub-term; Based on the still water stiffness of the swaying system, the horizontal component of the mooring system and the extreme values ​​of the environmental load, a quasi-static equilibrium residual equation is constructed, and the square integral operation is performed on the residual equation as the third physical constraint term. The first physical constraint sub-item, the second physical constraint sub-item, and the third physical constraint sub-item are superimposed to form a physical constraint penalty item; A multi-objective optimization framework is established, and the PINN surrogate model is embedded in the multi-objective optimization framework. The multi-objective optimization framework includes defining design variables, objective function vectors, and hard constraints of engineering specifications. The NSGA-III multi-objective optimization algorithm is invoked, and co-evolutionary optimization is performed based on the PINN surrogate model to output the Pareto optimal solution set. Based on the Pareto optimal solution set, the final optimized design scheme of the mooring system is output.

2. The optimization method for a deep-sea semi-submersible cage mooring system according to claim 1, characterized in that, The high-fidelity dataset for constructing the semi-submersible cage mooring system includes design variables such as mooring cable diameter, adjustable length, total mooring cable length, and horizontal span of anchor points, and determines the coupling relationship between each design variable and sets the physical value range of each design variable. A parameterized model template is constructed, design variables are defined as variable parameters, a cross-software time-domain solution mapping mechanism coupled with three-dimensional potential flow theory and Morrison equations is constructed, and hydrodynamic response characteristics are extracted. Halton's low-bias sequence is introduced to perform deterministic sampling of the multidimensional design space. The standard spatial coordinates are mapped to the physical parameter space based on the mirror inversion mapping function to generate the mooring system parameter matrix. The adjustable length is used instead of the total length of the mooring cable as an independent design variable, and the spatial parameterization mechanism of the mooring system is reconstructed based on the absolute straight-line distance constraint between the anchor point and the guide hole. Perform time-domain physical simulations on all samples to extract the static water pretension of the cable, the maximum tension over time, the sway value, heave value, and pitch value of the net cage, and construct a high-fidelity dataset.

3. The optimization method for a deep-sea semi-submersible cage mooring system according to claim 2, characterized in that, The construction of the PINN proxy model that integrates the physical constraints of the mooring system includes setting the input layer to receive a preprocessed normalized geometric feature vector, wherein the geometric feature vector includes the mooring cable diameter, adjustable length, horizontal span of the anchor point and total length of the mooring cable; A deep network topology containing multiple hidden layers is constructed. Each hidden layer performs batch normalization and nonlinear activation operations in sequence, and performs nonlinear forward propagation to map low-dimensional mooring parameters to a high-dimensional feature space. An inverse normalization and physical truncation mapping mechanism is introduced at the output layer. Based on the statistics of the training dataset and a preset physical rigid boundary, the normalized output of the network is mapped to a physically meaningful predicted value. The expression for the physical truncation mapping mechanism is as follows: ， in, This is the normalized output for the k-th target feature. and Let be the mean and standard deviation of the k-th physical feature in the training dataset, respectively. and These are rigid upper and lower boundaries set based on actual physical constraints and preset operating conditions.

4. The optimization method for a deep-sea semi-submersible cage mooring system according to claim 3, characterized in that, The construction of the PINN proxy model for integrating the physical constraints of the mooring system also includes: The nonlinear activation operation is performed using a modified linear unit activation function; During the network initialization phase, the He initialization strategy is adopted for the modified linear unit activation function, and the variance of the initial weights is dynamically adjusted according to the number of neurons in the previous layer. A random deactivation mechanism based on Bernoulli distribution is embedded between each hidden layer. During the training phase, a mask matrix is ​​generated with a preset retention probability. Element-wise multiplication is performed on the feature output. During the inference and prediction phase, the expected value scaling operation is performed on the feature output.

5. The optimization method for a deep-sea semi-submersible cage mooring system according to claim 1, characterized in that, The establishment of the multi-objective optimization framework includes using the mooring cable diameter, adjustable length and horizontal span of the anchor point as decision variables to construct a continuous multi-dimensional optimization space. A multidimensional objective function vector is constructed, which includes the total cost of the mooring system, the sway value of the cage, and the maximum tension of the mooring cable. A Pareto non-dominated sorting rule is established to preserve the non-dominated attributes among the objectives. A mathematical constraint function is established, including a safety factor, maximum heave displacement, and still water prestressing range. The trained surrogate model is embedded into a multi-objective optimization framework to predict the objective function response value. The multi-dimensional objective function vector satisfies: ， in, The total cost of the mooring system. This is the cage sway value. This represents the maximum tension experienced by the mooring cable.

6. The optimization method for a deep-sea semi-submersible cage mooring system according to claim 1, characterized in that, The co-evolutionary optimization based on the PINN proxy model includes generating reference points in the three-dimensional target space based on simplex lattice design to guide the direction of population evolution. Perform ideal point translation normalization on individuals in the population, calculate the vertical distance from the normalized target vector to the direction vector of the preset reference point, and perform a niche preservation operation based on the vertical distance; The trained surrogate model is invoked to predict the objective function response value, driving the NSGA-III algorithm to perform co-evolutionary optimization and output a Pareto optimal solution set. The formula for calculating the vertical distance is: ， in, Let x be the vertical distance from the j-th reference point. The target vector is a normalized translation of the ideal point. Let be the direction vector of the j-th reference point.

7. The optimization method for a deep-sea semi-submersible cage mooring system according to claim 6, characterized in that, The output Pareto optimal solution set also includes a dynamic adaptive constraint violation penalty mechanism based on evolutionary algebra, which uses the ratio of the power function of the current iteration algebra to the maximum evolutionary algebra as a pre-multiplier to perform exponential accumulation operation on the violation amount of each engineering specification constraint function. Based on the nonlinear increasing characteristics of the pre-multipliers in the evolutionary generations, the intensity of the constraint violation penalty is dynamically adjusted, and the cooperative feasibility rule outputs the Pareto optimal solution set. The expression for the dynamic adaptive constraint violation penalty mechanism is: ， in, Let x be the violation function of individual x in the t-th generation population. For the maximum number of generations, Let the current iteration algebra be... For algebraic scaling factor, To constrain the depth penalty index, Let be the constraint function for the k-th engineering specification.

8. An optimized structure for a deep-sea semi-submersible cage mooring system, based on the method described in claim 1, characterized in that, Includes semi-submersible cages, cable guides, mooring lines, and anchor points; The semi-submersible cage is a floating aquaculture platform with a watertight compartment structure. The semi-submersible operation draft is achieved by adjusting the ballast water, and multiple cable guide holes are fixedly installed on the edge of the lower structure of the semi-submersible cage. The cable guide hole is configured to fix and guide the upper end of the mooring cable and to transmit the mooring restoring force to the semi-submersible cage. The number of mooring lines corresponds to the number of guide holes. The upper end of each mooring line is connected to the corresponding guide hole, and the lower end extends outward and connects to the anchor point fixed to the seabed. The mooring cable has a mooring cable diameter and an adjustable length. The horizontal straight-line distance between the vertical projection point of the guide hole on the seabed and the corresponding anchor point is defined as the horizontal span of the anchor point. The actual total length of the mooring cable is determined by the absolute spatial straight-line distance from the anchor point to the guide hole and the adjustable length of the mooring cable.

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