Trapezoidal sail multi-target size optimization method based on NSGA-II algorithm

Abstract

The invention discloses a trapezoidal sail multi-target size optimization method based on an NSGA-II algorithm, and relates to the technical field of unmanned sailboats. According to the method, the aspect ratio, the taper ratio and the camber ratio are selected as design parameters of the trapezoidal sail, after multiple sets of design parameters are sampled and obtained within the value range of the design parameters based on a Latin hypercube sampling method, a trapezoidal sail model is constructed by utilizing fluid simulation analysis software for each set of design parameters, and the trapezoidal sail model is obtained. Performance evaluation parameters corresponding to each group of design parameters are obtained through simulation, a database is constructed, the database is utilized to train a Kriging agent model for replacement, multiple groups of trapezoidal sail design parameters to be preferentially selected are selected, and multi-target size optimization is performed on the trapezoidal sail design parameters based on an NSGA-II algorithm and the trained Kriging agent model. And determining optimal trapezoidal sail design parameters and verifying the accuracy of the optimal trapezoidal sail design parameters. According to the method, trapezoidal sail design parameters and performance evaluation parameters are combined, and a basis is provided for optimization of a sail design scheme by using an NSGA-II method and a Kriging agent model.

Description

Technical Field

[0001] The invention relates to the technical field of unmanned sailboats, and in particular to a multi-objective size optimization method for a trapezoidal sail based on an NSGA-II algorithm. Background Art

[0002] An unmanned sailboat is a marine robot that uses wind energy to sail autonomously. The wing sail is a key component of the unmanned sailboat, and its design directly affects the sailing efficiency and stability of the unmanned sailboat.

[0003] At present, size optimization has become one of the important means to improve the performance of unmanned sailboats. Size optimization helps to design more efficient wing sails, reduce energy consumption and ensure the stable navigation of unmanned sailboats in different ocean conditions. In addition, size optimization also helps to reduce the use of materials, reduce costs and improve the load capacity of unmanned sailboats.

[0004] Therefore, it is urgent to propose a multi-objective size optimization method for trapezoidal sails based on the NSGA-II algorithm. By studying the relationship between the resultant force, strength and multiple design variables of the trapezoidal sail, the multi-objective size optimization of the trapezoidal sail can be achieved, and the optimal size that can provide the maximum resultant force and sufficient strength can be obtained, providing a new solution for the optimal design of the trapezoidal sail size. Summary of the invention

[0005] The present invention aims to determine the optimal size design parameters of a trapezoidal sail that can provide sufficient thrust for an unmanned sailboat and is lightweight and high-strength. A multi-objective size optimization method for a trapezoidal sail based on the NSGA-II algorithm is proposed. The design parameters of the trapezoidal sail are combined with the performance evaluation parameters. The Kriging proxy model is used to replace the fluid simulation analysis to accurately obtain the performance evaluation parameters of the trapezoidal sail. The NSGA-II algorithm is combined to optimize the design parameters of the trapezoidal sail, which realizes the rapid determination of the optimal design parameters of the trapezoidal sail and provides a new idea for optimizing the design scheme of unmanned sailboats.

[0006] The present invention specifically adopts the following technical solutions:

[0007] A multi-objective size optimization method for a trapezoidal sail based on the NSGA-II algorithm comprises the following steps:

[0008] Step 1, selecting aspect ratio, taper ratio and camber ratio as design parameters of the trapezoidal sail, and determining the value range of each design parameter;

[0009] Step 2, sampling is performed within the value range of each design parameter based on the Latin hypercube sampling method to obtain multiple groups of design parameters;

[0010] Step 3, for each set of design parameters, a trapezoidal sail model is constructed using fluid simulation analysis software, and the performance evaluation parameters corresponding to each set of design parameters are obtained through simulation, including the resultant force, stress and strain of the trapezoidal sail, and multiple trapezoidal sail sample data are obtained according to each set of design parameters and their corresponding performance evaluation parameters to construct a database;

[0011] Step 4, establishing a Kriging proxy model, using the trapezoidal sail sample data in the database to train the Kriging proxy model, so that the prediction results of the trained Kriging proxy model for the performance evaluation parameters of the trapezoidal sail meet the preset accuracy requirements, and using the trained Kriging proxy model to directly predict the performance evaluation parameters of the trapezoidal sail according to the design parameters of the trapezoidal sail;

[0012] Step 5, selecting multiple groups of trapezoidal sail design parameters to be optimized, performing multi-objective size optimization on the trapezoidal sail design parameters based on the NSGA-II algorithm and the Kriging proxy model, and obtaining the optimal trapezoidal sail design parameters;

[0013] Step 6: Use fluid simulation analysis software to determine the performance evaluation parameters of the optimal trapezoidal sail design parameters, and verify the accuracy of the optimal trapezoidal sail design parameters obtained by multi-objective size optimization of the trapezoidal sail design parameters based on the NSGA-II algorithm and the Kriging proxy model.

[0014] Preferably, in step 3, the trapezoidal sail model includes a skin and a frame; the skin is installed on the frame to form a sail surface; the frame includes a plurality of ribs and spars, the ribs are evenly spaced on the spars, the bottom ends of the spars are fixed to the bottom of the trapezoidal sail model, and the cross-section of the sail surface consists of a trapezoidal cross-section and a rectangular cross-section, wherein the trapezoidal cross-section is located above the rectangular cross-section, and the width of the trapezoidal cross-section gradually increases from the top to the bottom.

[0015] Preferably, based on the fluid simulation analysis software, a trapezoidal sail model is used to perform simulation analysis for each set of design parameters, and the specific process is as follows:

[0016] A trapezoidal sail model is established in a three-dimensional coordinate system according to design parameters, structural parameters and material properties, wherein the origin of the three-dimensional coordinate system is located at the leading edge of the trapezoidal sail model, the x-axis is arranged along the chord length direction of the wing spar of the trapezoidal sail model, the y-axis is arranged along the thickness direction of the trapezoidal sail model, and the z-axis is arranged along the span direction of the trapezoidal sail model;

[0017] Set the flow field calculation domain and initial parameters of the trapezoidal sail model, set the inlet boundary, outlet boundary, flow direction and flow velocity of the fluid in the flow field, and use the inlet boundary of the fluid as the velocity inlet of the flow field calculation domain and the outlet boundary of the fluid as the pressure outlet of the flow field calculation domain, and set the distance between the trapezoidal sail model and the inlet boundary and outlet boundary of the fluid;

[0018] Set the total simulation time and time step of the fluid simulation analysis.

[0019] In each time step, the trapezoidal sail model is used for simulation and transient dynamic analysis until the preset total simulation time is reached and the simulation is terminated, the force condition of the trapezoidal sail model is obtained, and the resistance, lift and resultant force of the trapezoidal sail model are obtained. According to the resultant force of the trapezoidal sail model, the stress and strain of the trapezoidal sail model are calculated using finite element analysis software, and the performance evaluation parameters corresponding to the design parameters of the trapezoidal sail model are obtained, including the resultant force, stress and strain of the trapezoidal sail model;

[0020] The design parameters of the trapezoidal sail model are combined with the corresponding performance evaluation parameters, and the performance evaluation parameters are used as labels for the design parameters to form trapezoidal sail sample data. A database is constructed based on the trapezoidal sail sample data determined by all design parameters for training the Kriging proxy model.

[0021] Preferably, the flow field calculation domain of the trapezoidal sail model is based on the mass conservation equation and the momentum conservation equation, and the flow field calculation domain is:

[0022]

[0023] in,

[0024]

[0025] In the formula, ρ is; t is time; is the velocity vector, where u is the velocity vector The component in the x direction, v is the velocity vector The component in the y direction, w is the velocity vector component in the z direction; div(·) is the divergence; p is the pressure; τ xx , τ yx , τ zx , τ xy , τ yy , τ zy , τ xz , τ yz , τ zz are the components of the viscous force τ generated by the molecular viscosity acting on the surface of the microelement; F x is the mass force of the microelement in the x direction, F y is the mass force of the microelement in the y direction, F z is the mass force of the microelement in the z direction.

[0026] Preferably, the step 4 includes the following sub-steps:

[0027] Step 4.1, establishing a Kriging proxy model, using a database to train the Kriging proxy model, randomly extracting trapezoidal sail sample data from the database and inputting it into the Kriging proxy model, using the Kriging proxy model to predict the performance evaluation parameters of the trapezoidal sail according to the design parameters of the trapezoidal sail in the trapezoidal sail sample data, and obtaining the predicted values ​​of the resultant force, stress and strain of the trapezoidal sail;

[0028] Step 4.2, compare the predicted values ​​of the resultant force, stress and strain of the trapezoidal sail with the simulated calculated values ​​of the performance evaluation parameters in the trapezoidal sail sample data label, calculate the accuracy value predicted by the Kriging proxy model, and compare it with the preset accuracy; if the prediction accuracy of the Kriging proxy model is not lower than the preset accuracy, it indicates that the prediction result of the Kriging proxy model is accurate, and proceed to step 4.3; otherwise, adjust the kernel function of the Kriging proxy model, return to step 4.1, and continue to use the trapezoidal sail sample data in the database to train the Kriging proxy model until the prediction accuracy of the Kriging proxy model is not lower than the preset accuracy;

[0029] Step 4.3, obtain the Kriging proxy model trained by the database, and use the trained Kriging proxy model to replace the fluid simulation analysis software to directly predict the performance evaluation parameters of the trapezoidal sail according to the design parameters of the trapezoidal sail.

[0030] Preferably, the Kriging proxy model is:

[0031]

[0032] Where I is the serial number of the trapezoidal sail sample data, X I is the input trapezoidal sail sample data; is the predicted value of the Kriging proxy model; f(·) is the kernel function; β * is the kernel function coefficient; r(·) is the correlation vector; T is the transposed matrix; γ * is the relevant factor.

[0033] Preferably, the step 5 comprises the following sub-steps:

[0034] Step 5.1, set the maximum number of iterations and initialize the number of iterations to 0, and start iterative optimization;

[0035] Step 5.2, constructing an initial population with a population size of N according to the trapezoidal sail design parameters to be optimized;

[0036] Step 5.3, taking the individuals in the initial population as the parents to generate the parent population P, using the trained Kriging proxy model to predict the performance evaluation parameters corresponding to each individual in the parent population P, and combining the preset evaluation order of the performance evaluation parameters and the crowding degree of each individual to perform non-dominated quick sorting on all individuals in the parent population P;

[0037] Step 5.4, according to the non-dominated quick sort result, select and retain the individuals in the first N / 2 of the non-dominated quick sort in the parent population P to obtain the updated parent population P t , using the updated parent population P t Perform crossover and mutation processing to generate a sub-population Q with a population size of N t ;

[0038] Step 5.5: Combine the parent population P with the offspring population Q t Merge to generate a new offspring population R t , the offspring population R t The number of individuals in is 2N;

[0039] Step 5.6: Use the trained Kriging proxy model to predict the offspring population R t The performance evaluation parameters corresponding to each individual in the offspring population R are combined with the preset evaluation order of the performance evaluation parameters and the crowding degree of each individual. t Perform non-dominated quick sorting on all individuals in the population, select and retain the first N individuals in the non-dominated quick sorting as the initial population, and update the initial population and the current number of iterations;

[0040] Step 5.7, determine whether the current number of iterations is greater than the maximum number of iterations. If the current number of iterations is not less than the maximum number of iterations, proceed to step 5.8; otherwise, return to step 5.3;

[0041] Step 5.8, end the iterative optimization and output the optimal trapezoidal sail design parameters and their corresponding performance evaluation parameters.

[0042] Preferably, the crossover-mutation process is based on simulated binary crossover and polynomial mutation;

[0043] In the binary crossover process, randomly in the parent population P t Select two parent individuals and obtain the trapezoidal sail design parameters of the parent individuals and in, is the aspect ratio of the first parent individual, is the taper ratio of the first parent individual, is the thickness ratio of the first parent individual, is the aspect ratio of the second parent individual, is the taper ratio of the second parent individual, is the thickness ratio of the second parent individual, and two offspring individuals are generated by simulating binary crossover of the two parent individuals and for:

[0044]

[0045] in,

[0046]

[0047] In the formula, Design parameters for the i-th trapezoidal sail of the first offspring individual; Design parameters for the i-th trapezoidal sail of the first parent individual; Design parameters for the i-th trapezoidal sail of the second parent individual; Design parameters for the i-th trapezoidal sail of the second offspring individual; β is the generation factor; rand is a random number, rand∈[0,1]; η is the distribution factor;

[0048] During the polynomial mutation process, the mutated offspring individuals are updated by calculating the mutation factor:

[0049] C'=C+δ (6)

[0050] in,

[0051]

[0052] In the formula, C2 is the offspring individual before mutation, C is the offspring individual after mutation; δ is the mutation factor; a is a random number, a∈[0,1); q is the mutation distribution index, which is used to control the degree of mutation.

[0053] Preferably, in step 6, a trapezoidal sail model is constructed for each group of trapezoidal sail design parameters to be optimized, and the performance evaluation parameters corresponding to different groups of trapezoidal sail design parameters are simulated using fluid simulation analysis software to obtain the optimal trapezoidal sail design parameters, and compared with the optimal trapezoidal sail design parameters obtained by multi-objective size optimization of the trapezoidal sail design parameters based on the NSGA-II algorithm and the Kriging proxy model, to verify the accuracy of the optimal trapezoidal sail design parameters obtained by multi-objective size optimization of the trapezoidal sail design parameters based on the NSGA-II algorithm and the Kriging proxy model.

[0054] The present invention has the following beneficial effects:

[0055] The present invention proposes a multi-objective size optimization method for a trapezoidal sail based on the NSGA-II algorithm. By adopting the Latin hypercube sampling method for random sampling, the uniform coverage of the sampling space of the trapezoidal sail design parameters is effectively guaranteed, and the aggregation and blank of the trapezoidal sail design parameter sample extraction are avoided, which lays a foundation for improving the subsequent Kriging proxy model training speed.

[0056] The present invention proposes a multi-objective size optimization method for a trapezoidal sail based on the NSGA-II algorithm. By adopting a trained Kriging proxy model to replace the fluid simulation analysis software to directly obtain the performance evaluation parameters of the trapezoidal sail during the optimization process, the workload of simulation in the process of optimizing the optimal trapezoidal sail design parameters is greatly reduced, the computational efficiency of multi-objective high-dimensional optimization is improved, and the rapid prediction of the performance evaluation parameters corresponding to the trapezoidal sail design parameters is realized.

[0057] The present invention proposes a multi-objective size optimization method for a trapezoidal sail based on the NSGA-II algorithm. The NSGA-II method is used to select the optimal design parameters of the trapezoidal sail. In the optimization process, the non-dominated quick sort is used to maintain the diversity of the population, thereby avoiding the local optimum in the optimization process. Combined with the exploration and utilization of crowding distance balance, the optimal Pareto front is accurately approached, and the comprehensive optimization of the design parameters of the trapezoidal sail is achieved, which provides a new idea for the sail optimization of unmanned sailboats. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 Schematic diagram of the trapezoidal sail model of the present invention; in the figure, (a) is a front view of the trapezoidal sail model, and (b) is a top view of the trapezoidal sail model.

[0059] Figure 2 The present invention is a multi-objective size optimization flow chart of trapezoidal sail design parameters based on NSGA-II algorithm and Kriging proxy model. DETAILED DESCRIPTION

[0060] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and specific embodiments:

[0061] This embodiment proposes a multi-objective size optimization method for a trapezoidal sail based on the NSGA-II algorithm, comprising the following steps:

[0062] Step 1: Select aspect ratio, taper ratio and camber ratio as the design parameters of the trapezoidal sail, and determine the value range of each design parameter, as shown in Table 1.

[0063] Table 1 Range of values ​​of trapezoidal sail design parameters

[0064]

[0065] Step 2: In order to obtain multiple sets of design parameters in a better and more uniform manner, sampling is performed within the value range of each design parameter based on the Latin hypercube sampling method.

[0066] The Latin hypercube sampling method used in this embodiment is a stratified random sampling method that can perform efficient sampling in the distribution interval of variables. When there are K variables and M samples need to be selected from the distribution interval of each variable, the distribution interval of each variable is divided into the same M small intervals, and values ​​are randomly selected from each small interval, and the M values ​​selected from the K variables are randomly combined to obtain K×M design parameter samples. The Latin hypercube sampling method used in this embodiment is different from traditional random sampling. This method effectively ensures full coverage of the variable range by maximizing the coverage of the edges of each value interval.

[0067] In this embodiment, according to the value ranges of the aspect ratio, taper ratio, and camber ratio, the values ​​of the aspect ratio, taper ratio, and camber ratio are determined by sampling based on the Latin hypercube sampling method, as shown in Table 2.

[0068] Table 2 Trapezoidal sail design parameter values

[0069]

[0070] Step 3: For each set of design parameters, a trapezoidal sail model is constructed using fluid simulation analysis software. The performance evaluation parameters corresponding to each set of design parameters are obtained through simulation, including the resultant force, stress and strain of the trapezoidal sail. Sample data of multiple trapezoidal sails are obtained according to each set of design parameters and their corresponding performance evaluation parameters to construct a database.

[0071] In this embodiment, the trapezoidal sail model is as follows: Figure 1 As shown, it includes a skin and a frame. The skin is installed on the frame to form a sail surface; the frame includes a plurality of ribs and spars, the ribs are arranged on the spars at equal intervals, and the bottom end of the spars is fixed to a quarter of the bottom chord length of the trapezoidal sail model, and the cross section of the sail surface consists of a trapezoidal cross section and a rectangular cross section, wherein the trapezoidal cross section is located above the rectangular cross section, and the width of the trapezoidal cross section gradually increases from the top to the bottom.

[0072] Based on the fluid simulation analysis software STAR-CCM+, the trapezoidal sail model is used to perform fluid dynamics simulation analysis for each set of design parameters. The specific process is as follows:

[0073] A trapezoidal sail model is established in a three-dimensional coordinate system according to design parameters, structural parameters and material properties, wherein the origin of the three-dimensional coordinate system is located at the leading edge of the trapezoidal sail model, the x-axis is set along the chord length direction of the wing beam of the trapezoidal sail model, the y-axis is set along the thickness direction of the trapezoidal sail model, and the z-axis is set along the span direction of the trapezoidal sail model.

[0074] In this embodiment, the design parameters of the trapezoidal sail model include aspect ratio, taper ratio and camber ratio. The structural parameters of the trapezoidal sail model include upper chord length C1, lower chord length C2, upper camber t1, lower camber t2 and span L. The structural material used in the trapezoidal sail model is T300 carbon fiber / epoxy resin-based composite material, and its density is 1760 kg·m 3 , Poisson's ratio is 0.27, the longitudinal tensile modulus is 138 GPa, and the transverse tensile modulus is 8.36 GPa.

[0075] Set the flow field calculation domain and initial parameters of the trapezoidal sail model, set the inlet boundary, outlet boundary, flow direction and flow velocity of the fluid in the flow field, and use the inlet boundary of the fluid as the velocity inlet of the flow field calculation domain and the outlet boundary of the fluid as the pressure outlet of the flow field calculation domain. Set the distance between the trapezoidal sail model and the fluid inlet boundary and fluid outlet boundary, and set the total simulation time and time step of the fluid simulation analysis.

[0076] In this embodiment, the length of the flow field calculation domain of the trapezoidal sail model is 15 times the length of the lower chord, the width is 10 times the length of the lower chord, and the height is 10 times the length of the lower chord. The fluid inlet boundary and the fluid outlet boundary of the flow field calculation domain correspond to the two end faces of the flow field calculation domain along the x-axis, wherein the distance between the trapezoidal sail model and the fluid inlet boundary is 5 times the length of the lower chord, and the distance between the trapezoidal sail model and the fluid outlet boundary is 10 times the length of the lower chord. The fluid in the flow field calculation domain is set to flow along the positive direction of the x-axis, the fluid flow rate is 4.5m / s, and the rotation angle of the trapezoidal sail model is 30°.

[0077] In this embodiment, the flow field calculation domain of the trapezoidal sail model is based on the mass conservation equation and the momentum conservation equation, and the flow field calculation domain is:

[0078]

[0079] in,

[0080]

[0081] In the formula, ρ is; t is time; is the velocity vector, where u is the velocity vector The component in the x direction, v is the velocity vector The component in the y direction, w is the velocity vector component in the z direction; div(·) is the divergence; p is the pressure; τ xx , τ yx , τ zx , τ xy , τ yy , τ zy , τ xz , τ yz , τzz are the components of the viscous force τ generated by the molecular viscosity acting on the surface of the microelement; F x is the mass force of the microelement in the x direction, F y is the mass force of the microelement in the y direction, F z is the mass force of the microelement in the z direction.

[0082] During the simulation process, at each time step, the trapezoidal sail model is used to simulate and perform transient dynamic analysis to obtain the force condition of the trapezoidal sail model, wherein the force on the trapezoidal sail model in the x-axis direction is resistance, and the force on the y-axis direction is lift, thereby obtaining the resistance, lift and resultant force on the trapezoidal sail model, and according to the resultant force on the trapezoidal sail model, the stress and strain of the trapezoidal sail model are calculated with the bottom surface of the trapezoidal sail as the fixed surface, until the preset total simulation time is reached and the simulation is terminated, and the performance evaluation parameters corresponding to the design parameters of the trapezoidal sail model are obtained, including the resultant force, stress and strain of the trapezoidal sail model, wherein the stress and strain are used to represent the strength of the trapezoidal sail model.

[0083] The design parameters of the trapezoidal sail model are combined with the corresponding performance evaluation parameters, and the performance evaluation parameters are used as labels for the design parameters to form trapezoidal sail sample data. A database is constructed based on the trapezoidal sail sample data determined by all design parameters for training the Kriging proxy model.

[0084] Step 4, establish a Kriging proxy model, use the trapezoidal sail sample data in the database to train the Kriging proxy model, so that the prediction results of the trained Kriging proxy model for the performance evaluation parameters of the trapezoidal sail meet the preset accuracy requirements, and use the trained Kriging proxy model to directly predict the performance evaluation parameters of the trapezoidal sail according to the design parameters of the trapezoidal sail, which specifically includes the following sub-steps:

[0085] Step 4.1, establish a Kriging proxy model, the Kriging proxy model is:

[0086]

[0087] Where I is the serial number of the trapezoidal sail sample data, X I is the input trapezoidal sail sample data; is the predicted value of the Kriging proxy model; f(·) is the kernel function; β * is the kernel function coefficient; r(·) is the correlation vector, which consists of the trapezoidal sail sample data and the Kriging proxy model prediction value; T is the transposed matrix; γ * is the relevant factor.

[0088] The Kriging proxy model is trained using the database. Trapezoidal sail sample data are randomly extracted from the database and input into the Kriging proxy model. The Kriging proxy model is then used to predict the performance evaluation parameters of the trapezoidal sail according to the design parameters of the trapezoidal sail in the trapezoidal sail sample data, and the predicted values ​​of the resultant force, stress and strain of the trapezoidal sail are obtained.

[0089] Step 4.2, compare the predicted values ​​of the resultant force, stress and strain of the trapezoidal sail with the simulated calculated values ​​of the performance evaluation parameters in the trapezoidal sail sample data label, calculate the accuracy value of the Kriging proxy model prediction, and compare it with the preset accuracy of 95%; if the prediction accuracy of the Kriging proxy model is not lower than the preset accuracy, it indicates that the prediction result of the Kriging proxy model is accurate, and proceed to step 4.3; otherwise, adjust the kernel function of the Kriging proxy model, return to step 4.1, and continue to use the trapezoidal sail sample data in the database to train the Kriging proxy model until the prediction accuracy of the Kriging proxy model is not lower than the preset accuracy.

[0090] Step 4.3, obtain the Kriging proxy model trained by the database, and use the trained Kriging proxy model to predict the performance evaluation parameters of the trapezoidal sail.

[0091] This embodiment trains the Kriging proxy model and uses the Kriging proxy model to replace the fluid simulation analysis software to directly and accurately obtain the resultant force, stress and strain of the trapezoidal sail according to the design parameters of the trapezoidal sail, which greatly reduces the workload of fluid simulation analysis, improves the work efficiency of multi-objective high-dimensional optimization, and provides technical support for the rapid prediction of the performance evaluation parameters of the trapezoidal sail.

[0092] Step 5, select multiple groups of trapezoidal sail design parameters to be optimized, perform multi-objective size optimization on the trapezoidal sail design parameters based on the NSGA-II algorithm (i.e., multi-objective genetic algorithm) and the Kriging agent model, and obtain the optimal trapezoidal sail design parameters, such as Figure 2 As shown, the objective function for optimizing the design parameters of the trapezoidal sail in this embodiment is:

[0093]

[0094] In the formula, δ i are the design parameters of the trapezoidal sail, where δ1 is the aspect ratio, δ2 is the taper ratio, and δ3 is the camber ratio; F is the resultant force of the trapezoidal sail; σ is the maximum stress of the trapezoidal sail; ε is the maximum strain of the trapezoidal sail; a is the lower limit of the design parameters of the trapezoidal sail; b is the upper limit of the design parameters of the trapezoidal sail; A is the area of ​​the trapezoidal sail.

[0095] The multi-objective size optimization of the trapezoidal sail design parameters is carried out based on the NSGA-II algorithm and the Kriging proxy model, which specifically includes the following sub-steps:

[0096] Step 5.1, set the maximum number of iterations and initialize the number of iterations to 0, and start iterative optimization.

[0097] Step 5.2, construct an initial population with a population size of N according to the trapezoidal sail design parameters to be optimized, and initialize each individual in the initial population.

[0098] In step 5.3, the individuals in the initial population are taken as parents to generate the parent population P. The trained Kriging proxy model is used to predict the performance evaluation parameters corresponding to each individual in the parent population P. Combined with the preset evaluation order of the performance evaluation parameters and the crowding degree of each individual, all individuals in the parent population P are subjected to non-dominated quick sorting.

[0099] In this embodiment, when performing non-dominated quick sorting on individuals in a population, the number of disposable individuals of each individual in the population is first determined. Taking individuals A and B in the population as an example, according to the preset evaluation order of the performance evaluation parameters, if the performance evaluation parameters of individual A are better than those of individual B, it means that individual A dominates individual B. When performing non-dominated quick sorting on individuals in a population, the number of disposable individuals of all individuals in the population is first obtained, and individuals that are not dominated by other individuals are determined as the first-layer non-dominated solution, and the remaining individuals are placed in the next layer, and individuals that are not dominated by other individuals are selected as the second-layer non-dominated solution according to the number of disposable individuals of each individual, and so on, non-dominated quick sorting is performed on all individuals in the population to obtain the non-dominated quick sorting of the population.

[0100] In the non-dominated quick sorting process, if there are multiple individuals with the same number of disposable individuals in the same layer, they are further sorted based on the crowding degree of each individual, where the crowding degree is the number of individuals in the target space with the specified individual P. i Adjacent individuals P j and individual P k The specific sorting process is:

[0101] First, the distances of all individuals in the same layer are initialized, and the initialization distances of all individuals are set to 0.

[0102] Secondly, the objective function values ​​of the individuals in the same layer are arranged in ascending order. That is, in this embodiment, the individuals with the same number of disposable individuals in the same layer are sorted in ascending order according to the performance evaluation parameter values ​​based on the resultant force value, stress value and strain value of each individual respectively under the conditions of each performance evaluation parameter, and the selection advantage of the individuals at the edge of the sorting is maintained. The crowding distance of each individual is calculated based on the resultant force value, stress value and strain value respectively, as shown in formula (9):

[0103]

[0104] In the formula, d[rankj(P i )] is the individual P i The crowding distance; F(P j ) is the individual P j Performance evaluation parameters; F(P k ) is the individual P j Performance evaluation parameters; F max is the maximum value of the performance evaluation parameter in this layer; F min It is the minimum value of the performance evaluation parameter in this layer.

[0105] Then, the crowding distances calculated for the same individual based on the resultant force value, stress value and strain value are accumulated to obtain the individual's crowding degree, and the individuals with the same number of disposable individuals are sorted in descending order according to the crowding degree of each individual. That is, by selecting individuals with larger crowding distances in the population, the calculated results are evenly distributed in the target space, thereby maintaining the diversity of the population.

[0106] Step 5.4, according to the non-dominated quick sort result, select and retain the individuals in the first N / 2 of the non-dominated quick sort in the parent population P to obtain the updated parent population P t , using the updated parent population P t Perform crossover and mutation processing to generate a sub-population Q with a population size of N t .

[0107] In this embodiment, the crossover-mutation process is based on simulating binary crossover and polynomial mutation.

[0108] In the binary crossover process, randomly in the parent population P t Select two parent individuals and obtain the trapezoidal sail design parameters of the parent individuals and in, is the aspect ratio of the first parent individual, is the taper ratio of the first parent individual, is the thickness ratio of the first parent individual, is the aspect ratio of the second parent individual, is the taper ratio of the second parent individual, is the thickness ratio of the second parent individual, and two offspring individuals are generated by simulating binary crossover of the two parent individuals and for:

[0109]

[0110] in,

[0111]

[0112] In the formula, Design parameters for the i-th trapezoidal sail of the first offspring individual; Design parameters for the i-th trapezoidal sail of the first parent individual; Design parameters for the i-th trapezoidal sail of the second parent individual; are the design parameters of the i-th trapezoidal sail of the second offspring individual; β is the generation factor; rand is a random number, rand∈[0,1]; η is the distribution factor, which is a custom parameter. The larger the value of the distribution factor η is, the greater the probability that the generated offspring individual approaches the parent individual. In this embodiment, the distribution factor η is 10.

[0113] During the polynomial mutation process, the mutated offspring individuals are updated by calculating the mutation factor:

[0114] C'=C+δ (6)

[0115] in,

[0116]

[0117] Wherein, C' is the offspring individual before mutation, C is the offspring individual after mutation; δ is the mutation factor; a is a random number, a∈[0,1); q is the mutation distribution index, which is used to control the degree of mutation. In this embodiment, the mutation distribution index q is 10.

[0118] Step 5.5: Combine the parent population P with the offspring population Q t Merge to generate a new offspring population R t , the offspring population R t The number of individuals in is 2N.

[0119] Step 5.6: Use the trained Kriging proxy model to predict the offspring population R t The performance evaluation parameters corresponding to each individual in the offspring population R are combined with the preset evaluation order of the performance evaluation parameters and the crowding degree of each individual. t Perform non-dominated quick sorting on all individuals in the population, select and retain the first N individuals in the non-dominated quick sorting as the initial population, and update the initial population and the current number of iterations.

[0120] Step 5.7, determine whether the current number of iterations Gen is greater than the maximum number of iterations Gen Max , if the current iteration number Gen is not less than the maximum iteration number Gen Max , then go to step 5.8, otherwise, return to step 5.3.

[0121] Step 5.8, end the iterative optimization and output the optimal trapezoidal sail design parameters and their corresponding performance evaluation parameters.

[0122] Step 6: Use fluid simulation analysis software to determine the performance evaluation parameters of the optimal trapezoidal sail design parameters, and verify the accuracy of the optimal trapezoidal sail design parameters obtained by multi-objective size optimization of the trapezoidal sail design parameters based on the NSGA-II algorithm and the Kriging proxy model.

[0123] In this embodiment, a trapezoidal sail model is constructed for each group of trapezoidal sail design parameters to be optimized, and the performance evaluation parameters corresponding to different groups of trapezoidal sail design parameters are simulated by using fluid simulation analysis software to obtain the optimal trapezoidal sail design parameters, and the optimal trapezoidal sail design parameters are compared with the optimal trapezoidal sail design parameters obtained by multi-objective size optimization of the trapezoidal sail design parameters based on the NSGA-II algorithm and the Kriging proxy model. Through the comparison, it is found that the optimal trapezoidal sail design parameters determined according to the simulation results of the fluid simulation analysis software are consistent with the optimal trapezoidal sail design parameters determined by the method of the present invention, thereby verifying the accuracy of the method of the present invention applied to the multi-objective size optimization of trapezoidal sail design parameters.

[0124] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A multi-objective size optimization method for a trapezoidal sail based on the NSGA-II algorithm, characterized in that: The following steps are involved: Step 1, selecting aspect ratio, taper ratio and camber ratio as design parameters of the trapezoidal sail, and determining the value range of each design parameter; Step 2, sampling is performed within the value range of each design parameter based on the Latin hypercube sampling method to obtain multiple groups of design parameters; Step 3, for each set of design parameters, a trapezoidal sail model is constructed using fluid simulation analysis software, and the performance evaluation parameters corresponding to each set of design parameters are obtained through simulation, including the resultant force, stress and strain of the trapezoidal sail, and multiple trapezoidal sail sample data are obtained according to each set of design parameters and their corresponding performance evaluation parameters to construct a database; Step 4, establishing a Kriging proxy model, using the trapezoidal sail sample data in the database to train the Kriging proxy model, so that the prediction results of the trained Kriging proxy model for the performance evaluation parameters of the trapezoidal sail meet the preset accuracy requirements, and using the trained Kriging proxy model to directly predict the performance evaluation parameters of the trapezoidal sail according to the design parameters of the trapezoidal sail; Step 5, selecting multiple groups of trapezoidal sail design parameters to be optimized, performing multi-objective size optimization on the trapezoidal sail design parameters based on the NSGA-II algorithm and the Kriging proxy model, and obtaining the optimal trapezoidal sail design parameters; Step 6: Use fluid simulation analysis software to determine the performance evaluation parameters of the optimal trapezoidal sail design parameters, and verify the accuracy of the optimal trapezoidal sail design parameters obtained by multi-objective size optimization of the trapezoidal sail design parameters based on the NSGA-II algorithm and the Kriging proxy model.

2. The multi-objective size optimization method of a trapezoidal sail based on the NSGA-II algorithm according to claim 1, characterized in that: In step 3, the trapezoidal sail model includes a skin and a frame; the skin is installed on the frame to form a sail surface; the frame includes a plurality of ribs and spars, the ribs are evenly spaced on the spars, the bottom ends of the spars are fixed to the bottom of the trapezoidal sail model, and the cross-section of the sail surface consists of a trapezoidal cross-section and a rectangular cross-section, wherein the trapezoidal cross-section is located above the rectangular cross-section, and the width of the trapezoidal cross-section gradually increases from the top to the bottom.

3. The multi-objective size optimization method of a trapezoidal sail based on the NSGA-II algorithm as claimed in claim 2, characterized in that: Based on the fluid simulation analysis software, the trapezoidal sail model is used to perform simulation analysis for each set of design parameters. The specific process is as follows: A trapezoidal sail model is established in a three-dimensional coordinate system according to design parameters, structural parameters and material properties, wherein the origin of the three-dimensional coordinate system is located at the leading edge of the trapezoidal sail model, the x-axis is arranged along the chord length direction of the wing spar of the trapezoidal sail model, the y-axis is arranged along the thickness direction of the trapezoidal sail model, and the z-axis is arranged along the span direction of the trapezoidal sail model; Set the flow field calculation domain and initial parameters of the trapezoidal sail model, set the inlet boundary, outlet boundary, flow direction and flow velocity of the fluid in the flow field, and use the inlet boundary of the fluid as the velocity inlet of the flow field calculation domain and the outlet boundary of the fluid as the pressure outlet of the flow field calculation domain, and set the distance between the trapezoidal sail model and the inlet boundary and outlet boundary of the fluid; Set the total simulation time and time step of the fluid simulation analysis; In each time step, the trapezoidal sail model is used for simulation and transient dynamic analysis until the preset total simulation time is reached and the simulation is terminated, the force condition of the trapezoidal sail model is obtained, and the resistance, lift and resultant force of the trapezoidal sail model are obtained. According to the resultant force of the trapezoidal sail model, the stress and strain of the trapezoidal sail model are calculated using finite element analysis software, and the performance evaluation parameters corresponding to the design parameters of the trapezoidal sail model are obtained, including the resultant force, stress and strain of the trapezoidal sail model; The design parameters of the trapezoidal sail model are combined with the corresponding performance evaluation parameters, and the performance evaluation parameters are used as labels for the design parameters to form trapezoidal sail sample data. A database is constructed based on the trapezoidal sail sample data determined by all design parameters for training the Kriging proxy model.

4. The multi-objective size optimization method of a trapezoidal sail based on the NSGA-II algorithm as claimed in claim 3, characterized in that: The flow field calculation domain of the trapezoidal sail model is based on the mass conservation equation and the momentum conservation equation. The flow field calculation domain is: in, In the formula, ρ is; t is time; is the velocity vector, where u is the velocity vector The component in the x direction, v is the velocity vector The component in the y direction, w is the velocity vector component in the z direction; div(·) is the divergence; p is the pressure; τ xx , τ yx , τ zx , τ xy , τ yy , τ zy , τ xz , τ yz , τ zz are the components of the viscous force τ generated by the molecular viscosity acting on the surface of the microelement; F x is the mass force of the microelement in the x direction, F y is the mass force of the microelement in the y direction, F z is the mass force of the microelement in the z direction.

5. The multi-objective size optimization method of a trapezoidal sail based on the NSGA-II algorithm as claimed in claim 1, characterized in that: The step 4 includes the following sub-steps: Step 4.1, establishing a Kriging proxy model, using a database to train the Kriging proxy model, randomly extracting trapezoidal sail sample data from the database and inputting it into the Kriging proxy model, using the Kriging proxy model to predict the performance evaluation parameters of the trapezoidal sail according to the design parameters of the trapezoidal sail in the trapezoidal sail sample data, and obtaining the predicted values ​​of the resultant force, stress and strain of the trapezoidal sail; Step 4.2, compare the predicted values ​​of the resultant force, stress and strain of the trapezoidal sail with the simulated calculated values ​​of the performance evaluation parameters in the trapezoidal sail sample data label, calculate the accuracy value predicted by the Kriging proxy model, and compare it with the preset accuracy; if the prediction accuracy of the Kriging proxy model is not lower than the preset accuracy, it indicates that the prediction result of the Kriging proxy model is accurate, and proceed to step 4.3; otherwise, adjust the kernel function of the Kriging proxy model, return to step 4.1, and continue to use the trapezoidal sail sample data in the database to train the Kriging proxy model until the prediction accuracy of the Kriging proxy model is not lower than the preset accuracy; Step 4.3, obtain the Kriging proxy model trained by the database, and use the trained Kriging proxy model to replace the fluid simulation analysis software to directly predict the performance evaluation parameters of the trapezoidal sail according to the design parameters of the trapezoidal sail.

6. The multi-objective size optimization method of a trapezoidal sail based on the NSGA-II algorithm as claimed in claim 5, characterized in that: The Kriging proxy model is: Where I is the serial number of the trapezoidal sail sample data, X I is the input trapezoidal sail sample data; is the predicted value of the Kriging proxy model; f(·) is the kernel function; β * is the kernel function coefficient; r(·) is the correlation vector; T is the transposed matrix; γ * is the relevant factor.

7. The multi-objective size optimization method of a trapezoidal sail based on the NSGA-II algorithm as claimed in claim 1, characterized in that: The step 5 comprises the following sub-steps: Step 5.1, set the maximum number of iterations and initialize the number of iterations to 0, and start iterative optimization; Step 5.2, constructing an initial population with a population size of N according to the trapezoidal sail design parameters to be optimized; Step 5.3, taking the individuals in the initial population as the parents to generate the parent population P, using the trained Kriging proxy model to predict the performance evaluation parameters corresponding to each individual in the parent population P, and combining the preset evaluation order of the performance evaluation parameters and the crowding degree of each individual to perform non-dominated quick sorting on all individuals in the parent population P; Step 5.4, according to the non-dominated quick sort result, select and retain the first N / 2 individuals in the non-dominated quick sort in the parent population P to obtain the updated parent population P t , using the updated parent population P t Perform crossover and mutation processing to generate a sub-population Q with a population size of N t ; Step 5.5: Combine the parent population P with the offspring population Q t Merge to generate a new offspring population R t , the offspring population R t The number of individuals in is 2N; Step 5.6: Use the trained Kriging proxy model to predict the offspring population R t The performance evaluation parameters corresponding to each individual in the offspring population R are combined with the preset evaluation order of the performance evaluation parameters and the crowding degree of each individual. t Perform non-dominated quick sorting on all individuals in the population, select and retain the first N individuals in the non-dominated quick sorting as the initial population, and update the initial population and the current number of iterations; Step 5.7, determine whether the current number of iterations is greater than the maximum number of iterations. If the current number of iterations is not less than the maximum number of iterations, proceed to step 5.8; otherwise, return to step 5.3; Step 5.8, end the iterative optimization and output the optimal trapezoidal sail design parameters and their corresponding performance evaluation parameters.

8. The multi-objective size optimization method of a trapezoidal sail based on the NSGA-II algorithm as claimed in claim 7, characterized in that: The crossover-mutation process is based on simulating binary crossover and polynomial mutation; In the binary crossover process, randomly in the parent population P t Select two parent individuals and obtain the trapezoidal sail design parameters of the parent individuals and in, is the aspect ratio of the first parent individual, is the taper ratio of the first parent individual, is the thickness ratio of the first parent individual, is the aspect ratio of the second parent individual, is the taper ratio of the second parent individual, is the thickness ratio of the second parent individual, and two offspring individuals are generated by simulating binary crossover of the two parent individuals and for: in, In the formula, Design parameters for the i-th trapezoidal sail of the first offspring individual; Design parameters for the i-th trapezoidal sail of the first parent individual; Design parameters for the i-th trapezoidal sail of the second parent individual; Design parameters for the i-th trapezoidal sail of the second offspring individual; β is the generation factor; rand is a random number, rand∈[0,1]; η is the distribution factor; During the polynomial mutation process, the mutated offspring individuals are updated by calculating the mutation factor: C'=C+δ (6) in, In the formula, C′ is the offspring individual before mutation, C is the offspring individual after mutation; δ is the mutation factor; a is a random number, a∈[0,1); q is the mutation distribution index, which is used to control the degree of mutation.

9. The multi-objective size optimization method of a trapezoidal sail based on the NSGA-II algorithm as claimed in claim 1, characterized in that: In step 6, a trapezoidal sail model is constructed for each group of trapezoidal sail design parameters to be optimized, and the performance evaluation parameters corresponding to different groups of trapezoidal sail design parameters are simulated using fluid simulation analysis software to obtain the optimal trapezoidal sail design parameters, and compared with the optimal trapezoidal sail design parameters obtained by multi-objective size optimization of the trapezoidal sail design parameters based on the NSGA-II algorithm and the Kriging proxy model, to verify the accuracy of the optimal trapezoidal sail design parameters obtained by multi-objective size optimization of the trapezoidal sail design parameters based on the NSGA-II algorithm and the Kriging proxy model.

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