Column structure response prediction method and system based on residual connection neural network

Abstract

The present invention belongs to the field of marine engineering technology, and discloses a column structure response prediction method and system based on a residual connection neural network. The present invention combines the physical information neural network (PINN) with the Kolmogorov‑Arnold (KAN) theorem, and significantly improves the accuracy and computational efficiency of the prediction model through a multi-layer nonlinear mapping framework and residual connection optimization. By introducing physical equation constraint losses and environmental parameter inputs, the model can more accurately simulate the dynamic response characteristics in extreme marine environments, effectively solving the limitations of traditional methods in nonlinear factor processing and real-time calculations. Experiments show that the present invention has significant advantages in accuracy, generalization ability and computational efficiency, and provides reliable and efficient technical support for marine platform structure design and operation status monitoring, and has important theoretical value and broad application prospects.

Description

Technical Field

[0001] The invention belongs to the field of marine engineering technology, and in particular relates to a column structure response prediction method and system based on a residual connection neural network. Background Art

[0002] Marine engineering, especially the development and operation of offshore platforms, is the core of achieving sustainable utilization of marine resources. As the core facility of marine development, offshore platforms play an important role in key tasks such as oil and gas collection and wind power support. Their structural safety is crucial to promoting the sustainable development of marine resource development. It can be said that the stability of platform structures is the key to global marine resource development, especially in the context of application in offshore projects such as oil, gas, and wind power, which places extremely high demands on their safety.

[0003] In the design of marine engineering structures, it is required to strengthen the monitoring of structures and responses during the design and construction process to ensure that the platform can remain stable under severe conditions such as extreme weather and earthquakes. To this end, improving the prediction capability of marine platform structural responses has become an important means to ensure the safety of the platform. At the same time, the intelligence level of marine engineering equipment has become an important direction for promoting the high-quality development of the marine economy. In recent years, with the promotion of digital transformation and intelligent upgrading, technologies such as artificial intelligence and big data have been applied in engineering monitoring and forecasting. Improved engineering efficiency and safety. Therefore, applying intelligent monitoring and forecasting technologies such as neural networks to real-time monitoring and forecasting of marine platform structural responses can not only help effectively reduce the risk of safety accidents, ensure the long-term stability and environmental adaptability of the platform, but also improve the operating efficiency of the platform and reduce maintenance costs. The marine platform monitoring system based on artificial intelligence not only improves the independent innovation capability of marine engineering technology, but also provides a solid guarantee for resource development in complex marine environments.

[0004] In recent years, the field of marine engineering has developed rapidly, but it still faces many challenges in predicting the structural response of platforms. Due to the complex and changeable marine environment, the load and pressure fluctuations on the platform are large, which puts higher requirements on structural safety. Especially in the fields of deep-sea oil drilling, offshore wind power, floating LNG, etc., the column structure is subjected to multiple loads from wind, waves, currents, etc., which can easily cause fatigue and structural damage. It is urgent to use intelligent means to predict the structural response in real time to support the design, operation and maintenance of the platform and disaster response. As the supporting part of the offshore platform, the column structure needs to have good strength and stability under dynamic loads such as wind, waves and currents. Therefore, the structural response prediction not only affects the platform's disaster resistance, but is also a necessary means to extend the platform's life and optimize the structural design.

[0005] Traditional analysis methods mostly rely on numerical methods such as finite element modeling, but such methods have high computational costs and are difficult to achieve real-time prediction. Deep learning, especially residual connection technology, has shown significant advantages in solving prediction and calculation problems. Residual connection technology has been proven to be effective in dealing with the gradient vanishing problem in deep networks and has performed well in large-scale data processing and complex relationship modeling. Therefore, in the prediction of offshore platform structural response, residual connection technology helps to build a deep network structure and achieve accurate prediction of column structural response by learning nonlinear relationships. This method maintains smooth information flow during the multi-layer feature extraction process, making the model more adaptable in processing large-scale data and capturing the impact of environmental variables on column structural response. The technology based on neural network intelligent prediction can efficiently and accurately simulate structural response, and can quickly provide response prediction of column structure under different environmental conditions and complex load combinations, thus providing a new solution for offshore platform structural response prediction and has broad application prospects.

[0006] Through the above analysis, the problems and defects of the existing technology are: the response prediction accuracy and real-time performance of the existing offshore platform columns in extreme marine environments are poor, and the structural response of the platform columns cannot be effectively and accurately predicted. Summary of the invention

[0007] In order to overcome the problems existing in the related art, the disclosed embodiments of the present invention provide a method and system for predicting the response of a column structure based on a residual connection neural network. The present invention is particularly directed to the response prediction technology of column structures in marine engineering under the action of waves and other external loads. Specifically, the present invention belongs to the intersection of structural engineering, marine engineering and artificial intelligence technology, and pays particular attention to the dynamic response prediction technology of column structures in marine engineering under complex environmental loads such as waves, wind waves and ocean currents, aiming to improve the response prediction accuracy of the column structure and optimize the design and safety assessment of marine engineering structures. Through this technology, more efficient intelligent analysis tools can be provided for marine platforms, deep-sea column structures and other offshore projects, thereby improving the reliability of engineering design, reducing risks, and helping to ensure the safety of offshore work.

[0008] The technical solution is as follows: A column structure response prediction method based on a residual connection neural network comprises the following steps:

[0009] S1, preprocessing the environmental data of the offshore platform columns, and initializing the environmental loads using the physical information neural network PINN based on the preprocessed environmental data;

[0010] S2, based on the Komogorov-Arnold KA theorem, a multi-layer nonlinear mapping model KAN is established to describe the environmental load to structural response;

[0011] S3, based on the constructed multi-layer nonlinear mapping model KAN, introduces a composite loss function to make the multi-layer nonlinear mapping model KAN adapt to actual observation data while following physical laws; introduces residual connections to optimize the network;

[0012] S4, ablation experiments are used to optimize the performance of the multi-layer nonlinear mapping model KAN for predicting the response of column structures under complex sea conditions.

[0013] In step S1, the environmental data is derived from monitoring equipment and experimental data, including: environmental load parameters of wind speed, wave, and flow speed;

[0014] Preprocessing of environmental data of offshore platform columns includes: resampling data of different time steps to ensure that the data has a uniform time interval; interpolation filling of missing data and normalization of all input data.

[0015] In step S1, the physical information neural network PINN is used to initialize the environmental load, including the following steps:

[0016] Step 1.1, based on the time series, establish the mapping relationship between wind speed, flow velocity, structural force area and load, and construct a fully connected network. The input is time, wind or wave flow velocity, effective force area or volume, and the output is the predicted load value;

[0017] Step 1.2, find the constraints of the physical equations, and the wind load is calculated as:

[0018] ;

[0019] In the formula, Indicates the air density; Indicates the drag coefficient; represents the windward area; Indicates wind speed;

[0020] In the windward area Integrate the above to calculate the total wind load when the wind speed changes with position and time:

[0021] ;

[0022] In the formula, Indicates the wind speed value at each position and time variable on the column;

[0023] Wave load calculation:

[0024] ;

[0025] In the formula, Indicates water density; Indicates the diameter of the structure; Indicates the absolute value of flow velocity; Indicates flow rate; represents the coefficient of inertia; represents the action volume; represents acceleration;

[0026] For the effective action volume, the integral is performed along the direction of wave velocity to obtain the resultant wave load on the structure:

[0027] ;

[0028] The wind load equation and the wave load resultant force equation are added as constraints to the loss function of the physical neural network. It consists of two parts:

[0029] ;

[0030] In the formula, is the physical loss constrained by the physical equations, is the network mean square error data loss.

[0031] In step S2, a multi-layer nonlinear mapping model KAN is established to describe the environmental load to structural response, including:

[0032] Based on the Komogorov-Arnold KA theorem, complex nonlinear characteristics are approximated through layer-by-layer nonlinear mapping; the relationship between environmental loads and structural responses is gradually decomposed through multi-level mapping, and the output of each layer gradually captures deeper nonlinear characteristics; at the same time, residual connections are added to each layer of the multi-layer nonlinear mapping model KAN; through residual connections, the physical information output by PINN is embedded in each layer of the multi-layer nonlinear mapping model KAN, so that the physical impact of environmental loads can be continuously transmitted and retained in the entire network structure.

[0033] In step S3, the composite loss function includes a physical loss function constructed based on the physical model of wind load and wave load, which is used to ensure that the network output conforms to the known physical laws; and a data loss function, which is used to measure the error between the model prediction and the actual observation data through the mean square error loss MSE.

[0034] Furthermore, the physical loss function is expressed as follows:

[0035] ;

[0036] In the formula, Indicates the number of monitoring points, represents the windward area, represents the action volume;

[0037] The data loss function is expressed as follows:

[0038] ;

[0039] In the formula, It represents the predicted value of wave load; represents wave load; represents the wind load forecast value, Indicates the actual value of wind load; represents the predicted value of structural response; Indicates the actual value of the structural response.

[0040] Furthermore, the composite loss function is:

[0041] ;

[0042] In the formula, It represents the L2 regularization loss function in the neural network. represents the regularization strength, represents the weight matrix of the lth layer, l represents the number of network layers, Represents the sum of squares of the weight matrix of the lth layer.

[0043] In step S4, an ablation experiment is used to optimize the performance of the multi-layer nonlinear mapping model KAN, including:

[0044] Conduct ablation experiments on input features, gradually eliminate different environmental load features, analyze the impact of each feature on the column response prediction, and further optimize the input data;

[0045] Hyperparameter adjustment: AdamW optimization algorithm is used for hyperparameter optimization. During training, if the loss converges slowly, switch to L-BFG-S optimizer for adjustment.

[0046] Another object of the present invention is to provide a column structure response prediction system based on a residual connection neural network, the system implements the column structure response prediction method based on a residual connection neural network, and the system comprises:

[0047] The environmental data preprocessing module is used to preprocess the environmental data of the offshore platform columns and initialize the environmental loads using the physical information neural network PINN based on the preprocessed environmental data;

[0048] A multi-layer nonlinear mapping model building module is used to build a multi-layer nonlinear mapping model KAN for describing the environmental load to the structural response according to the Komogorov-Arnold KA theorem;

[0049] The composite loss function introduction module is used to introduce a composite loss function based on the constructed multi-layer nonlinear mapping model KAN, so that the multi-layer nonlinear mapping model KAN can adapt to the actual observation data while following the physical laws; residual connections are introduced to optimize the network;

[0050] The optimization module is used to optimize the performance of the multi-layer nonlinear mapping model KAN using ablation experiments for predicting the response of column structures under complex sea conditions.

[0051] Furthermore, the system is mounted on a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it can realize the functions of the above-mentioned column structure response prediction system based on residual connection neural network.

[0052] In combination with all the above technical solutions, the beneficial effects of the present invention are as follows:

[0053] The present invention aims to improve the response prediction accuracy and real-time performance of offshore platform columns in extreme marine environments. By combining physical information neural network (PINN) with Kolmogorov-Arnold (KAN) network, the present invention can accurately predict the structural response of platform columns using deep learning technology while ensuring physical rationality.

[0054] The present invention introduces a column structural response prediction method based on residual connection neural network, which is specially designed for predicting the nonlinear structural response of marine platform columns under environmental loads in complex marine environments, and shows significant innovation and practical value. Compared with the prior art, the present invention has the characteristics of simple structure and clear algorithm, and provides accurate and reliable decision support for marine platform structural safety assessment and design optimization. In addition, this method effectively improves the accuracy and reliability of column structural response prediction under severe sea conditions by accurately simulating the impact of environmental loads on column response, and solves the limitations of traditional prediction models in dealing with complex nonlinear responses. Therefore, the present invention not only provides an advanced technical means for the structural health monitoring and early warning system of marine platforms, but also opens up a new path for research and application in related fields, and has important theoretical significance and broad application prospects.

[0055] The present invention significantly improves the accuracy and computational efficiency of the prediction of the response of the offshore platform column structure by integrating the physical information neural network and the Kolmogorov-Arnold (KAN) theorem and combining the residual connection mechanism. This innovative technology can be widely used in the safety assessment and maintenance of offshore platforms, providing real-time and efficient prediction tools for engineering structures in complex marine environments, and reducing potential accident risks. At the same time, compared with traditional numerical simulation methods, the present invention reduces the consumption of computing resources and prediction time, greatly improves the efficiency of industrial application, and is expected to bring significant economic benefits and technical competitiveness to the marine engineering industry. In addition, the technology is also extensible and can be applied to the prediction of other nonlinear structural responses such as bridges and wind power pile foundations, with huge market application potential. International prediction methods for nonlinear structural responses in complex marine environments mainly rely on traditional numerical simulation and experimental methods, which have problems such as low computational efficiency, insufficient prediction accuracy, and difficulty in real-time response. The present invention combines the physical information neural network with the KAN network for the first time, and further optimizes the network performance through residual connection, overcoming the limitations of the existing technology in terms of stability and real-time performance in extreme environments. This method fills the technical gap in the field of nonlinear and dynamic response prediction, especially in the structural response problem of offshore platform columns, and provides a new, efficient and accurate solution with important academic value and engineering application significance.

[0056] In the field of marine engineering, accurately predicting the dynamic response of structures under complex environmental loads has always been a key but not fully solved technical problem, especially the real-time prediction under nonlinear factors and extreme sea conditions. Traditional methods often find it difficult to balance computational efficiency and prediction accuracy, and lack the effective integration of physical constraints and data-driven methods. The present invention successfully overcomes this problem by introducing physical information constraints and the KAN network, combined with a residual connection structure, and achieves real-time and high-precision response prediction, meeting the urgent needs of the engineering community for efficient and reliable prediction tools.

[0057] Traditional nonlinear response prediction methods tend to rely on single data-driven or pure physical modeling, while ignoring the advantages of combining the two, forming a certain technical bias. The present invention effectively integrates physical information and data-driven methods, uses PINN to capture environmental physical characteristics, combines the powerful nonlinear mapping capabilities of the KAN network, and optimizes model performance through residual connections, breaking the limitations of a single method. Through this multi-dimensional innovative fusion, the present invention achieves an organic unity of accuracy, generalization ability, and real-time performance, opens up a new research path for nonlinear response prediction, and effectively overcomes long-standing technical biases. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The accompanying drawings herein are incorporated in and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the description, serve to explain the principles of the present disclosure;

[0059] Figure 1 It is a flow chart of a column structure response prediction method based on a residual connection neural network provided by an embodiment of the present invention;

[0060] Figure 2 It is a physical information neural network structure diagram for predicting environmental loads provided by an embodiment of the present invention;

[0061] Figure 3 It is a network architecture diagram of column structure response prediction based on KA theorem provided by an embodiment of the present invention;

[0062] Figure 4 It is a residual neural network architecture diagram integrating KA theorem and physical constraints provided by an embodiment of the present invention;

[0063] Figure 5 Schematic diagram of a column structure response prediction system based on a residual connection neural network provided in an embodiment of the present invention;

[0064] In the figure: 1. Environmental data preprocessing module; 2. Multi-layer nonlinear mapping model building module; 3. Composite loss function introduction module; 4. Optimization module. DETAILED DESCRIPTION

[0065] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention, so the present invention is not limited by the specific implementation disclosed below.

[0066] The innovation of the present invention is that it combines the advantages of physical information neural network and KAN network, and optimizes network performance by introducing residual connection. This method uses a combination of physical constraints and data-driven to construct a multi-layer nonlinear mapping model, and achieves high-precision and high-efficiency prediction of the response of column structures under complex marine environments. Through the design of a composite loss function of physical equation constraints and data loss, the present invention overcomes the shortcomings of low computational efficiency and poor real-time performance of traditional numerical methods, while improving the stability and generalization ability of the prediction model. Compared with the prior art, the present invention shows significant prediction accuracy and engineering applicability under extreme sea conditions, providing an innovative technical path for marine platform structural safety assessment, design optimization and operation monitoring.

[0067] The present invention combines the physical information neural network (PINN) with the Kolmogorov-Arnold (KAN) theorem, and significantly improves the accuracy and computational efficiency of the prediction model through a multi-layer nonlinear mapping framework and residual connection optimization. The present invention includes environmental load estimation based on the physical information neural network, column response prediction based on the KAN network, and residual connection to optimize the network, and constructs a hybrid model that integrates physical constraints and data-driven. By introducing physical equation constraint losses and environmental parameter inputs, the model can more accurately simulate the dynamic response characteristics in extreme marine environments, effectively solving the limitations of traditional methods in nonlinear factor processing and real-time calculations. Experiments show that the present invention has significant advantages in accuracy, generalization ability and computational efficiency, and provides reliable and efficient technical support for marine platform structure design and operation status monitoring, and has important theoretical value and broad application prospects.

[0068] Embodiment 1, as Figure 1 As shown, the column structure response prediction method based on residual connection neural network provided by the embodiment of the present invention includes:

[0069] S1, preprocessing the environmental data of the offshore platform columns, and initializing the environmental loads using the physical information neural network PINN based on the preprocessed environmental data;

[0070] The environmental data is derived from a variety of monitoring equipment and experimental data, including environmental load parameters such as wind speed, waves, and flow velocity.

[0071] The specific steps of preprocessing the environmental data of the offshore platform columns are: first, resampling the data of different time steps to ensure that the data has a uniform time interval; at the same time, interpolating and filling the missing data to ensure the integrity and consistency of the data;

[0072] Then, in order to eliminate the physical dimension differences between different data sources, all input data are normalized to ensure that the influence of various input parameters on the neural network is balanced.

[0073] The use of physical information neural network (PINN) to initialize environmental loads includes: using PINN to embed physical formulas (such as wind load and wave load formulas) to convert physical constraints into physical loss parts in the physical neural network loss function. This process allows the model to be trained in accordance with physical laws and to make full use of actual data, thereby improving the accuracy and interpretability of the model.

[0074] S2, based on the Komogorov-Arnold KA theorem, a multi-layer nonlinear mapping model KAN is established to describe the environmental load to structural response;

[0075] Establishing a multi-layer nonlinear mapping model KAN (Kolmogorov-Arnold Networks) includes: based on the KA theorem, approximating complex nonlinear features through layer-by-layer nonlinear mapping. The relationship between environmental loads and structural responses is gradually decomposed through multi-level mapping, and the output of each layer gradually captures deeper nonlinear features; at the same time, in order to avoid gradient disappearance and ensure the stable transmission of physical information, the present invention adds residual connections to each layer of the multi-layer nonlinear mapping model KAN (KAN network). The introduction of residual connections ensures that each layer of the network can effectively transmit the physical information of the environmental load. Through residual connections, the physical information output by PINN is embedded in each layer of the multi-layer nonlinear mapping model KAN (KAN network), ensuring that the physical impact of the environmental load is continuously transmitted and retained in the entire network structure.

[0076] S3, based on the constructed multi-layer nonlinear mapping model KAN, introduces a composite loss function to make the multi-layer nonlinear mapping model KAN adapt to actual observation data while following physical laws; introduces residual connections to optimize the network;

[0077] Specifically, in order to ensure that the output of the multi-layer nonlinear mapping model KAN conforms to physical laws, the present invention designs a composite loss function. The loss function includes two parts. The physical loss is a loss part constructed based on physical models such as wind loads and wave loads, which is used to ensure that the network output conforms to known physical laws. It also includes data loss, which measures the error between the model prediction and the actual observation data through the mean square error loss (MSE) to ensure that the model has a high degree of fit.

[0078] During the training process, the weight coefficients of physical loss and data loss are dynamically adjusted according to the experimental results to ensure a balance between data fitting and physical constraints. This design enables the multi-layer nonlinear mapping model KAN to accurately adapt to actual observation data while following physical laws.

[0079] Among them, the physical loss function is expressed as follows:

[0080] ;

[0081] In the formula, Indicates the air density; It represents the drag coefficient, which depends on the shape of the object; represents the windward area; Indicates wind speed, Indicates water density; Indicates the drag coefficient; Indicates the diameter of the structure; Indicates the absolute value of flow velocity; Indicates flow rate; represents the coefficient of inertia; represents the action volume; Indicates acceleration.

[0082] The present invention innovatively proposes that the data loss function is expressed as follows:

[0083] ;

[0084] In the formula, It represents the predicted value of wave load; represents wave load; represents the wind load forecast value, Indicates the actual value of wind load; represents the predicted value of structural response; Indicates the actual value of the structural response.

[0085] The innovative proposal of the present invention is that the composite function is:

[0086] ;

[0087] In the formula, represents the regularization strength, represents the weight matrix of the lth layer, l represents the number of network layers, Represents the sum of squares of the weight matrix of the lth layer. It represents the L2 regularization loss function in the neural network;

[0088] S4, using ablation experiments to optimize the performance of the multi-layer nonlinear mapping model KAN for the prediction of the response of column structures under complex sea conditions;

[0089] The ablation experiment of the model input features is carried out to gradually eliminate different environmental load features, analyze the impact of each feature on the column response prediction, and further optimize the model input. Hyperparameter adjustment: The AdamW optimization algorithm is used for hyperparameter optimization. During the training process, if the loss convergence speed of the model is slow, switch to the L-BFG-S optimizer for fine adjustment to ensure the stability and convergence of the model training. Multi-condition comparison experiments, as shown in Table 1, are carried out under different marine conditions (such as the combined action of wind, waves and currents, etc.) Model prediction accuracy is tested and compared with traditional finite element models and other neural network models (PINN, MLP, LSTM, etc.) to verify the response accuracy and real-time performance of the method of the present invention under complex sea conditions.

[0090] Table 1 Model prediction accuracy test under different ocean conditions

[0091]

[0092] In summary, the column structure response prediction method based on residual connection neural network proposed in the present invention not only proposes a new multi-layer nonlinear mapping model in theory, but also provides an effective offshore platform column response prediction method in practical applications. By optimizing model design, introducing physical constraints, dynamically adjusting loss functions and other means, the present invention can provide accurate and physically interpretable prediction results under complex marine conditions, significantly improving the safety and reliability of offshore platform structures.

[0093] Example 2, as another implementation of the present invention, the column structure response prediction method based on residual connection neural network provided in the embodiment of the present invention includes:

[0094] Step 1: Estimation of environmental loads based on physical information neural network.

[0095] In this step, the environmental load needs to be estimated first through the physical information neural network. The physical information neural network uses the marine environment monitoring sensor data (such as wave speed, wind speed, etc.) and the force area of ​​the structure as input, and obtains an accurate estimate of the environmental load by combining the physical equation constraints. The core of this step is to process and optimize environmental factors through the physical information neural network to obtain the most representative load data, providing accurate input for subsequent structural response prediction;

[0096] Step 2: Predict the column response based on the multi-layer nonlinear mapping model KAN (KAN network).

[0097] In this step, the Kolmogorov-Arnold neural network architecture is used to predict the structural response of the column. The multi-layer nonlinear mapping model KAN (KAN network) can learn the dynamic response of the column from complex environmental loads and structural parameters through nonlinear feature extraction and pattern recognition capabilities. This network structure improves the prediction accuracy and computational efficiency by efficiently capturing the mapping relationship between input data and structural response, and further enhances the model's understanding and simulation capabilities of complex physical phenomena;

[0098] Step 3: Introduce residual connection to optimize the multi-layer nonlinear mapping model KAN (KAN network).

[0099] In this step, residual connections are introduced to further improve the prediction ability of the model in order to solve the potential optimization problems of the multi-layer nonlinear mapping model KAN (KAN network). The introduction of residual connections not only helps solve the gradient vanishing problem in deep networks, but also enables the network to process complex input data more efficiently. Specifically, the input of the multi-layer nonlinear mapping model KAN (KAN network) no longer depends solely on environmental loads, but also includes environmental parameters. The residual connection is used to enhance the performance of the network and optimize the learning process of the model.

[0100] Step 4: Evaluation, iterative optimization and application of the multi-layer nonlinear mapping model KAN (KAN network).

[0101] In this step, the multi-layer nonlinear mapping model KAN (KAN network) is first evaluated and its prediction results are verified. The evaluation work includes comparing the model prediction results with the existing experimental data to check the accuracy and stability of the model. According to the evaluation results, the model is iteratively optimized, including adjusting the network structure, optimizing the loss function, and selecting a suitable optimization algorithm. Finally, the optimized model is applied to the prediction of column structure response in extreme marine environments, providing high-precision support for marine engineering design and operation.

[0102] Exemplarily, the method of constructing a physical information neural network in step 1 is specifically as follows:

[0103] In this step, the basic theory of physical information neural network is combined to build an intelligent prediction model of environmental loads on offshore platform columns, and study how to effectively learn and approximate the real-time loads of columns under the combined action of wind and flow based on the environmental loads (wind load and wave load) on the columns through physical information neural network. Using the real-time monitoring data of the offshore platform, the loss function of the physical information neural network is constructed with the wind load calculation formula and the wave load calculation formula (Morrison equation), and the physical model is combined with the data-driven method to develop an intelligent prediction algorithm for column environmental loads based on physical information neural network.

[0104] Step 1.1, firstly, based on the time series, establish the mapping relationship between wind speed, flow velocity, structural stress area and load, and construct a fully connected network. The input is time, wind or wave velocity, effective stress area or volume, and the output is the predicted load value.

[0105] Step 1.2, then find the constraints of the physical equations:

[0106] Wind load calculation:

[0107] ;

[0108] In the formula, Indicates the air density; It represents the drag coefficient, which depends on the shape of the object; represents the windward area; Indicates wind speed.

[0109] Since wind speed varies with height or time, Integrate above to calculate the sum of wind loads as wind speed varies with location and time:

[0110] ;

[0111] In the formula, Indicates the wind speed value at each position and time variable on the column;

[0112] Wave load calculation:

[0113] ;

[0114] In the formula, Indicates water density; Indicates the drag coefficient; Indicates the diameter of the structure; Indicates the absolute value of flow velocity; Indicates flow rate; represents the coefficient of inertia; represents the action volume; Indicates acceleration.

[0115] In actual calculation, the effective action volume is considered and integrated along the direction of wave velocity to obtain the resultant wave load on the structure:

[0116] ;

[0117] The present invention adds the wind load equation and the wave load resultant force equation as constraints into the loss function of the physical neural network, wherein the loss function consists of two parts: is the physical loss constrained by the physical equations, is the network mean square error data loss;

[0118]

[0119] ;

[0120] ;

[0121] The network framework of the method in step 1 of the present invention is detailed in Figure 2 .

[0122] Furthermore, the method of constructing the multi-layer nonlinear mapping model KAN (KAN network) in step 2 is specifically as follows:

[0123] In this step, a multi-layer nonlinear mapping model KAN (KAN network) based on the Kolmogorov-Arnold theorem is constructed to predict the nonlinear structural response characteristics of offshore platform columns under complex environmental loads. This method gradually decomposes and approximates the response law of the column structure through the multi-layer nonlinear mapping framework provided by the KA theorem, and integrates ablation experiments and comparative experiments to optimize and verify the performance of the model to ensure the accuracy, robustness and real-time performance of the model. Specifically include:

[0124] (1) The present invention selects characteristic vectors of environmental loads and column structural responses and designs the model mapping order. By analyzing the physical effects of different environmental parameters (wind, waves) in marine conditions, the main load characteristics are extracted, including variables such as wind force and wave force. These characteristic vectors constitute the input of the model to accurately describe the stress conditions of the column in a complex environment. In the KAN network architecture, the determination of the number of mapping layers and the mapping order is crucial to the model performance. Based on the layer-by-layer mapping theory in the KA theorem, the model will use a multi-layer mapping method to gradually decompose complex nonlinear features to approximate the mapping relationship from environmental loads to structural responses. The output of each layer of the network gradually approaches the response characteristics of the column under specific working conditions, ensuring that the model has sufficient resolution to capture the impact of environmental parameters on structural responses.

[0125] For example, for the layer-by-layer mapping theory based on the KA (Kolmogorov-Arnold) theorem, the model will use a multi-layer mapping method to gradually decompose complex nonlinear features, including:

[0126] According to the KA theorem, any continuous multivariable function can be decomposed into a combination of a series of single-variable functions through a finite number of layers of nonlinear mapping. The present invention uses this feature to construct a layer-by-layer mapping structure in the multi-layer nonlinear mapping model KAN (KAN network). Through each layer of the network, the complex multidimensional environmental load characteristics are gradually decomposed into processable low-dimensional nonlinear feature mappings. The nonlinear activation function of each layer of the network is approximated as a single-variable function, and the weights and biases connecting different layers characterize the coupling relationship between the variables.

[0127] The details are as follows: Includes major influencing factors such as wind , wave force

[0128] , wave height , wave period These characteristics describe the load characteristics of complex marine environments.

[0129] First, feature extraction of environmental loads is performed through the initial mapping of the input layer:

[0130] ;

[0131] in: is the input layer weight matrix, which is used to perform weighted combination of environmental load characteristics; is the bias vector; is a nonlinear activation function, such as ReLU or tanh. The output Represent the main influencing features in environmental loads and gradually extract the significant contributions to the structural response.

[0132] In the multi-layer nonlinear mapping model KAN (KAN network), each layer has a certain effect on the environmental load characteristics. Further decomposition and approximation are performed to output the feature representation of the next layer :

[0133] ;

[0134] The weight matrix of each layer and the bias vector Learning the nonlinear relationship between environmental loads and structural responses; activation function Simulate nonlinear characteristics and approximate the influence of environmental loads on the structural response of columns layer by layer.

[0135] Through layer-by-layer nonlinear mapping, the multi-layer nonlinear mapping model KAN (KAN network) gradually decouples the action mechanism of complex loads and approximates the dynamic response characteristics of the column. For example, the first layer may focus on identifying the independent effects of wind and wave forces, the second layer begins to capture the coupling effect of the two, and the third layer further analyzes their superposition effect on the nonlinear response.

[0136] In order to approximate the mapping relationship from environmental load to structural response, the mapping is realized by the layer-by-layer nonlinear mapping framework based on the Kolmogorov-Arnold neural network. The mapping relationship is decomposed into the mapping of environmental load characteristics to network input, layer-by-layer nonlinear mapping, and the mapping of the final output layer.

[0137] (2) The present invention will construct a multi-layer nonlinear mapping model KAN (KAN network), and train the multi-layer nonlinear mapping model KAN (KAN network) based on the actual measured marine platform environmental data and structural response data. The multi-layer nonlinear mapping provided by the KA theorem has high expressive power. Therefore, in the network design, the output of each layer will be processed by a regularization optimization method to prevent overfitting. At the same time, the structural response loss is introduced into the loss function of the model so that the model always keeps close to the original physical constraints during the training process. In the training optimization process, the AdamW optimization algorithm is used in combination to perform hyperparameter optimization to ensure the stability of the network and the convergence of the training.

[0138] For example, in network design, the output of each layer is processed by regularization optimization methods including:

[0139] First, the weight decay (L2 regularization) method in the network limits the excessive growth of network weights by adding the sum of squares of weights to the loss function, avoiding the model from being too complex, which leads to overfitting of the training data. Secondly, the Dropout technique is used to randomly "discard" the output of some neurons during the training process, reduce the interdependence between neurons, enhance the robustness of the network, and enable the model to have better generalization capabilities. At the same time, batch normalization is applied before the activation function of each layer. By normalizing the output of each layer, the changes in the output distribution of each layer are reduced, thereby accelerating the convergence of the model and further reducing the risk of overfitting.

[0140] Exemplarily, the structural response loss introduced into the loss function of the physical neural network is expressed as:

[0141] ;

[0142] The total loss can be expressed as:

[0143] ;

[0144] The network framework of the method in step 2 of the present invention is detailed in Figure 3 .

[0145] Specifically, (a) the input data includes environmental load characteristics, such as wind speed, wave force, and current velocity, which are collected by sensors on the ocean platform and converted into feature vectors. In the data preprocessing stage, normalization and time resampling are performed to ensure data consistency and standardization, so that environmental data from different sources can be effectively combined in the model.

[0146] (b) The above environmental load characteristics will be processed through the multi-layer nonlinear mapping structure of the KAN network. Based on the Kolmogorov-Arnold theorem, each layer of the network will gradually deconstruct the complex environmental data and approximate the nonlinear relationship between environmental loads and column structural responses through multi-layer mapping. The output of each layer gradually extracts higher-order features to ensure that the network can capture the impact of environmental factors on structural responses.

[0147] During the training process, the model's loss function introduces structural response loss. The loss term helps the network maintain its approximation to physical laws during training, ensuring that the model can not only fit the data but also follow the actual physical constraints. In this way, the model can avoid overfitting while ensuring accuracy.

[0148] (c) The AdamW optimization algorithm is used to optimize the model's hyperparameters and promote the acceleration and stability of the training process. During the training process, when the model gradually converges, the AdamW optimizer accelerates parameter updates by dynamically adjusting the learning rate to ensure that the model can achieve high-precision training in a relatively short period of time. Through this series of data processing and optimization strategies, the model can efficiently and stably complete the prediction task of the column structure response.

[0149] Exemplarily, in step 3, the method of the multi-layer nonlinear mapping model KAN (KAN network) based on residual connection is specifically as follows:

[0150] In step 3, the physical information neural network and the Kolmogorov-Arnold network are combined to further optimize the column structure response prediction model by fusing physical constraints and residual connections, including:

[0151] (i) In the data preprocessing stage, multi-source environmental monitoring data are integrated, and the consistency of data steps is ensured through time resampling and interpolation filling. At the same time, data normalization is performed to ensure the physical consistency between different data sources.

[0152] (ii) Use physical information neural networks to predict environmental loads and convert environmental data such as wind speed, flow rate and waves into initial load values ​​through physical models (such as the Morrison equation). These physical constraints are embedded in the loss function of the neural network to ensure that the network output during training not only conforms to physical laws but also accurately fits the actual data. The output of PINN provides physical rationality for the subsequent KAN network and ensures the physical consistency of the entire model.

[0153] Exemplarily, the physical constraint is embedded into the loss function expression of the neural network as follows:

[0154] ;

[0155] For example, in the design of the multi-layer nonlinear mapping model KAN (KAN network), a multi-layer mapping structure based on the KA theorem is first used to decompose the mapping of complex environmental parameters to column structural responses into multi-level nonlinear relationships. At each layer, the input environmental features will be gradually decomposed to ensure that the network can gradually approach the real structural response. In order to avoid the gradient vanishing problem and ensure the stable transmission of physical information between network levels, residual connections are introduced between each layer of mapping. The addition of residual connections enables the network to retain physical information at each layer, thereby better learning nonlinear mapping.

[0156] Exemplarily, the mapping of complex environmental parameters to column structural responses is decomposed into multi-level nonlinear relationships including:

[0157] According to the Kolmogorov-Arnold theorem, any continuous multivariable function can be decomposed into a combination of a series of single variable functions through a finite number of layers of nonlinear mapping. The present invention uses this feature to construct a layer-by-layer mapping structure in the KAN network. Through each layer of the network, the complex multidimensional environmental load characteristics are gradually decomposed into processable low-dimensional nonlinear feature maps. The nonlinear activation function of each layer of the network is approximated as a single variable function, and the weights and biases connecting different layers characterize the coupling relationship between the variables.

[0158] Exemplarily, the residual connection is introduced between each layer of mapping, including: in order to ensure the stable transmission of physical information, a residual connection is added to each layer, and the mapping relationship becomes:

[0159] ;

[0160] In the formula, is the output of the previous layer or the initial input, is the weight matrix of the current layer, is the bias vector, The output of the previous layer is directly transferred to the current layer, forming a residual connection. The present invention enables the network to learn the incremental information of each layer, rather than the absolute information of each layer, through the above solution, thus avoiding the gradient vanishing problem.

[0161] As another example, in addition, the design of residual connections not only helps to stabilize the gradient transfer, but also ensures the adaptive update of environmental parameters at each layer. By dynamically adjusting the parameter distribution between network layers, the residual term enables the network to automatically adapt environmental parameters and physical constraints when processing loads under different working conditions. In this way, the model can automatically adjust parameters according to actual data, so that the mapping process of each layer can better reflect the impact of the environment on the structural response.

[0162] Exemplarily, the dynamic adjustment of parameter distribution between network layers includes: (1) the introduction of residual connections. In the network design, the input of each layer not only comes from the output of the previous layer, but also retains the original input of the previous layer. This design ensures that while information is transmitted between layers, the original representation of environmental parameters and physical constraints is retained through residual connections. This provides a basis for dynamically adjusting parameter distribution, allowing the model to adaptively adjust the degree of attention to features in each layer. (2) Parameter update drives dynamic adjustment; during the training process, the parameters of the network (including weights and biases) are updated through the back propagation algorithm. Back propagation calculates the gradient of the parameters of each layer according to the loss function, and gradually updates the weights of each layer in combination with the optimization algorithm (such as AdamW). In this way, the parameter distribution of different layers can dynamically adapt to the input data characteristics, so that the network gradually approaches the target mapping relationship.

[0163] The automatic adaptation of environmental parameters and physical constraints includes:

[0164] (1) Standardization and dynamic weight allocation of environmental parameter characteristics: In the input stage, different environmental parameters (such as wind speed, wave, flow rate, etc.) are normalized to ensure that they have the same magnitude and scale. This processing is not only conducive to the numerical stability of the model, but also can adjust the weights according to the influence of different environmental parameters on the response in each training iteration through the dynamic weight allocation mechanism. For example:

[0165] If the wind speed has a more significant effect on the structural response, the network will assign higher weights to wind speed related features.

[0166] Dynamic adjustment is achieved through a weighted attention mechanism (e.g., weighted feature maps), which dynamically updates these weights based on the gradient information from each backpropagation.

[0167] (2) Physical constraint embedding loss function;

[0168] Introducing items related to physical constraints into the loss function makes the model output not only fit the actual data but also satisfy the known physical laws. For example, using the Morrison equation, the environmental parameters are converted into actual load data, and the error between it and the network prediction value is calculated.

[0169] Environmental parameter feature loss and structural response feature loss are added to the loss function to force the model to learn physical laws during training. The above technical solution enables the network to adjust the internal parameter distribution to fit the physical laws under different environmental parameter inputs.

[0170] Exemplarily, in order to further improve the prediction accuracy of the model, the present invention also designs a composite loss function that combines physical loss and data loss. The physical loss part is based on physical models such as wind load and wave load to ensure that the network output conforms to physical laws; the data loss part uses mean square error (MSE) to ensure a high degree of fit of the network on the training data. By dynamically adjusting the weight coefficients of physical loss and data loss, the present invention can balance the physical constraints and data-driven fitting effects and optimize the prediction ability of the model.

[0171] Exemplarily, the composite loss function includes:

[0172] ;

[0173] In the optimization process of the multi-layer nonlinear mapping model KAN (KAN network), the present invention adopts multiple strategies. First, the secondary features are eliminated one by one through ablation experiments, the influence of key variables on the structural response prediction is analyzed, and the environmental load factors that are most important for the prediction accuracy are identified. Secondly, by adjusting the hyperparameters, the AdamW optimization algorithm is used to accelerate the training process. When the number of training steps is large and the loss converges slowly, the L-BFGS optimizer is switched to further improve the training accuracy and efficiency.

[0174] Exemplarily, eliminating minor features one by one through ablation experiments includes: the process of eliminating minor features one by one is to first list all environmental features that may affect the structural response, such as wind speed, flow rate, etc. Then, by evaluating the impact of each feature on the prediction results, determine which features contribute less to the model. Next, gradually eliminate these features with small contributions to observe whether the performance of the model is affected. If the model performance does not change much after removing a certain feature, it can be confirmed that this feature is minor. Ultimately, through this process, the present invention can find the most important features, simplify the model, and improve training efficiency and prediction accuracy.

[0175] The method of accelerating the training process by adjusting hyperparameters and using the AdamW optimization algorithm includes: By adjusting hyperparameters and using the AdamW optimization algorithm, the training process can be accelerated and the accuracy can be improved. First, select initial hyperparameters, such as learning rate, batch size, and weight decay. The AdamW optimizer combines momentum and adaptive learning rate to help adjust parameters more efficiently. During the training process, AdamW dynamically adjusts the learning rate based on the gradient information to avoid excessive update steps, while controlling overfitting through weight decay. By continuously adjusting these hyperparameters, the model can converge faster and improve prediction accuracy. When the number of training steps is large and the loss converges slowly, you can further adjust the hyperparameters or switch to other optimizers (such as L-BFGS) to improve efficiency and accuracy.

[0176] The network framework of the method in step 3 of the present invention is detailed in Figure 4 .

[0177] Through the method described above and its experimental verification, the present invention provides an effective solution for predicting the nonlinear structural response of marine platform columns under environmental loads in complex marine environments. It has the characteristics of high-precision prediction and strong physical foundation, and provides a new technical path and development basis for marine platform structural safety assessment and design optimization.

[0178] Embodiment 3, as Figure 5 As shown, an embodiment of the present invention provides a column structure response prediction system based on a residual connection neural network, the system comprising:

[0179] Environmental data preprocessing module 1 is used to preprocess environmental data of offshore platform columns, and based on the preprocessed environmental data, a physical information neural network PINN is used to initialize environmental loads;

[0180] A multi-layer nonlinear mapping model building module 2 is used to build a multi-layer nonlinear mapping model KAN for describing the environmental load to the structural response according to the Komogorov-Arnold KA theorem;

[0181] The composite loss function introduction module 3 is used to introduce a composite loss function based on the constructed multi-layer nonlinear mapping model KAN, so that the multi-layer nonlinear mapping model KAN can adapt to the actual observation data while following the physical laws; residual connection is introduced to optimize the network;

[0182] The optimization module 4 is used to optimize the performance of the multi-layer nonlinear mapping model KAN by using ablation experiments, and is used for predicting the response of the column structure under complex sea conditions.

[0183] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered within the protection scope of the present invention.

Claims

1. A column structure response prediction method based on residual connection neural network, characterized in that: The method comprises the steps of: S1, preprocessing the environmental data of the offshore platform columns, and initializing the environmental loads using the physical information neural network PINN based on the preprocessed environmental data; S2, based on the Komogorov-Arnold KA theorem, a multi-layer nonlinear mapping model KAN is established to describe the environmental load to structural response; S3, based on the constructed multi-layer nonlinear mapping model KAN, introduces a composite loss function to make the multi-layer nonlinear mapping model KAN adapt to actual observation data while following physical laws; introduces residual connections to optimize the network; S4, using ablation experiments to optimize the performance of the multi-layer nonlinear mapping model KAN for the prediction of the response of column structures under complex sea conditions; In step S1, the physical information neural network PINN is used to initialize the environmental load, including the following steps: Step 1.1, based on the time series, establish the mapping relationship between wind speed, flow velocity, structural force area and load, and construct a fully connected network. The input is time, wind or wave flow velocity, effective force area or volume, and the output is the predicted load value; Step 1.2, find the constraints of the physical equations, and the wind load is calculated as: In the formula, ρ a Indicates air density; C d It represents the drag coefficient; A represents the windward area; V represents the wind speed; Integrate over the windward area A to calculate the total wind load when the wind speed changes with position and time: Where V 2 (x, t) represents the wind speed value at each position and time variable on the column; Wave load calculation: In the formula, ρ w represents water density; D represents the diameter of the structure; |U| represents the absolute value of the flow rate; U represents the flow rate; C m Represents the inertia coefficient; V v represents the action volume; represents acceleration; For the effective action volume, the integral is performed along the direction of wave velocity to obtain the resultant wave load on the structure: The wind load equation and the wave load resultant force equation are added as constraints to the loss function of the physical neural network. total Composed of two parts composition: Loss total =Loss function +Loss data In the formula, Loss function is the physical loss constrained by the physical equation, Loss data is the network mean square error data loss; In step S2, a multi-layer nonlinear mapping model KAN is established to describe the environmental load to structural response, including: Based on the Komogorov-Arnold KA theorem, complex nonlinear features are approximated by layer-by-layer nonlinear mapping; The relationship between environmental load and structural response is gradually decomposed through multi-level mapping, and the output of each layer gradually captures deeper nonlinear characteristics; at the same time, residual connections are added to each layer of the multi-layer nonlinear mapping model KAN; through residual connections, the physical information output by PINN is embedded in each layer of the multi-layer nonlinear mapping model KAN, so that the physical impact of environmental loads can be continuously transmitted and retained in the entire network structure; In step S3, the composite loss function includes a physical loss function constructed based on the physical model of wind load and wave load, which is used to ensure that the network output conforms to the known physical laws; and a data loss function, which is used to measure the error between the model prediction and the actual observation data through the mean square error loss MSE.

2. The column structure response prediction method based on residual connection neural network according to claim 1 is characterized in that: In step S1, the environmental data is derived from monitoring equipment and experimental data, including: environmental load parameters of wind speed, wave, and flow speed; Preprocessing of environmental data of offshore platform columns includes: resampling data of different time steps to ensure that the data has a uniform time interval; interpolation filling of missing data and normalization of all input data.

3. The column structure response prediction method based on residual connection neural network according to claim 1 is characterized in that: The physical loss function is expressed as follows: In the formula, N represents the number of monitoring points, A n Represents the frontal area, V n represents the action volume; The data loss function is expressed as follows: In the formula, Indicates the predicted value of wave load; F s represents wave load; Indicates the wind load forecast value, F w represents wind load; Represents the predicted value of structural response; F d Indicates the actual value of the structural response.

4. The column structure response prediction method based on residual connection neural network according to claim 1 is characterized in that: The composite loss function is: In the formula, Loss reg It represents the L2 regularization loss function in the neural network, λ represents the regularization strength, and W (l) represents the weight matrix of the lth layer, l represents the number of network layers, |W (l) | 2 Represents the sum of squares of the weight matrix of the lth layer.

5. The column structure response prediction method based on residual connection neural network according to claim 1 is characterized in that: In step S4, an ablation experiment is used to optimize the performance of the multi-layer nonlinear mapping model KAN, including: Conduct ablation experiments on input features, gradually eliminate different environmental load features, analyze the impact of each feature on the column response prediction, and further optimize the input data; Hyperparameter adjustment: AdamW optimization algorithm is used for hyperparameter optimization. During training, if the loss converges slowly, switch to L-BFG-S optimizer for adjustment.

6. A column structure response prediction system based on residual connection neural network, characterized in that: The system implements the column structure response prediction method based on residual connection neural network according to any one of claims 1 to 5, and the system comprises: An environmental data preprocessing module (1) is used to preprocess environmental data of an offshore platform column, and based on the preprocessed environmental data, a physical information neural network PINN is used to initialize environmental loads; A multi-layer nonlinear mapping model building module (2) is used to build a multi-layer nonlinear mapping model KAN for describing the environmental load to the structural response according to the Komogorov-Arnold KA theorem; The composite loss function introduction module (3) is used to introduce a composite loss function based on the constructed multi-layer nonlinear mapping model KAN, so that the multi-layer nonlinear mapping model KAN can adapt to the actual observation data while following the physical laws; residual connection is introduced to optimize the network; The optimization module (4) is used to optimize the performance of the multi-layer nonlinear mapping model KAN by using ablation experiments, and is used for predicting the response of the column structure under complex sea conditions.

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