A machine learning-guided dynamic population optimization design method

Abstract

The present invention discloses a dynamic population optimization design method guided by machine learning, which is applicable to the lightweight design problem of the drive shaft of an azimuth propeller, including: considering the structural parameters and service constraints of the drive shaft to initialize the population and parameters; determining the dynamic population based on iterative information and multi-objective non-dominated sorting method; constructing an evolutionary operation that adapts to the potential of the population individuals to generate a candidate offspring pool; determining a machine learning model modeling sample within the neighborhood of each candidate offspring individual; constructing a Gaussian process machine learning model, and deriving the expected improvement of the candidate offspring individual; screening the real offspring individuals according to the relaxation factor and the multi-objective non-dominated sorting method, and updating the population; constructing a local search based on a Gaussian process to locate the local high-potential individuals, and updating the iterative information. The present invention comprehensively considers the weight target and fatigue constraints to design the algorithm optimization trajectory, which improves the global adaptability and convergence speed of the algorithm for the lightweight design problem of the drive shaft of an azimuth propeller.

Description

Technical Field

[0001] The present invention relates to the general technical field of artificial intelligence in the field of electronic information, and more specifically, to a dynamic population optimization design method guided by machine learning. Background Art

[0002] The lightweight design problem of the drive shaft of an omni-rotating propeller requires minimizing the weight of the drive shaft while satisfying the fatigue life constraint. This type of problem is a classic expensive constrained optimization problem involving time-consuming simulation analysis. The fatigue simulation evaluation time for the drive shaft of an omni-rotating propeller is between half an hour and one hour, which means that the solution to this type of problem can only withstand a small number of calls to the real target and constraint simulation model. For this reason, common metaheuristic algorithms will not be able to obtain a satisfactory optimization solution within an acceptable design cycle, while other optimization algorithms such as gradient-based methods are unable to escape the complex feasible domain of the expensive constrained optimization problem corresponding to the lightweight design problem of the drive shaft of an omni-rotating propeller and the local optimum caused by the highly nonlinear objective function.

[0003] Machine learning models can build a mapping relationship from input space to output space by learning the intrinsic connections between data, thus providing an efficient approximate model for complex objectives or constraint problems involving simulation. To this end, existing research focuses on integrating machine learning models into metaheuristic methods to accelerate convergence. The core is that machine learning models can provide fast and accurate predictions, which can replace many unnecessary and time-consuming simulation analysis calls in the metaheuristic optimization process, greatly improving the overall optimization efficiency.

[0004] In the process of implementing the technical method of the embodiment of the present invention, the inventor of this patent found at least the following technical problems in the prior art:

[0005] Researchers have only used experimental design methods to minimize the weight of the azimuth propeller drive shaft while meeting service requirements, resulting in poor performance. In addition, the existing machine learning-guided meta-heuristic algorithms ignore the fact that real-time search should adapt to the real-time optimization state of the algorithm when designing optimization strategies, resulting in poor adaptability of the algorithm and failure to provide real-time controllable adaptive search for the lightweight design problem of the azimuth propeller drive shaft, resulting in low optimization efficiency.

[0006] Therefore, the present invention considers dynamically reconstructing the current population in combination with the real-time optimization state of the algorithm, and updating the constraint relaxation factor in real time in combination with the iterative information, so as to improve the adaptability of the algorithm to the lightweight design problem of the full-rotation propeller drive shaft. Furthermore, how to use the predictive ability of machine learning to speed up the algorithm to conduct rapid local exploration of specific high-potential areas is also the focus of the present invention. Summary of the invention

[0007] In view of the above limitations of the prior art or the need for improved technology, the present invention proposes a dynamic population optimization design method guided by machine learning, which studies and designs a dynamic population optimization design method guided by machine learning based on the characteristics of the lightweight design problem of the existing full-rotation propeller drive shaft involving time-consuming fatigue simulation constraints and complex objectives. The method designs a dynamic population reconstruction and adaptive evolution operation that adapts to the real-time optimization state of the method to improve the adaptability of the method to complex constraint problems, and effectively combines the machine learning prediction ability to accelerate the rapid convergence ability of the method in local areas.

[0008] To achieve the above objectives, an embodiment of the present invention provides a dynamic population optimization design method guided by machine learning, which is applicable to the lightweight design problem of a full-rotation propeller drive shaft, and the method includes:

[0009] Step 1: Convert the lightweight design problem of the full-rotation propeller drive shaft into an expensive constrained optimization problem that minimizes the computational time of the drive shaft weight while satisfying the fatigue life constraint. The diameter and length of each shaft section of the drive shaft correspond to the structural parameters that need to be optimized during the lightweight design of the drive shaft. Combined with the matching relationship between the drive shaft and the bearing, the value range of the diameter and length structural parameters of each shaft section of the drive shaft is given. Therefore, the structural parameters and the value range constitute the design space of the expensive constraint optimization problem. The target value of the drive shaft weight obtained in ANSYS Workbench is used as the optimization target of the expensive constraint optimization problem. The fatigue life of the drive shaft obtained by fatigue life analysis in ANSYS nCode DesignLife is used as the optimization constraint of the expensive constraint optimization problem. Find the optimal combination of structural parameter values ​​within the design space to minimize the target value of the drive shaft weight while satisfying the fatigue life constraint of the drive shaft. First, initialize the population within the design space composed of the structural parameters and the value range to generate a population containing multiple population individuals. Each individual contains a set of diameter and length values ​​of each shaft section of the drive shaft, corresponding to a drive shaft. Then, import the drive shaft corresponding to each individual into ANSYS Static analysis is performed in Workbench to obtain the weight target value of the drive shaft, and the static analysis results and the periodic alternating load of the drive shaft are imported into ANSYS nCode DesignLife for fatigue life analysis to obtain the fatigue life constraint value of the drive shaft. All individuals in the current population and the corresponding weight target value and fatigue life constraint value are used to build a database. The iteration parameters of population evolution including the total number of iterations and convergence conditions are initialized according to the lightweight design index of the drive shaft, and then the initial constraint relaxation factor in the optimization process is calculated based on the fatigue life constraint value of the drive shaft corresponding to each individual in the population.

[0010] Step 2: Calculate the truncation parameter based on the current iteration number and the fatigue life constraint value and weight target value of the drive shaft in the database, select individuals in the database containing all the drive shaft information according to the truncation parameter to form the current database, and select individuals from the current database based on the multi-objective non-dominated sorting method to form a dynamic population, with the individual diversity, drive shaft weight target value and drive shaft fatigue life constraint and drive shaft load boundary condition constraint violation value as three goals in the current database;

[0011] Step 3: Using the weight target value, fatigue life and boundary condition constraint violation value of individuals in the dynamic population as indicators, the feasibility rules are used to sort the individuals in the dynamic population, and the corresponding differential mutation operations are designed according to the sorting values ​​to generate a candidate offspring pool. In the candidate offspring pool, each candidate offspring corresponds to a new combination of structural parameter values ​​of the drive shaft obtained through the differential mutation operation. The feasibility rules include the following three rules:

[0012] (1) Individuals that satisfy all constraints are better than individuals that do not satisfy all constraints;

[0013] (2) If both individuals satisfy all constraints, the individual with a smaller objective value is better;

[0014] (3) If both individuals do not satisfy all constraints, the individual with a smaller constraint violation value is better;

[0015] Step 4: Determine the neighborhood of each candidate offspring individual based on the Euclidean distance, and select modeling samples from the neighborhood for constructing the Gaussian process machine learning model by considering the individual weight target value, fatigue life, feasibility of boundary condition constraints, and diversity;

[0016] Step 5: For each candidate offspring individual, a Gaussian process machine learning model is constructed using the determined modeling sample, and the expected improvement of the candidate offspring individual is derived;

[0017] Step 6: Update the current constraint relaxation factor based on the iteration information and the initial constraint relaxation factor, select the real offspring individuals from the candidate offspring pool using the constraint dominance criterion, evaluate the real offspring individuals, and update the current population according to the weight target value and fatigue life constraint value corresponding to the evaluated real offspring individuals;

[0018] Step 7: Construct a local search based on Gaussian process to locate the local area offspring individuals, update the iteration information, and judge whether the drive shaft corresponding to the optimal structural parameters obtained by the method in the current iteration reaches the weight and fatigue life indicators of the lightweight design of the full-rotation propeller drive shaft. If so, output the optimal structural parameters obtained by the method, otherwise go to step 2 until the weight and fatigue life indicators are reached.

[0019] Furthermore, the initial constraint relaxation factor in the optimization process is calculated based on the fatigue life constraint value of the drive shaft corresponding to each individual in the population in step 1. The specific calculation formula is as follows:

[0020] ,

[0021] In the above formula, represents the initial constraint relaxation factor when the number of iterations is equal to 0, It means that the individuals in the population are sorted in descending order according to the fatigue life constraint violation value. Individuals, It also corresponds to the current population The drive shaft is formed by the combination of the diameter and length structural parameter values ​​of each shaft section of the drive shaft corresponding to each individual. Indicates individual Fatigue life constraint violation value.

[0022] Furthermore, the step 2 calculates the truncation parameter based on the current iteration number and the fatigue life constraint value and weight target value of the drive shaft in the database, and selects the individuals in the database containing all the drive shaft information according to the truncation parameter to form the current database, which specifically includes the following sub-steps:

[0023] Calculate the attenuation parameter that changes with the number of iterations. The specific formula is as follows:

[0024] ,

[0025] In the above formula, represents the attenuation parameter value, t represents the number of iterations, Maxt Indicates the maximum number of iterations allowed by the method;

[0026] Calculate the cutoff parameter. The specific formula is as follows:

[0027] ,

[0028] In the above formula, Indicates truncated parameter value, and are two constants;

[0029] Calculate the comprehensive constraint violation value of individuals in the database containing all drive shaft information. The specific formula is as follows:

[0030] ,

[0031] In the above formula, Represents the database Individual, also the The drive shaft is formed by the combination of the diameter and length structural parameter values ​​of each shaft section of the drive shaft corresponding to each individual. Indicates individual The fatigue life and the combined constraint violation value of the boundary condition constraints are: Indicates individual The fatigue life constraint value of the azimuth thruster is Indicates the first Boundary conditions constrain individual The constraint value of Indicates the number of boundary condition constraints;

[0032] Sort all individuals in the database according to the comprehensive constraint violation value from small to large, and select the top Individuals form the current database, where Represents the number of all individuals in the database.

[0033] Furthermore, in the step 2, the individual diversity in the current database, the target value of the drive shaft weight and the drive shaft fatigue life constraint and the drive shaft load boundary condition constraint violation value are taken as three objectives, and individuals are selected from the current database based on the multi-objective non-dominated sorting method to form a dynamic population, which specifically includes the following sub-steps:

[0034] For any individual in the current database , the diversity calculation formula is as follows:

[0035] ,

[0036] In the above formula, Indicates individual Diversity, Indicates the current database. Indicates the current database individual;

[0037] Taking the diversity, weight target value, fatigue life and boundary condition constraint violation value of any individual in the current database as three objectives, a multi-objective non-dominated sorting method is used to sort the individuals in the current database, and the optimal non-dominated solution set is used as a dynamic population.

[0038] Furthermore, the step three specifically includes the following sub-steps:

[0039] In the feasibility rule, all individuals with zero constraint violation values ​​are ranked ahead of all individuals with non-zero constraint violation values. In the set of individuals with zero constraint violation values, individuals with smaller target values ​​are ranked ahead. In the set of individuals with non-zero constraint violation values, individuals with smaller constraint violation values ​​are ranked ahead.

[0040] For any individual in a dynamic population, the following differential mutation operations are performed to generate candidate offspring:

[0041] ,

[0042] In the above formula, Indicates for The generated Candidate offspring, express The sort value of represents the maximum ranking value of all individuals in the dynamic population, Represents a random number between 0 and 1. and They represent two different individuals randomly selected from the dynamic population.

[0043] Furthermore, the step 4 specifically includes the following sub-steps:

[0044] For any individual in a dynamic population , calculate all individuals in the current database and the corresponding candidate offspring The Euclidean distance between

[0045] Select the top 200 individuals from the current database according to the Euclidean distance from small to large to form candidate offspring individuals Neighborhood of;

[0046] In the candidate offspring In the neighborhood of , the optimal non-dominated set is determined by fast non-dominated sorting method with the individual target value, constraint violation value and diversity as three goals to form a modeling sample.

[0047] Furthermore, the calculation formula for the expected improvement in step 5 is as follows:

[0048] ,

[0049] In the above formula, Indicates for The expected increase in represents the minimum target value of all individuals in the modeling sample, Represents the Gaussian process machine learning model for The predicted value of represents the normal cumulative distribution function with mean 0 and variance 1, represents the probability density function of a normal distribution with mean 0 and variance 1, Represents the Gaussian process machine learning model for The prediction variance of .

[0050] Furthermore, in step 6, the current constraint relaxation factor is updated based on the iteration information and the initial constraint relaxation factor, and the specific calculation formula is as follows:

[0051] ,

[0052] In the above formula, It means the number of iterations is The constraint relaxation factor when Indicates the maximum number of iterations allowed by the method.

[0053] Furthermore, in step 6, the constraint dominance criterion is used to select real offspring individuals from the candidate offspring pool, the real offspring individuals are evaluated, and the current population is updated according to the weight target value and fatigue life constraint value corresponding to the evaluated real offspring individuals. The specific steps are as follows:

[0054] For each individual in the candidate offspring pool, in the constraint dominance criterion, first, the Gaussian process machine learning model is used to predict the weight target value and fatigue life constraint value of the drive shaft represented by each individual. Then, the best individual is selected from the candidate offspring pool as the real offspring individual according to the constraint dominance criterion. The sub-steps of the constraint dominance criterion are as follows:

[0055] (1) If the fatigue life constraint values ​​of all individuals are greater than zero, the individual with the Gaussian process machine learning prediction value of the minimum fatigue life constraint is taken as the best individual;

[0056] (2) Among the individuals whose fatigue life constraint value is less than zero, the individual with the Gaussian process machine learning prediction value of the minimum weight target is selected as the best individual;

[0057] Import the drive shaft corresponding to the real offspring individual into ANSYS Workbench for static analysis and obtain the weight target value of the drive shaft. Import the static analysis results and the periodic alternating load of the drive shaft into ANSYS nCodeDesignLife for fatigue life analysis and obtain the fatigue life constraint value of the drive shaft.

[0058] According to the feasibility rule, the individuals in the dynamic population are compared with their corresponding real offspring individuals after evaluation, and the better ones are used to replace the individuals in the dynamic population.

[0059] Furthermore, the construction in step seven locates the local area offspring individuals based on the local search of the Gaussian process and updates the iteration information, specifically including the following sub-steps:

[0060] Using the Gaussian process machine learning model, the following optimization problem is constructed:

[0061] ,

[0062] In the above formula, represents the Gaussian process machine learning model built for the azimuth thruster weight target, represents the Gaussian process machine learning model constructed for the fatigue life constraint of the azimuth thruster. Indicates the following information for the azimuth thruster: The Gaussian process machine learning model constructed by the boundary condition constraint function, and They represent the lower and upper limits of the length and diameter structural parameters of each shaft section of the azimuth thruster in the design space, To minimize the Gaussian process machine learning model, are the constraints that need to be satisfied;

[0063] The particle swarm optimization method is used to solve the above-constructed optimization problem and obtain local individuals. The drive shaft corresponding to the local individuals is imported into ANSYS Workbench for static analysis and the weight target value of the drive shaft is obtained. The static analysis results and the periodic alternating load of the drive shaft are imported into ANSYS nCode DesignLife for fatigue life analysis to obtain the fatigue life constraint value of the drive shaft.

[0064] Update iterations And other iteration information.

[0065] In summary, compared with the prior art, the above technical solution conceived by the present invention provides a machine learning-guided dynamic population optimization design method which mainly has the following beneficial effects:

[0066] 1. Considering the complex sub-feasible domain problem corresponding to the complex characteristics of fatigue life constraints, a constraint relaxation factor that adapts to the iterative state is designed to balance the degree of exploration of the target and constraints during the search process, thereby significantly reducing the possibility of falling into some complex sub-feasible domains.

[0067] 2. In the framework of multi-objective fast non-dominated sorting, the dynamic population is constructed by fully considering the diversity of individuals, the feasibility of fatigue life constraints and boundary condition constraints, and the convergence of weight objectives. This ensures that the population in each generation has high potential and good distribution, which provides the method with a strong global exploration capability.

[0068] 3. Constructing the Gaussian process machine learning model in the neighborhood of candidate offspring individuals rather than in the entire design space effectively reduces the modeling time of the Gaussian process machine learning model, improves the model's adaptability to candidate offspring individuals, and enhances the model's screening ability.

[0069] 4. With the help of the accurate prediction ability of the Gaussian process machine learning model, an efficient local search strategy is constructed to effectively avoid the oscillation phenomenon that may be caused by insufficient convergence speed in local areas.

[0070] 5. The present invention can accurately predict and search for the lightweight design problem of the azimuth propeller drive shaft, improve the accuracy of the optimization solution, and can be widely used in the design optimization of expensive problems, which is conducive to promotion and application. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 A simplified flow chart of a machine learning-guided dynamic population optimization design method provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0072] In order to make the purpose, technical scheme and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0073] See also Figure 1 The present invention provides a machine learning-guided dynamic population optimization design method, which is applicable to the lightweight design problem of the full-rotation propeller drive shaft. Specifically, the method mainly includes the following steps 1 to 7.

[0074] Step 1: Convert the lightweight design problem of the full-rotation propeller drive shaft into an expensive constrained optimization problem that minimizes the computational time of the drive shaft weight while satisfying the fatigue life constraint. The diameter and length of each shaft section of the drive shaft correspond to the structural parameters that need to be optimized during the lightweight design of the drive shaft. Combined with the matching relationship between the drive shaft and the bearing, the value range of the diameter and length structural parameters of each shaft section of the drive shaft is given. Therefore, the structural parameters and the value range constitute the design space of the expensive constraint optimization problem. The target value of the drive shaft weight obtained in ANSYS Workbench is used as the optimization target of the expensive constraint optimization problem. The fatigue life of the drive shaft obtained by fatigue life analysis in ANSYS nCode DesignLife is used as the optimization constraint of the expensive constraint optimization problem. Find the optimal combination of structural parameter values ​​within the design space to minimize the target value of the drive shaft weight while satisfying the fatigue life constraint of the drive shaft. First, initialize the population within the design space composed of the structural parameters and the value range to generate a population containing multiple population individuals. Each individual contains a set of diameter and length values ​​of each shaft section of the drive shaft, corresponding to a drive shaft. Then, import the drive shaft corresponding to each individual into ANSYS Static analysis is performed in Workbench to obtain the weight target value of the drive shaft, and the static analysis results and the periodic alternating load of the drive shaft are imported into ANSYS nCode DesignLife for fatigue life analysis to obtain the fatigue life constraint value of the drive shaft. All individuals in the current population and the corresponding weight target value and fatigue life constraint value are used to build a database. The iterative parameters of population evolution including the total number of iterations and convergence conditions are initialized according to the lightweight design indicators of the drive shaft. Then, the initial constraint relaxation factor in the optimization process is calculated based on the fatigue life constraint value of the drive shaft corresponding to each individual in the population.

[0075] Among them, the initial constraint relaxation factor in the optimization process is calculated based on the fatigue life constraint value of the drive shaft corresponding to each individual in the population. The specific calculation formula is as follows:

[0076] ,

[0077] In the above formula, represents the initial constraint relaxation factor when the number of iterations is equal to 0, It means that the individuals in the population are sorted in descending order according to the fatigue life constraint violation value. Individuals, It also corresponds to the current population The drive shaft is formed by the combination of the diameter and length structural parameter values ​​of each shaft section of the drive shaft corresponding to each individual. Indicates individual Fatigue life constraint violation value.

[0078] Step 2: Calculate the truncation parameter based on the current number of iterations and the fatigue life constraint value and weight target value of the drive shaft in the database. According to the truncation parameter, select individuals in the database containing all the drive shaft information to form the current database. With the individual diversity, drive shaft weight target value and drive shaft fatigue life constraint and drive shaft load boundary condition constraint violation value in the current database as three goals, select individuals from the current database based on the multi-objective non-dominated sorting method to form a dynamic population.

[0079] The truncation parameter is calculated based on the current iteration number and the fatigue life constraint value and weight target value of the drive shaft in the database, and the individuals in the database containing all the drive shaft information are selected according to the truncation parameter to form the current database, which specifically includes the following sub-steps:

[0080] Calculate the attenuation parameter that changes with the number of iterations. The specific formula is as follows:

[0081] ,

[0082] In the above formula, represents the attenuation parameter value, t represents the number of iterations, Maxt Indicates the maximum number of iterations allowed by the method;

[0083] Calculate the cutoff parameter. The specific formula is as follows:

[0084] ,

[0085] In the above formula, Indicates truncated parameter value, and are two constants;

[0086] Calculate the comprehensive constraint violation value of individuals in the database containing all drive shaft information. The specific formula is as follows:

[0087] ,

[0088] In the above formula, Represents the database Individual, also the The drive shaft is formed by the combination of the diameter and length structural parameter values ​​of each shaft section of the drive shaft corresponding to each individual. Indicates individual The fatigue life and the combined constraint violation value of the boundary condition constraints are: Indicates individual The fatigue life constraint value of the azimuth thruster is Indicates the first Boundary conditions constrain individual The constraint value of Indicates the number of boundary condition constraints;

[0089] Sort all individuals in the database according to the comprehensive constraint violation value from small to large, and select the top Individuals form the current database, where Represents the number of all individuals in the database.

[0090] With the three objectives of individual diversity in the current database, target value of drive shaft weight, fatigue life constraint of drive shaft, and violation value of drive shaft load boundary condition constraint, individuals are selected from the current database based on the multi-objective non-dominated sorting method to form a dynamic population, which specifically includes the following sub-steps:

[0091] For any individual in the current database , the diversity calculation formula is as follows:

[0092] ,

[0093] In the above formula, Indicates individual Diversity, Indicates the current database. Indicates the current database individual;

[0094] Taking the diversity, weight target value, fatigue life and boundary condition constraint violation value of any individual in the current database as three objectives, a multi-objective non-dominated sorting method is used to sort the individuals in the current database, and the optimal non-dominated solution set is used as a dynamic population.

[0095] Step 3: Using the weight target value, fatigue life and boundary condition constraint violation value of individuals in the dynamic population as indicators, the feasibility rules are used to sort the individuals in the dynamic population, and the corresponding differential mutation operations are designed according to the sorting values ​​to generate a candidate offspring pool. In the candidate offspring pool, each candidate offspring corresponds to a new combination of structural parameter values ​​of the drive shaft obtained through the differential mutation operation. The feasibility rules include the following three rules:

[0096] (1) Individuals that satisfy all constraints are better than individuals that do not satisfy all constraints;

[0097] (2) If both individuals satisfy all constraints, the individual with a smaller objective value is better;

[0098] (3) If two individuals do not satisfy all constraints, the individual with the smaller constraint violation value is better.

[0099] Among them, step three specifically includes the following sub-steps:

[0100] In the feasibility rule, all individuals with zero constraint violation values ​​are ranked ahead of all individuals with non-zero constraint violation values. In the set of individuals with zero constraint violation values, individuals with smaller target values ​​are ranked ahead. In the set of individuals with non-zero constraint violation values, individuals with smaller constraint violation values ​​are ranked ahead.

[0101] For any individual in a dynamic population, the following differential mutation operations are performed to generate candidate offspring:

[0102] ,

[0103] In the above formula, Indicates for The generated Candidate offspring, express The sort value of represents the maximum ranking value of all individuals in the dynamic population, Represents a random number between 0 and 1. and They represent two different individuals randomly selected from the dynamic population.

[0104] Step 4: Determine the neighborhood of each candidate offspring individual based on the Euclidean distance, and select modeling samples from the neighborhood for constructing the Gaussian process machine learning model considering the individual weight target value, fatigue life and boundary condition constraint feasibility and diversity.

[0105] Among them, step 4 specifically includes the following sub-steps:

[0106] For any individual in a dynamic population , calculate all individuals in the current database and the corresponding candidate offspring The Euclidean distance between

[0107] Select the first 200 individuals from the current database according to the Euclidean distance from small to large to form candidate offspring individuals Neighborhood of;

[0108] In the candidate offspring In the neighborhood of , the optimal non-dominated set is determined by fast non-dominated sorting method with the individual target value, constraint violation value and diversity as three goals to form a modeling sample.

[0109] Step 5: For each candidate offspring individual, a Gaussian process machine learning model is constructed using the determined modeling sample, and the expected improvement of the candidate offspring individual is derived.

[0110] The calculation formula for the expected improvement in step 5 is as follows:

[0111] ,

[0112] In the above formula, Indicates for The expected increase in represents the minimum target value of all individuals in the modeling sample, Represents the Gaussian process machine learning model for The predicted value of represents the normal cumulative distribution function with mean 0 and variance 1, represents the probability density function of a normal distribution with mean 0 and variance 1, Represents the Gaussian process machine learning model for The prediction variance of .

[0113] Step 6: Update the current constraint relaxation factor based on the iteration information and the initial constraint relaxation factor, use the constraint dominance criterion to select the real offspring individuals from the candidate offspring pool, evaluate the real offspring individuals, and update the current population according to the weight target value and fatigue life constraint value corresponding to the evaluated real offspring individuals.

[0114] Among them, step six updates the current constraint relaxation factor based on the iteration information and the initial constraint relaxation factor. The specific calculation formula is as follows:

[0115] ,

[0116] In the above formula, It means the number of iterations is The constraint relaxation factor when Indicates the maximum number of iterations allowed by the method.

[0117] In step 6, the constraint dominance criterion is used to select real offspring individuals from the candidate offspring pool, the real offspring individuals are evaluated, and the current population is updated according to the weight target value and fatigue life constraint value corresponding to the evaluated real offspring individuals. The specific steps are as follows:

[0118] For each individual in the candidate offspring pool, in the constraint dominance criterion, first, the Gaussian process machine learning model is used to predict the weight target value and fatigue life constraint value of the drive shaft represented by each individual. Then, the best individual is selected from the candidate offspring pool as the real offspring individual according to the constraint dominance criterion. The sub-steps of the constraint dominance criterion are as follows:

[0119] (1) If the fatigue life constraint values ​​of all individuals are greater than zero, the individual with the Gaussian process machine learning prediction value of the minimum fatigue life constraint is taken as the best individual;

[0120] (2) Among the individuals whose fatigue life constraint value is less than zero, the individual with the Gaussian process machine learning prediction value of the minimum weight target is selected as the best individual;

[0121] Import the drive shaft corresponding to the real offspring individual into ANSYS Workbench for static analysis and obtain the weight target value of the drive shaft. Import the static analysis results and the periodic alternating load of the drive shaft into ANSYS nCodeDesignLife for fatigue life analysis and obtain the fatigue life constraint value of the drive shaft.

[0122] According to the feasibility rule, the individuals in the dynamic population are compared with their corresponding real offspring individuals after evaluation, and the better ones are used to replace the individuals in the dynamic population.

[0123] Step 7: Construct a local search based on Gaussian process to locate the local area offspring individuals, update the iteration information, and judge whether the drive shaft corresponding to the optimal structural parameters obtained by the method in the current iteration reaches the weight and fatigue life indicators of the lightweight design of the full-rotation propeller drive shaft. If so, output the optimal structural parameters obtained by the method, otherwise go to step 2 until the weight and fatigue life indicators are reached.

[0124] Among them, the construction of step seven is based on the local search of the Gaussian process to locate the offspring individuals in the local area and update the iteration information, which specifically includes the following sub-steps:

[0125] Using the Gaussian process machine learning model, the following optimization problem is constructed:

[0126] ,

[0127] In the above formula, represents the Gaussian process machine learning model built for the azimuth thruster weight target, represents the Gaussian process machine learning model constructed for the fatigue life constraint of the azimuth thruster. Indicates the following information for the azimuth thruster: The Gaussian process machine learning model constructed by the boundary condition constraint function, and They represent the lower and upper limits of the length and diameter structural parameters of each shaft section of the azimuth thruster in the design space, To minimize the Gaussian process machine learning model, are the constraints that need to be satisfied;

[0128] The particle swarm optimization method is used to solve the above-constructed optimization problem and obtain local individuals. The drive shaft corresponding to the local individuals is imported into ANSYS Workbench for static analysis and the weight target value of the drive shaft is obtained. The static analysis results and the periodic alternating load of the drive shaft are imported into ANSYS nCode DesignLife for fatigue life analysis to obtain the fatigue life constraint value of the drive shaft.

[0129] Update iterations And other iteration information.

[0130] Example

[0131] This embodiment uses the classic test problem g06 in CEC2006 to illustrate a machine learning-guided dynamic population optimization design method provided in this embodiment. The optimization problem expression of g06 in CEC2006 in this embodiment is as follows:

[0132] ;

[0133] In the formula, For the design variables, To optimize the objective function, and They are the first optimization constraint function and the second optimization constraint function, To find the optimal solution to the classic testing problem, To minimize the classic test problem, are the constraints that need to be satisfied in the classic test problem.

[0134] In view of the above problems, a dynamic population optimization design method guided by machine learning in an embodiment of the present invention is used for processing. In order to further illustrate this embodiment, the maximum number of calls to the real simulation model is set to 1000, and the experimental results are shown in the following table. According to the results in the table, the optimal solution obtained by the method of this embodiment is infinitely close to the real optimal solution, which reflects the effectiveness of this embodiment in improving the optimization accuracy. It can be considered that the method of this embodiment has a good effect on the classical constrained optimization problem involved in the lightweight design problem of the full-rotation propeller drive shaft.

[0135] Comparison table of optimization results of different methods

[0136] The optimal solution obtained by this method The real optimal solution Target value -6961.83 -6961.81

[0137] The present invention provides a machine learning-guided dynamic population optimization design method for the lightweight design problem of the full-revolving propeller drive shaft. The method can effectively construct a constraint relaxation factor that adapts to the feasibility changes of the fatigue life constraint and the boundary constraint of the population in the iterative process, avoid falling into the local sub-feasible domain defined by the fatigue life constraint, construct a dynamic population that adapts to the iterative process based on individual distribution and potential information, and design an evolutionary operation that adapts to its search potential for each population individual, thereby enhancing the global adaptability to the lightweight design problem of the full-revolving propeller drive shaft. With the help of a high-potential individual refining strategy based on a Gaussian process machine learning model, the high-potential individuals in the current area are quickly located, and the convergence speed is accelerated. The method has strong applicability to the lightweight design problem of the full-revolving propeller drive shaft.

[0138] It will be easily understood by those skilled in the art that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A machine learning-guided dynamic population optimization design method, characterized in that: The method is applicable to the lightweight design problem of the azimuth propeller drive shaft, and the method comprises: Step 1: Convert the lightweight design problem of the full-rotation propeller drive shaft into an expensive constrained optimization problem that minimizes the computational time of the drive shaft weight while satisfying the fatigue life constraint. The diameter and length of each shaft section of the drive shaft correspond to the structural parameters that need to be optimized during the lightweight design of the drive shaft. Combined with the matching relationship between the drive shaft and the bearing, the value range of the diameter and length structural parameters of each shaft section of the drive shaft is given. Therefore, the structural parameters and the value range constitute the design space of the expensive constraint optimization problem. The target value of the drive shaft weight obtained in ANSYS Workbench is used as the optimization target of the expensive constraint optimization problem. The fatigue life of the drive shaft obtained by fatigue life analysis in ANSYS nCode DesignLife is used as the optimization constraint of the expensive constraint optimization problem. Find the optimal combination of structural parameter values ​​within the design space to minimize the target value of the drive shaft weight while satisfying the fatigue life constraint of the drive shaft. First, initialize the population within the design space composed of the structural parameters and the value range to generate a population containing multiple population individuals. Each individual contains a set of diameter and length values ​​of each shaft section of the drive shaft, corresponding to a drive shaft. Then, import the drive shaft corresponding to each individual into ANSYS Static analysis is performed in Workbench to obtain the weight target value of the drive shaft, and the static analysis results and the periodic alternating load of the drive shaft are imported into ANSYS nCode DesignLife for fatigue life analysis to obtain the fatigue life constraint value of the drive shaft. All individuals in the current population and the corresponding weight target value and fatigue life constraint value are used to build a database. The iteration parameters of population evolution including the total number of iterations and convergence conditions are initialized according to the lightweight design index of the drive shaft, and then the initial constraint relaxation factor in the optimization process is calculated based on the fatigue life constraint value of the drive shaft corresponding to each individual in the population. Step 2: Calculate the truncation parameter based on the current number of iterations and the fatigue life constraint value and weight target value of the drive shaft in the database, select individuals in the database containing all the drive shaft information according to the truncation parameter to form the current database, and select individuals from the current database based on the multi-objective non-dominated sorting method to form a dynamic population with the three objectives of individual diversity, drive shaft weight target value, drive shaft fatigue life constraint, and drive shaft load boundary condition constraint violation value in the current database; the truncation parameter is calculated based on the current number of iterations and the fatigue life constraint value and weight target value of the drive shaft in the database, and the individuals in the database containing all the drive shaft information are selected according to the truncation parameter to form the current database, which specifically includes the following sub-steps: Calculate the attenuation parameter that changes with the number of iterations. The specific formula is as follows: ， In the above formula, represents the attenuation parameter value, t represents the number of iterations, Maxt Indicates the maximum number of iterations allowed by the method; Calculate the cutoff parameter. The specific formula is as follows: ， In the above formula, Indicates truncated parameter value, and are two constants; Calculate the comprehensive constraint violation value of individuals in the database containing all drive shaft information. The specific formula is as follows: ， In the above formula, Represents the database Individual, also the The drive shaft is formed by the combination of the diameter and length structural parameter values ​​of each shaft section corresponding to each individual drive shaft. Indicates individual The fatigue life and the combined constraint violation value of the boundary condition constraints are: Indicates individual The fatigue life constraint value of the azimuth thruster is Indicates the first Boundary conditions constrain individual The constraint value of Indicates the number of boundary condition constraints; It means the number of iterations is Constraint relaxation factor when ; Sort all individuals in the database according to the comprehensive constraint violation value from small to large, and select the top Individuals form the current database, where Represents the number of all individuals in the database; Step 3: Using the weight target value, fatigue life and boundary condition constraint violation value of individuals in the dynamic population as indicators, the feasibility rules are used to sort the individuals in the dynamic population, and the corresponding differential mutation operations are designed according to the sorting values ​​to generate a candidate offspring pool. In the candidate offspring pool, each candidate offspring corresponds to a new combination of structural parameter values ​​of the drive shaft obtained through the differential mutation operation. The feasibility rules include the following three rules: (1) Individuals that satisfy all constraints are better than individuals that do not satisfy all constraints; (2) If both individuals satisfy all constraints, the individual with a smaller objective value is better; (3) If both individuals do not satisfy all constraints, the individual with a smaller constraint violation value is better; Step 4: Determine the neighborhood of each candidate offspring individual based on the Euclidean distance, and select modeling samples from the neighborhood for constructing the Gaussian process machine learning model by considering the individual weight target value, fatigue life, feasibility of boundary condition constraints, and diversity; Step 5: For each candidate offspring individual, a Gaussian process machine learning model is constructed using the determined modeling sample, and the expected improvement of the candidate offspring individual is derived; Step 6: Update the current constraint relaxation factor based on the iteration information and the initial constraint relaxation factor, select the real offspring individuals from the candidate offspring pool using the constraint dominance criterion, evaluate the real offspring individuals, and update the current population according to the weight target value and fatigue life constraint value corresponding to the evaluated real offspring individuals; the specific calculation formula for updating the current constraint relaxation factor based on the iteration information and the initial constraint relaxation factor in step 6 is as follows: ， In the above formula, It means the number of iterations is The constraint relaxation factor when Indicates the maximum number of iterations allowed by the method; Step 7: Construct a local search based on Gaussian process to locate the local area offspring individuals, update the iteration information, and judge whether the drive shaft corresponding to the optimal structural parameters obtained by the method in the current iteration reaches the weight and fatigue life indicators of the lightweight design of the full-rotation propeller drive shaft. If so, output the optimal structural parameters obtained by the method, otherwise go to step 2 until the weight and fatigue life indicators are reached.

2. The method according to claim 1, characterized in that In the step 1, the initial constraint relaxation factor in the optimization process is calculated based on the fatigue life constraint value of the drive shaft corresponding to each individual in the population. The specific calculation formula is as follows: ， In the above formula, represents the initial constraint relaxation factor when the number of iterations is equal to 0, It means that the individuals in the population are sorted in descending order according to the fatigue life constraint violation value. Individuals, It also corresponds to the current population The drive shaft is formed by the combination of the diameter and length structural parameter values ​​of each shaft section corresponding to each individual drive shaft. Indicates individual Fatigue life constraint violation value.

3. The method according to claim 1, characterized in that The step 2 is based on the three objectives of individual diversity in the current database, the target value of the drive shaft weight and the fatigue life constraint of the drive shaft and the violation value of the drive shaft load boundary condition constraint, and selects individuals from the current database based on the multi-objective non-dominated sorting method to form a dynamic population, which specifically includes the following sub-steps: For any individual in the current database , the diversity calculation formula is as follows: ， In the above formula, Indicates individual Diversity, Indicates the current database. Indicates the current database individual; Taking the diversity, weight target value, fatigue life and boundary condition constraint violation value of any individual in the current database as three objectives, a multi-objective non-dominated sorting method is used to sort the individuals in the current database, and the optimal non-dominated solution set is used as a dynamic population.

4. The method according to claim 1, characterized in that The step three specifically includes the following sub-steps: In the feasibility rule, all individuals with zero constraint violation values ​​are ranked ahead of all individuals with non-zero constraint violation values. In the set of individuals with zero constraint violation values, individuals with smaller target values ​​are ranked ahead. In the set of individuals with non-zero constraint violation values, individuals with smaller constraint violation values ​​are ranked ahead. For any individual in a dynamic population, the following differential mutation operations are performed to generate candidate offspring: ， In the above formula, Indicates for The generated Candidate offspring, express The sort value of represents the maximum ranking value of all individuals in the dynamic population, Represents a random number between 0 and 1. and They represent two different individuals randomly selected from the dynamic population.

5. The method according to claim 1, characterized in that The step 4 specifically includes the following sub-steps: For any individual in a dynamic population , calculate all individuals in the current database and the corresponding candidate offspring The Euclidean distance between Select the first 200 individuals from the current database according to the Euclidean distance from small to large to form candidate offspring individuals Neighborhood of; In the candidate offspring In the neighborhood of , the optimal non-dominated set is determined by fast non-dominated sorting method with the three objectives of individual target value, constraint violation value and diversity to form modeling samples.

6. The method according to claim 1, characterized in that The calculation formula of the expected lift in step 5 is as follows: ， In the above formula, Indicates for The expected increase in represents the minimum target value of all individuals in the modeling sample, Represents the Gaussian process machine learning model for The predicted value of represents the normal cumulative distribution function with mean 0 and variance 1, represents the probability density function of a normal distribution with mean 0 and variance 1, Represents the Gaussian process machine learning model for The prediction variance of .

7. The method according to claim 1, characterized in that In step 6, the constraint dominance criterion is used to select real offspring individuals from the candidate offspring pool, the real offspring individuals are evaluated, and the current population is updated according to the weight target value and fatigue life constraint value corresponding to the evaluated real offspring individuals. The specific steps are as follows: For each individual in the candidate offspring pool, in the constraint dominance criterion, first, the Gaussian process machine learning model is used to predict the weight target value and fatigue life constraint value of the drive shaft represented by each individual. Then, the best individual is selected from the candidate offspring pool as the real offspring individual according to the constraint dominance criterion. The sub-steps of the constraint dominance criterion are as follows: (1) If the fatigue life constraint values ​​of all individuals are greater than zero, the individual with the Gaussian process machine learning prediction value of the minimum fatigue life constraint is taken as the best individual; (2) Among the individuals whose fatigue life constraint value is less than zero, the individual with the Gaussian process machine learning prediction value of the minimum weight target is selected as the best individual; Import the drive shaft corresponding to the real offspring individual into ANSYS Workbench for static analysis and obtain the weight target value of the drive shaft. Import the static analysis results and the periodic alternating load of the drive shaft into ANSYS nCodeDesignLife for fatigue life analysis and obtain the fatigue life constraint value of the drive shaft. According to the feasibility rule, the individuals in the dynamic population are compared with their corresponding real offspring individuals after evaluation, and the better ones are used to replace the individuals in the dynamic population.

8. The method according to claim 1, characterized in that The construction in step 7 is based on the local search of the Gaussian process to locate the offspring individuals in the local area and update the iteration information, which specifically includes the following sub-steps: Using the Gaussian process machine learning model, the following optimization problem is constructed: ， In the above formula, represents the Gaussian process machine learning model built for the azimuth thruster weight target, represents the Gaussian process machine learning model constructed for the fatigue life constraint of the azimuth thruster. Indicates the following information for the azimuth thruster: The Gaussian process machine learning model constructed by the boundary condition constraint function, and They represent the lower and upper limits of the length and diameter structural parameters of each shaft section of the azimuth thruster in the design space, To minimize the Gaussian process machine learning model, are the constraints that need to be satisfied; It means the number of iterations is Constraint relaxation factor when ; The particle swarm optimization method is used to solve the above-constructed optimization problem and obtain local individuals. The drive shaft corresponding to the local individuals is imported into ANSYS Workbench for static analysis and the weight target value of the drive shaft is obtained. The static analysis results and the periodic alternating load of the drive shaft are imported into ANSYS nCode DesignLife for fatigue life analysis to obtain the fatigue life constraint value of the drive shaft. Update iterations And other iteration information.

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