Method for service life and lightweight design of ml-based z-peller drive shaft

Abstract

The application discloses a method for service life and lightweight design of a full-rotation propeller drive shaft based on ML, which comprises the following steps: (1) obtaining the service life and weight of the full-rotation propeller drive shaft through geometric modeling, statics analysis and fatigue analysis simulation, and establishing a mathematical model; (2) generating an optimization population in a multidimensional design space; (3) constructing an evolution starting point set based on the simulation result distribution state of the optimization population, and designing two-step progressive evolution operations to generate candidate offspring individual vectors; (4) designing inner evolution to accelerate the optimization speed, and screening by using Chebyshev aggregation functions; (5) performing simulation evaluation on the screened optimal candidate offspring individual vectors, and updating the accurate population; and (6) updating the optimization population, returning to step (3), and continuing until the optimized structure meets the design requirements. The application can efficiently solve the service life and lightweight optimization design problems of the full-rotation propeller drive shaft structure.

Description

Technical Field

[0001] This invention relates to the fields of artificial intelligence and swarm intelligence, and more specifically, to a method for improving the service life and lightweight design of a full-rotation propeller drive shaft based on machine learning. Background Technology

[0002] The azimuth thruster drive shaft is a key component of a ship's propulsion system, and its design significantly impacts a ship's fuel efficiency, range, and load capacity. Achieving a lightweight design for the azimuth thruster drive shaft can effectively reduce the overall weight of the ship, improving both economic efficiency and environmental friendliness. Simultaneously, the azimuth thruster drive shaft operates in the complex marine environment, requiring sufficient service life and reliability to ensure safe operation under prolonged, high-load conditions. Therefore, how to achieve a lightweight design for the azimuth thruster drive shaft while ensuring its service life has become an important issue in the field of marine engineering.

[0003] Traditional optimization design methods typically employ heuristic algorithms, such as genetic algorithms and particle swarm optimization. While these algorithms possess good global search capabilities, they often suffer from significant computational costs when dealing with complex multi-objective optimization problems. This is especially true when each evaluation requires calling time-consuming finite element simulation models, necessitating substantial computational resources and time for population evolution and fitness assessment. This leads to a substantial reduction in overall optimization efficiency, limiting the reduction of design cycles and the improvement of optimization results. The simulation evaluation of the azimuth thruster drive shaft involves complex mechanical analysis and service life calculations, where traditional heuristic algorithms are inefficient due to their high computational cost.

[0004] Machine learning (ML) technology can build rapid approximate models by learning from and analyzing existing simulation data, replacing complex simulation processes by simulating only the best candidate vectors. This approach not only significantly reduces computational costs and time consumption but also improves optimization efficiency within a limited design cycle, enabling engineers to explore and evaluate more design options and accelerate product development and innovation. However, many current optimization algorithms have not fully integrated the capabilities of machine learning, failing to fully realize its potential advantages in complex structural design. Furthermore, traditional methods mostly optimize for a single objective, making it difficult to simultaneously consider the service life and lightweight design of the azimuth thruster drive shaft, thus failing to meet the multi-objective optimization needs of practical engineering. Summary of the Invention

[0005] To address the limitations of existing technologies and the need for improved technologies, this invention proposes a machine learning-based (ML) method for the service life and lightweight design of azimuth thruster drive shafts. This method addresses the time-consuming and complex simulation characteristics of azimuth thruster drive shaft structural optimization design, as well as the design requirements of two objectives: service life and lightweight design. It researches and designs a machine learning optimization design method that determines different evolutionary starting point sets based on the distribution of the optimization population in the target space. The method determines different evolutionary starting point sets by analyzing the distribution of service life and weight information obtained from optimization population simulation in the target space. An evolutionary process is constructed based on a radial basis function machine learning model. Combined with a Chebyshev aggregation function constructed from two types of reference points, the optimal candidate individual offspring vectors are selected for service life and weight simulation, improving the optimization efficiency for both service life and lightweight design objectives of the azimuth thruster drive shaft structure. The ML-based azimuth thruster drive shaft service life and lightweight design method designed in this invention can simultaneously optimize multiple objectives for complex structures. It can not only be used for the service life and lightweight design of azimuth thruster drive shaft structures but also provides a usable algorithmic structure for the multi-performance design of other complex structures.

[0006] To achieve the above objectives, according to one aspect of the present invention, a method for improving the service life and lightweight design of a full-rotation thruster drive shaft based on ML is provided, the method comprising:

[0007] Step (1): Based on the static load on the azimuth thruster drive shaft, construct the geometric model of the azimuth thruster drive shaft in Pro / E and perform force decomposition. Import the geometric model into ANSYS Workbench for static analysis and read the weight of the azimuth thruster drive shaft. Import the static analysis results and the time-series load on the azimuth thruster drive shaft into ANSYS nCode DesignLife. The static load is the support load on the azimuth thruster drive shaft when it is fixed, and the time-series load is the dynamic load on the azimuth thruster drive shaft that changes with time when it is working. Based on the material properties of the azimuth thruster drive shaft, use the Goodman method to correct the service life SN curve in ANSYS nCode DesignLife software. Perform simulation in ANSYS nCode DesignLife to obtain the service life of the azimuth thruster drive shaft. Use the radius of each shaft segment, the length of each shaft segment, and the number of shaft segments as structural design parameters. Use the service life and weight of the azimuth thruster drive shaft as two optimization objectives. Derive the mathematical optimization model of the service life and lightweight design problem of the azimuth thruster drive shaft.

[0008] Step (2): Considering material strength, manufacturing process, and space constraints, determine the range of values ​​for the radius, length, and number of each shaft segment, and construct a multi-dimensional design space composed of the radius, length, and number of each shaft segment, where one dimension represents a structural design parameter; based on the dimensions of the multi-dimensional design space and computational resources, determine the number of individual vectors to be sampled. N Within a multidimensional design space, the simplex method is used to generate... N A uniformly distributed reference vector is generated within the multidimensional design space using a uniform sampling method. N Each vector contains individual vectors containing values ​​for the radius, length, and number of each axis segment. N The individual vectors form an optimization population; ANSYS nCodeDesignLife is used to simulate the service life and weight of each individual vector in the optimization population to obtain two target values: service life and weight, and all individual vector information is stored in the database.

[0009] Step (3): Based on the optimized population simulation results, construct an evolutionary starting point set in the distribution state of the target space composed of the two optimization objectives of service life and weight of the azimuth thruster drive shaft. For each evolutionary starting point set, within the multi-dimensional design space composed of structural design parameters such as the radius of each shaft segment, the length of each shaft segment, and the number of shaft segments, randomly select an initial individual vector in the evolutionary starting point set and perform a two-step progressive evolution operation to generate candidate offspring individual vectors. In the two-step progressive evolution operation, the first subpopulation and the best first-class candidate offspring individual vector are selected from the candidate offspring individual vectors generated by the first-step dimensional perturbation mutation operation according to the Chebyshev aggregation function constructed based on the ideal reference point. The best first-class candidate offspring individual vector is used as the starting point of the second-step dimensional perturbation mutation operation to perform the second-step dimensional perturbation mutation operation. The second subpopulation is selected from the candidate offspring individual vectors generated by the second-step dimensional perturbation mutation operation according to the Chebyshev aggregation function constructed based on the nadir reference point.

[0010] Step (4): For each subpopulation, inner evolution based on radial basis function machine learning model is used to obtain the optimal candidate subpopulation, and two Chebyshev aggregation functions are constructed based on the two reference points. Based on each Chebyshev aggregation value, the corresponding optimal candidate offspring individual vector is selected from the optimal candidate subpopulation.

[0011] Step (5): Use the simulation model of the service life and weight of the full-rotation propeller drive shaft structure to simulate and evaluate the optimal candidate offspring individual vectors, and update the accurate population and database;

[0012] Step (6): Design an optimized population update strategy. Use the best candidate subpopulation obtained in step (4) for the first type of subpopulation to update the optimized population. Also, judge the simulation evaluation results in step (5). If the service life and weight meet the design requirements, output the optimized structure of the azimuth thruster drive shaft corresponding to all individual vectors in the Pareto set selected from the database. Otherwise, go to step (3) until the optimized structure meets the design requirements.

[0013] Further, in step (1), the service life SN curve in ANSYS nCode DesignLife software is corrected according to the material properties of the azimuth thruster drive shaft using the Goodman method. The service life of the azimuth thruster drive shaft is obtained by simulation in ANSYS nCode DesignLife. The radius, length, and number of shaft segments are used as structural design parameters. The service life and weight of the azimuth thruster drive shaft are used as two optimization objectives. The mathematical optimization model of the service life and lightweight design problem of the azimuth thruster drive shaft is derived. The specific steps are as follows:

[0014] The first step is to correct the service life (SN) curve in ANSYS nCodeDesignLife software using the Goodman method based on the material properties of the azimuth thruster drive shaft. The Goodman method specifically includes the following steps:

[0015] Plot a Goodman diagram with the stress range corresponding to the material on the horizontal axis and the average stress corresponding to the material on the vertical axis. The straight line in the diagram represents the allowable stress line of the material, which is obtained by calculating the ultimate tensile strength and 0.2% yield strength of the material.

[0016] Based on the various load conditions that the azimuth thruster drive shaft actually bears during operation, calculate the actual stress range and average stress of the azimuth thruster drive shaft;

[0017] Plot the actual stress points on the Goodman diagram and correct the service life SN curve of the azimuth thruster drive shaft by comparing it with the allowable stress line.

[0018] The service life of the azimuth thruster drive shaft was obtained by simulation in ANSYS nCode DesignLife based on the modified service life SN curve.

[0019] The second step involves using the radius, length, and number of shaft segments as structural design parameters, and the service life and weight of the azimuth thruster drive shaft as two optimization objectives. A mathematical optimization model for the service life and lightweight design problem of the azimuth thruster drive shaft is derived, with the specific expression as follows:

[0020] ,

[0021] In the above formula, X represents the structural design parameters of the azimuth thruster drive shaft. This represents the radius of the first axis segment. Indicates the first M The radius of each shaft segment, This indicates the length of the first shaft segment. Indicates the first M The length of each shaft segment Indicates the number of shaft segments. This indicates the weight of the drive shaft of the azimuth thruster. This indicates the density of the drive shaft of the azimuth thruster. Indicates structural design parameters X The volume of the corresponding full-rotation thruster drive shaft, This indicates that the structural design parameters are X The corresponding full-rotation thruster drive shaft shape function at that time, This represents the service life of the azimuth thruster drive shaft under the Goodman method, with the constant C for material matching ranging from 2.56 to 3.85. This indicates the yield strength load of the material used in the drive shaft of the azimuth thruster. This indicates the yield stress of the material used in the drive shaft of the azimuth thruster. This represents the yield strain of the material used in the drive shaft of the azimuth thruster. k, m, and n correspond to the adjustment coefficients of the yield strength load, yield stress, and yield strain of the material used in the drive shaft of the azimuth thruster, respectively. The multidimensional design space is represented by the structural design parameters of the azimuth thruster drive shaft. Find represents finding the optimal solution of the structural optimization parameters. Min represents minimizing the weight of the azimuth thruster drive shaft and maximizing its service life. St represents the constraints that need to be satisfied.

[0022] Furthermore, step (3) specifically includes the following steps:

[0023] The first step is to perform a normalization operation based on the maximum and minimum values ​​of the two target values ​​of service life and weight obtained from the ANSYS nCode DesignLife simulation.

[0024] The second step is to calculate the minimum perpendicular distance between the normalized target value and each reference vector, and then connect each individual vector in the optimization population with the reference vector that has the minimum perpendicular distance:

[0025] The third step is to take all the individual vectors that are related to the reference vector as the starting point for the evolution of the reference vector.

[0026] The fourth step is to select the nearest neighboring reference vector based on the vertical distance from smallest to largest, and take all the individual vectors connected to the neighboring reference vector as the evolutionary starting set of the reference vector.

[0027] The fifth step involves randomly selecting an initial individual vector from the evolutionary starting point set of each reference vector, performing the first step of dimensional perturbation mutation operation within the multidimensional design space composed of structural design parameters such as the radius of each axis segment, the length of each axis segment, and the number of axis segments, and constructing a Chebyshev aggregation function based on the ideal reference point. The first type of subpopulation and the best first type of candidate offspring individual vector are then selected from the candidate offspring individual vectors generated by the first step of dimensional perturbation mutation operation.

[0028] The sixth step involves taking the best candidate offspring vectors selected based on the ideal reference point as the starting point, performing the second step of dimensional perturbation mutation operation within the multidimensional design space composed of structural design parameters such as the radius of each axis segment, the length of each axis segment, and the number of axis segments, and constructing a Chebyshev aggregation function based on the nadir reference point, and selecting the second type of subpopulation from the candidate offspring vectors generated by the second step of dimensional perturbation mutation operation.

[0029] The ideal reference point and the nadir reference point are determined by the following two equations:

[0030] ,

[0031] ,

[0032] In the above formula, The ideal reference point is at the th j The values ​​of each target, This indicates that the nadir reference point is at the 1st ytterbium position. j The values ​​of each target, DB For database, OP To optimize the population, Represents the first in the database j One target value, Represents the first machine learning model based on radial basis functions. j There are 1 target value, where m is the number of targets;

[0033] The Chebyshev convergence function based on the ideal reference point and the nadir reference point is determined by the following two equations:

[0034] ,

[0035] ,

[0036] In the above formula, It is a Chebyshev aggregation function constructed based on an ideal reference point. It is a Chebyshev aggregation function constructed based on the nadir reference point. Is the reference vector at the th i The weight of each goal The target value for the current individual. This indicates that the ideal reference point in the database is at the [number]th [position]. i One target value, This indicates the position of the nadir reference point in the database. i One target value, m That is the target number.

[0037] Furthermore, step (4) specifically involves the following steps:

[0038] The first step, for each subpopulation, sets a maximum number of approximate evaluations based on the radial basis function machine learning model in the inner evolutionary process. Within this maximum number of approximate evaluations, an adaptive differential evolution operation is used to generate candidate offspring individual vectors. The formula is as follows:

[0039] ,

[0040] In the above formula, Indicates the previous subpopulation p Randomly select an individual vector from %. Represents the current individual vector. and This represents two individual vectors randomly selected from the set consisting of the current subpopulation and the vector of the individual being replaced; the scaling factor is used. F Control the magnitude of individual vector variation;

[0041] The second step involves designing a two-layer screening strategy for the generated candidate offspring individual vectors. This strategy combines the distance between candidate offspring individual vectors with the aggregation degree information calculated by two Chebyshev aggregation functions constructed based on the reference point types corresponding to the two subpopulations. This yields the optimal candidate offspring individual vectors and the optimal candidate subpopulations for the first and second subpopulations, respectively. The specific steps of the two-layer screening strategy are as follows:

[0042] Based on the reference point type of the generated candidate offspring individual vectors, 3 were selected using Chebyshev aggregation values. N One candidate offspring individual vector;

[0043] Calculate the distance between the nearest candidate offspring vectors, and perform non-dominated sorting to obtain the ranking level with distance and Chebyshev aggregation value as two objectives;

[0044] Based on the ascending order of ranking levels, and using Chebyshev aggregation value as the screening criterion, the following were selected. N The vectors of each candidate offspring individual are used to form the optimal candidate subpopulation;

[0045] Select an optimal candidate individual vector from the optimal candidate subpopulation corresponding to each reference vector, and merge the optimal candidate individual vectors corresponding to all reference vectors to form a set of offspring individuals.

[0046] A Chebyshev aggregation function is constructed based on an ideal reference point, and the optimal candidate offspring individual vectors for the first type of subpopulation are selected from the offspring individual set.

[0047] A Chebyshev aggregation function is constructed based on the nadir reference point, and the optimal candidate offspring vectors for the second type of subpopulation are selected from the offspring individual set.

[0048] Furthermore, the step of updating the precise population in step (5) is as follows:

[0049] The first step is to perform static analysis on each optimal candidate offspring individual vector in ANSYS Workbench and read the weight of the azimuth thruster drive shaft. The static analysis results and the time-series load on the azimuth thruster drive shaft are then imported into ANSYS nCode DesignLife for service simulation to obtain the service life and weight of the optimal candidate offspring individual vector. The optimal candidate offspring individual vector information is then stored in the database. The optimal candidate offspring individual vectors saved in the database are all uniformly named individual vectors in subsequent steps.

[0050] The second step is to update the precise population based on the non-dominated sorting method.

[0051] Furthermore, step (6) specifically includes the following steps:

[0052] The first step is to find the individual vectors that are related to the reference vector based on the vertical distance in the updated precise population and the first type of subpopulation obtained from the inner evolution for each subinterval.

[0053] The second step is to calculate the Chebyshev aggregation value of the exact population individual vector associated with the reference vector, and select the individual vector with the smallest Chebyshev aggregation value as the optimal candidate offspring individual vector.

[0054] The third step is to calculate the Chebyshev aggregation value of the first subpopulation individual vectors associated with the reference vector, and select the individual vector with the smallest Chebyshev aggregation value as the optimal candidate offspring individual vector.

[0055] Fourth step: When the reference vector is not associated with an individual in the exact population, use the optimal candidate offspring individual vector in the first subpopulation for that reference vector as the updated optimized population individual vector.

[0056] Fifth step: When the reference vector is associated with an individual in the exact population, compare the Chebyshev aggregation values ​​of the best candidate offspring individual vector in the first subpopulation for the reference vector with those of the best candidate offspring individual vector in the exact population for the reference vector, and select the best candidate offspring individual vector with the smallest Chebyshev aggregation value as the updated optimized population individual vector.

[0057] The sixth step is to obtain the Pareto set of individual vectors in the database based on the non-dominated sorting, and to determine the service life and weight values ​​corresponding to all individual vectors in the Pareto set and the service life and lightweight design index of the azimuth thruster drive shaft under actual working conditions. If the design index is met, the optimized structure of the azimuth thruster drive shaft corresponding to all individual vectors in the currently obtained Pareto set is output; otherwise, the next iteration loop is entered until the design index is met.

[0058] On the other hand, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the ML-based azimuth thruster drive shaft service life and lightweight design method described in the foregoing embodiments.

[0059] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the steps of the ML-based method for service life and lightweight design of a full-rotation thruster drive shaft as described in the foregoing embodiments.

[0060] In summary, compared with the prior art, the ML-based method for improving the service life and lightweight design of the azimuth thruster drive shaft provided by this invention has the following improvements over the limitations of the prior art:

[0061] 1. Considering the problem that the service life and weight target values ​​obtained by simulation of the optimized population generated by the uniform sampling method are not uniformly distributed in the target space, a method is designed to construct the evolutionary starting point set based on the distribution state of the optimized population simulation results in the target space, so as to ensure that the two target values ​​of service life and weight are uniformly considered in the subspace divided by the reference vector.

[0062] 2. Randomly select an initial individual vector from the evolutionary starting point set to implement a two-step incremental evolution strategy, and use the optimal individual vector obtained in the first step as the starting point of the second step, thereby improving the quality of the optimized individuals in a targeted manner; at the same time, in the two evolutionary steps, Chebyshev aggregation functions constructed with different reference point types are used for screening, thereby obtaining two types of subpopulations with different convergence characteristics in a targeted manner.

[0063] 3. Chebyshev aggregation functions constructed based on two types of reference points were used to select the optimal candidate offspring individual vectors for service life and quality simulation. During the optimization process, only the optimal candidate offspring individual vectors were simulated for service life and quality. The service life and target values ​​of the remaining candidate individual vectors were predicted by the radial basis function machine learning model, which effectively accelerated the optimization efficiency and enabled the structural design parameters that meet the design requirements of the azimuth thruster drive shaft structure to be obtained within a limited design cycle.

[0064] 4. An optimized population update strategy was designed, which uses the optimal candidate subpopulation to update the optimized population. Taking into account both the simulated individual vectors and the individual vectors generated during the evolution process, it helps to provide a better starting point in the evolution process, thereby improving the optimization quality.

[0065] 5. This invention can optimize multi-objective problems involving complex simulations, improve the optimization efficiency of complex simulations, and can optimize multiple objectives simultaneously to achieve overall optimality. It is beneficial for the optimization application of various complex structures and has practicality. Attached Figure Description

[0066] Figure 1 A simplified flowchart of a ML-based method for service life and lightweight design of a full-rotation thruster drive shaft provided by the present invention. Detailed Implementation

[0067] To more clearly illustrate the objectives, technical solutions, and advantages of this invention, we will describe them in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. Furthermore, the technical features in the following embodiments can be combined with each other as long as they do not conflict with each other.

[0068] Please see Figure 1 This invention provides a method for designing the service life and lightweight design of a full-rotation thruster drive shaft based on machine learning (ML), which is applicable to the dual-objective optimization problem of service life and lightweight design of a full-rotation thruster drive shaft structure. Specifically, the method includes steps (1) to (6).

[0069] Step (1): Based on the static load on the azimuth thruster drive shaft, construct the geometric model of the azimuth thruster drive shaft in Pro / E and perform force decomposition. Import the geometric model into ANSYS Workbench for static analysis and read the weight of the azimuth thruster drive shaft. Import the static analysis results and the time-series load on the azimuth thruster drive shaft into ANSYS nCode DesignLife. The static load is the support load on the azimuth thruster drive shaft when it is fixed, and the time-series load is the dynamic load on the azimuth thruster drive shaft that changes with time when it is working. Based on the material properties of the azimuth thruster drive shaft, use the Goodman method to correct the service life SN curve in ANSYS nCode DesignLife software. Perform simulation in ANSYS nCode DesignLife to obtain the service life of the azimuth thruster drive shaft. Using the radius of each shaft segment, the length of each shaft segment, and the number of shaft segments as structural design parameters, and the service life and weight of the azimuth thruster drive shaft as two optimization objectives, derive the mathematical optimization model of the service life and lightweight design problem of the azimuth thruster drive shaft.

[0070] In step (1), the service life SN curve in ANSYS nCodeDesignLife software is corrected according to the material properties of the azimuth thruster drive shaft using the Goodman method. The service life of the azimuth thruster drive shaft is obtained by simulation in ANSYS nCodeDesignLife. The radius, length and number of shaft segments are used as structural design parameters. The service life and weight of the azimuth thruster drive shaft are used as two optimization objectives. The mathematical optimization model of the service life and lightweight design problem of the azimuth thruster drive shaft is derived. The specific steps are as follows:

[0071] The first step is to correct the service life (SN) curve in ANSYS nCodeDesignLife software using the Goodman method based on the material properties of the azimuth thruster drive shaft. The Goodman method specifically includes the following steps:

[0072] Plot a Goodman diagram with the stress range corresponding to the material on the horizontal axis and the average stress corresponding to the material on the vertical axis. The straight line in the diagram represents the allowable stress line of the material, which is obtained by calculating the ultimate tensile strength and 0.2% yield strength of the material.

[0073] Based on the various load conditions that the azimuth thruster drive shaft actually bears during operation, calculate the actual stress range and average stress of the azimuth thruster drive shaft;

[0074] Plot the actual stress points on the Goodman diagram and correct the service life SN curve of the azimuth thruster drive shaft by comparing it with the allowable stress line.

[0075] The service life of the azimuth thruster drive shaft was obtained by simulation in ANSYS nCode DesignLife based on the modified service life SN curve.

[0076] The second step involves using the radius, length, and number of shaft segments as structural design parameters, and the service life and weight of the azimuth thruster drive shaft as two optimization objectives. A mathematical optimization model for the service life and lightweight design problem of the azimuth thruster drive shaft is derived, with the specific expression as follows:

[0077] ,

[0078] In the above formula, X represents the structural design parameters of the azimuth thruster drive shaft. This represents the radius of the first axis segment. Indicates the first M The radius of each shaft segment, This indicates the length of the first shaft segment. Indicates the first M The length of each shaft segment Indicates the number of shaft segments. This indicates the weight of the drive shaft of the azimuth thruster. This indicates the density of the drive shaft of the azimuth thruster. Indicates structural design parameters X The volume of the corresponding full-rotation thruster drive shaft, This indicates that the structural design parameters are X The corresponding full-rotation thruster drive shaft shape function at that time, This represents the service life of the azimuth thruster drive shaft under the Goodman method, with the constant C for material matching ranging from 2.56 to 3.85. This indicates the yield strength load of the material used in the drive shaft of the azimuth thruster. This indicates the yield stress of the material used in the drive shaft of the azimuth thruster. This represents the yield strain of the material used in the drive shaft of the azimuth thruster. k, m, and n correspond to the adjustment coefficients of the yield strength load, yield stress, and yield strain of the material used in the drive shaft of the azimuth thruster, respectively. The multidimensional design space is represented by the structural design parameters of the azimuth thruster drive shaft. Find represents finding the optimal solution of the structural optimization parameters. Min represents minimizing the weight of the azimuth thruster drive shaft and maximizing its service life. St represents the constraints that need to be satisfied.

[0079] Step (2): Considering material strength, manufacturing process, and space constraints, determine the range of values ​​for the radius, length, and number of each shaft segment, and construct a multi-dimensional design space composed of the radius, length, and number of each shaft segment, where one dimension represents a structural design parameter; based on the dimensions of the multi-dimensional design space and computational resources, determine the number of individual vectors to be sampled. N Within a multidimensional design space, the simplex method is used to generate... N A uniformly distributed reference vector is generated within the multidimensional design space using a uniform sampling method. N Each vector contains individual vectors containing values ​​for the radius, length, and number of each axis segment. N An optimization population is formed by individual vectors; ANSYS nCodeDesignLife is used to simulate the service life and weight of each individual vector in the optimization population to obtain two target values: service life and weight, and all individual vector information is stored in the database.

[0080] Step (3): Based on the optimized population simulation results, construct an evolutionary starting point set in the distribution state of the target space composed of the two optimization objectives of the service life and weight of the azimuth thruster drive shaft. For each evolutionary starting point set, within the multi-dimensional design space composed of structural design parameters such as the radius of each shaft segment, the length of each shaft segment, and the number of shaft segments, randomly select an initial individual vector in the evolutionary starting point set and perform a two-step progressive evolution operation to generate candidate offspring individual vectors. In the two-step progressive evolution operation, the first type of subpopulation and the best first type of candidate offspring individual vector are selected from the candidate offspring individual vectors generated by the first step of the dimensional perturbation mutation operation according to the Chebyshev aggregation function constructed based on the ideal reference point. The best first type of candidate offspring individual vector is used as the starting point of the second step of the dimensional perturbation mutation operation to perform the second step of the dimensional perturbation mutation operation. The second type of subpopulation is selected from the candidate offspring individual vectors generated by the second step of the dimensional perturbation mutation operation according to the Chebyshev aggregation function constructed based on the nadir reference point.

[0081] The specific steps of step (3) are as follows:

[0082] The first step is to perform a normalization operation based on the maximum and minimum values ​​of the two target values ​​of service life and weight obtained from the ANSYS nCode DesignLife simulation.

[0083] The second step is to calculate the minimum perpendicular distance between the normalized target value and each reference vector, and then connect each individual vector in the optimization population with the reference vector that has the minimum perpendicular distance:

[0084] The third step is to take all the individual vectors that are related to the reference vector as the starting point for the evolution of the reference vector.

[0085] The fourth step is to select the nearest neighboring reference vector based on the vertical distance from smallest to largest, and take all the individual vectors connected to the neighboring reference vector as the evolutionary starting set of the reference vector.

[0086] The fifth step involves randomly selecting an initial individual vector from the evolutionary starting point set of each reference vector, performing the first step of dimensional perturbation mutation operation within the multidimensional design space composed of structural design parameters such as the radius of each axis segment, the length of each axis segment, and the number of axis segments, and constructing a Chebyshev aggregation function based on the ideal reference point. The first type of subpopulation and the best first type of candidate offspring individual vector are then selected from the candidate offspring individual vectors generated by the first step of dimensional perturbation mutation operation.

[0087] The sixth step involves taking the best candidate offspring vectors selected based on the ideal reference point as the starting point, performing the second step of dimensional perturbation mutation operation within the multidimensional design space composed of structural design parameters such as the radius of each axis segment, the length of each axis segment, and the number of axis segments, and constructing a Chebyshev aggregation function based on the nadir reference point, and selecting the second type of subpopulation from the candidate offspring vectors generated by the second step of dimensional perturbation mutation operation.

[0088] The ideal reference point and the nadir reference point are determined by the following two equations:

[0089] ,

[0090] ,

[0091] In the above formula, The ideal reference point is at the th j The values ​​of each target, This indicates that the nadir reference point is at the 1st ytterbium position. j The values ​​of each target, DB For database, OP To optimize the population, Represents the first in the database j One target value, Represents the first machine learning model based on radial basis functions. j There are 1 target value, where m is the number of targets;

[0092] The Chebyshev convergence function based on the ideal reference point and the nadir reference point is determined by the following two equations:

[0093] ,

[0094] ,

[0095] In the above formula, It is a Chebyshev aggregation function constructed based on an ideal reference point. It is a Chebyshev aggregation function constructed based on the nadir reference point. Is the reference vector at the th i The weight of each goal The target value for the current individual. This indicates that the ideal reference point in the database is at the [number]th [position]. i One target value, This indicates the position of the nadir reference point in the database. i One target value, m That is the target number.

[0096] Step (4): For each subpopulation, inner evolution based on radial basis function machine learning model is used to obtain the optimal candidate subpopulation. Two Chebyshev aggregation functions are constructed based on the two reference points. Based on each Chebyshev aggregation value, the corresponding optimal candidate offspring individual vector is selected from the optimal candidate subpopulation.

[0097] The specific steps of step (4) are as follows:

[0098] The first step, for each subpopulation, sets a maximum number of approximate evaluations based on the radial basis function machine learning model in the inner evolutionary process. Within this maximum number of approximate evaluations, an adaptive differential evolution operation is used to generate candidate offspring individual vectors. The formula is as follows:

[0099] ,

[0100] In the above formula, Indicates the previous subpopulation p Randomly select an individual vector from %. Represents the current individual vector. and This represents two individual vectors randomly selected from the set consisting of the current subpopulation and the vector of the individual being replaced; the scaling factor is used. F Control the magnitude of individual vector variation;

[0101] The second step involves designing a two-layer screening strategy for the generated candidate offspring individual vectors. This strategy combines the distance between candidate offspring individual vectors with the aggregation degree information calculated by two Chebyshev aggregation functions constructed based on the reference point types corresponding to the two subpopulations. This yields the optimal candidate offspring individual vectors and the optimal candidate subpopulations for the first and second subpopulations, respectively. The specific steps of the two-layer screening strategy are as follows:

[0102] Based on the reference point type of the generated candidate offspring individual vectors, 3 were selected using Chebyshev aggregation values.N One candidate offspring individual vector;

[0103] Calculate the distance between the nearest candidate offspring vectors, and perform non-dominated sorting to obtain the ranking level with distance and Chebyshev aggregation value as two objectives;

[0104] Based on the ascending order of ranking levels, and using Chebyshev aggregation value as the screening criterion, the following were selected. N The vectors of each candidate offspring individual are used to form the optimal candidate subpopulation;

[0105] Select an optimal candidate individual vector from the optimal candidate subpopulation corresponding to each reference vector, and merge the optimal candidate individual vectors corresponding to all reference vectors to form a set of offspring individuals.

[0106] A Chebyshev aggregation function is constructed based on an ideal reference point, and the optimal candidate offspring individual vectors for the first type of subpopulation are selected from the offspring individual set.

[0107] A Chebyshev aggregation function is constructed based on the nadir reference point, and the optimal candidate offspring vectors for the second type of subpopulation are selected from the offspring individual set.

[0108] Step (5): Use the simulation model of the service life and weight of the full-rotation propeller drive shaft structure to simulate and evaluate the optimal candidate offspring individual vectors, and update the accurate population and database.

[0109] The steps for updating the precise population in step (5) are as follows:

[0110] The first step is to perform static analysis on each optimal candidate offspring individual vector in ANSYS Workbench and read the weight of the azimuth thruster drive shaft. The static analysis results and the time-series load on the azimuth thruster drive shaft are then imported into ANSYS nCode DesignLife for service simulation to obtain the service life and weight of the optimal candidate offspring individual vector. The optimal candidate offspring individual vector information is then stored in the database. The optimal candidate offspring individual vectors saved in the database are all uniformly named individual vectors in subsequent steps.

[0111] The second step is to update the precise population based on the non-dominated sorting method.

[0112] Step (6): Design an optimized population update strategy. Use the best candidate subpopulation obtained in step (4) for the first type of subpopulation to update the optimized population. Also, judge the simulation evaluation results in step (5). If the service life and weight meet the design requirements, output the optimized structure of the azimuth thruster drive shaft corresponding to all individual vectors in the Pareto set selected from the database. Otherwise, go to step (3) until the optimized structure meets the design requirements.

[0113] The specific steps of step (6) are as follows:

[0114] The first step is to find the individual vectors that are related to the reference vector based on the vertical distance in the updated precise population and the first type of subpopulation obtained from the inner evolution for each subinterval.

[0115] The second step is to calculate the Chebyshev aggregation value of the exact population individual vector associated with the reference vector, and select the individual vector with the smallest Chebyshev aggregation value as the optimal candidate offspring individual vector.

[0116] The third step is to calculate the Chebyshev aggregation value of the first subpopulation individual vectors associated with the reference vector, and select the individual vector with the smallest Chebyshev aggregation value as the optimal candidate offspring individual vector.

[0117] Fourth step: When the reference vector is not associated with an individual in the exact population, use the optimal candidate offspring individual vector in the first subpopulation for that reference vector as the updated optimized population individual vector.

[0118] Fifth step: When the reference vector is associated with an individual in the exact population, compare the Chebyshev aggregation values ​​of the best candidate offspring individual vector in the first subpopulation for the reference vector with those of the best candidate offspring individual vector in the exact population for the reference vector, and select the best candidate offspring individual vector with the smallest Chebyshev aggregation value as the updated optimized population individual vector.

[0119] The sixth step is to obtain the Pareto set of individual vectors in the database based on the non-dominated sorting, and to determine the service life and weight values ​​corresponding to all individual vectors in the Pareto set and the service life and lightweight design index of the azimuth thruster drive shaft under actual working conditions. If the design index is met, the optimized structure of the azimuth thruster drive shaft corresponding to all individual vectors in the currently obtained Pareto set is output; otherwise, the next iteration loop is entered until the design index is met.

[0120] Example

[0121] This embodiment uses the benchmark function ZDT1 to illustrate the optimized performance of a machine learning-based method for optimizing the service life and lightweight design of a full-radius thruster drive shaft. The expression for the benchmark function ZDT1, which has two objectives, is as follows:

[0122] ,

[0123] In this embodiment, and These are two objective function expressions. This represents the first design variable. These are the remaining design variables in the multidimensional design space, excluding the first design variable. As an auxiliary constructor, f 1 is the first value of the objective function. It is the i-th design variable among the remaining design variables, where n is the dimension, i.e., the number of design variables.

[0124] The above benchmark test function ZDT1 was processed through steps (1) to (6) of the ML-based full-rotation thruster drive shaft service life and lightweight design method provided by the present invention to obtain the experimental results.

[0125] To illustrate this embodiment in more detail, the ML-based method for optimizing the service life and lightweight design of the azimuth thruster drive shaft in this embodiment is compared with another excellent Kriging-assisted Guided Evolutionary Algorithm (K-RVEA). The maximum number of simulation evaluations in this embodiment is set to 300, and the number of design variables is set to 30. The experimental results are shown in Table 1. The comparison method used is the average IGD value after 25 independent runs. With the same number of simulations, the method in this embodiment significantly outperforms the Kriging-assisted Guided Evolutionary Algorithm (K-RVEA). Therefore, it can be considered that the method in this embodiment can effectively solve the problem of optimizing the service life and lightweight design of the azimuth thruster drive shaft structure.

[0126] Table 1 Comparison of optimization results of different algorithms

[0127]

[0128] The ML-based method for service life and lightweight design of azimuth thruster drive shafts provided by this invention provides a systematic solution for the dual-objective design of service life and lightweight design of azimuth thruster drive shaft structures by constructing different evolutionary starting point sets based on the distribution state of target information obtained from simulation in the target space, adopting a two-step progressive evolution, and selecting a Chebyshev aggregation function constructed from two types of reference points.

[0129] In a second aspect, the present invention provides a computer device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the ML-based azimuth thruster drive shaft service life and lightweight design method of the aforementioned embodiments.

[0130] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the steps of the ML-based azimuth thruster drive shaft service life and lightweight design method of the aforementioned embodiments.

[0131] Those skilled in the art will readily understand that the above are merely 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 within the scope of protection of the present invention.

Claims

1. A method for improving the service life and lightweight design of a full-rotation thruster drive shaft based on ML, characterized in that, The method includes: Step (1): Based on the static load on the azimuth thruster drive shaft, construct the geometric model of the azimuth thruster drive shaft in Pro / E and perform force decomposition. Import the geometric model into ANSYS Workbench for static analysis and read the weight of the azimuth thruster drive shaft. Import the static analysis results and the time-series load on the azimuth thruster drive shaft into ANSYS nCode DesignLife. The static load is the support load on the azimuth thruster drive shaft when it is fixed, and the time-series load is the dynamic load on the azimuth thruster drive shaft that changes with time when it is working. Based on the material properties of the azimuth thruster drive shaft, use the Goodman method to correct the service life SN curve in ANSYS nCode DesignLife software. Perform simulation in ANSYS nCode DesignLife to obtain the service life of the azimuth thruster drive shaft. Use the radius of each shaft segment, the length of each shaft segment, and the number of shaft segments as structural design parameters. Use the service life and weight of the azimuth thruster drive shaft as two optimization objectives. Derive the mathematical optimization model of the service life and lightweight design problem of the azimuth thruster drive shaft. Step (2): Considering material strength, manufacturing process, and space constraints, determine the range of values ​​for the radius, length, and number of each shaft segment, and construct a multi-dimensional design space composed of the radius, length, and number of each shaft segment, where one dimension represents a structural design parameter; based on the dimensions of the multi-dimensional design space and computational resources, determine the number of individual vectors to be sampled. N Within a multidimensional design space, the simplex method is used to generate... N A uniformly distributed reference vector is generated within the multidimensional design space using a uniform sampling method. N Each vector contains individual vectors containing values ​​for the radius, length, and number of each axis segment. N The individual vectors form an optimization population; ANSYS nCode DesignLife is used to simulate the service life and weight of each individual vector in the optimization population to obtain two target values: service life and weight, and all individual vector information is stored in the database. Step (3): Based on the optimized population simulation results, construct an evolutionary starting point set in the distribution state of the target space composed of the two optimization objectives of service life and weight of the azimuth thruster drive shaft. For each evolutionary starting point set, within the multi-dimensional design space composed of structural design parameters such as the radius of each shaft segment, the length of each shaft segment, and the number of shaft segments, randomly select an initial individual vector in the evolutionary starting point set and perform a two-step progressive evolution operation to generate candidate offspring individual vectors. In the two-step progressive evolution operation, the first subpopulation and the best first-class candidate offspring individual vector are selected from the candidate offspring individual vectors generated by the first-step dimensional perturbation mutation operation according to the Chebyshev aggregation function constructed based on the ideal reference point. The best first-class candidate offspring individual vector is used as the starting point of the second-step dimensional perturbation mutation operation to perform the second-step dimensional perturbation mutation operation. The second subpopulation is selected from the candidate offspring individual vectors generated by the second-step dimensional perturbation mutation operation according to the Chebyshev aggregation function constructed based on the nadir reference point. Step (4): For each subpopulation, inner evolution based on radial basis function machine learning model is used to obtain the optimal candidate subpopulation, and two Chebyshev aggregation functions are constructed based on the two reference points. Based on each Chebyshev aggregation value, the corresponding optimal candidate offspring individual vector is selected from the optimal candidate subpopulation. Step (5): Use the simulation model of the service life and weight of the full-rotation propeller drive shaft structure to simulate and evaluate the optimal candidate offspring individual vectors, and update the accurate population and database; Step (6): Design an optimized population update strategy. Use the best candidate subpopulation obtained in step (4) for the first type of subpopulation to update the optimized population. Also, judge the simulation evaluation results in step (5). If the service life and weight meet the design requirements, output the optimized structure of the azimuth thruster drive shaft corresponding to all individual vectors in the Pareto set selected from the database. Otherwise, go to step (3) until the optimized structure meets the design requirements.

2. The method as described in claim 1, characterized in that, In step (1), the service life SN curve in ANSYS nCode DesignLife software is corrected according to the material properties of the azimuth thruster drive shaft using the Goodman method. The service life of the azimuth thruster drive shaft is obtained by simulation in ANSYS nCode DesignLife. The radius, length, and number of shaft segments are used as structural design parameters. The service life and weight of the azimuth thruster drive shaft are used as two optimization objectives. The mathematical optimization model of the service life and lightweight design problem of the azimuth thruster drive shaft is derived. The specific steps are as follows: The first step is to correct the service life (SN) curve in ANSYS nCodeDesignLife software using the Goodman method based on the material properties of the azimuth thruster drive shaft. The Goodman method specifically includes the following steps: Plot a Goodman diagram with the stress range corresponding to the material on the horizontal axis and the average stress corresponding to the material on the vertical axis. The straight line in the diagram represents the allowable stress line of the material, which is obtained by calculating the ultimate tensile strength and 0.2% yield strength of the material. Based on the various load conditions that the azimuth thruster drive shaft actually bears during operation, calculate the actual stress range and average stress of the azimuth thruster drive shaft; Plot the actual stress points on the Goodman diagram and correct the service life SN curve of the azimuth thruster drive shaft by comparing it with the allowable stress line. The service life of the azimuth thruster drive shaft was obtained by simulation in ANSYS nCode DesignLife based on the modified service life SN curve. The second step involves using the radius, length, and number of shaft segments as structural design parameters, and the service life and weight of the azimuth thruster drive shaft as two optimization objectives. A mathematical optimization model for the service life and lightweight design problem of the azimuth thruster drive shaft is derived, with the specific expression as follows: ， In the above formula, X represents the structural design parameters of the azimuth thruster drive shaft. This represents the radius of the first axis segment. Indicates the first M The radius of each shaft segment, This indicates the length of the first shaft segment. Indicates the first M The length of each shaft segment Indicates the number of shaft segments. This indicates the weight of the drive shaft of the azimuth thruster. This indicates the density of the drive shaft of the azimuth thruster. Indicates structural design parameters X The volume of the corresponding full-rotation thruster drive shaft, This indicates that the structural design parameters are X The corresponding full-rotation thruster drive shaft shape function at that time, This represents the service life of the azimuth thruster drive shaft under the Goodman method, with the constant C for material matching ranging from 2.56 to 3.

85. This indicates the yield strength load of the material used in the drive shaft of the azimuth thruster. This indicates the yield stress of the material used in the drive shaft of the azimuth thruster. This represents the yield strain of the material used in the drive shaft of the azimuth thruster. k, m, and n correspond to the adjustment coefficients of the yield strength load, yield stress, and yield strain of the material used in the drive shaft of the azimuth thruster, respectively. The multidimensional design space is represented by the structural design parameters of the azimuth thruster drive shaft. Find represents finding the optimal solution of the structural optimization parameters. Min represents minimizing the weight of the azimuth thruster drive shaft and maximizing its service life. St represents the constraints that need to be satisfied.

3. The method as described in claim 1, characterized in that, The specific steps of step (3) are as follows: The first step is to perform a normalization operation based on the maximum and minimum values ​​of the two target values ​​of service life and weight obtained from the ANSYS nCode DesignLife simulation. The second step is to calculate the minimum perpendicular distance between the normalized target value and each reference vector, and then connect each individual vector in the optimization population with the reference vector that has the minimum perpendicular distance: The third step is to take all the individual vectors that are related to the reference vector as the starting point for the evolution of the reference vector. The fourth step is to select the nearest neighboring reference vector based on the vertical distance from smallest to largest, and take all the individual vectors connected to the neighboring reference vector as the evolutionary starting set of the reference vector. The fifth step involves randomly selecting an initial individual vector from the evolutionary starting point set of each reference vector, performing the first step of dimensional perturbation mutation operation within the multidimensional design space composed of structural design parameters such as the radius of each axis segment, the length of each axis segment, and the number of axis segments, and constructing a Chebyshev aggregation function based on the ideal reference point. The first type of subpopulation and the best first type of candidate offspring individual vector are then selected from the candidate offspring individual vectors generated by the first step of dimensional perturbation mutation operation. The sixth step involves taking the best candidate offspring vectors selected based on the ideal reference point as the starting point, performing the second step of dimensional perturbation mutation operation within the multidimensional design space composed of structural design parameters such as the radius of each axis segment, the length of each axis segment, and the number of axis segments, and constructing a Chebyshev aggregation function based on the nadir reference point, and selecting the second type of subpopulation from the candidate offspring vectors generated by the second step of dimensional perturbation mutation operation. The ideal reference point and the nadir reference point are determined by the following two equations: ， ， In the above formula, The ideal reference point is indicated at the th... j The values ​​of each target, This indicates that the nadir reference point is at the 1st ytterbium position. j The values ​​of each target, DB For database, OP To optimize the population, Represents the first in the database j One target value, Represents the first machine learning model based on radial basis functions. j There are 1 target values, where m is the number of targets; The Chebyshev convergence function based on the ideal reference point and the nadir reference point is determined by the following two equations: ， ， In the above formula, It is a Chebyshev aggregation function constructed based on an ideal reference point. It is a Chebyshev aggregation function constructed based on the nadir reference point. Is the reference vector at the th i The weight of each goal The target value for the current individual. This indicates that the ideal reference point in the database is at the [number]th [position]. i One target value, This indicates the position of the nadir reference point in the database. i One target value, m That is the target number.

4. The method as described in claim 1, characterized in that, The specific steps of step (4) are as follows: The first step, for each subpopulation, sets a maximum number of approximate evaluations based on the radial basis function machine learning model in the inner evolutionary process. Within this maximum number of approximate evaluations, an adaptive differential evolution operation is used to generate candidate offspring individual vectors. The formula is as follows: ， In the above formula, Indicates the previous subpopulation p Randomly select an individual vector from %. Represents the current individual vector. and This represents two individual vectors randomly selected from the set consisting of the current subpopulation and the vector of the individual being replaced; the scaling factor is used. F Control the magnitude of individual vector variation; The second step involves designing a two-layer screening strategy for the generated candidate offspring individual vectors. This strategy combines the distance between candidate offspring individual vectors with the aggregation degree information calculated by two Chebyshev aggregation functions constructed based on the reference point types corresponding to the two subpopulations. This yields the optimal candidate offspring individual vectors and the optimal candidate subpopulations for the first and second subpopulations, respectively. The specific steps of the two-layer screening strategy are as follows: Based on the reference point type of the generated candidate offspring individual vectors, 3 were selected using Chebyshev aggregation values. N One candidate offspring individual vector; Calculate the distance between the nearest candidate offspring vectors, and perform non-dominated sorting to obtain the ranking level with distance and Chebyshev aggregation value as two objectives; Based on the ascending order of ranking levels, and using Chebyshev aggregation value as the screening criterion, the following were selected. N The vectors of each candidate offspring individual are used to form the optimal candidate subpopulation; Select an optimal candidate individual vector from the optimal candidate subpopulation corresponding to each reference vector, and merge the optimal candidate individual vectors corresponding to all reference vectors to form a set of offspring individuals. A Chebyshev aggregation function is constructed based on an ideal reference point, and the optimal candidate offspring individual vectors for the first type of subpopulation are selected from the offspring individual set. A Chebyshev aggregation function is constructed based on the nadir reference point, and the optimal candidate offspring vectors for the second type of subpopulation are selected from the offspring individual set.

5. The method as described in claim 1, characterized in that, The step of updating the precise population in step (5) is as follows: The first step is to perform static analysis on each optimal candidate offspring individual vector in ANSYS Workbench and read the weight of the azimuth thruster drive shaft. The static analysis results and the time-series load on the azimuth thruster drive shaft are then imported into ANSYS nCode DesignLife for service simulation to obtain the service life and weight of the optimal candidate offspring individual vector. The optimal candidate offspring individual vector information is then stored in the database. The optimal candidate offspring individual vectors saved in the database are all uniformly named individual vectors in subsequent steps. The second step is to update the precise population based on the non-dominated sorting method.

6. The method as described in claim 1, characterized in that, The specific steps of step (6) are as follows: The first step is to find the individual vectors that are related to the reference vector based on the vertical distance in the updated precise population and the first type of subpopulation obtained from the inner evolution for each subinterval. The second step is to calculate the Chebyshev aggregation value of the exact population individual vector associated with the reference vector, and select the individual vector with the smallest Chebyshev aggregation value as the optimal candidate offspring individual vector. The third step is to calculate the Chebyshev aggregation value of the first subpopulation individual vectors associated with the reference vector, and select the individual vector with the smallest Chebyshev aggregation value as the optimal candidate offspring individual vector. Fourth step: When the reference vector is not associated with an individual in the exact population, use the optimal candidate offspring individual vector in the first subpopulation for that reference vector as the updated optimized population individual vector. Fifth step: When the reference vector is associated with an individual in the exact population, compare the Chebyshev aggregation values ​​of the best candidate offspring individual vector in the first subpopulation for the reference vector with those of the best candidate offspring individual vector in the exact population for the reference vector, and select the best candidate offspring individual vector with the smallest Chebyshev aggregation value as the updated optimized population individual vector. The sixth step is to obtain the Pareto set of individual vectors in the database based on the non-dominated sorting, and to determine the service life and weight values ​​corresponding to all individual vectors in the Pareto set and the service life and lightweight design index of the azimuth thruster drive shaft under actual working conditions. If the design index is met, the optimized structure of the azimuth thruster drive shaft corresponding to all individual vectors in the currently obtained Pareto set is output; otherwise, the next iteration loop is entered until the design index is met.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-6.

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