Multi-objective optimization design method for layout shape of UUV fin rudder

Abstract

The invention discloses a UUV fin rudder layout appearance multi-objective optimization design method, and particularly relates to the field of underwater vehicle design. Comprising the following steps: taking shape parameters of a fin rudder as variables to be optimized, and establishing an objective function and constraint conditions; building a real function calculation framework; taking the initial value of the design variable as an initial sample, and constructing a first set with the initial target value; constructing a second set by using non-dominated solutions in the initial sample; establishing an RBF proxy model by using the samples in the first set and the objective function value; sequentially executing a constraint domain search strategy, a convergence exploration strategy and a diversity improvement strategy in a multi-objective evolutionary algorithm based on the RBF proxy model to obtain a potential global optimal solution set; and when the potential global optimal solution set reaches a first preset condition, outputting the potential global optimal solution set as the most expected solution set. The calling times of the real function can be effectively reduced, so that the calculation cost of simulation optimization is reduced.

Description

Technical Field

[0001] This application relates to the field of underwater vehicle shape design, and particularly to a multi-objective optimization design method for the shape of a UUV fin-rudder layout. Background Art

[0002] Unmanned Underwater Vehicles (UUVs) are widely used in scenarios such as seabed mapping, marine environment monitoring, marine resource development, and underwater obstacle search and positioning. The fin-rudder layout form of a UUV is an important part of the entire design process and is an intuitive manifestation of the UUV's shape characteristics. At the same time, the quality of the fin-rudder layout design directly determines the hydrodynamic performance and navigation characteristics of the UUV. Traditional UUV shape optimization design is driven by numerical simulation methods such as CFD analysis and directly outputs results. However, since CFD simulation calculations are very time-consuming and the simulation analysis needs to be repeatedly called for comprehensive evaluation during the optimization process, the computational cost generated by the simulation-driven optimization method is extremely high and the computational efficiency is significantly reduced. Summary of the Invention

[0003] The main purpose of this application is to provide a multi-objective optimization design method for the shape of a UUV fin-rudder layout, aiming to solve the problem of reduced computational efficiency caused by excessive calls to simulation analysis in existing methods.

[0004] To achieve the above object, this application provides a multi-objective optimization design method for the shape of a UUV fin-rudder layout, including: Step 1, taking the shape parameters of the fin-rudder as variables to be optimized, establishing an objective function, where the objective function includes the equilibrium angle of attack and the equilibrium rudder angle, and using the longitudinal dynamic stability of the UUV as a constraint condition; Step 2, generating initial variables to be optimized, performing real function calculations on the initial variables to be optimized to obtain real objective values, and updating the number of real function calculations; where the objective values include objective function values and constraint condition values; Step 3, taking the initial variables to be optimized as initial samples, and constructing a first set with the corresponding real objective values; constructing a second set using the non-dominated solutions in the initial samples; Step 4, establishing an RBF surrogate model using the samples in the first set and the corresponding real objective values; Step 5, taking all non-dominated solutions in the second set as the initial population; Step 6, according to the real objective values and predicted objective values, performing a convergence exploration strategy on the initial population to determine potentially better individuals; where the predicted objective values are predicted through the RBF surrogate model; Step 7, performing a diversity improvement strategy on the potentially better individuals to obtain a potentially globally optimal solution set; Step 8, when it is determined that the potentially globally optimal solution set meets the first preset condition, outputting the potentially globally optimal solution set as the most promising solution set.

[0005] Optionally, step 8 includes: performing a true function calculation on the samples in the potential global optimal solution set that have not undergone a true function calculation to obtain true objective values, and updating the number of true function calculations; when it is determined that the number of true function calculations reaches a preset number value, outputting the potential global optimal solution set as the most promising solution set.

[0006] Optionally, step 5 further includes: when it is determined that there is no feasible solution in the second set, performing a constrained domain search strategy on the space composed of the samples in the first set to obtain a local optimal solution; step 7 further includes, after obtaining the potential global optimal solution set: adding the local optimal solution to the potential global optimal solution set; step 8 includes: performing a true function calculation on the samples in the potential global optimal solution set that have not undergone a true function calculation to obtain true objective values, and updating the number of true function calculations; when it is determined that the number of true function calculations reaches a preset number value, outputting the potential global optimal solution set as the most promising solution set.

[0007] Optionally, performing a constrained domain search strategy on the space composed of the samples in the first set includes: determining the constraint violation values of each sample in the first set according to the constraint condition values, and selecting the individual with the smallest constraint violation value as the base point; calculating the Euclidean distances between the remaining individuals in the first set and the base point, sorting [constraint violation value, -Euclidean distance] in ascending order, and determining the potential space according to the constraint violation value or the Euclidean distance; using the sequential quadratic programming algorithm to locate the feasible domain in the potential space, and combining the multi-start search strategy to search for the local optimal solution.

[0008] Optionally, step 8 further includes, when it is determined that the number of true function calculations has not reached the preset number value, adding the evaluated true objective values and the corresponding samples to the first set, performing non-dominated sorting on the samples in the first set based on the true objective values, and updating the second set; returning to step 4 until the potential global optimal solution set meets the first preset condition.

[0009] Optionally, in step 8, when it is determined that the number of samples that have not undergone a true function calculation is 0, forming a number of new samples based on the optimized Latin hypercube sampling method, performing a true function calculation on the new samples to obtain true objective values, and updating the number of true function calculations.

[0010] Optionally, the fin-rudder shape parameters include the chord length of the fin plate, the distance from the leading edge of the fin to the head of the UUV, the chord length of the rudder plate, the distance from the leading edge of the rudder to the head of the UUV, the leading edge and trailing edge angle of the fin plate, and the leading edge and trailing edge angle of the rudder plate.

[0011] Optionally, the real function calculation is obtained by calling an automatic simulation framework. The simulation method of the automatic simulation framework includes: determining the profile points of the upper and lower surfaces of the fin rudder according to the input variables to be optimized; using the profile points of the upper and lower surfaces of the fin rudder to establish a UUV geometric model and generate a flow domain model; on the flow domain model, determining the hydrodynamic parameters of the UUV at different angles of attack, different rudder angles, and different non-dimensional angular velocities respectively; wherein, the hydrodynamic parameters include lift coefficient and pitching moment coefficient; respectively determining the position derivatives of the hydrodynamic parameters with respect to the angle of attack and the rudder angle, and determining the rotational derivatives of the hydrodynamic parameters with respect to the non-dimensional angular velocity, and determining the objective function value according to the position derivatives of the hydrodynamic parameters with respect to the angle of attack and the rudder angle; determining the constraint condition value according to the rotational derivative.

[0012] Optionally, step 6 includes: step 6.1, taking the initial population as the parental individuals; step 6.2, generating offspring individuals by using the parental individuals, and determining the objective values of the offspring individuals by using the RBF surrogate model, and forming a new population by fusing the parental individuals and the offspring individuals; step 6.3, normalizing the population by using the objective values of the new population and determining the convergence index of each individual; step 6.4, generating a set of uniformly distributed reference vector sets; step 6.5, determining the angles between the individuals of the current population and each reference vector, and performing an association operation on the individuals and the nearest adjacent reference vectors; step 6.6, determining the constraint violation value and the convergence index according to the objective values of the individuals, and performing non-dominated sorting on the individuals associated with the reference vectors by using the constraint violation value and the convergence index, and taking the individual with the smallest constraint violation value or convergence index as the next-generation parental individuals; step 6.7, returning to step 6.2 until a second preset condition is reached to obtain potentially better individuals.

[0013] Optionally, step 7 includes: determining the number of non-dominated solutions among the potentially better individuals. When it is determined that the number of non-dominated solutions is less than the preset value, taking all non-dominated solutions as new samples; when it is determined that the number of non-dominated solutions is greater than the preset value, performing secondary selection among all non-dominated solutions by using the maximum penalty angle, and taking the selection result as new samples.

[0014] Compared with the prior art, the beneficial effects of the present application are as follows:

[0015] The multi-objective optimization design method for the UUV fin-rudder layout shape takes the airfoils of the fins and rudders and the relative positions of the fins and rudders as design variables, models the UUV body, fins and rudders, takes the minimum balanced angle of attack and balanced rudder angle of the UUV as the design objectives, and the longitudinal dynamic stability as the constraint condition, and builds an automatic simulation calculation framework for the hydrodynamic force of the UUV shape; combined with the surrogate-assisted constrained multi-objective evolutionary algorithm to optimize the design variables. During the optimization process, the surrogate-assisted prediction of the objective function and constraint conditions reduces the number of CFD simulations, and can obtain a UUV fin-rudder shape with excellent comprehensive performance under a limited number of real function calculations, improving the efficiency of the UUV fin-rudder shape design. Brief Description of the Drawings

[0016] Figure 1 It is a schematic flow chart of a multi-objective optimization design method for the UUV fin-rudder layout shape of this application;

[0017] Figure 2 It is an external view of the fin and rudder of an underwater vehicle in an embodiment of a multi-objective optimization design method for the UUV fin-rudder layout shape of this application.

[0018] The realization, functional features and advantages of the purpose of this application will be further described in conjunction with the embodiments with reference to the drawings. Detailed Embodiments

[0019] To make the purpose, technical solutions and advantages of this application clearer, the technical solutions in this application will be clearly and completely described below in conjunction with the drawings in this application. Obviously, the described embodiments are part of the embodiments of this application, rather than all of them. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of this application.

[0020] The first embodiment of the present invention provides a multi-objective optimization design method for the UUV fin-rudder layout shape, as Figure 1 shown, specifically including the following steps:

[0021] Step 1: Take the shape parameters of the fin and rudder as the variables to be optimized, establish objective functions respectively. The objective functions include the balanced angle of attack and the balanced rudder angle, and take the longitudinal dynamic stability of the UUV as the constraint condition;

[0022] Among them, the fin-rudder shape parameters include the chord length L of the fin plate F , the distance R1 from the leading edge of the fin to the head of the UUV, the chord length R of the rudder plate F , the distance R2 from the leading edge of the rudder to the head of the UUV, the leading-edge trailing-edge angle x0 of the fin plate and the leading-edge trailing-edge angle x1 of the rudder plate. Then the variables to be optimized X = [L F , R1, R F, R2, x0, x1]; The objective function and constraints are as follows:

[0023] Minimize f m (X) for m = 1, 2;

[0024] subject to -g(X) < 0

[0025] g(X) - 1 < 0

[0026] where X is the variable to be optimized; f m (X) is the objective function, representing the equilibrium angle of attack when m = 1 and the equilibrium rudder angle when m = 2; g(X) is the constraint.

[0027] Step 2: Generate the initial variable to be optimized, perform real - function calculations on the initial variable to be optimized to obtain the real objective values, where the objective values include the objective - function value and the constraint values, and update the real - function calculation times. The real - function calculation times NFE = NFE0. Among them, the real - function calculation is obtained by calling the automatic simulation framework, and the automatic simulation framework is the UUV external - shape hydrodynamic real - function calculation framework, which can realize inputting the variable to be optimized X, automatically performing hydrodynamic simulation, extracting hydrodynamic parameters, and calculating f m (X) and g(X). Step 2 specifically includes the following steps:

[0028] Step 2.1, use the optimized Latin - hypercube sampling to generate the initial variable to be optimized, that is, the fin - rudder shape parameters;

[0029] Step 2.2, input the initial variable to be optimized into the automatic simulation framework to obtain the real objective values. The specific steps are as follows:

[0030] Step 2.2.1, through the MATLAB programming software, determine the profile points of the upper and lower surfaces of the fin - rudder according to the fin - rudder shape parameters;

[0031] Step 2.2.2, use the profile points of the upper and lower surfaces of the fin - rudder, call the CAD secondary - development technology to establish the UUV geometric model, generate the flow - domain model, perform mesh division on the flow - domain model, and appropriately encrypt the mesh in the fin - rudder area;

[0032] Step 2.2.3, on the mesh elements of the flow - domain model, respectively determine the hydrodynamic parameters of the UUV at different angles of attack, different rudder angles, and different non - dimensional angular velocities; among them, the hydrodynamic parameters include the lift coefficient and the pitching - moment coefficient;

[0033] Step 2.2.4: Determine the position derivative of the lift coefficient with respect to the angle of attack, and determine the position derivative of the lift coefficient with respect to the rudder angle; determine the position derivative of the pitching moment coefficient with respect to the angle of attack, and determine the position derivative of the pitching moment coefficient with respect to the rudder angle; determine the rotational derivative of the lift coefficient with respect to the non-dimensional angular velocity, and determine the rotational derivative of the pitching moment coefficient with respect to the non-dimensional angular velocity; according to the position derivatives and rotational derivatives obtained above, correspondingly determine the longitudinal dynamic stability (i.e., the constraint condition value) and the objective function value, and the specific formulas are as follows:

[0034] The calculation formulas for the equilibrium angle of attack f1(X) and the equilibrium rudder angle f2(X) are:

[0035]

[0036] In the formula, ΔG is the negative buoyancy of the UUV, and G is the gravity of the UUV; is the relative longitudinal distance between the center of gravity and the center of buoyancy. If the center of gravity is in front of the center of buoyancy, it is positive; is the position derivative of the pitching moment coefficient with respect to the rudder angle, is the position derivative of the lift coefficient with respect to the rudder angle, is the position derivative of the pitching moment coefficient with respect to the angle of attack, is the position derivative of the lift coefficient with respect to the angle of attack;

[0037] The calculation formula for the longitudinal dynamic stability g(X) is:

[0038]

[0039] In the formula, is the relative density; C x is the drag coefficient, with the maximum cross-sectional area S of the UUV as the characteristic area; is the rotational derivative of the lift coefficient with respect to the non-dimensional angular velocity; is the rotational derivative of the pitching moment coefficient with respect to the non-dimensional angular velocity.

[0040] Step 3: Use the initial variables to be optimized as the initial samples, and construct the first set with the corresponding true target values; use the non-dominated solutions in the initial samples to construct the second set;

[0041] Specifically, a first set is constructed using the initial samples and the initial target values; the initial samples are non-dominated sorted according to the dominance relationship to obtain the Pareto non-dominated solution set, i.e., the second set. Specifically, if sample A is superior to sample B in at least one objective or constraint and is not worse than sample B in all objectives and constraints, then sample A dominates sample B. The dominance levels of the sample points in the sample library are divided according to the dominance relationship, and a Pareto non-dominated solution set from the sample points to the dominance levels is established according to the sorting results of the sample points. The Pareto non-dominated solution set consists of the sample points with a dominance level of 1, and this solution set is called the Pareto front.

[0042] Step 4: Establish an RBF surrogate model using the samples in the first set and the corresponding true target values;

[0043] Step 5: Use the non-dominated solutions in the second set as the initial population; and when it is determined that there are no feasible solutions in the second set, in combination with the constraint conditions, perform a constraint domain search strategy on the space formed by all the samples in the first set. When a feasible solution is found, the constraint domain search strategy stops, and the local optimal solution Local is obtained;

[0044] Among them, the constraint domain search strategy uses a space reduction method to reduce the search range of the domain, which can improve the search efficiency of feasible solutions. The constraint domain search strategy specifically includes:

[0045] Determine the constraint violation values of each sample in the first set according to the constraint conditions, and select the individual with the smallest constraint violation value as the base point; the definition of the constraint violation value (CV) is:

[0046]

[0047] In the formula, g j (x) and h k (x) are the j inequality constraints and the k equality constraints respectively.

[0048] In the fin-rudder layout optimization problem, there are only inequality constraint conditions, so the specific calculation method of the CV value is as follows:

[0049] CV(x) = max{0, -g(x)} + max{0, g(x) - 1}

[0050] Calculate the Euclidean distance between the remaining individuals in the first set and the base point as I1; the CV values of the remaining individuals are marked as I2. Sort [I2, -I1] in ascending order, that is, first sort in ascending order according to the CV value. When the CV values are the same, select the individual with a larger Euclidean distance. Finally, select the first Number2 individuals with smaller CV values or larger Euclidean distances (when the CV values are equal). Mark the range of these selected individuals as the potential space;

[0051] Determine the feasible solution in the potential space by combining the sequential quadratic programming (SQP) algorithm and the multi-start search strategy. Combining the multi-start search strategy to determine the feasible solution can prevent the SQP algorithm from falling into a local optimum. The multi-start search strategy is specifically as follows: In the potential space, use the Latin sampling method to sample multiple starting points and start searching for the feasible solution simultaneously.

[0052] Step 6: Execute the convergence exploration strategy on the initial population to determine potentially better individuals; among them, during the execution process, obtain the predicted objective value of the individual through the RBF surrogate model; the specific steps are as follows:

[0053] Step 6.1: Take the initial population as the parental individuals.

[0054] Step 6.2: Generate offspring individuals using the parental individuals, and use the RBF surrogate model to determine the objective values of the offspring individuals. Combine the parental individuals and the offspring individuals to form a new population.

[0055] Step 6.3: Perform population normalization using the objective function values of the new population and determine the convergence index for each individual; the calculation formula for the convergence index CI is:

[0056]

[0057] In the formula, f i (x) - z i * is the conversion value of the objective function value for each individual, and z i * = min{f i (x)|x ∈ P}, which refers to the minimum value of each objective function in the current population.

[0058] The detailed steps of population normalization are as follows:

[0059] (i) Calculate the ideal point: The ideal point refers to the minimum value of each objective function value in the current population. For each objective function f i , the ideal point is calculated as follows: where P is the current population.

[0060] (ii) Calculate the extreme point: The extreme point refers to the point that is farthest along each objective function direction in the objective space. These points are used to construct a hyperplane for normalization. For each objective function f i , find the individual x that maximizes f i (x).

[0061] (iii) Construct a hyperplane: Use the extreme points to construct a hyperplane that will be used to normalize the objective function values. The equation of the hyperplane can be determined by the coordinates of the extreme points. Using the hyperplane equation, the intercept a of the hyperplane on each objective can be obtained. i .

[0062] (iv) Normalize the objective function values: Normalize the objective function value f i (x) of each individual to the same scale. The normalization formula is usually:

[0063] Step 6.4: Generate a set of reference vectors that cover the entire objective function space; specifically, the number of vectors is where M is the number of objective functions and H is the number of parts into which the objectives are divided. The magnitude of each value in the vector coordinates can be where j is the j-th objective. And the vector coordinates should satisfy For example, there are 2 objective functions in this problem. If each objective is divided into 5 parts, the number of vectors should be vectors. The magnitude of each value in the vector coordinates can be S j ∈ {0, 0.2, 0.4, 0.6, 0.8, 1}, and the sum should be 1. For example, 6 reference vectors are: (0, 1), (1, 0), (0.2, 0.8), (0.8, 0.2), (0.4, 0.6), (0.6, 0.4).

[0064] Step 6.5: Determine the angle between the individuals in the current population and each reference vector, and perform an association operation between the individual and the nearest (with the smallest angle) reference vector.

[0065] Step 6.6: Use the constraint violation value and the convergence index to perform a non-dominated sorting on the individuals associated with the reference vectors, and take the individual with the smallest constraint violation value or convergence index as the parent of the next generation; the sorting process is as follows:

[0066]

[0067] Step 6.7: Return to Step 6.2 until the second preset condition is reached to obtain potentially better individuals. Among them, the second preset condition can be the preset number of loops.

[0068] Step 7: Perform a diversity improvement strategy on the potentially better individuals to obtain a set of potentially global optimal solutions; in another embodiment, that is, when there is no feasible solution in the second set in Step 5, add the local optimal solution to the set of potentially global optimal solutions as the final set of potentially global optimal solutions.

[0069] Specifically, in step 7.1, non-dominated sorting is performed on the potentially better individuals according to the objective function values to obtain a non-dominated solution set O, and the number of non-dominated solutions among the potentially better individuals is determined, that is, the number of samples in the non-dominated solution set O. When it is determined that the number of non-dominated solutions is less than the preset value Number1, all non-dominated solutions are used as new samples; if it is determined that the number of non-dominated solutions is greater than the preset value Number1, secondary selection is performed among all non-dominated solutions using the maximum penalty angle to make the number of non-dominated solutions less than the preset value Number1, and new samples are obtained.

[0070] Among them, the specific method of the "maximum penalty angle" secondary selection includes:

[0071] Step a, convert the objective function values of each individual in the non-dominated solution set O and the second set into f i (x)-z i * ;

[0072] Step b, calculate the CV value of each individual in O and perform normalization processing to serve as the penalty factor λ(x); the calculation formula of the penalty factor λ(x) is:

[0073]

[0074] In the formula, CV max =max{CV(x)|x∈O}, which is the maximum value of the CV value in the current solution set; CV min =min{CV(x)|x∈O}, which is the minimum value of the CV value in the current solution set.

[0075] Step c, calculate the Euclidean distance between each individual in O and all individuals in the second set, find the second set sample point closest to each sample point in O, and calculate the included angle size α(x) between the two sample points. α(x) is the selection index for the "maximum penalty angle" secondary selection. The penalty factor λ(x) is used to correct α(x) to reduce the possibility of infeasible or individuals with larger CV values being selected, and the penalty angle is obtained. Its calculation formula is:

[0076] fitness(x)=[1-λ(x)]α(x)

[0077] Step d, in order to enhance the diversity of the algorithm, select the sample in O with the largest penalty angle, remove it from O, and form a potential global optimal solution set with it, and add it to the second set;

[0078] Step f, loop and execute steps a to f until the number of samples in the potential global optimal solution set reaches the design value, and define the potential global optimal solution set as Global.

[0079] Step 7.2, add the samples in Global that have not undergone real function calculations to new; if there is no feasible solution in the second set in Step 5, Global includes Local and Global; if the samples in new are not zero, that is, new samples are generated, perform real function calculations on the new samples (i.e., samples that have not undergone real function calculations) in new to obtain the real objective values, and update the real function calculation times NFE, NFE = NFE + |new|;

[0080] If new is empty and the new samples are 0, form several new samples based on the optimized Latin hypercube sampling method, add them to new, perform real function calculations on the samples in new to obtain the real objective values, and update the real function calculation times.

[0081] It should be noted that after each loop is completed, clear new.

[0082] Step 8, when it is determined that the set of potential global optimal solutions reaches the first preset condition, output the set of potential global optimal solutions as the most promising solution set. Specifically, it includes:

[0083] When it is determined that the real function calculation times have not reached the preset number of times, add the samples and corresponding real objective values in the set new to the first set, perform non-dominated sorting on the samples in the first set based on the real objective values, and update the second set; return to Step 4 until the real function calculation times reach the preset number of times, and output the set of potential global optimal solutions as the most promising solution set.

[0084] In order to select the optimal solution in the fin-rudder layout optimization problem, the most promising solution set can be further processed. Specifically, calculate the CV value of each individual in the most promising solution. If the CV value is not 0, it indicates that the individual does not meet the constraint conditions, and remove it from the solution set; perform non-dominated sorting on the remaining individuals based on the objective function values to obtain the Pareto solution set. Further, according to actual needs, select the optimal solution to the problem from the Pareto solution set and output the fin-rudder shape of the vehicle with excellent comprehensive performance.

[0085] In this embodiment, the constrained multi-objective evolutionary algorithm CE-SAEA based on proxy-assisted is used for optimization. This algorithm uses the RBF proxy model for prediction, which can effectively reduce the number of calls to the real function, thereby reducing the computational cost of simulation optimization; the constrained domain search strategy can quickly locate the feasible region through multi-start search and space contraction techniques, and at the same time improve the continuity of the algorithm in the case where the feasible region is infeasible; the convergence exploration strategy selects promising individuals related to each effective reference vector to drive the population to converge to the global optimal solution; the diversity improvement strategy reduces the possibility of infeasible solutions or individuals with large CV values being selected through the concept of "maximum penalty angle", enhancing the diversity of the algorithm.

[0086] Embodiment

[0087] Step 1: Establish a parametric model of the fin and rudder shape

[0088] In this embodiment, the UUV body selects the MK46 vehicle, the fin and rudder layout adopts a "cross" fin and an "X" rudder, and the fin and rudder shapes are flat plates. The total length of the UUV is 2790 mm, and the maximum diameter is 323.85 mm. The value range of the design variables is determined according to the main dimensions of the UUV. The design variables of the fin and rudder shape are the chord length of the fin plate, the distance from the leading edge of the fin to the head of the UUV, the chord length of the rudder plate, the distance from the leading edge of the rudder to the head of the UUV, the leading and trailing edge angle of the fin plate, and the leading and trailing edge angle of the rudder plate. Therefore, the design variable X = [L F , R1, R F , R2, x0, x1] The parameterization results are as Figure 2 shown.

[0089] Step 2: Establish a multi-objective optimization problem for the fin and rudder shape

[0090] Under the working condition of a rotational speed of 405 RPM, taking the minimum of the balanced angle of attack and the balanced rudder angle as the optimization objective and the longitudinal dynamic stability as the constraint condition, and using the design variables of the fin and rudder shape as the variables to be optimized, a multi-objective optimization problem for the UUV fin and rudder shape is constructed. The objective function and constraint conditions are as follows:

[0091] Minimize f m (X) m = 1, 2;

[0092] subject to -g(X) < 0

[0093] g(X) - 1 < 0

[0094] where X is the variable to be optimized; f m (X) is the objective function, when m = 1, it represents the balanced angle of attack, and when m = 2, it represents the balanced rudder angle; g(X) is the constraint condition.

[0095] Step 3: Build a real function calculation framework for the hydrodynamic performance of the UUV's outer shape

[0096] Use Latin hypercube sampling to obtain the initial values of the design variables for the fin and rudder layout of the UUV. Through CAD secondary development technology, call the 3D modeling software in the CFD simulation management platform to update the geometric model corresponding to the initial values of the design variables, and automatically realize the geometric modeling of different fin and rudder shapes; call Fluent Meshing to perform mesh division on the flow domain model, and perform mesh refinement in the fin and rudder areas; call Fluent to perform CFD simulation on the UUV to obtain the corresponding hydrodynamic parameters, including lift coefficient and pitching moment coefficient; and automatically complete the extraction of hydrodynamic parameters and process the hydrodynamic parameters in the programming software, and finally output the objective function value and constraint condition value.

[0097] Step 4: Initialize the optimization model

[0098] Take the initial values of the design variables as the initial samples, and construct the first set with the initial objective values; use the non-dominated solutions in the initial samples to construct the second set;

[0099] Step 5: Optimization algorithm for searching

[0100] Use the samples and objective function values in the first set to establish an RBF surrogate model; based on the RBF surrogate model, sequentially execute the constraint domain search strategy, convergence exploration strategy, and diversity improvement strategy in the multi-objective evolutionary algorithm to obtain a set of potential global optimal solutions; and when the set of potential global optimal solutions meets the first preset condition, output the set of potential global optimal solutions as the most promising solution set.

[0101] The above are only the preferred embodiments of the present application, and do not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made by using the content of the specification and drawings of the present application, or directly or indirectly applied in other related technical fields, shall be equally included in the patent protection scope of the present application.

Claims

1. A multi-objective optimization design method for UUV fin and rudder layout, characterized in that: include: Step 1: Taking the shape parameters of the fin rudder as the variables to be optimized, establishing an objective function, wherein the objective function includes a balanced attack angle and a balanced rudder angle, and taking the longitudinal dynamic stability of the UUV as a constraint condition; Step 2: Generate initial variables to be optimized, perform real function calculation on the initial variables to be optimized, obtain real target values, and update the number of real function calculations; wherein the target value includes the target function value and the constraint condition value; Step 3: Use the initial variables to be optimized as initial samples and construct a first set with the corresponding true target values; and construct a second set using the non-dominated solutions in the initial samples; Step 4: Establish an RBF proxy model using the samples in the first set and the corresponding true target values; Step 5, taking all non-dominated solutions in the second set as the initial population; Step 6: According to the real target value and the predicted target value, a convergent exploration strategy is executed on the initial population to determine a potential superior individual; Wherein, the predicted target value is predicted by the RBF proxy model; Step 7: Execute the diversity improvement strategy on the potential superior individuals to obtain a potential global optimal solution set; Step 8: When it is determined that the potential global optimal solution set meets the first preset condition, output the potential global optimal solution set as the most promising solution set.

2. The multi-objective optimization design method for UUV fin and rudder layout according to claim 1 is characterized in that: Step 8 includes: Perform true function calculation on samples that have not been calculated for the true function in the potential global optimal solution set to obtain the true target value, and update the number of true function calculations; When it is determined that the number of true function calculations reaches a preset number, the potential global optimal solution set is output as the most promising solution set.

3. The multi-objective optimization design method for UUV fin and rudder layout according to claim 1 is characterized in that: Step 5 also includes: When it is determined that no feasible solution exists in the second set, a constrained domain search strategy is performed on the space composed of samples in the first set to obtain a local optimal solution; Step 7, after obtaining the potential global optimal solution set, further includes: adding the local optimal solution to the potential global optimal solution set; Step 8 includes: performing true function calculation on samples in the potential global optimal solution set that have not been subjected to true function calculation, obtaining true target values, and updating the number of true function calculations; When it is determined that the number of true function calculations reaches a preset number, the potential global optimal solution set is output as the most promising solution set.

4. The multi-objective optimization design method for UUV fin and rudder layout according to claim 3 is characterized in that: The executing of the constraint domain search strategy on the space composed of samples in the first set includes: Determine the constraint violation value of each sample in the first set according to the constraint condition value, and select the individual with the smallest constraint violation value as the base point; Calculate the Euclidean distance between the remaining individuals in the first set and the base point, sort [constraint violation value, -Euclidean distance] in ascending order, and determine the potential space according to the constraint violation value or Euclidean distance; The sequential quadratic programming algorithm is used to locate the feasible region in the potential space, and the local optimal solution is obtained by combining the multi-starting point search strategy.

5. The multi-objective optimization design method for the UUV fin-rudder layout shape according to claim 2 or 3, characterized in that: Step 8 also includes, when it is determined that the number of true function calculations does not reach a preset number of times, adding the evaluated true target value and the corresponding sample to the first set, performing non-dominated sorting on the samples in the first set based on the true target value, and updating the second set; Return to step 4 until the potential global optimal solution set meets the first preset condition.

6. The multi-objective optimization design method for UUV fin and rudder layout according to claim 2 or 3, characterized in that: In step 8, when it is determined that the number of samples for which the true function calculation has not been performed is 0, a number of new samples are formed based on the optimized Latin hypercube sampling method, and the true function calculation is performed on the new samples to obtain the true target value, and the number of true function calculations is updated.

7. The multi-objective optimization design method for UUV fin and rudder layout according to claim 1, characterized in that: The fin rudder shape parameters include the chord length of the fin, the distance from the leading edge of the fin to the UUV head, the chord length of the rudder, the distance from the leading edge of the rudder to the UUV head, the leading edge and trailing edge angle of the fin, and the leading edge and trailing edge angle of the rudder.

8. The multi-objective optimization design method for UUV fin and rudder layout according to claim 1, characterized in that: The real function calculation is obtained by calling an automatic simulation framework, and the simulation method of the automatic simulation framework includes: According to the input variables to be optimized, determine the shape value points of the upper and lower surfaces of the fin rudder; Using the type value points on the upper and lower surfaces of the fin rudder, a UUV geometric model is established and a watershed model is generated; On the flow domain model, respectively determining the fluid dynamic parameters of the UUV at different angles of attack, the fluid dynamic parameters at different rudder angles, and the fluid dynamic parameters at different dimensionless angular velocities; Wherein, the fluid dynamic parameters include lift coefficient and pitch moment coefficient; Determine the position derivatives of the fluid dynamic parameters as the angle of attack and the rudder angle change, respectively, and determine the rotational derivatives of the fluid dynamic parameters as the dimensionless angular velocity changes, and determine the objective function value according to the position derivatives of the fluid dynamic parameters as the angle of attack and the rudder angle change; A constraint condition value is determined based on the rotation derivative.

9. The multi-objective optimization design method for UUV fin and rudder layout according to claim 1, characterized in that: Step 6 includes: Step 6.1, taking the initial population as the parent individuals; Step 6.2: Generate offspring individuals using the parent individuals, determine target values ​​of offspring individuals using the RBF proxy model, and fuse parent individuals and offspring individuals to form a new population; Step 6.3, using the target value of the new population to normalize the population, and determining the convergence index of each individual; Step 6.4, generating a set of uniformly distributed reference vectors; Step 6.5, determine the angle between the individual of the current population and each reference vector, and associate the individual with the nearest adjacent reference vector; Step 6.6, determine the constraint violation value and convergence index according to the target value of the individual, use the constraint violation value and convergence index to perform non-dominated sorting on the individuals associated with the reference vector, and take the individual with the smallest constraint violation value or convergence index as the parent of the next generation; Step 6.7: Return to step 6.2 until the second preset condition is met to obtain a potentially superior individual.

10. The multi-objective optimization design method for UUV fin and rudder layout according to claim 1, characterized in that: Step 7 includes: Determine the number of non-dominated solutions among the potential superior individuals, and when it is determined that the number of non-dominated solutions is less than a preset value, take all non-dominated solutions as new samples; When it is determined that the number of non-dominated solutions is greater than a preset value, a secondary selection is performed among all non-dominated solutions using the maximum penalty angle, and the selection result is used as a new sample.

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