Optimization design method of coordinated similarity model of marine structure in wave environment
By combining the Navier-Stokes equations with an efficient global optimization algorithm, a scaled model of marine structures in a wave environment is optimized, solving the problems of non-scalable water density and limitations of theoretical applicability, and achieving high-precision and efficient scaled model design.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HARBIN INST OF TECH AT WEIHAI
- Filing Date
- 2026-05-28
- Publication Date
- 2026-07-21
AI Technical Summary
Existing technologies for designing scaled models of marine structures in wave environments suffer from large errors due to the non-scalability of water density, and the Morrison equation and diffraction theory have limited applicability, making it difficult to achieve efficient coordinated similarity model design under arbitrary working conditions.
By combining the Navier-Stokes equations (NS equations) with the efficient global optimization algorithm (EGO), the wave height or the width of the frontal surface is optimized. The Kriging model and the desired improved EI criterion are used to perform iterative optimization and select the optimal value to approximate the wave force of the prototype structure.
It effectively reduces the error of scaled models, improves the prediction accuracy of prototype structure responses, is applicable to arbitrary Reynolds numbers, scales and flow states, reduces computational costs and improves computational efficiency.
Smart Images
Figure CN122263748B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of marine engineering technology and testing methods. Specifically, it is an optimization design method for coordinated similarity models of marine structures in wave environments. This method combines the Navier-Stokes equations with an efficient global optimization algorithm and is applicable to the design of scaled models of flexible upright structures under wave action. It can effectively improve the prediction accuracy of the scaled model for the key responses of the prototype structure. Background Technology
[0002] With the development of marine engineering, renewable energy, and underwater structure construction, a large number of vertical elastic structures are widely used in complex sea conditions. If we want to obtain the critical response of these structures, experimental analysis is one of the most common and effective methods. However, marine structures are often characterized by large size, heavy weight, and high manufacturing cost, making prototype testing impractical. Therefore, in most engineering problems, scaled-down model tests are usually used to study the critical response of the target structure.
[0003] Based on the structural motion equations and the principle of dimensional compatibility, traditional similarity laws generally use the elastic modulus similarity coefficient. Density similarity coefficient Dimensional similarity coefficient And acceleration similarity coefficient These four are independent similarity coefficients, and their relationship is shown in Equation 1: (1) Only three of these can be freely chosen, and the fourth can be derived from Equation 1 by selecting three similarity coefficients. Besides these four physical quantities, the similarity coefficients of the remaining physical quantities can all be derived from these four independent similarity coefficients. Usually, the acceleration similarity coefficient of the scaled-down model is set to 1 to ensure consistency with the gravitational acceleration similarity coefficient; the prototype and scaled-down model usually use the same material, and the elastic modulus similarity coefficient is set to 1; while the size similarity coefficient of the scaled-down model... It must be smaller than 1. Therefore, in order to ensure that Formula 1 holds true, the density similarity coefficient of scaled-down structures is usually the reciprocal of the size similarity coefficient. The structure usually needs to add counterweights to achieve an increase in equivalent density.
[0004] Unlike conventional structures, marine engineering structures involve water in their model tests. According to the principle of dimensional similarity, the similarity coefficient of water density in a scaled-down model should be the reciprocal of the geometric similarity ratio, meaning the water density needs to be increased. However, this requirement is usually difficult to achieve in practice. To compensate for the systematic errors caused by the inability to change the water density, the conventional method is to calculate the forces acting on the prototype and the scaled-down model before the test, based on the Morrison equation or diffraction theory. Then, using the scaled-down model as a basis, the wave height or the width of the upstream face is adjusted to ensure that the wave forces acting on the adjusted scaled-down model, after retrospective analysis, are consistent with those of the prototype. This method often effectively reduces the scaling errors caused by the inability to change the water density. The model obtained through such parameter adjustments is called a compatible similarity model.
[0005] Existing designs for coordinated similarity models primarily rely on Morrison's equations and diffraction theory to achieve rapid model construction. However, both theories have clearly defined limitations in their applicability. When the environment in which the structure operates exceeds these limitations, the obtained wave force results become unreliable. To date, a method that is not constrained by applicability and can efficiently design coordinated similarity models under arbitrary working conditions remains lacking. Summary of the Invention
[0006] This invention addresses the shortcomings and deficiencies of existing technologies by proposing an optimization design method for coordinated similarity models of marine structures in wave environments, which can effectively improve the prediction accuracy of scaled models for key responses of prototype structures.
[0007] This invention achieves its purpose through the following measures: An optimization design method for a coordinated similarity model of marine structures in a wave environment is characterized by the following steps: First, determining the structural and environmental information of the prototype structure and the scaled-down model, and then calculating the wave forces corresponding to the prototype structure based on the Navier-Stokes equations. Wave forces corresponding to the scaled-down model The optimization indices for the coordinated similarity model are determined, including wave height or frontal width; the error evaluation index between the inverse force calculation of the coordinated similarity model and the force of the prototype is determined; then, based on the structural and environmental information of the scaled-down model, a number of [items / items] are selected according to the determined optimization indices. n The trial sample points were used to obtain the corresponding optimization index values. The error evaluation index RMSE between the model force calculated based on the NS equation and the prototype force is as follows: Furthermore, an efficient global optimization algorithm, EGO, consisting of the Kriging model and the desired improved EI criterion, is introduced to iteratively optimize the optimization index until the preset maximum number of iterations is reached or the Kriging model stably converges to its minimum value. The sample point with the smallest RMSE is selected from the resulting dataset as the optimal value of the optimization index, thus coordinating the wave forces of similar models. Approximating the wave forces corresponding to the prototype structure .
[0008] The present invention introduces an efficient global optimization (EGO) algorithm consisting of a Kriging model and an expected improvement EI criterion, which iteratively optimizes the optimization index until a preset maximum number of iterations is reached or the Kriging model stably converges to a minimum value. Specifically, this includes the following steps: Step 1: Using the Kriging model, assume that the optimization index takes any value within the optimization interval. x The relationship with RMSE is used This means that the function can be written as: (2), where, Represents the mean of an unknown constant. Let the Gaussian random process with mean 0 satisfy: (3), (4), of which, Represents the mathematical expectation. Describing covariance, Indicates process variance. Represents sample points The correlation function value between and is commonly expressed as the Gaussian correlation function: (5), where represents the relevant parameters, also called hyperparameters, when When approaching, Approaching 1; when and When they are far apart, Approaching 0; Step 2: Construct a correlation matrix using all sample points: (6), where represents The sample correlation matrix, the first i Line 1 j Column elements are For any optimization index value x The correlation vector between it and all sample points is defined as: (7), among which, Indicates any value of the optimization index xThe correlation column vector between the optimization index values and all known sample points; Combine existing sample points with any optimization index value x The corresponding function values are incorporated into the same probability model and written as: (8), among which, Represents a multivariate normal distribution. This represents the mean vector corresponding to the sample points; Step 3: In the Kriging model, Generalized least squares estimation is used: (9), among which, express The estimated value, A vector consisting entirely of 1s represents The column vector, i.e. The process variance estimate is written as: (10), among which, Representing process variance The estimated value, This represents the deviation vector of the sample output relative to the mean; From the conditional distribution of the joint Gaussian distribution, we can obtain that any optimization index value can be... x The predicted mean at: (11), among which, This indicates a local correction to the global mean based on existing samples; Similarly, based on the conditional Gaussian distribution, the prediction variance is: (12); Step 4: Let the optimal value among the existing samples be: ,in The optimal sample is the one with the smallest known objective function value. For the RMSE of the i-th sample, for any value of the optimization index... x Its "improvement amount" is defined as: (13), among which, To optimize any index value within the interval x The amount of improvement that can be obtained at this point, due to Since it is unknown, we use a Gaussian distribution established by Kriging to calculate its expectation: (14) Combining with step 1, we obtain the following under the Gaussian process assumption: Represented as: (15) The desired improved analytical expression is obtained as follows: (16), among which, The cumulative distribution function (CDF) of the standard normal distribution. PDF is the probability density function of the standard normal distribution. Step 5: Search the entire design space to find the point that maximizes EI. ; Step 6: At the newly selected point The calculations based on the Navier-Stokes equations were performed, and the corresponding RMSE was obtained. ; Step 7: Transfer the newly obtained sample points Incorporate into the initial sample point set, that is: (17) (18) to form an updated sample set and ; Step 8: Then repeat steps 1 to 7 until the preset maximum number of iterations is reached or the Kriging model stably converges to its minimum value. Finally, select the sample point with the smallest RMSE from the obtained dataset as the optimal value of the optimization index, thereby coordinating the wave forces of similar models. Approximate the wave forces corresponding to the prototype structure as closely as possible. .
[0009] The structural information of the prototype structure and scaled-down model described in this invention includes geometric dimensions and material constitutive information, and the environmental information includes water depth and wave parameter information.
[0010] Compared with existing technologies, this invention has the following advantages: First, by introducing a coordinated similarity model, it effectively alleviates the problem of excessive scaling error in marine structures caused by the non-scalability of water density. Second, compared with existing research, it is based on the fundamental governing equations of fluid motion, namely the Navier-Stokes equations, without relying on specific flow assumptions. It is applicable to any Reynolds number, any scale, and any flow state, thus enabling the design of coordinated similarity models for marine structures under any working condition, avoiding the limitations of applicability of the Morrison equations and diffraction theory in existing research. Third, by combining the Navier-Stokes equations with the EGO algorithm, it effectively reduces computational costs while ensuring high-precision numerical solutions, achieving synergistic optimization of computational accuracy and efficiency. Attached Figure Description
[0011] Appendix Figure 1 A flowchart of the present invention.
[0012] Appendix Figure 2This invention relates to a fluid-structure interaction platform based on waves2Foam–preCICE–CalculiX for calculating wave forces, wherein the waves2Foam solver is constructed based on the Navier-Stokes equations.
[0013] Appendix Figure 3 This is a modeling of the prototype structure in a fluid-structure interaction platform in an embodiment of the present invention.
[0014] Appendix Figure 4 The above are comparison results of the traditional similar model with the prototype in terms of base shear force, base bending moment, and top displacement in the embodiments of the present invention. Figure 4 (a) corresponds to the base shear force. Figure 4 (b) corresponds to the base bending moment. Figure 4 (c) corresponds to the top displacement.
[0015] Appendix Figure 5 The wave force time history curves of six initial sample points with different wave heights in this embodiment of the invention are shown after the wave development has stabilized.
[0016] Appendix Figure 6 This shows the correspondence between the wave height and RMSE of the six initial sample points in this embodiment of the invention.
[0017] Appendix Figure 7 This refers to the five iterative optimizations performed based on the initial samples in this embodiment of the invention, wherein... Figure 7 In the middle (a), the result of the optimization after 0 iterations is shown. Figure 7 (b) corresponds to one iteration of optimization. Figure 7 (c) corresponds to 2 iterations. Figure 7 The middle (d) corresponds to 3 iterations. Figure 7 (e) corresponds to 4 iterations. Figure 7 The interval (f) corresponds to 5 iterations.
[0018] Appendix Figure 8 This invention presents the relationship between the number of newly added sample points and the current optimal wave height, as well as the relationship between the number of newly added sample points and RMSE, during the five iterative optimization processes based on the initial samples in this embodiment of the invention.
[0019] Appendix Figure 9 This is a time history comparison of the final coordinated similar model, traditional similar model and prototype structure in terms of base shear force, base bending moment and top displacement in the embodiments of the present invention. Detailed Implementation
[0020] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0021] This invention addresses the shortcomings of existing research by proposing a design method for coordinated similarity models of marine structures based on the Navier-Stokes equations (NS equations) and an efficient global optimization algorithm (EGO). This invention is based on the fundamental governing equations of fluid motion, the NS equations, and is independent of specific flow assumptions. It is applicable to any Reynolds number, any scale, and any flow state, enabling the design of coordinated similarity models for marine structures under any working condition. However, the calculation of the NS equations itself incurs high time and computational costs. Furthermore, optimizing wave height or frontal width based on the NS equations to ensure that the forces on the coordinated similarity model are consistent with those on the prototype scale can be considered a computationally expensive black-box function optimization problem. To improve solution efficiency, EGO, a classic black-box optimization strategy consisting of the Kriging model and the Expected Improvement (EI) criterion, is introduced. This accelerates the optimization process, allowing the coordinated similarity model to be designed with only a few iterations based on a certain initial sample, thereby improving the prediction accuracy of the scaled model test on the prototype structure response. The specific steps include: Step a: Determine the structural information of the prototype structure and the scaled-down model, including geometric dimensions and material constitutive properties, as well as environmental information, including water depth and wave parameters, and calculate the wave forces corresponding to the prototype structure based on the Navier-Stokes equations. Wave forces corresponding to the scaled-down model ; Step b: Define the optimization indices for coordinating similar models, which are usually wave height, frontal width, or a combination of both; Step c: Determine the error evaluation index between the force of the coordinated similar model after back-calculation and the force of the prototype. In this example, the root mean square error (RMSE) between the force of the coordinated similar model and the force of the prototype after the wave field has stabilized is selected. Step d: Based on the structural and environmental information of the scaled model, and according to the optimization indicators determined in Step 2, select a quantity of... n The trial sample points were used to obtain the corresponding optimization index values. The corresponding RMSE of the model force calculated based on the Navier-Stokes equations and the prototype force is obtained by reverse calculation. ; Step e: Assume that the relationship between the optimization index x, which takes any value within the optimization interval, and RMSE is expressed as follows: This indicates that the function does not have an explicit analytical expression and can only be obtained through trial and error. Using the Kriging model, we assume the function is written as follows: (2), where, Represents the mean of an unknown constant. Let the Gaussian random process with mean 0 satisfy: (3), (4), of which, Represents the mathematical expectation. Describing covariance, Indicates process variance. Represents sample points and The correlation function values between them, the commonly used Gaussian correlation function is written as: (5), among which, This refers to the relevant parameters, also called hyperparameters, when... When very close, Approaching 1; when and When they are far apart, Approaching 0; Construct a correlation matrix using all sample points: (6), among which, express The sample correlation matrix, the first i Line 1 j Column elements are ; For any optimization index value x The correlation vector between it and all sample points is defined as: (7), among which, This represents the correlation column vector between any optimization index value x and all known sample points; To infer the function value of the unknown point by utilizing the relationships between existing sample points and the relationships between the unknown point and existing sample points, the function values of the existing sample points and the unknown point are placed into the same probability model, thus written as: (8), among which, Represents a multivariate normal distribution. This represents the mean vector corresponding to the sample points; In the Kriging model, Generalized least squares estimation is used: (9), among which, express The estimated value, A vector consisting entirely of 1s represents The column vector, i.e. ; The process variance estimate is written as: (10), among which, Representing process variance The estimated value, This represents the deviation vector of the sample output relative to the mean; From the conditional distribution of the joint Gaussian distribution, we can obtain that any optimization index value can be... x The predicted mean at: (11), among which, This indicates a local correction to the global mean based on existing samples; Similarly, based on the conditional Gaussian distribution, the prediction variance is: (12); Step f: Let the optimal value among the existing samples be: ,in The minimum known objective function value (optimal sample) is given. For the first i The RMSE of a sample for any value of the optimization metric. x Its "improvement amount" is defined as: (13), among which, To optimize the value of any optimization index within the interval x The amount of improvement that can be obtained at this point; because Since it is unknown, we use a Gaussian distribution established by Kriging to calculate its expectation: (14) Combining with step e, we obtain the result under the Gaussian process assumption. Represented as: (15) The desired improved analytical expression is obtained as follows: (16), among which, The cumulative distribution function (CDF) of the standard normal distribution. The probability density function (PDF) is the standard normal distribution. Step g: Search the entire design space to find the point that maximizes EI. ; Step h: at the newly selected point The calculations based on the Navier-Stokes equations were performed, and the corresponding RMSE was obtained. ; Step i: Transfer the newly obtained sample points Incorporate into the initial sample point set, that is: (17) (18) to form an updated sample set and ; Step j: Then repeat steps e to i until the preset maximum number of iterations is reached or the Kriging model stably converges to the minimum value. Finally, select the sample point with the smallest RMSE from the obtained dataset as the optimal value of the optimization index, thereby coordinating the wave forces of similar models. Approximate the wave forces corresponding to the prototype structure as closely as possible. ; The method proposed in this example will be verified below: This example uses a flexible upright cylinder under the action of a regular wave as a verification case. The flexible upright cylinder is a typical test structure composed of an aluminum core, an aerodynamic shape, and a counterweight. The key parameters are an equivalent elastic modulus of 194 MPa and an equivalent density of 792 kg / m³. 3 The damping ratio is 0.65%, the diameter is 0.15m, and the height is 2.4m.
[0022] like Figure 2 As shown, this invention utilizes a wave2Foam-preCICE- CalculiX's fluid-structure interaction numerical tank is used for wave force calculations. The waves2Foam solver, based on the Navier-Stokes equations, is a widely used and mature solution tool in current scientific research and engineering. Using this solver avoids the need to develop a custom Navier-Stokes equations solver, thus improving computational efficiency and reliability. Furthermore, the constructed fluid-structure interaction platform enables bidirectional coupled structural analysis, thereby more realistically simulating the dynamic response of marine structures under wave action.
[0023] like Figure 3 The diagram shows the modeling of the prototype of the verification example of this invention in a fluid-structure interaction platform. The water tank is 7.8m long, 3m wide, 3.6m high, and 0.6m deep. The relaxation zone is 1.1m behind the Inlet, which is used to gradually generate waves and prevent numerical divergence. The damping zone is 2.7m in front of the Outlet, which is used to absorb waves and prevent wave reflection from affecting the incident wave. The waves are regular waves with a wave height of 0.04m and a wave period of 0.8s.
[0024] Appendix 1 lists the conventional similarity design parameters used to verify the present invention and to construct a conventional similarity model. The size similarity coefficient is 1 / 2, the elastic modulus similarity coefficient is 1, the acceleration similarity coefficient is 1, the density similarity coefficient is calculated from the similarity relationship and is 2, and the water density, which cannot be changed, is set to 1. The remaining similarity coefficients are shown in Appendix 1.
[0025] Appendix 1: Physical quantities used to construct traditional similarity models
[0026] like Figure 4As shown, the comparison results of the traditional similar model used to verify the present invention in terms of base shear force, base bending moment and top displacement show that the error is extremely large, and it is necessary to design a coordinated similar model to reduce the error caused by the scaled-down model.
[0027] There are many design strategies for coordinating similar models, among which common ones include adjusting wave height, adjusting the width of the oncoming surface, or adjusting both wave height and oncoming surface width simultaneously. The optimization strategy for this validation case is to adjust the wave height, such as... Figure 5 The figure shows the wave force time history curves of six initial sample points with different wave heights in the verification case of this invention after the wave development has stabilized; Appendix Figure 6 To verify the relationship between the wave height and RMSE of the six initial sample points in the case, it can be seen that the optimal wave height is in the range of 20mm to 60mm.
[0028] In this embodiment, the RMSE (Recovery Mean Squared Error) of the forces on the coordinated similar model 7 seconds after wave development stabilizes, after back-calculation, and the forces on the prototype structure is selected as the error evaluation standard. For example... Figure 7 As shown in (a), the Kriging model in EGO can obtain the predicted mean and variance of all points in the design space based on the information of 6 initial sample points. Then, the EI criterion in EGO can calculate the expected improvement (EI) of each point in the entire design space based on the mean and variance provided by the Kriging model. The point with the largest EI value indicates that obtaining the RMSE of that point is most conducive to finding the optimal wave height; as shown in (a), the expected improvement (EI) of each point in EGO is the expected improvement (EI) of each point in EGO. Figure 7 (b), (c), (d), (e), and (f) show the iterative process of the EGO algorithm in order to find the optimal wave height. It can be seen that the final selected points are basically concentrated in a narrow interval, which proves that the optimization process is proceeding in the right direction.
[0029] like Figure 8 As shown, the EGO algorithm can successfully identify the final optimal wave height with the lowest RMSE with only one new sample iteration, demonstrating the high efficiency of the EGO method.
[0030] like Figure 9 As shown in Appendix Table 2, the final coordinated similar model and the prototype structure have a good time history fitting effect in terms of base shear force, base bending moment and top displacement, and the error is much smaller than that of the traditional similar model. Among them, compared with the traditional similar model, the final coordinated similar model reduces the RMSE of base shear force by 89.68%, the RMSE of base bending moment by 75.01%, and the RMSE of top displacement by 85.14%.
[0031] Appendix 2 shows the comparison of RMSE results between the final coordinated similar model, the traditional similar model, and the prototype structure in terms of base shear, base bending moment, and top displacement, as well as the reduction rate of RMSE by the final coordinated similar model.
[0032]
[0033] Compared with the prior art, the present invention has the following advantages: (1) Compared with the existing research, the present invention uses the basic governing equation of fluid motion, the NS equation, as the theoretical basis for analysis. It does not rely on specific flow assumptions and can be applied to different Reynolds numbers, different scales and various flow states, thereby realizing the construction of a coordinated similarity model of marine structures under any working condition, overcoming the limitations of the Morrison equation and diffraction theory in terms of applicability. (2) By integrating the NS equation with the EGO algorithm, the computational efficiency is effectively improved and the computational cost is reduced while ensuring the accuracy of numerical calculation, thus achieving a synergistic improvement in accuracy and efficiency.
Claims
1. An optimization design method for a coordinated similarity model of marine structures in a wave environment, characterized in that, include: First, the structural and environmental information of the prototype and scaled-down models is determined, and the wave forces corresponding to the prototype structure are calculated based on the Navier-Stokes equations. Wave forces corresponding to the scaled-down model Determine the optimization indices for the coordinated similarity model, including wave height or frontal width; determine the error evaluation index between the force calculation results of the coordinated similarity model and the force of the prototype. Then, based on the structural and environmental information of the scaled-down model, and according to the determined optimization indices, a quantity of [number missing] was selected. n The trial sample points were used to obtain the corresponding optimization index values. The error evaluation index RMSE between the model force calculated based on the Navier-Stokes equations and the prototype force is as follows: Furthermore, an efficient global optimization algorithm, EGO, consisting of the Kriging model and the desired improved EI criterion, is introduced to iteratively optimize the optimization index until the preset maximum number of iterations is reached or the Kriging model stably converges to its minimum value. The sample point with the smallest RMSE is selected from the resulting dataset as the optimal value of the optimization index, thus coordinating the wave forces of similar models. Approximating the wave forces corresponding to the prototype structure ; The introduction of the efficient global optimization EGO algorithm, which consists of the Kriging model and the desired improvement EI criterion, to iteratively optimize the optimization index until the preset maximum number of iterations is reached or the Kriging model stably converges to the minimum value, specifically includes the following steps: Step 1: Using the Kriging model, assume that the optimization index takes any value within the optimization interval. x The relationship with RMSE is used This means that the function can be written as: (2), where, Represents the mean of an unknown constant. Let the Gaussian random process with mean 0 satisfy: (3), (4), of which, Represents the mathematical expectation. Describing covariance, Indicates process variance. Represents sample points and The correlation function values between them, the commonly used Gaussian correlation function is written as: (5), among which, This refers to the relevant parameters, also called hyperparameters, when... and When approaching, Approaching 1; when and When they are far apart, Approaching 0; Step 2: Construct a correlation matrix using all sample points: (6), among which, express The sample correlation matrix, the first i Line number j Column elements are , For any optimization index value x, its correlation vector with all sample points is defined as: (7), among which, Indicates any value of the optimization index x The correlation column vector between the optimization index values and all known sample points; Combine existing sample points with any optimization index value x The corresponding function values are incorporated into the same probability model and written as: (8), among which, Represents a multivariate normal distribution. This represents the mean vector corresponding to the sample points; Step 3: In the Kriging model, Generalized least squares estimation is used: (9), among which, express The estimated value, A vector consisting entirely of 1s represents The column vector, i.e. , The process variance estimate is written as: (10), among which, Representing process variance The estimated value, This represents the deviation vector of the sample output relative to the mean; From the conditional distribution of the joint Gaussian distribution, we can obtain that any optimization index value can be... x The predicted mean at this location is: (11), among which, This indicates a local correction to the global mean based on existing samples; Similarly, based on the conditional Gaussian distribution, the prediction variance is: （12）； Step 4: Let the optimal value among the existing samples be: ,in The optimal sample is the one with the smallest known objective function value. For the RMSE of the i-th sample, for any value of the optimization index... x Its "improvement amount" is defined as: (13), among which, To optimize the value of any optimization index within the interval x The amount of improvement that can be obtained at this point, due to Since it is unknown, we use a Gaussian distribution established by Kriging to calculate its expectation: (14) Combining with step 1, we obtain the following under the Gaussian process assumption: Represented as: (15) The desired improved analytical expression is obtained as follows: (16), among which, The cumulative distribution function (CDF) of the standard normal distribution. PDF is the probability density function of the standard normal distribution. Step 5: Search the entire design space to find the point that maximizes EI. ; Step 6: At the newly selected point The calculations based on the Navier-Stokes equations were performed, and the corresponding RMSE was obtained. ; Step 7: Transfer the newly obtained sample points Incorporate into the initial sample point set, that is: (17) (18) to form an updated sample set and ; Step 8: Then repeat steps 1 to 7 until the preset maximum number of iterations is reached or the Kriging model stably converges to its minimum value. Finally, select the sample point with the smallest RMSE from the obtained dataset as the optimal value of the optimization index, thereby coordinating the wave forces of similar models. Approximating the wave forces corresponding to the prototype structure .
2. The optimization design method for a coordinated similarity model of marine structures in a wave environment according to claim 1, characterized in that, The structural information of the prototype structure and the scaled-down model includes geometric dimensions and material constitutive information, while the environmental information includes water depth and wave parameters.