Method for predicting corrosion degradation of offshore engineering structures

Abstract

The application provides a corrosion degradation prediction method of a marine engineering structure, and relates to the field of marine engineering structures, and comprises the following steps: constructing a finite element model representing the three-dimensional random corrosion morphology of the marine engineering structure; establishing a surrogate model with material parameters as input and multi-order dynamic responses as output; for each group of candidate statistical characteristic quantities, generating multiple groups of material parameter samples to input the surrogate model, and obtaining a set of multi-order dynamic response prediction values; taking the relative error between the mean value of each order dynamic response prediction value and the mean value of the target response distribution of each order dynamic response target value as an optimization target, and obtaining a Pareto non-dominated solution set; calculating the KL divergence between the joint prediction distribution of the multi-order dynamic response corresponding to each candidate solution in the Pareto non-dominated solution set and the target response distribution, and selecting the candidate solution with the minimum KL divergence as the optimal solution. The method takes into account the efficiency, accuracy and calculation cost of the corrosion degradation prediction of the marine engineering structure.

Description

Technical Field

[0001] This invention relates to the field of marine engineering structures, and in particular to a method for predicting corrosion degradation of marine engineering structures. Background Technology

[0002] During their long service life of 25-30 years, marine engineering structures are continuously subjected to multiple loads, including waves, wind, and currents. Their structural safety faces multiple hidden dangers such as fatigue accumulation, localized damage propagation, and sudden failure. If the performance degradation of critical components is not identified in time, it can easily lead to a decrease in the overall load-bearing capacity of the structure or even catastrophic failure. Therefore, conducting highly reliable structural health monitoring is of significant engineering importance. As the core support for structural health monitoring, the finite element model needs to accurately reflect the actual service state of the structure. However, among numerous damage factors, corrosion, as the most common and continuously developing degradation mechanism of marine engineering structures, exhibits significant spatial randomness and morphological irregularities, especially in the splash zone where it manifests as a three-dimensional non-uniform degradation characteristic developing along the wall thickness. This complex corrosion morphology has a profound impact on the local stiffness and overall dynamic response of the structure, and traditional modeling methods are insufficient to effectively characterize its true mechanism.

[0003] Moreover, in complex corrosive environments, structural responses often exhibit stronger nonlinear coupling and multi-scale characteristics, placing higher demands on both model expressive power and computational efficiency. Therefore, it is necessary to develop corrosion degradation prediction methods that can describe the time-varying evolution of three-dimensional stochastic corrosion morphology, in order to accurately predict the trend of structural performance degradation while taking into account computational overhead. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a method for predicting the corrosion and degradation of marine engineering structures. This method balances the efficiency, accuracy, and computational cost of predicting the corrosion and degradation of marine engineering structures.

[0005] This invention provides a method for predicting the corrosion degradation of marine engineering structures, comprising: A finite element model characterizing the three-dimensional random corrosion morphology of marine engineering structures was constructed, and the target values ​​of the multi-order dynamic response of the marine engineering structures under different corrosion degradation states were obtained as the target response distribution. Based on the finite element model, a surrogate model is established with material parameters as input and multi-order dynamic response as output, using the statistical characteristics of the material parameters of the structure as the variables to be identified. For each set of candidate statistical features, multiple sets of material parameter samples are generated based on the truncated normal distribution corresponding to the candidate statistical features. The material parameter samples are input into the surrogate model to obtain the corresponding set of multi-order dynamic response prediction values, and the mean of each order dynamic response prediction value is calculated. Using the relative error between the mean of the predicted values ​​of each order of dynamic response and the mean of the target values ​​of each order of dynamic response in the target response distribution as the optimization objective, a multi-objective evolutionary algorithm is used to optimize and solve the statistical characteristics of the material parameters to obtain the Pareto non-dominated solution set. Calculate the KL divergence between the joint prediction distribution of the multi-order dynamic response corresponding to each candidate solution in the Pareto non-dominated solution set and the target response distribution, select the candidate solution with the smallest KL divergence as the optimal solution, and obtain the optimal statistical feature quantity. The corrosion degradation state is assessed based on the aforementioned optimal statistical characteristic quantities.

[0006] In one embodiment of the present invention, the step of establishing a surrogate model based on the finite element model, using the statistical characteristics of the material parameters of the structure as the variables to be identified, and taking the material parameters as input and the multi-order dynamic response as output, includes: Using the material parameters of the marine engineering structure as input and the multi-order dynamic response of the structure as output, an initial training sample set is generated in the material parameter space through Latin hypercube sampling. For each initial training sample set, the corresponding dynamic response value is calculated by modal analysis using the finite element model, and an initial surrogate model is established. The initial surrogate model outputs the predicted dynamic response value corresponding to any material parameter; wherein, the material parameters include elastic modulus and density. For each candidate material parameter in the candidate sample pool, the minimum Euclidean distance from the candidate material parameter to all known material parameters in the current training sample set is calculated as an exploration term, and the deviation norm between the predicted dynamic response value output by the surrogate model at the candidate material parameter and the reference dynamic response value is calculated as an development term. The exploration term and the development term are normalized and then weighted and summed according to preset weights to obtain the comprehensive acquisition function value. The candidate material parameter with the largest comprehensive acquisition function value is selected from the candidate sample pool as a new sample point. The dynamic response value corresponding to the new sample point is calculated by the finite element model. The new sample point and its corresponding dynamic response value are added to the training sample set, and the initial surrogate model is updated so that the dynamic response prediction value output by the updated surrogate model at the new sample point is close to the dynamic response value obtained by the finite element model.

[0007] In one embodiment of the present invention, the surrogate model adopts a Gaussian process regression model, wherein: The initial surrogate model outputs the following predicted dynamic response values ​​at arbitrary material parameters: ; in, For the regression term, For regression coefficients, The vector represents the basis functions, and the superscript T indicates the matrix transpose. With a mean of zero and a standard deviation of Gaussian process; The material parameters of the training samples, any two material parameters and covariance between , The correlation function uses a Gaussian squared exponential kernel, and its expression is:

[0008] in, For the hyperparameters of the correlation function, Let be the dimension of the material parameter space; Let p be the component value of the p-th material parameter in the j-th dimension. Let q be the component value of the q-th material parameter in the j-th dimension. Let j be the hyperparameters in the j-th dimension; The regression coefficients are estimated using the generalized squares method, and the calculation formula is as follows: ; Where R is the correlation matrix, and the elements are... F is the regression matrix, with elements of... , , ; The updated surrogate model, for any material parameters to be predicted The predicted dynamic response value is calculated as follows: ; in, For the material parameters to be predicted With sample The correlation vector between them; The formula for calculating the variance of the predicted dynamic response output by the surrogate model is as follows: ; in, , This is an estimate of the standard deviation.

[0009] In one embodiment of the present invention, the calculation formula for the exploration item is: ; in, The current number of training samples, Indicates the first A known sample point, For any candidate material parameters, For exploration purposes; The calculation formula for the development item is: ; in, For the surrogate model in candidate material parameters Predicted dynamic response values ​​at the location, The dynamic response reference value is the dynamic response value of the marine engineering structure in the uncorroded state, or the dynamic response value of the marine engineering structure in the current corroded state. For development purposes; The formula for calculating the comprehensive acquisition function value is as follows: ; in, For the normalized exploration term, For the normalized development items, To explore weights.

[0010] In one embodiment of the present invention, multiple sets of material parameter samples are generated based on the truncated normal distribution corresponding to the candidate statistical features. The formula for generating the material parameter samples is as follows: ； ； ; in, , The number of samples generated in each evaluation. These are the lower and upper limits of the elastic modulus E. density The lower limit and upper limit, , Here, represents the mean and standard deviation of the elastic modulus, and represents statistical characteristics. Here, represents the mean and standard deviation of the density, and represents statistical characteristics. To truncate the normal distribution, , For the first Elastic modulus and density of the sample materials; For the first A set of material parameter samples, consisting of elastic modulus and density; The material parameter samples are input into the surrogate model to obtain the corresponding set of multi-order dynamic response prediction values:

[0011] in, This is the predicted value of the m-th order dynamic response. For the first lA set of predicted m-th order dynamic response values ​​for a group of material parameter samples. It is the set of predicted multi-order dynamic response values ​​for all groups of material parameter samples.

[0012] In one embodiment of the present invention, the relative error between the mean of the predicted values ​​of each order of dynamic response and the mean of the target values ​​of each order of dynamic response in the target response distribution is used as the optimization objective, and the calculation formula is as follows: ; in, Variables to be identified The optimization objective function of order i, , Let be the mean of the predicted values ​​of the i-th order dynamic response. Let be the mean of the target value of the i-th order dynamic response; The corresponding multi-objective optimization problem is expressed as: ; in, These are the variables to be identified. The lower limit and upper limit; The NSGA-II multi-objective evolutionary algorithm is used to solve the multi-objective optimization problem, and the Pareto non-dominated solution set is obtained.

[0013] In one embodiment of the present invention, the KL divergence between the joint prediction distribution of the multi-order dynamic response corresponding to each candidate solution in the Pareto non-dominated solution set and the target response distribution is calculated using the following formula: ; in, Let KL divergence be the KL divergence. This represents the joint prediction distribution of the multi-order dynamic responses of the current candidate solution. For the target response distribution, These are the mean vector and covariance matrix of the predicted distribution, respectively. , Let be the mean vector and covariance matrix of the target distribution, respectively. Let be the dimension of the joint distribution. for The inverse matrix, Let be the trace of the matrix.

[0014] In one embodiment of the present invention, before selecting the candidate solution with the smallest KL divergence, the method further includes: normalizing the relative errors corresponding to the predicted values ​​of each order dynamic response of each candidate solution in the Pareto non-dominated solution set, calculating the Euclidean distance from each candidate solution to the given ideal point, retaining the candidate solutions whose Euclidean distance does not exceed a preset multiple of the minimum Euclidean distance as the candidate solution set, and then selecting the candidate solution with the smallest KL divergence from the candidate solution set.

[0015] In one embodiment of the present invention, the step of evaluating the corrosion degradation state based on the optimal statistical characteristic quantity includes: The mean value of the material parameters of the optimal statistical characteristic quantity is compared with the mean value of the material parameters before corrosion, and the degree of corrosion degradation of the marine engineering structure is assessed based on the change in the mean value. The standard deviation of the material parameters of the optimal statistical characteristic quantity is compared with the standard deviation of the material parameters before corrosion, and the degree of non-uniformity of the corrosion morphology is evaluated based on the change in standard deviation. The statistical characteristics include the mean and standard deviation.

[0016] In one embodiment of the present invention, the step of constructing a finite element model characterizing the three-dimensional random corrosion morphology of a marine engineering structure includes: Based on the overall geometric dimensions and component arrangement of the marine engineering structure, a beam element finite element model with beam elements as the main body is established; In the finite element model of the beam element, the beam element region corresponding to the target component located within the splash zone is separated, and a solid element sub-model is established at the location of the beam element region. The coordinates of the outer surface nodes of the solid unit sub-model are offset in the radial direction, and the offset amount is taken according to a preset random distribution law to form a three-dimensional random corrosion morphology on the outer surface of the solid unit sub-model. Multi-point constraints are established at the connection sections between the solid element sub-model and the remaining beam elements in the beam element finite element model, so that the boundary node degrees of freedom of the solid element sub-model and the boundary node degrees of freedom of the beam element satisfy the displacement compatibility relationship. Based on the degree of corrosion degradation, the statistical distribution parameters of the radial offset of the outer surface nodes of the solid element sub-model are set to generate a multi-scale finite element model characterizing the three-dimensional random corrosion morphology.

[0017] As can be seen from the above solutions, the advantages of the present invention are: This invention discloses a method for predicting corrosion degradation of marine engineering structures. Based on the finite element model, it establishes a surrogate model with the statistical characteristics of the structure's material parameters as the variables to be identified, taking the material parameters as input and multi-order dynamic responses as outputs. For each set of candidate statistical characteristics, multiple sets of material parameter samples are generated and input into the surrogate model to obtain the corresponding set of predicted multi-order dynamic responses. Treating the material parameters as random variables and predicting the corrosion degradation state at the distribution level can comprehensively characterize the material performance degradation and its uncertainty caused by corrosion. Simultaneously, a nonlinear mapping between material parameters and structural dynamic responses is established through the surrogate model, enabling the identification of corrosion degradation states based on observable dynamic response data. The surrogate model also replaces the finite element model for repeated calculations, significantly reducing the computational cost during distribution propagation. Furthermore, the relative error between the mean of each order of dynamic response predicted values ​​and the mean of each order of dynamic response target values ​​in the target response distribution is used as the optimization objective. Combined with KL divergence, the closeness between the predicted distribution and the target distribution is evaluated, while constraining the distribution's central location, dispersion, and correlation, making the prediction results closer to the true state at the distribution level. This method can effectively improve the consistency of response distribution in corroded and degraded marine engineering structures while taking into account computational costs. Attached Figure Description

[0018] Figure 1 A schematic diagram of the overall process of a corrosion degradation prediction method for marine engineering structures provided in an embodiment of the present invention; Figure 2 for Figure 1 A detailed flowchart of step S1 is shown below; Figure 3 A schematic diagram of the underwater support structure for the jacket platform; Figure 4 for Figure 1 A detailed flowchart of step S2 is shown below; Figure 5 To verify the prediction accuracy of the surrogate model, a comparison chart of predicted and calculated values ​​using five-fold cross-validation was used. Figure 6 Offline comparison and weighted ablation results for different sampling strategies; Figure 7 Scattered point distribution and confidence ellipse under different corrosion conditions; The attached figures are labeled as follows: 10: Guide frame platform; 11: Main pile leg; 12: Horizontal strut; 13: Diagonal bracing components; 131: Horizontal diagonal brace; 132: Vertical brace. Detailed Implementation

[0019] It should be noted that, in this invention, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0020] In the absence of further restrictions, an element defined by the phrase "comprising a..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0021] refer to Figure 1 As shown, Figure 1 A schematic diagram of the overall process of the corrosion degradation prediction method for marine engineering structures provided in one embodiment of the present invention is shown.

[0022] A method for predicting corrosion degradation of marine engineering structures includes the following steps: Step S1: Construct a finite element model characterizing the three-dimensional random corrosion morphology of the marine engineering structure, and obtain the target values ​​of the multi-order dynamic response of the marine engineering structure under different corrosion degradation states as the target response distribution.

[0023] Step S2: Based on the finite element model, a surrogate model is established with the material parameters as input and the multi-order dynamic response as output, using the statistical characteristics of the material parameters of the structure as the variables to be identified.

[0024] Step S3: For each set of candidate statistical features, generate multiple sets of material parameter samples according to the truncated normal distribution corresponding to the candidate statistical features, input the material parameter samples into the surrogate model to obtain the corresponding set of multi-order dynamic response prediction values, and calculate the mean of each order dynamic response prediction value.

[0025] Step S4: Using the relative error between the mean of the predicted values ​​of each order of dynamic response and the mean of the target values ​​of each order of dynamic response in the target response distribution as the optimization objective, a multi-objective evolutionary algorithm is used to optimize and solve the statistical characteristic quantities of the material parameters to obtain the Pareto non-dominated solution set.

[0026] Step S5: Calculate the KL divergence between the joint prediction distribution of the multi-order dynamic response corresponding to each candidate solution in the Pareto non-dominated solution set and the target response distribution, select the candidate solution with the smallest KL divergence as the optimal solution, and obtain the optimal statistical feature quantity.

[0027] Step S6: Evaluate the corrosion degradation state based on the optimal statistical characteristic quantity.

[0028] In this embodiment, material parameters are treated as random variables to predict the corrosion degradation state at the distribution level, comprehensively characterizing the material performance degradation and its uncertainty caused by corrosion. Simultaneously, a nonlinear mapping between material parameters and structural dynamic response is established through a surrogate model, enabling the identification of the corrosion degradation state based on observable dynamic response data. The surrogate model also replaces the finite element model for repetitive calculations, significantly reducing computational costs during distribution propagation. Furthermore, the relative error of the mean values ​​of each order of dynamic response is used as the optimization objective. Based on the mean error optimization, the KL divergence is further used to evaluate the closeness between the predicted and target distributions, while constraining the distribution's central location, dispersion, and correlation, making the prediction results closer to the true state at the distribution level. This method effectively improves the consistency of the response distribution of corroded and degraded marine engineering structures while considering computational costs, providing a reference for health monitoring and probabilistic model calibration of in-service marine engineering structures.

[0029] In one embodiment, reference Figure 2 As shown, Figure 2 A detailed flowchart of step S1 is shown.

[0030] Step S11: Based on the overall geometric dimensions and component layout of the marine engineering structure, establish a beam element finite element model with beam elements as the main body.

[0031] Step S12: In the finite element model of the beam element, separate the beam element region corresponding to the target component located within the splash zone, and establish a solid element sub-model at the location of the beam element region.

[0032] Step S13: Offset the coordinates of the outer surface nodes of the solid unit sub-model in the radial direction. The offset amount is taken according to a preset random distribution law to form a three-dimensional random corrosion morphology on the outer surface of the solid unit sub-model.

[0033] Step S14: Establish multi-point constraints at the connection sections between the solid element sub-model and the remaining beam elements in the beam element finite element model, so that the boundary node degrees of freedom of the solid element sub-model and the boundary node degrees of freedom of the beam element satisfy the displacement compatibility relationship.

[0034] Step S15: Set the statistical distribution parameters of the radial offset of the outer surface nodes of the solid unit sub-model according to the degree of corrosion degradation, and generate a multi-scale finite element model characterizing the three-dimensional random corrosion morphology.

[0035] In this embodiment, only key components in the splash zone are modeled using solid elements for refined detailing, while beam elements are used in other areas. This approach accurately captures the structural performance degradation caused by corrosion damage, ensuring the characterization accuracy of corrosion-sensitive areas, while avoiding the enormous computational overhead of a full solid model. Furthermore, by dynamically adjusting the radial offset of the outermost node coordinates in the splash zone, the random corrosion morphology can characterize the irregular unevenness of the corroded surface, overcoming the limitation of traditional simplified models with uniform wall thickness that cannot reflect the spatial randomness of corrosion morphology. This achieves a refined depiction of three-dimensional random corrosion morphology, enabling dynamic updates of local mass distribution while adjusting local structural stiffness. Simultaneously, multi-point constraints connect solid elements and beam elements, ensuring load transfer and deformation continuity at the connection interfaces between elements of different dimensions, achieving coordinated deformation between multi-scale elements.

[0036] In one embodiment, a jacket platform, a marine engineering structure, is used as an example for multi-scale finite element modeling. (Reference) Figure 3 As shown, Figure 3 This is a schematic diagram of the underwater support structure of the jacket platform 10. The jacket platform 10 includes an underwater support structure, a typical jacket structure, mainly composed of main pile legs 11, horizontal struts 12, and diagonal bracing members 13. The main pile legs 11, horizontal struts 12, and diagonal bracing members are 13-beam units. Multiple main pile legs 11 are arranged in an upwardly inward incline along the height direction to form a frame structure. The horizontal struts 12 are located at different elevations of the main pile legs, connecting the main pile legs 11 to form a multi-layered platform. The diagonal bracing members 13 include horizontal diagonal braces 131 and vertical diagonal braces 132. The horizontal diagonal braces 131 are arranged within each layer of the platform, connecting the horizontal struts 12; the vertical diagonal braces 132 are arranged between the multi-layered platforms, connecting the horizontal struts 12 and the main pile legs 11. For example, four main pile legs are provided, arranged in an upwardly inward incline. The planar dimensions at elevation -11.9m are 16.7m × 11.7m, decreasing to 15.12m × 10.12m at elevation -4.0m. The pile leg cross-section is 1350mm × 24mm. There are three layers of horizontal bracing, located at elevations of 4.0m, -4.0m, and -11.9m, with a cross-section of 700mm × 22mm. Horizontal diagonal bracing is arranged within each platform level, while vertical diagonal bracing is mainly distributed between the -4.0m and -11.9m platforms.

[0037] For this jacket platform, firstly, based on the overall geometry and component layout of the jacket platform, a beam element finite element model is established, primarily using beam elements. Then, the beam element regions corresponding to the target components within the splash zone are separated, and solid element sub-models are created at the locations of these beam element regions. For example, the splash zone is set as a preset length interval along the structural height direction, such as 3.0m, and the main pile leg segment located within this splash zone is designated as the target component. In the splash zone of the jacket platform, refined modeling is performed using solid elements to create solid element sub-models, while beam elements are used for modeling in other areas.

[0038] After corrosion occurs in the splash zone, marine engineering structures exhibit uneven wall thinning and surface irregularities. This irregular corrosion morphology is difficult to describe directly using a single wall thickness value. Therefore, we characterize the impact of corrosion on the overall structural stiffness using an equivalent wall thickness.

[0039] In one embodiment, the radial offset of the outer surface nodes of the solid element sub-model follows a Gaussian distribution, the mean of the offset is determined by the equivalent wall thickness loss caused by corrosion, and the standard deviation of the offset is used to characterize the irregularity of the corroded surface.

[0040] In practice, the equivalent wall thickness loss is determined by matching the displacement-reaction curve under static analysis. For a given corrosion condition, the bottom nodes of the beam element finite element model are first fixed, and a preset displacement is applied to the top of the structure along the horizontal direction. The displacement-reaction curve between the average top displacement and the total horizontal reaction force is extracted. Then, the displacement-reaction curve obtained for this condition is compared with the displacement-reaction curves of different wall thicknesses. The wall thickness with the highest matching degree is selected as the equivalent wall thickness for this condition, and the difference between the initial wall thickness in the uncorroded state and the equivalent wall thickness is taken as the wall thickness loss.

[0041] The degree of corrosion degradation is divided into several levels based on the equivalent wall thickness loss, including no corrosion, slight corrosion, moderate corrosion, and severe corrosion. As shown in Table 1, Table 1 illustrates the settings for different corrosion conditions.

[0042] Table 1. Settings for different corrosion conditions

[0043] Based on different degrees of corrosion degradation, the statistical distribution parameters of the radial offset of the outer surface nodes of the solid unit sub-model are set, namely the statistical distribution parameters such as mean and standard deviation, to generate a multi-scale finite element model that characterizes the three-dimensional random corrosion morphology.

[0044] In one embodiment, MPC multi-point constraints are established at the connection sections between the solid element sub-model and the remaining beam elements in the beam element finite element model, so that the boundary node degrees of freedom of the solid element sub-model and the boundary node degrees of freedom of the beam element satisfy the displacement coordination relationship, thereby ensuring load transfer and deformation continuity between models of different dimensions.

[0045] In one embodiment, the mesh density of the solid unit sub-model is determined based on the spatial wavelength of the corrosion morphology, which can be determined by the standard deviation of the offset, so that each corrosion bump feature is covered by at least one unit layer.

[0046] Furthermore, using this finite element model, with the material parameters of the marine engineering structure as input, the target values ​​of the multi-order dynamic responses of the marine engineering structure under different corrosion and degradation states are obtained, serving as the target response distribution. The material parameters can be selected as elastic modulus and density. The elastic modulus directly affects the overall stiffness of the marine engineering structure, while the density directly affects the mass distribution of the structure. The output dynamic responses of each order are jointly determined by stiffness and mass.

[0047] After establishing the aforementioned finite element model, each high-fidelity analysis requires sequential parameter input, modeling, modal solving, and frequency extraction. Even if this process can be automated, relying solely on one-time static sampling still necessitates a large number of training samples to cover the parameter domain, resulting in high computational costs. Therefore, further refinement of the finite element model is necessary. However, repeated finite element analyses with numerous parameter combinations during model refinement still incur significant computational overhead. Thus, model refinement requires a reasonable balance between accuracy and computational efficiency. To address this issue, an approximate analysis approach centered on the response surface is considered. By constructing a mapping relationship between finite element inputs and outputs, rapid prediction of structural responses can be achieved. Based on this, surrogate models become crucial tools for improving model refinement efficiency. However, establishing high-precision surrogate models typically relies on large-scale sample support, leading to high initial sample acquisition costs. The purpose of introducing active learning is to prioritize supplementing the surrogate model with sample points that are more beneficial to its accuracy when the sample size is limited.

[0048] Specifically, in step S2, based on the finite element model, a surrogate model is established with the statistical characteristics of the structure's material parameters as the variables to be identified, using the material parameters as input and the multi-order dynamic response as output. (Reference) Figure 4 As shown, Figure 4 A schematic diagram of the specific process for step S2 is shown.

[0049] Step S21: Using the material parameters of the marine engineering structure as input and the multi-order dynamic response of the structure as output, an initial training sample set is generated in the material parameter space through Latin hypercube sampling. For each initial training sample, the corresponding dynamic response value is calculated by modal analysis through the finite element model, and an initial surrogate model is established. The initial surrogate model outputs the predicted dynamic response value corresponding to any material parameter; wherein, the material parameters include elastic modulus and density.

[0050] Step S22: For each candidate material parameter in the candidate sample pool, calculate the minimum Euclidean distance from the candidate material parameter to all known material parameters in the current training sample set as an exploration term, and calculate the deviation norm between the predicted dynamic response value output by the surrogate model at the candidate material parameter and the reference dynamic response value as an development term. After normalizing the exploration term and the development term, sum them according to the preset weights to obtain the comprehensive acquisition function value.

[0051] Step S23: Select the candidate material parameter with the largest comprehensive acquisition function value from the candidate sample pool as the new sample point, calculate the dynamic response value corresponding to the new sample point through the finite element model, add the new sample point and its corresponding dynamic response value to the training sample set, update the initial surrogate model, so that the dynamic response prediction value output by the updated surrogate model at the new sample point is close to the dynamic response value obtained by the finite element model.

[0052] In one specific implementation, the surrogate model adopts a Gaussian process regression model, wherein: The initial surrogate model outputs the following predicted dynamic response values ​​at arbitrary material parameters: ; in, For the regression term, For regression coefficients, The vector represents the basis functions, and the superscript T indicates the matrix transpose. With a mean of zero and a standard deviation of Gaussian process; The material parameters of the training samples, any two material parameters and covariance between , The correlation function uses a Gaussian squared exponential kernel, and its expression is: ; in, For the hyperparameters of the correlation function, Let be the dimension of the material parameter space; Let p be the component value of the p-th material parameter in the j-th dimension. Let q be the component value of the q-th material parameter in the j-th dimension. Let j be the hyperparameters in the j-th dimension; The regression coefficients are estimated using the generalized squares method, and the calculation formula is as follows: ; Where R is the correlation matrix, and the elements are... F is the regression matrix, with elements of... , , ; The updated surrogate model, for any material parameters to be predicted The predicted dynamic response value is calculated as follows: ; in, For the material parameters to be predicted With sample The correlation vector between them; The formula for calculating the variance of the predicted dynamic response output by the surrogate model is as follows: ; in, , This is an estimate of the standard deviation.

[0053] Furthermore, within the active learning framework, the acquisition function determines the selection location of new samples, and its design directly impacts the construction efficiency and accuracy of the surrogate model. New samples not only need to improve the global coverage of the input space but should also focus on key regions that are more sensitive to structural responses and their distribution propagation. To further improve the construction efficiency and accuracy of the surrogate model, this embodiment constructs an acquisition function that integrates exploration and development mechanisms. This acquisition function includes two parts: an exploration term and a development term. The exploration term reflects the dispersion of candidate points from existing samples. A larger exploration term indicates that the candidate point is farther from existing samples, which is more conducive to supplementing sparse sample regions and thus helps improve global spatial coverage. The development term measures the potential contribution of candidate points to response changes.

[0054] For each candidate material parameter in the candidate sample pool, the minimum Euclidean distance from that candidate material parameter to all known material parameters in the current training sample set is calculated as an exploration term, and the calculation formula is as follows: ; in, This represents the current number of training samples. Indicates the first A known sample point, For any candidate material parameters, For exploration purposes.

[0055] The deviation norm between the predicted dynamic response value output by the surrogate model and the reference dynamic response value at the candidate material parameter is calculated as an development term. The formula for calculating the development term is:

[0056] in, For the surrogate model in candidate material parameters Predicted dynamic response values ​​at the location, The dynamic response reference value is the dynamic response value of the marine engineering structure in the uncorroded state, or the dynamic response value of the marine engineering structure in the current corroded state. As an development term, unlike traditional uncertainty indicators based on prediction variance, this development term directly reflects the degree of influence of candidate points on changes in the response surface and subsequent distribution propagation.

[0057] To achieve a balance between exploration and development, the above exploration and development items are normalized to construct a comprehensive acquisition function, calculated as follows: The formula for calculating the comprehensive acquisition function value is as follows: ; in, For the normalized exploration term, For normalized development items, To explore the weights, in one preferred approach, an equal weighting is adopted: By setting equal weights, a balance is achieved between the coverage of the input space and the enhancement of the response-sensitive region, thus avoiding the sampling process being dominated by a single factor and improving the overall modeling capability of the surrogate model under limited sample conditions.

[0058] The candidate material parameter with the largest comprehensive acquisition function value is selected from the candidate sample pool as a new sample point. The dynamic response value corresponding to the new sample point is calculated using the finite element model. The new sample point and its corresponding dynamic response value are added to the training sample set to update the initial surrogate model. This update ensures that the dynamic response prediction value output by the surrogate model at the new sample point approximates the dynamic response value obtained by the finite element model. This process does not simply involve uniformly densifying the samples, but rather, while controlling the sample distribution to avoid excessive concentration, it focuses on supplementing regions that are more sensitive to changes in frequency response.

[0059] After obtaining the surrogate model, the repetitive calculations of the finite element method can be replaced by the surrogate model, and the correction of the stochastic model is correspondingly transformed into the problem of identifying the distribution of material parameters. Therefore, [the following is a continuation of the previous sentence]. As a variable to be identified, , These are the mean and standard deviation of the elastic modulus. The mean and standard deviation of the density are given. These are statistical features. Given a set of candidate parameters... Then, several sets of elasticity variables and density samples are randomly generated, then input into the surrogate model to obtain the predicted frequency distribution, and finally compared with the target frequency distribution.

[0060] Specifically, in step S3, for each set of candidate statistical features, multiple sets of material parameter samples are generated according to the truncated normal distribution corresponding to the candidate statistical features. The material parameter samples are input into the surrogate model to obtain the corresponding set of multi-order dynamic response prediction values, and the mean of each order dynamic response prediction value is calculated.

[0061] Multiple sets of material parameter samples are generated based on the truncated normal distribution corresponding to the candidate statistical features. The formula for generating the material parameter samples is as follows: ； ； ; in, , The number of samples generated in each evaluation. These are the lower and upper limits of the elastic modulus E. density The lower limit and upper limit, , Here, represents the mean and standard deviation of the elastic modulus, and represents statistical characteristics. Here, represents the mean and standard deviation of the density, and represents statistical characteristics. To truncate the normal distribution, , For the first Elastic modulus and density of the sample materials; For the first A sample of material parameters, consisting of elastic modulus and density.

[0062] The material parameter samples are input into the updated surrogate model to obtain the corresponding set of multi-order dynamic response prediction values:

[0063] in, This is the predicted value of the m-th order dynamic response. For the first l A set of predicted m-th order dynamic response values ​​for a group of material parameter samples. It is the set of predicted multi-order dynamic response values ​​for all groups of material parameter samples.

[0064] Calculate the mean vector of the predicted frequency distribution. The mean vector and covariance matrix of the target frequency distribution are denoted as follows: and .

[0065] In one embodiment, in step S4, the relative error between the mean of the predicted values ​​of each order of dynamic response and the mean of the target values ​​of each order of dynamic response in the target response distribution is used as the optimization objective. A multi-objective evolutionary algorithm is used to optimize and solve the statistical characteristic quantities of the material parameters to obtain the Pareto non-dominated solution set.

[0066] The formula for calculating the optimization objective is as follows: ; in, Variables to be identified The optimization objective function of order i, , Let be the mean of the predicted values ​​of the i-th order dynamic response. Let be the mean of the target value of the i-th order dynamic response; The corresponding multi-objective optimization problem is expressed as: ; in, These are the variables to be identified. The lower limit and upper limit.

[0067] In one embodiment, the NSGA-II multi-objective evolutionary algorithm is used to solve the multi-objective optimization problem to obtain the Pareto non-dominated solution set.

[0068] In one embodiment, only the first three frequencies may be used. The mean expansion is used to construct a multi-objective optimization problem based on the predicted values ​​of the first three-order dynamic responses. These represent the relative errors of the mean values ​​of the three frequencies, with the optimization direction being minimization. Since lower-order natural frequencies are primarily controlled by the overall structural stiffness and mass, they can reflect the impact of changes in material statistical parameters on the overall dynamic response. This avoids the correction results only fitting a single mode. During optimization, instead of directly pursuing that every material parameter equals its true value, the goal is to first ensure that the updated parameter distribution can recover the mean values ​​of the first three frequencies. Separate constraints The mean error is used to obtain a set of Pareto candidate solutions. Then, the mean error is used... The divergence is compared to identify the differences in the joint distribution of the third-order frequencies, and the final corrected solution is selected from the candidate solutions. This approach is more in line with the goal of stochastic model correction: first ensure that the frequency response matches, and then determine whether the parameter distribution is reasonable.

[0069] In one specific implementation, in step S5, after obtaining the Pareto non-dominated solution, the KL divergence between the joint prediction distribution of the multi-order dynamic response corresponding to each candidate solution in the Pareto non-dominated solution set and the target response distribution is further calculated as a post-screening index to evaluate the degree of similarity between the predicted frequency distribution and the target frequency distribution at the distribution level. The KL divergence is not used as a Pareto optimization objective; it is only used to screen the final results after obtaining the non-dominated solution.

[0070] Specifically, the KL divergence between the joint prediction distribution of the multi-order dynamic response corresponding to each candidate solution in the Pareto non-dominated solution set and the target response distribution is calculated using the following formula:

[0071] in, Let KL divergence be the KL divergence. This represents the joint prediction distribution of the multi-order dynamic responses of the current candidate solution. For the target response distribution, These are the mean vector and covariance matrix of the predicted distribution, respectively. , Let be the mean vector and covariance matrix of the target distribution, respectively. To determine the dimension of the joint distribution, when using the joint distribution of the first three frequencies, ; for The inverse matrix, Let be the trace of the matrix.

[0072] Then, the relative errors corresponding to the predicted values ​​of each order dynamic response of each candidate solution in the Pareto non-dominated solution set are normalized, the Euclidean distance from each candidate solution to the given ideal point is calculated, and the candidate solutions whose Euclidean distance does not exceed a preset multiple of the minimum Euclidean distance are retained as the candidate solution set. Then, the candidate solution with the smallest KL divergence is selected from the candidate solution set as the optimal solution, and the optimal statistical feature quantity is obtained.

[0073] The smaller the KL divergence, the closer the predicted frequency distribution is to the target frequency distribution. This KL divergence index is no longer the primary objective of Pareto optimization, but rather used to further filter solutions with better distribution consistency from candidate solutions with relatively good mean errors. This ensures that the first three frequency means are directly constrained, while also preserving a comprehensive evaluation of the distribution center, dispersion, and correlation through the joint KL divergence.

[0074] In one embodiment, in step S6, the corrosion degradation state is further assessed based on the optimal statistical characteristic quantity. Specifically, the mean value of the material parameters of the optimal statistical characteristic quantity is compared with the mean value of the material parameters before corrosion, and the degree of corrosion degradation of the marine engineering structure is assessed based on the change in the mean value. The standard deviation of the material parameters of the optimal statistical characteristic quantity is compared with the standard deviation of the material parameters before corrosion, and the degree of non-uniformity of the corrosion morphology is assessed based on the change in the standard deviation.

[0075] In practical applications, stochastic model correction requires extensive sample calculations at the parameter distribution level. Relying on manual modeling and post-processing for each sample is not only time-consuming but also makes it difficult to ensure consistency in modeling and data extraction processes across different samples. To address this, an automated evaluation workflow was established using MATLAB, Python, and Abaqus / CAE to generate high-fidelity samples in batches, record computational status, and organize results. In this workflow, each software module performs a different task. MATLAB handles Latin hypercube sampling (LHS) in the parameter space, surrogate model training, and control of NSGA-II multi-objective optimization; Python scripts are used for secondary development of Abaqus / CAE, handling parametric modeling and data transfer; and Abaqus / CAE is responsible for finite element calculations and outputting the corresponding structural responses. Through this coupled workflow, parameter sampling, finite element calculations, surrogate modeling, and optimization updates can be completed within the same computational chain. This reduces errors caused by manual operation and improves the efficiency of sample calculations and data management, providing a computational foundation for subsequent uncertainty analysis and stochastic model correction.

[0076] The following specific example demonstrates the effectiveness of the method described above in this invention.

[0077] The basic dynamic characteristics of the jacket platform under different corrosion and degradation states are explained. Four operating conditions are set as shown in Table 1: Condition D1: New state (i.e., uncorroded state), Condition D2: Slightly corroded state, Condition D3: Moderately corroded state, and Condition D4: Severely corroded state.

[0078] The first three natural frequencies of the structure under loading conditions D1–D4 were extracted and compared. Abaqus modal analysis results show that the first three natural frequencies of the newly built structure in condition D1 are 3.5001Hz, 3.9015Hz, and 4.6694Hz, respectively; with increasing corrosion, the frequencies generally show a decreasing trend. Under condition D2, the third natural frequencies decrease to 3.4240Hz, 3.8216Hz, and 4.5799Hz; under condition D3, they are 3.3378Hz, 3.7307Hz, and 4.4781Hz, respectively; and under condition D4, they further decrease to 3.2152Hz, 3.6009Hz, and 4.3329Hz. Compared with D1, the decrease in the first three natural frequencies under condition D4 is approximately 8.14%, 7.70%, and 7.21%, respectively. This change indicates that corrosion degradation reduces the overall stiffness of the structure, causing lower-order frequencies to shift towards lower frequencies.

[0079] Figure 5 The parity plot, showing the comparison between predicted and calculated values ​​using five-fold cross-validation, is used to verify the accuracy of the surrogate model's predictions. Figure 5 (a) Figure 5 (b) and Figure 5 (c) are respectively Cross-validation, cross-validation The values ​​are 0.9999993933, 0.9999993808, and 0.9999995297, respectively; the corresponding RMSEs are 0.103623, 0.111911, and 0.110983 mHz, respectively. It can be seen that the predicted values ​​and calculated values ​​generally agree well, indicating that the established surrogate model can accurately predict the low-order frequency response of the structure.

[0080] Besides geometric modeling, the selection of training samples also affects the efficiency of surrogate model construction. To compare the impact of different sampling strategies on the distribution propagation results under corrosion degradation conditions, four strategies—Random-LHS, pure exploration, pure exploitation, and the fusion exploration and exploitation mechanism (EEB-ALK) of this invention—were compared under the same initial samples, candidate pool, and independent test set conditions. Furthermore, the weights of the exploration and exploitation terms in EEB-ALK were further adjusted to analyze their impact on the sampling effect. Figure 6 The offline comparison and weighted ablation results of different sampling strategies are shown. Figure 6 visible, Figure 6 In the middle (a), the accuracy of the global proxy model is represented. Figure 6 (b) represents the distribution and propagation of corrosion in critical operating conditions. Figure 6 (c) indicates a comparison of key areas under different working conditions. Figure 6In the figure (d), the EEB weighted ablation experiment is shown. Among the distribution propagation indices of corrosion degradation conditions D3–D4, EEB-ALK exhibits a lower KL divergence, demonstrating its superiority. When the sample size is 120, the average KL of EEB-ALK for D3–D4 is 45.70, which is lower than 88.61 for Random-LHS and 55.83 for the pure exploration strategy.

[0081] At the stochastic model correction level, the KL divergence of the joint distribution of the first two frequencies is the primary objective, with the mean error of the first two frequencies as the secondary objective. The final update results are obtained through the NSGA-II and Pareto knee criterion. Under the D1–D4 conditions, the mean error of the first three frequencies before correction was 0.98%–4.56%, which decreased to 0.00055%–0.04224% after correction; the KL divergence of the joint distribution of the first two frequencies decreased from 7.99–148.00 to 0.0019–0.0064. Figure 7 The distribution of scattered points and confidence ellipses in the f1-f2 plane under the D1–D4 working conditions are shown. Figure 7 It can be seen that there is a significant offset between the initial distribution and the target distribution, especially in cases D3 and D4, where the gray ellipse is located to the upper right of the target distribution. After correction, the center of the blue ellipse basically coincides with the red ellipse, indicating that the updated random parameters bring the first two frequency distributions closer to the target distribution, thus improving the consistency of the joint response.

[0082] In summary, the corrosion degradation prediction method for marine engineering structures provided by this invention can accurately capture the structural performance degradation caused by corrosion damage, ensure the characterization accuracy of corrosion-sensitive areas, improve the consistency of response distribution in corrosion-degraded marine engineering structures, and take into account computational costs. Specifically: Firstly, a finite element model based on beam elements is established, and the beam element regions corresponding to the target components within the splash zone are separated to create solid element sub-models. The coordinates of the outer surface nodes of the solid element sub-models are offset radially to form a three-dimensional random corrosion morphology. MPC multi-point constraints are established at the connection sections between the solid element sub-models and the remaining beam elements. This method uses solid elements for refined modeling only in key components within the splash zone, while beam elements are used in other areas. This approach accurately captures the structural performance degradation caused by corrosion damage, ensuring the characterization accuracy of corrosion-sensitive areas, while avoiding the huge computational overhead of a full solid model. Furthermore, by dynamically adjusting the radial offset of the outermost node coordinates in the splash zone, the random corrosion morphology can characterize the irregular unevenness of the corroded surface in the splash zone. This overcomes the shortcomings of traditional simplified models with uniform wall thickness that cannot reflect the spatial randomness of corrosion morphology, achieving a refined characterization of the three-dimensional random corrosion morphology. This allows for the adjustment of local structural stiffness while simultaneously updating the local mass distribution. Meanwhile, by connecting solid elements and beam elements through MPC multi-point constraints, the load transfer and deformation continuity of elements of different dimensions at the connection interface are ensured, and coordinated deformation between multi-scale elements is achieved.

[0083] Secondly, based on the aforementioned finite element model, a surrogate model is established, using the statistical characteristics of the structure's material parameters as the variables to be identified. This surrogate model takes the material parameters as input and the multi-order dynamic response as output. For each set of candidate statistical characteristics, multiple sets of material parameter samples are generated and input into the surrogate model to obtain the corresponding set of predicted multi-order dynamic response values. Treating the material parameters as random variables and predicting the corrosion degradation state at the distribution level can comprehensively characterize the material performance degradation caused by corrosion and its uncertainty. Simultaneously, the surrogate model establishes a nonlinear mapping between material parameters and the structural dynamic response, enabling the identification of the corrosion degradation state based on observable dynamic response data. Furthermore, the surrogate model replaces the finite element model in performing repetitive calculations, significantly reducing the computational cost during the distribution propagation process.

[0084] Third, the relative error between the mean of the predicted values ​​of each order of dynamic response and the mean of the target values ​​of each order of dynamic response in the target response distribution is used as the optimization objective. Combined with KL divergence, the degree of closeness between the predicted distribution and the target distribution is evaluated. At the same time, the central position, dispersion and correlation of the distribution are constrained, so that the prediction results are closer to the real state at the distribution level.

[0085] In addition, embodiments of the present invention also provide a readable storage medium storing a program or instructions that, when executed by a processor, implement the steps of the above-described method for predicting the corrosion and degradation of marine engineering structures, and achieve the same technical effect.

[0086] It should be noted that the scope of the methods in the embodiments of the present invention is not limited to performing functions in the order shown or discussed, but may also include performing functions substantially simultaneously or in the reverse order, depending on the functions involved. For example, the described methods may be performed in a different order than described, and various steps may be applied, omitted, or combined. In addition, features described with reference to certain examples may be combined in other examples.

[0087] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of the present invention.

Claims

1. A method for predicting corrosion degradation of marine engineering structures, characterized in that, include: A finite element model characterizing the three-dimensional random corrosion morphology of marine engineering structures was constructed, and the target values ​​of the multi-order dynamic response of the marine engineering structures under different corrosion degradation states were obtained as the target response distribution. Based on the finite element model, a surrogate model is established with material parameters as input and multi-order dynamic response as output, using the statistical characteristics of the material parameters of the structure as the variables to be identified. For each set of candidate statistical features, multiple sets of material parameter samples are generated based on the truncated normal distribution corresponding to the candidate statistical features. The material parameter samples are input into the surrogate model to obtain the corresponding set of multi-order dynamic response prediction values, and the mean of each order dynamic response prediction value is calculated. Using the relative error between the mean of the predicted values ​​of each order of dynamic response and the mean of the target values ​​of each order of dynamic response in the target response distribution as the optimization objective, a multi-objective evolutionary algorithm is used to optimize and solve the statistical characteristics of the material parameters to obtain the Pareto non-dominated solution set. Calculate the KL divergence between the joint prediction distribution of the multi-order dynamic response corresponding to each candidate solution in the Pareto non-dominated solution set and the target response distribution, select the candidate solution with the smallest KL divergence as the optimal solution, and obtain the optimal statistical feature quantity. The corrosion degradation state is assessed based on the aforementioned optimal statistical characteristic quantities; The steps for constructing a finite element model characterizing the three-dimensional stochastic corrosion morphology of marine engineering structures include: Based on the overall geometric dimensions and component arrangement of the marine engineering structure, a finite element model of beam elements is established, with beam elements as the main body. In the finite element model of the beam element, the beam element region corresponding to the target component located within the splash zone is separated, and a solid element sub-model is established at the location of the beam element region. The coordinates of the outer surface nodes of the solid unit sub-model are offset in the radial direction, and the offset amount is taken according to a preset random distribution law to form a three-dimensional random corrosion morphology on the outer surface of the solid unit sub-model. Multi-point constraints are established at the connection sections between the solid element sub-model and the remaining beam elements in the beam element finite element model, so that the boundary node degrees of freedom of the solid element sub-model and the boundary node degrees of freedom of the beam element satisfy the displacement compatibility relationship. Based on the degree of corrosion degradation, the statistical distribution parameters of the radial offset of the outer surface nodes of the solid element sub-model are set to generate a multi-scale finite element model characterizing the three-dimensional random corrosion morphology.

2. The corrosion degradation prediction method for marine engineering structures according to claim 1, characterized in that, Based on the finite element model, the steps of establishing a surrogate model with material parameters as input and multi-order dynamic response as output, using the statistical characteristics of the structure's material parameters as the variables to be identified, include: Using the material parameters of the marine engineering structure as input and the multi-order dynamic response of the structure as output, an initial training sample set is generated in the material parameter space through Latin hypercube sampling. For each initial training sample set, the corresponding dynamic response value is calculated by modal analysis using the finite element model, and an initial surrogate model is established. The initial surrogate model outputs the predicted dynamic response value corresponding to any material parameter; wherein, the material parameters include elastic modulus and density. For each candidate material parameter in the candidate sample pool, the minimum Euclidean distance from the candidate material parameter to all known material parameters in the current training sample set is calculated as an exploration term, and the deviation norm between the predicted dynamic response value output by the surrogate model at the candidate material parameter and the reference dynamic response value is calculated as an development term. The exploration term and the development term are normalized and then weighted and summed according to preset weights to obtain the comprehensive acquisition function value. The candidate material parameter with the largest comprehensive acquisition function value is selected from the candidate sample pool as a new sample point. The dynamic response value corresponding to the new sample point is calculated by the finite element model. The new sample point and its corresponding dynamic response value are added to the training sample set, and the initial surrogate model is updated so that the dynamic response prediction value output by the updated surrogate model at the new sample point is close to the dynamic response value obtained by the finite element model.

3. The corrosion degradation prediction method for marine engineering structures according to claim 2, characterized in that, The surrogate model employs a Gaussian process regression model, wherein: The initial surrogate model outputs the following predicted dynamic response values ​​at arbitrary material parameters: ； in, For the regression term, For regression coefficients, The vector represents the basis functions, and the superscript T indicates the matrix transpose. With a mean of zero and a standard deviation of Gaussian process; The material parameters of the training samples, any two material parameters and Covariance between , The correlation function uses a Gaussian squared exponential kernel, and its expression is: ； in, For the hyperparameters of the correlation function, Let be the dimension of the material parameter space; Let p be the component value of the p-th material parameter in the j-th dimension. Let q be the component value of the q-th material parameter in the j-th dimension. Let j be the hyperparameters in the j-th dimension; The regression coefficients are estimated using the generalized squares method, and the calculation formula is as follows: ； Where R is the correlation matrix, and the elements are... F is the regression matrix, with elements of... , , ; The updated surrogate model, for any material parameters to be predicted The predicted dynamic response value is calculated as follows: ； in, For the material parameters to be predicted With sample The correlation vector between them; The formula for calculating the variance of the predicted dynamic response output by the surrogate model is as follows: ； in, , This is an estimate of the standard deviation.

4. The corrosion degradation prediction method for marine engineering structures according to claim 3, characterized in that, The formula for calculating the exploration item is: ； in, This represents the current number of training samples. Indicates the first A known sample point, For any candidate material parameters, For exploration purposes; The calculation formula for the development item is: ； in, For the surrogate model in candidate material parameters Predicted dynamic response values ​​at the location, The dynamic response reference value is the dynamic response value of the marine engineering structure in the uncorroded state, or the dynamic response value of the marine engineering structure in the current corroded state. For development purposes; The formula for calculating the comprehensive acquisition function value is as follows: ； in, For the normalized exploration term, For the normalized development items, To explore weights.

5. The corrosion degradation prediction method for marine engineering structures according to claim 3, characterized in that, Multiple sets of material parameter samples are generated based on the truncated normal distribution corresponding to the candidate statistical features. The formula for generating the material parameter samples is as follows: ； ； ； in, , The number of samples generated in each evaluation. These are the lower and upper limits of the elastic modulus E. density The lower limit and upper limit, , Here, represents the mean and standard deviation of the elastic modulus, and represents statistical characteristics. Here, represents the mean and standard deviation of the density, and represents statistical characteristics. To truncate the normal distribution, , For the first Elastic modulus and density of the sample materials; For the first A set of material parameter samples, consisting of elastic modulus and density; The material parameter samples are input into the surrogate model to obtain the corresponding set of multi-order dynamic response prediction values: ； in, This is the predicted value of the m-th order dynamic response. For the first l A set of predicted m-th order dynamic response values ​​for a group of material parameter samples. It is the set of predicted multi-order dynamic response values ​​for all groups of material parameter samples.

6. The corrosion degradation prediction method for marine engineering structures according to claim 5, characterized in that, The relative error between the mean of the predicted values ​​of each order of dynamic response and the mean of the target values ​​of each order of dynamic response in the target response distribution is used as the optimization objective, and the calculation formula is as follows: ； in, Variables to be identified The optimization objective function of order i, , Let be the mean of the predicted values ​​of the i-th order dynamic response. Let be the mean of the target value of the i-th order dynamic response; The corresponding multi-objective optimization problem is expressed as: ； in, These are the variables to be identified. The lower limit and upper limit; The NSGA-II multi-objective evolutionary algorithm is used to solve the multi-objective optimization problem, and the Pareto non-dominated solution set is obtained.

7. The corrosion degradation prediction method for marine engineering structures according to claim 6, characterized in that, The KL divergence between the joint prediction distribution of the multi-order dynamic response corresponding to each candidate solution in the Pareto non-dominated solution set and the target response distribution is calculated using the following formula: ； in, Let KL divergence be the KL divergence. This represents the joint prediction distribution of the multi-order dynamic responses of the current candidate solution. For the target response distribution, These are the mean vector and covariance matrix of the predicted distribution, respectively. , Let be the mean vector and covariance matrix of the target distribution, respectively. Let be the dimension of the joint distribution. for The inverse matrix, Let be the trace of the matrix.

8. The corrosion degradation prediction method for marine engineering structures according to claim 7, characterized in that, Before selecting the candidate solution with the smallest KL divergence, the following steps are also included: normalizing the relative errors corresponding to the predicted values ​​of each order of dynamic response of each candidate solution in the Pareto non-dominated solution set, calculating the Euclidean distance of each candidate solution to the given ideal point, retaining the candidate solutions whose Euclidean distance does not exceed a preset multiple of the minimum Euclidean distance as the candidate solution set, and then selecting the candidate solution with the smallest KL divergence from the candidate solution set.

9. The corrosion degradation prediction method for marine engineering structures according to claim 1, characterized in that, The steps for assessing the corrosion degradation state based on the optimal statistical characteristic quantity include: The mean value of the material parameters of the optimal statistical characteristic quantity is compared with the mean value of the material parameters before corrosion, and the degree of corrosion degradation of the marine engineering structure is assessed based on the change in the mean value. The standard deviation of the material parameters of the optimal statistical characteristic quantity is compared with the standard deviation of the material parameters before corrosion, and the degree of non-uniformity of the corrosion morphology is evaluated based on the change in standard deviation. The statistical characteristics include the mean and standard deviation.

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