An Optimization Method for the Surface Appendage Layout of an Autonomous Underwater Vehicle

Abstract

The present invention belongs to the technical field related to the optimization of the surface appendage layout of an underwater vehicle, and discloses a method for optimizing the surface appendage layout of an autonomous underwater vehicle, including the following steps: (1) constructing a parametric model of the appendages of the underwater vehicle; (2) constructing an optimization problem model; (3) constructing an automatic calculation framework for the objective function and a sample database; (4) using the global combined surrogate model to screen the best layout of the differential evolution algorithm population and putting the result into the database; (5) using the global combined surrogate model to screen the layout with the greatest uncertainty in the differential evolution population and putting the result into the database; (6) using an optimizer to search for the optimal solution of the local combined surrogate model and putting the result into the database; (7) judging whether the number of samples corresponding to the true function value reaches a preset value, thereby determining the best surface appendage layout or turning to step (4). The present invention reduces the number of calls to the simulation model and efficiently searches for the optimal layout design.

Description

Technical Field

[0001] The present invention belongs to the technical field related to the optimization of the surface appendage layout of an underwater vehicle, and more specifically, relates to a method for optimizing the surface appendage layout of an autonomous underwater vehicle. Background Art

[0002] As an underwater unmanned platform, an autonomous underwater vehicle has wide applications in the fields of ocean target tracking, ocean environment development, ocean resource exploration, etc. The vehicle relies on the energy carried by itself to complete the preset tasks, and requires it to have the characteristics of large range, long endurance, and high load. A body of revolution is a widely used shape for underwater vehicles. Due to the volume limitation of the vehicle, the amount of energy carried is limited, which restricts the mission execution time. Increasing the amount of energy carried will increase the volume and weight of the vehicle, increase the navigation resistance, and thus increase the energy consumption. By optimizing the layout of the surface appendages of the underwater vehicle, the navigation resistance can be reduced, and the effects of increasing the range and endurance can be achieved.

[0003] With the development of computational fluid dynamics (CFD), it has become a commonly used method to evaluate the advantages and disadvantages of the hydrodynamic layout of the underwater vehicle's shape by using computer simulation. Compared with empirical formulas, the CFD method can obtain accurate and reliable results. Although the simulation analysis using the CFD method is very effective, this process is time-consuming; when the optimization method calls the simulation model hundreds or thousands of times, it requires a large amount of computing resources, seriously affecting the product design cycle. Summary of the Invention

[0004] Aiming at the above defects or improvement requirements of the prior art, the present invention provides a method for optimizing the surface appendage layout of an autonomous underwater vehicle. The method establishes a parametric model of the distribution of appendages on the surface of the vehicle, representing the positions of the appendages on the surface of the vehicle. With the goal of minimizing the influence of the layout on the hydrodynamic performance of the vehicle, an optimization problem model is established, and an automatic simulation calculation framework is used to evaluate the quality of the appendage layout. The surrogate model-assisted evolutionary algorithm is used for optimization to obtain the optimal layout.

[0005] To achieve the above object, according to one aspect of the present invention, a method for optimizing the surface appendage layout of an autonomous underwater vehicle is provided. The method includes the following steps:

[0006] (1) Represent each appendage of the underwater vehicle using three-dimensional coordinates, and combine the variables representing the positions of the appendages together to form a design variable x = [x1, x2,..., x d , where x is a kind of appendage layout, and the upper and lower limits of each design variable are determined according to the actual situation, x i ∈[x l , x u ;

[0007] (2) Construct an optimization problem model with the minimum sailing resistance coefficient of the underwater vehicle as the optimization objective and the upper and lower limits of the design variables as the constraint conditions. The expression of this optimization problem model is as follows:

[0008] min C L =f(x)

[0009] s.t. x i ∈[x l , x u

[0010] i = 1, 2,..., d

[0011] In the formula, C L is the sailing resistance coefficient of the vehicle, obtained from simulation analysis, x is the design variable, and d is the number of variables;

[0012] (3) Construct an automatic calculation framework for the objective function. At the same time, generate N ini initial samples in the design space, use the automatic calculation framework of the objective function to calculate the corresponding objective function values, and put the samples and the corresponding function values into the database;

[0013] (4) Construct a global combined surrogate model, use the global combined surrogate model to screen the differential evolution algorithm population, and conduct a more optimal layout search. Select the individual with the minimum objective function value to calculate the true function value, and put the selected individual and the corresponding function value into the database;

[0014] (5) Use the global combined surrogate model to screen the layout with the greatest uncertainty in the differential evolution population for search, select the individual with the greatest uncertainty to calculate the true function value, and put the individual with the greatest uncertainty and the corresponding function value into the database;

[0015] (6) Construct a local combined surrogate model using a predetermined number of optimal samples, and use an optimizer to search for the optimal solution of the local combined surrogate model. Then, calculate the corresponding true function value for the optimal solution, and put the obtained optimal solution and the corresponding function value into the database;

[0016] (7) Judge whether the number of samples corresponding to the true function value in the current database reaches the preset value. If it reaches, the optimization process stops, and select the optimal sample in the database as the optimal surface appendage layout; otherwise, go to step (4).

[0017] ​Further, for each design variable x, using the secondary development technology of CAD software, an underwater vehicle outer shape geometric model is automatically generated. Using the script recording function of CAE software, the mesh generation steps and drag coefficient calculation steps of the geometric model are recorded to obtain an automatic calculation framework for the objective function, which is used to automatically output the objective function value of each design variable.

[0018] Further, step (4) includes the following sub-steps:

[0019] (41) Using all samples in the database as the initial modeling samples, a global combined surrogate model is constructed;

[0020] (42) Select n samples with the best layouts in the database to form the initial search population. The DE / best / 1 mutation strategy and binomial crossover strategy are used to generate offspring individuals. The mutation and crossover strategies are given by the following formula:

[0021] v i = x b + F·(x r1 - x r2 ) (4)

[0022]

[0023] In the formula, x b is the current best layout design, x r1 and x r2 are different layout designs randomly selected from the population, F is the scaling factor, and v i is the obtained mutant individual, that is, a kind of appendage layout design; As the j-th component of the individual after crossover, it comes from the j-th component of the mutant individual or the parent individual, and C r ∈[0,1] is the crossover probability factor;

[0024] (43) Use the global combined surrogate model to predict the offspring individuals, and select the design with a better layout among the corresponding individuals of the parent and offspring as the next generation population;

[0025] (44) Repeat steps (42) and (43) N times. Among the individuals in the last generation, select the individual with the smallest predicted function value to calculate the true function value, that is, calculate the drag coefficient of this layout, and put this individual and the corresponding true function value into the database.

[0026] Further, the construction of the global combined surrogate model includes the following sub-steps:

[0027] (411) Select m samples from the initial modeling samples using the sampling - with - replacement method. After removing duplicate samples, a set of training samples with the number m′ is formed, and the unselected samples are used as test samples;

[0028] (412) Repeat step (411) M times to obtain M sets of training samples and test samples;

[0029] (413) Use the M sets of training samples to establish corresponding RBF models, use the corresponding test samples to test the model accuracy, and select some models with high accuracy from them to establish a global combined surrogate model. The modeling form of the global combined surrogate model is:

[0030]

[0031]

[0032] In the formula, ||·|| is the Euclidean distance, represents the basis function, λ represents the basis - function coefficient, p(x) is a linear polynomial, and the predicted value of a layout design is the arithmetic average of the predicted values of M′ RBF models.

[0033] Further, step (5) includes the following sub - steps:

[0034] (51) Randomly select n samples from the database to form an initial search population. Use the DE / rand / 1 mutation strategy and the binomial crossover strategy to generate offspring individuals. The mutation strategy is given by the following formula:

[0035] v i =x r1 +F·(x r2 -x r3 ) (6)

[0036] In the formula, x r1 , x r2 and x r3 are different layout designs randomly selected from the current population;

[0037] (52) Use the global combined surrogate model to calculate the prediction variance of the offspring individuals and normalize it. The corresponding formula is:

[0038]

[0039]

[0040] (53) Calculate the minimum distance between the offspring individuals and the samples in the database and normalize it. Combine the two criteria of the normalized prediction variance and the minimum distance to form an uncertainty criterion. The corresponding expression is:

[0041]

[0042]

[0043]

[0044] where U(x) represents the uncertainty of an individual, and NFE represents the number of samples in the database;

[0045] (54) Compare the parent and offspring individuals, and retain the individuals with greater uncertainty as the next generation population; repeat steps (51) to (53) N times. Among the individuals in the last generation, select the individual with the greatest uncertainty for calculating the true function value, that is, calculate the drag coefficient corresponding to this layout, and put this individual and the true function value into the database.

[0046] Further, step (6) includes the following sub-steps:

[0047] (61) Use some of the best samples in the database as the initial modeling samples, and construct a local combined surrogate model;

[0048] (62) Use an optimizer to search for the optimal solution of the model, that is, the optimal appendage layout design, calculate the true function value for the appendage layout, and put the result into the database.

[0049] Further, use the optimal Latin hypercube design to generate N ini initial samples in the design space.

[0050] Further, in step (4), using RBF as the surrogate model, a global combined surrogate model is established by the Bagging method.

[0051] Generally speaking, compared with the prior art by the above technical solutions conceived by the present invention, the surface appendage layout optimization method for the autonomous underwater vehicle provided by the present invention mainly has the following beneficial effects:

[0052] 1. Parametrize the layout of the appendages on the surface of the underwater vehicle, represent a kind of appendage layout design with a set of design variables, and take the influence of the appendage layout on the hydrodynamic performance of the vehicle as the optimization goal to establish an optimization problem model.

[0053] 2. Use the surrogate model-assisted evolutionary algorithm to optimize the optimization problem, establish a global combined surrogate model to screen the evolutionary population, select the optimal and the most uncertain appendage layout designs, establish a local combined surrogate model, and use an optimizer to search for the optimal solution of the model, reducing the number of calls to the simulation model and efficiently searching for the optimal layout design. Description of the Drawings

[0054] Figure 1It is a schematic flow chart of the surface appendage layout optimization method for the autonomous underwater vehicle provided by the present invention;

[0055] Figure 2 It is a schematic diagram of the parametric layout of the surface appendages of the autonomous underwater vehicle;

[0056] Figure 3 It is a parametric schematic diagram of typical appendages;

[0057] Figure 4 It is a schematic flow chart of the calculation of hydrodynamic coefficients in the present invention;

[0058] Figure 5 It is a schematic modeling flow chart of the combined surrogate model of the present invention.

[0059] In all the drawings, the same reference numerals are used to represent the same elements or results, where: 1 - vehicle, 2 - side-scan sonar, 3 - antenna, 4 - hook, 5 - full-motion rudder. Detailed implementation manners

[0060] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0061] The surrogate model technology shows relatively obvious advantages in engineering optimization. As an approximate model, the surrogate model can establish the expression relationship between the design variables and the objective function. Select a certain number of samples in the design space, obtain the response values of the sample points through the simulation method, and rely on the samples and their response values to establish the surrogate model; for any input variable, the surrogate model can give its predicted value. The surrogate model optimization method is suitable for dealing with complex and expensive black-box problems, can reduce the number of calls to the simulation model, and improve the optimization efficiency of the problem. The surrogate model-assisted evolutionary algorithm combines the prediction ability of the surrogate model and the search ability of the evolutionary algorithm, and can obtain better designs under the condition of limited computing resources.

[0062] Please refer to Figure 1, the present invention provides a method for optimizing the surface appendage layout of an autonomous underwater vehicle. The method optimizes the parameters of the appendage layout on the vehicle surface, represents the positions of all appendages with design variables, takes the minimum influence of the appendage layout on the vehicle drag coefficient as the optimization goal, builds an automatic calculation framework for the objective function, conducts high-precision simulation on the quality of a layout, uses a surrogate model-assisted evolutionary algorithm to optimize the appendage layout, combines different levels of combined surrogate models to search for the optimal and most uncertain appendage layouts, reduces the number of calls to the simulation model, efficiently searches for the optimal layout design, solves the problem of optimal design of the surface appendages of the autonomous underwater vehicle, and obtains a better vehicle appendage layout under the condition of limited computing resources.

[0063] The method for optimizing the surface appendage layout design of the underwater autonomous vehicle provided by the present invention mainly includes the following steps:

[0064] Step 1, establish a parametric model of the appendages on the surface of the underwater vehicle.

[0065] Establish a three-dimensional coordinate system with the center of the head of the body of revolution as the origin. Each appendage can be represented by three-dimensional coordinates. Since the vehicle usually has symmetry, only one or two variables are needed to represent each type of appendage. Combine the variables representing the positions of the appendages together to form a design variable x = [x1, x2,..., x d , x is an appendage layout, and the upper and lower limits of each variable are determined according to the actual situation. x i ∈[x l , x u .

[0066] Step 2, establish an optimization problem model.

[0067] In the problem of optimizing the appendage layout design, the shape of each appendage is fixed, and only the layout design of the appendages on the vehicle surface needs to be considered. The optimization goal is to minimize the vehicle's navigation drag coefficient, and the constraint condition is the upper and lower limits of the design variables. The optimization problem can be summarized as:

[0068]

[0069] where C L is the vehicle's navigation drag coefficient, obtained by simulation analysis, x is the design variable, and d is the number of variables.

[0070] Step 3, construct an automatic calculation framework for the objective function.

[0071] For each design variable x, using the secondary development technology of CAD software, an underwater vehicle's external geometric model is automatically generated. Using the script recording function of CAE software, the mesh generation steps and drag coefficient calculation steps of the geometric model are recorded, and the objective function value of each design variable is automatically output.

[0072] Step 4, initialize the optimization process.

[0073] Using the Optimal Latin Hypercube Design (OLHD) to generate N ini initial samples in the design space, that is, N ini types of appendage layout designs; automatically calculate the corresponding objective function values of the framework using the objective function, that is, the vehicle's external drag coefficient, and put the samples and function values into the database.

[0074] Step 5, using the radial basis function as the surrogate model, adopt the Bagging method to establish a combined surrogate model, which specifically includes the following steps:

[0075] Step 5.1, select a certain number of samples (m) from the database as the initial modeling samples, and the number m is selected according to the modeling requirements of the surrogate model.

[0076] Step 5.2, use the sampling method with replacement to select m samples from the initial samples, and form a set of training samples with a quantity of m′ after removing duplicate samples. The unselected samples are used as test samples.

[0077] Step 5.3, repeat Step 5.2 M times to obtain M groups of training samples and test samples.

[0078] Step 5.4, use the M groups of training samples to establish the corresponding RBF models, use the corresponding test samples to test the model accuracy, and select the partial models with higher accuracy (M′) from them to establish a combined surrogate model. The modeling form of the combined surrogate model is:

[0079]

[0080]

[0081] where ||·|| is the Euclidean distance, represents the basis function, λ represents the basis function coefficient, p(x) is a linear polynomial, and the predicted value of a layout design is the arithmetic mean of the predicted values of M′ RBF models.

[0082] Step 6, use the global combined surrogate model to screen the differential evolution algorithm population and conduct a search for a better layout. Specifically, it includes the following steps:

[0083] Step 6.1, use all the samples in the database as the initial modeling samples, and establish a global combined surrogate model according to Step 5.

[0084] Step 6.2, Select n samples with the best layouts from the database to form the initial search population. Use the "DE / best / 1" mutation strategy and the binomial crossover strategy to generate offspring individuals. The mutation and crossover strategies are given by the following formula:

[0085] v i = x b + F · (x r1 - x r2 ) (4)

[0086]

[0087] In the formula, x b is the current best layout design, x r1 and x r2 are different layout designs randomly selected from the population. F is the scaling factor, and v i is the obtained mutant individual, that is, a kind of attachment layout design; As the j-th component of the individual after crossover, it comes from the j-th component of the mutant individual or the parent individual. C r ∈ [0, 1] is the crossover probability factor.

[0088] Step 6.3, Use the global combined surrogate model to predict the offspring individuals. Select the design with a better layout among the corresponding individuals of the parent and offspring as the next generation population. Repeat Step 6.2 and Step 6.3 N times. In the last generation of individuals, select the individual with the smallest predicted function value to calculate the true function value, that is, calculate the drag coefficient of this layout. Put this individual and the true function value into the database.

[0089] Step 7, Use the global combined surrogate model to screen the differential evolution population to search for layout designs with greater uncertainty, specifically including the following steps:

[0090] Step 7.1, Randomly select n samples from the database to form the initial search population. Use the "DE / rand / 1" mutation strategy and the binomial crossover strategy to generate offspring individuals. The crossover strategy is given by Equation (5), and the mutation strategy is given by the following formula:

[0091] v i = x r1 + F · (x r2 - x r3 ) (6)

[0092] In the formula, x r1 , x r2 and x r3 are different layout designs randomly selected from the current population.

[0093] Step 7.2: Calculate and normalize the prediction variance of the offspring individuals using the global combined surrogate model constructed in Step 6.1, which is given by the following formula:

[0094]

[0095]

[0096] Step 7.3: Calculate and normalize the minimum distance between the offspring individuals and the samples in the database, and combine the two criteria of the normalized prediction variance and the minimum distance to form an uncertainty criterion. The corresponding expression is:

[0097]

[0098]

[0099]

[0100] In the formula, U(x) represents the uncertainty of the individual, and NFE represents the number of samples in the database.

[0101] Step 7.4: Compare the parent and offspring individuals, and retain the individuals with greater uncertainty as the next generation population; repeat Steps 7.1 to 7.3 N times. Among the individuals in the last generation, select the individual with the greatest uncertainty to calculate the true function value, that is, calculate the drag coefficient corresponding to this layout, and put this individual and the true function value into the database.

[0102] Step 8: Establish a local combined surrogate model using a certain number of optimal samples, and use an optimizer to search for the optimum of the local combined surrogate model, which specifically includes the following steps:

[0103] Step 8.1: Use some of the best samples in the database as the initial modeling samples, and establish a local combined surrogate model according to Step 5.

[0104] Step 8.2: Use an optimizer to search for the optimal solution of the model, that is, the optimal appendage layout design, calculate the true function value of the appendage layout, and put the result into the database.

[0105] Step 9: During the optimization process, Steps 6 - 8 are carried out in sequence, and a new layout design and the corresponding function value are obtained respectively. When the number of true samples reaches the preset value, the optimization process stops, and the optimal sample in the database is selected as the best sample layout design; otherwise, return to Step 6, update the relevant data and model, and continue the optimization.

[0106] The following uses specific embodiments to further elaborate on the present invention in detail.

[0107] Please refer to Figure 2 、 Figure 3 、Figure 4 and Figure 5 An optimization method for the surface appendage layout of an underwater vehicle provided by an embodiment of the present invention mainly includes the following steps:

[0108] Step 1: Establish a parametric model of the appendages on the surface of the vehicle. Taking the head center of the rotating body as the origin, establish a three-dimensional coordinate system as shown in Figure 2 . The x-axis is the axis direction of the vehicle, and the y-axis and z-axis are the radial directions of the vehicle. The appendages of the vehicle 1 in the example include side-scan sonar 2, antenna 3, hook 4, and full-moving rudder 5. Among them, the number of side-scan sonars is 2, located on the abdomen of the vehicle, symmetrically distributed about the xz plane; the number of hooks is 2, used for the release and recovery of the vehicle, and the number of full-moving rudders is 4, symmetrically distributed. Figure 3 Parametrize the appendage positions, and uniquely represent the positions of the appendages with a set of variables; the hooks, antenna, and full-moving rudders can only vary along the x-axis, and their positions can be represented by x1, x2, x3, x4, all of which are the centroid positions of the appendages along the x direction; the side-scan sonar is located on the abdomen of the vehicle, parallel to the x-axis, and the position of its bottom center in the coordinate system can be represented by two components x5 and x6. The range of each variable component is determined according to the design situation. The units of the first five components are mm, and the unit of the sixth component is rad.

[0109] Step 2: Establish an optimization problem model. The number of design variables is 6, the optimization goal is to minimize the navigation resistance, and the constraint conditions are the upper and lower limits of the design variables; the navigation speed is 5 knots, and the navigation angle of attack is 2°.

[0110] Step 3: Build an automatic calculation framework for the objective function. For each design variable x, automatically output its function value. Using UG secondary development technology, automatically generate the corresponding geometric model of the vehicle's shape; use the ICEM CFD script recording function to record the mesh generation steps of the geometric model, and use the ANSYS CFX script recording function to record the calculation steps of the vehicle's shape resistance coefficient. The automatic calculation process is as shown in Figure 4 .

[0111] Step 4: Use the optimal Latin hypercube design (OLHD) to generate N ini initial samples in the design space, and obtain N ini appendage layout designs; use Step 3 to calculate the objective function values corresponding to each sample, that is, the shape resistance coefficient of the vehicle, and put the samples and function values into the database.

[0112] Step 5: Use RBF as the surrogate model and adopt the Bagging method to establish a combined surrogate model. The modeling process is as shown in Figure 5As shown in the figure. A certain number of samples are selected from the database using the sampling-with-replacement method for sampling M times to obtain corresponding training samples and test samples; the RBF model is trained using the training samples, and the model is tested using the test samples, and M' models with higher accuracy are selected from them to establish a combined surrogate model; the drag coefficient of each vehicle layout is the average of the M' predicted values.

[0113] Step 6: Use the global combined surrogate model to screen the differential evolution population and search for a better appendage layout; select n best samples from the database as the initial population, and use the "DE / best / 1" mutation strategy and the binomial crossover strategy to generate offspring individuals; select better individuals as the next generation population using the predicted values of the global combined model; after evolving N generations, select the individual with the smallest predicted function value for real value calculation and put the data into the database.

[0114] Step 7: Use the global combined surrogate model to screen the differential evolution population and search for an appendage layout with greater uncertainty; randomly select n samples from the database as the initial population, and use the "DE / rand / 1" mutation strategy and the binomial crossover strategy to generate offspring individuals; use a uncertainty criterion formed by the normalized predicted variance and the minimum distance of the global combined surrogate model to screen the next generation population; after evolving N generations, select the individual with the greatest uncertainty for real value calculation and put the data into the database.

[0115] Step 8: Establish a local combined surrogate model using a certain number of optimal samples, use the Fmincon optimizer to search for the optimal solution of the local combined surrogate model, that is, the optimal appendage layout, calculate the real function value of the appendage layout, and put the corresponding data into the database.

[0116] Step 9: During the optimization process, Steps 6, 7, and 8 are carried out in sequence, and a new layout design and the corresponding function value are obtained respectively; when the number of real samples reaches the preset value, the optimization process stops, and the optimal sample in the database is selected as the best appendage layout design, otherwise return to Step 6, update the relevant data and models, and continue the optimization.

[0117] Those skilled in the art can easily understand that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An optimization method for the surface attachment layout of an autonomous underwater vehicle, characterized in that, The method includes the following steps: (1) Represent each appendage of the underwater vehicle using three-dimensional coordinates, and combine the variables representing the appendage positions together to form a design variable \(x = [x_1, x_2,\cdots, x d \), where \(x\) is an appendage layout. The upper and lower limits of each design variable are determined according to the actual situation, and \(x i \in[x l , x u ; (2) Taking the minimum navigation resistance coefficient of the underwater vehicle as the optimization objective and the upper and lower limits of the design variables as the constraint conditions to construct an optimization problem model. The expression of the optimization problem model is: min C L = f(x) s.t.x i ∈[x l ,x u ​ i = 1, 2,..., d where C L is the navigation resistance coefficient of the vehicle, obtained from simulation analysis, x is the design variable, and d is the number of variables; (3)Construct an automatic calculation framework for the objective function, and at the same time generate N ini initial samples in the design space, use the automatic calculation framework of the objective function to calculate the corresponding objective function values, and put the samples and the corresponding function values into the database; (4) Constructing a global combined surrogate model, using the global combined surrogate model to screen the differential evolution algorithm population, and conducting a more optimal layout search. Select the individual with the minimum objective function value to calculate the true function value, and put the selected individual and the corresponding function value into the database; (5) Using the global combined surrogate model to screen the layout with the greatest uncertainty in the differential evolution population for search, select the individual with the greatest uncertainty to calculate the true function value, and put the individual with the greatest uncertainty and the corresponding function value into the database; (6) Using a predetermined number of optimal samples to construct a local combined surrogate model, and using an optimizer to search for the optimal solution of the local combined surrogate model. Then, calculate the corresponding true function value for the optimal solution, and put the obtained optimal solution and the corresponding function value into the database; (7) Judging whether the number of samples corresponding to the true function value in the current database reaches a preset value. If it reaches, the optimization process stops, and the optimal sample in the database is selected as the optimal surface attachment layout; otherwise, go to step (4).

2. The surface appendage layout optimization method of the autonomous underwater vehicle according to claim 1, wherein: For each design variable x, using the secondary development technology of CAD software to automatically generate the corresponding underwater vehicle external geometric model, and using the script recording function of CAE software to record the mesh generation steps and resistance coefficient calculation steps of the geometric model to obtain an automatic calculation framework for the target function. The automatic calculation framework for the target function is used to automatically output the target function value of each design variable.

3. The surface appendage layout optimization method for an autonomous underwater vehicle according to claim 1, characterized in that: Step (4) includes the following sub-steps: (41) Taking all samples in the database as the initial modeling samples to construct a global combined surrogate model; (42) Selecting n samples with the best layout in the database to form an initial search population, and using the DE / best / 1 mutation strategy and binomial crossover strategy to generate offspring individuals. The mutation and crossover strategies are given by the following formula: v i = x b + F·(x r1 - x r2 ) (4) where x b is the current best layout design, x r1 and x r2 are different layout designs randomly selected from the population, F is the scaling factor, v i is the obtained mutant individual, i.e., a kind of attachment layout design; As the j-th component of the individual after crossover, it comes from the j-th component of the mutant individual or the parent individual, C r ∈[0,1] is the crossover probability factor; (43) Using the global combined surrogate model to predict the offspring individuals, and selecting the design with a better layout in the corresponding individuals of the parent and offspring as the next generation population; (44) Repeating steps (42) and (43) N times. Among the individuals in the last generation, select the individual with the minimum predicted function value to calculate the true function value, that is, calculate the resistance coefficient of this layout, and put this individual and the corresponding true function value into the database.

4. The method for optimizing the surface appendage layout of the autonomous underwater vehicle according to claim 3, characterized in that: The construction of the global combined surrogate model includes the following sub-steps: (411) Using the sampling method with replacement to select m samples from the initial modeling samples, removing the repeated samples to form a set of training samples with a quantity of m′, and the unselected samples are used as test samples; (412) Repeating step (411) M times to obtain M sets of training samples and test samples; (413) Using M sets of training samples to establish the corresponding RBF model, using the corresponding test samples to test the model accuracy, and selecting the partial models with high accuracy from them to establish a global combined surrogate model. The modeling form of the global combined surrogate model is: where ||·|| is the Euclidean distance, represents the basis function, λ represents the basis function coefficient, p(x) is a linear polynomial, and the predicted value of a layout design is the arithmetic mean of the predicted values of M' RBF models.

5. The surface appendage layout optimization method for an autonomous underwater vehicle according to claim 3, wherein: Step (5) includes the following sub-steps: (51) Randomly select \(n\) samples from the database to form the initial search population. Use the DE / rand / 1 mutation strategy and binomial crossover strategy to generate offspring individuals. The mutation strategy is given by the following formula: v i = x r1 + F·(x r2 - x r3 ) (6) where x r1 , x r2 and x r3 are different layout designs randomly selected from the current population; (52) Calculate the predicted variance of the offspring individuals using the global combined surrogate model and normalize it. The corresponding formula is: (53) Calculate the minimum distance between the offspring individuals and the samples in the database and normalize it. Combine the two criteria of the normalized predicted variance and the minimum distance to form an uncertainty criterion. The corresponding expression is: In the formula, \(U(x)\) represents the uncertainty of an individual, and \(NFE\) represents the number of samples in the database; (54) Compare the parent and offspring individuals, and retain the individuals with greater uncertainty as the next generation population. Repeat steps (51) to (53) \(N\) times. Among the individuals in the last generation, select the individual with the greatest uncertainty to calculate the true function value, that is, calculate the drag coefficient corresponding to this layout. Put this individual and the true function value into the database.

6. The method for optimizing the surface appendage layout of the autonomous underwater vehicle according to claim 5, characterized in that: (6) The steps include the following sub-steps: (61) Use some of the best samples in the database as the initial modeling samples and construct a local combined surrogate model; (62) Use the optimizer to search for the optimal solution of the model, that is, the optimal appendage layout design. Calculate the true function value of the appendage layout and put the result into the database.

7. The surface appendage layout optimization method for an autonomous underwater vehicle according to any one of claims 1-6, characterized in that: Generate N initial samples in the design space using the optimized Latin hypercube design ini samples.

8. The method for optimizing the surface appendage layout of an autonomous underwater vehicle according to any one of claims 1-6, characterized in that: (4) In step (4), use RBF as the surrogate model and adopt the Bagging method to establish a global combined surrogate model.

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