ML-based full-revolving thruster driving shaft service life and lightweight design method

Abstract

The invention discloses an ML-based full-revolving thruster driving shaft service life and lightweight design method, which comprises the following steps: (1) obtaining the service life and weight of a full-revolving thruster driving shaft through geometric modeling, statics analysis and fatigue analysis simulation, and establishing a mathematical model; (2) generating an optimization population in the multi-dimensional design space; (3) constructing an evolution starting point set based on an optimized population simulation result distribution state, and designing a two-step progressive evolution operation to generate candidate offspring individual vectors; (4) inner layer evolution is designed to accelerate the optimization speed, and a Chebyshev aggregation function is adopted for screening; (5) performing simulation evaluation on the screened optimal candidate offspring individual vector, and updating the accurate population; and (6) updating the optimized population, and returning to the step (3) until the optimized structure meets the design requirements. According to the method, efficient solving can be carried out on the service life and lightweight optimization design problem of the driving shaft structure of the full-revolving thruster.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence and swarm intelligence technology, and in particular to a service life and lightweight design method for an azimuth propeller drive shaft based on ML. Background Art

[0002] The azimuth propeller drive shaft is a key component of the ship's propulsion system, and its design has a significant impact on the ship's fuel efficiency, range, and load capacity. Realizing the lightweight design of the azimuth propeller drive shaft can effectively reduce the overall weight of the ship and improve its economy and environmental protection. At the same time, the azimuth propeller drive shaft operates in a complex marine environment and needs to have sufficient service life and reliability to ensure safe operation under long-term, high-load conditions. Therefore, how to achieve lightweight design of the azimuth propeller drive shaft while ensuring its service life has become an important topic in the field of ship engineering.

[0003] Traditional optimization design methods usually use heuristic algorithms, such as genetic algorithms, particle swarm optimization algorithms, etc. These algorithms have good global search capabilities, but when dealing with complex multi-objective optimization problems, especially when each evaluation requires calling time-consuming finite element simulation models, they often require a lot of computing resources and time for population evolution and fitness evaluation, resulting in a significant reduction in overall optimization efficiency, limiting the shortening of the design cycle and the improvement of the optimization effect. The simulation evaluation of the full-rotation propeller drive shaft involves complex mechanical analysis and service life calculations. Traditional heuristic algorithms are less efficient in this high-computational cost environment.

[0004] ML (Machine Learning) technology can build a fast approximate model by learning and analyzing existing simulation data, replacing the complex simulation process and simulating only the best selected candidate individual vectors. This method not only greatly reduces the computing cost and time consumption, but also improves the optimization efficiency within a limited design cycle, allowing engineers to explore and evaluate more design options and accelerate product development and innovation. However, many current optimization algorithms have not yet fully integrated the capabilities of machine learning and have failed to fully realize their potential advantages in complex structural design; in addition, most traditional methods optimize for a single objective, making it difficult to simultaneously take into account the service life and lightweight design of the full-rotation propeller drive shaft, and cannot meet the needs of multi-objective optimization in actual engineering. Summary of the invention

[0005] In view of the limitations of the prior art or the need for improved technology, the present invention proposes a service life and lightweight design method for the drive shaft of an all-rotating propeller based on ML. Based on the time-consuming and complex simulation characteristics involved in the optimization design of the structure of the all-rotating propeller drive shaft, as well as the design requirements of the two goals of service life and lightweight, a machine learning optimization design method is studied and designed to determine different evolutionary starting point sets based on the distribution state of the optimized population in the target space. The method determines different evolutionary starting point sets by simulating the distribution state of the service life and weight information in the target space obtained by the optimization population, constructs an evolutionary process based on the radial basis function machine learning model, and combines the Chebyshev aggregation function constructed by two types of reference points to screen out the best candidate individual offspring vector for service life and weight simulation, thereby improving the optimization efficiency of the two goals of the service life and lightweight of the drive shaft structure of the all-rotating propeller. The service life and lightweight design method for the drive shaft of an all-rotating propeller based on ML designed by the present invention can simultaneously optimize multiple goals that adapt to complex structures. It can not only be used for the service life and lightweight design of the drive shaft structure of the all-rotating propeller, but also provides an available algorithm structure for the multi-performance design of other complex structures.

[0006] To achieve the above object, according to one aspect of the present invention, a method for designing the service life and lightweight of a drive shaft of an azimuth propeller based on ML is provided, the method comprising: Step (1): According to the static load on the azimuth propeller drive shaft, a geometric model of the azimuth propeller drive shaft is constructed in Pro / E and force decomposition is performed. The geometric model is imported into ANSYS Workbench for static analysis and the weight of the azimuth propeller drive shaft is read. The static analysis results and the sequential loads borne by the azimuth propeller drive shaft are imported into ANSYS nCode DesignLife together, wherein the static load is the support load borne by the azimuth propeller drive shaft when it is fixed, and the sequential load is the dynamic load that changes with time when the azimuth propeller drive shaft is working. According to the material properties of the azimuth propeller drive shaft, the service life SN curve in the ANSYS nCode DesignLife software is corrected by the Goodman method, and the service life of the azimuth propeller drive shaft is obtained by simulation in ANSYS nCode DesignLife. The radius of each shaft segment, the length of each shaft segment and the number of shaft segments are used as structural design parameters, and the service life and weight of the azimuth propeller drive shaft are used as two optimization targets. The mathematical optimization model of the service life and lightweight design problem of the azimuth propeller drive shaft is derived. Step (2): Considering the material strength, manufacturing process and space constraints, determine the range of values ​​of each shaft segment radius, each shaft segment length and the number of shaft segments, and construct a multidimensional design space consisting of each shaft segment radius, each shaft segment length and the number of shaft segments, where one dimension represents a structural design parameter; determine the number of individual vectors that need to be sampled based on the dimensions of the multidimensional design space and computing resources. N , in the multidimensional design space, the simplex method generates N uniformly distributed reference vectors; in the multidimensional design space, the uniform sampling method is used to generate N Each of these individual vectors contains the values ​​of the radius, length, and number of segments of each axis. N Individual vectors form an optimized population; ANSYS nCodeDesignLife is used to simulate the service life and weight of each individual vector in the optimized population to obtain the two target values ​​of service life and weight, and all individual vector information is stored in the database; Step (3): Based on the optimization population simulation results, an evolutionary starting point set is constructed in the distribution state of the target space composed of the two optimization objectives of the service life and weight of the full-rotation propeller drive shaft. For each evolutionary starting point set, an initial individual vector is randomly selected from the evolutionary starting point set within the multidimensional design space composed of the structural design parameters of the radius of each shaft segment, the length of each shaft segment and the number of shaft segments to implement a two-step progressive evolution operation to generate a candidate offspring individual vector. In the two-step progressive evolution operation, a first-class subpopulation and the best first-class candidate offspring individual vector are screened 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, and the second-step dimensional perturbation mutation operation is performed using the best first-class candidate offspring individual vector as the starting point of the second-step dimensional perturbation mutation operation, and the second-step dimensional perturbation mutation operation is performed according to the Chebyshev aggregation function constructed based on the nadir reference point. Step (4): For each type of subpopulation, the inner evolution based on the radial basis function machine learning model is used to obtain the optimal candidate subpopulation, and two Chebyshev aggregation functions are constructed according to the two types of 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 service life and weight simulation model of the azimuth propeller drive shaft structure to simulate and evaluate the optimal candidate offspring individual vectors, and update the precise population and database; Step (6): Design an optimization population update strategy, use the best candidate subpopulation obtained for the first type of subpopulation in step (4) to update the optimization population, and judge the simulation evaluation results in step (5). If the service life and weight meet the design requirements, output the optimized structure of the full-rotation propeller drive shaft corresponding to all individual vectors in the Pareto set screened by the database; otherwise, go to step (3) until the optimized structure meets the design requirements.

[0007] Furthermore, in the step (1), the service life SN curve in the ANSYS nCode DesignLife software is corrected by using the Goodman method according to the material properties of the azimuth propeller drive shaft, and the service life of the azimuth propeller drive shaft is obtained by simulation in the ANSYS nCode DesignLife. The radius of each shaft segment, the length of each shaft segment and the number of shaft segments are used as structural design parameters, and the service life and weight of the azimuth propeller drive shaft are used as two optimization targets. The mathematical optimization model of the service life and lightweight design problem of the azimuth propeller drive shaft is derived. The specific steps are as follows: The first step is to use the Goodman method to correct the service life SN curve in the ANSYS nCodeDesignLife software according to the material properties of the azimuth propeller drive shaft. The Goodman method specifically includes the following steps: ‌The stress range corresponding to the material is used as the horizontal axis, and the average stress corresponding to the material is used as the vertical axis to draw a Goodman diagram, where 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; ‌According to the various load conditions borne by the azimuth propeller drive shaft in actual operation, the actual stress range and average stress of the azimuth propeller drive shaft are calculated; ‌The actual stress points are plotted on the Goodman diagram and the service life SN curve of the azimuth propeller drive shaft is corrected by comparing it with the allowable stress line; Based on the modified service life SN curve, the service life of the azimuth propeller drive shaft is obtained by simulation in ANSYS nCode DesignLife. In the second step, the radius of each shaft segment, the length of each shaft segment and the number of shaft segments are used as structural design parameters, and the service life and weight of the azimuth propeller drive shaft are used as two optimization targets to derive the mathematical optimization model for the service life and lightweight design of the azimuth propeller drive shaft. The specific expression is as follows: , In the above formula, X represents the structural design parameters of the azimuth propeller drive shaft, represents the radius of the first axis segment, Indicates M The radius of the shaft segment, Indicates the length of the first axis segment, Indicates M The length of the shaft segment, Indicates the number of shaft segments, Indicates the weight of the azimuth propeller drive shaft, represents the density of the azimuth propeller drive shaft, Indicates the structural design parameters X The volume of the azimuth propeller drive shaft corresponding to Indicates that the structural design parameters are X The corresponding azimuth propeller drive shaft shape function is The service life of the azimuth propeller drive shaft under the Goodman method is represented by the constant C that matches the material, which ranges from 2.56 to 3.85. Indicates the yield strength load of the material used in the azimuth propeller drive shaft, Indicates the yield stress of the material used in the azimuth propeller drive shaft, represents the yield strain of the material used in the azimuth propeller drive shaft, 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 azimuth propeller drive shaft, respectively. It represents the multidimensional design space formed by the structural design parameters of the azimuth propeller drive shaft, Find represents the optimal solution of the structural optimization parameters, Min represents minimizing the weight of the azimuth propeller drive shaft and maximizing the service life of the azimuth propeller drive shaft, and St represents the constraints that need to be met.

[0008] Furthermore, the specific steps of step (3) are as follows: In the first step, a normalization operation based on the maximum and minimum values ​​is performed according to the two target values ​​of service life and weight obtained in the ANSYS nCode DesignLife simulation; The second step is to calculate the minimum vertical distance between the normalized target value and each reference vector, and connect each individual vector in the optimized population with the reference vector with the minimum vertical distance: The third step is, for the reference vectors that are associated with individual vectors, all the corresponding individual vectors are used as the evolutionary starting points of the reference vectors; Step 4: For reference vectors that have no individual vectors connected to them, select the neighboring reference vectors that are closest to the reference vectors according to the vertical distance from small to large, and use all individual vectors connected to the neighboring reference vectors as the evolutionary starting point set of the reference vectors; The fifth step is to randomly select an initial individual vector for each reference vector evolution starting point set, perform the first dimensional perturbation mutation operation in the multidimensional design space composed of the axis segment radius, the axis segment length and the axis segment number structural design parameters, and construct a Chebyshev aggregation function based on the ideal reference point, and select the first-class subpopulation and the best first-class candidate offspring individual vector from the candidate offspring individual vectors generated by the first dimensional perturbation mutation operation; The sixth step is to use the best first-class candidate offspring individual vectors selected based on the ideal reference point as the starting point, perform the second-step dimensional perturbation mutation operation within the multidimensional design space composed of the design parameters of the axis segment radius, the axis segment length, and the number of axis segments, and construct a Chebyshev aggregation function based on the nadir reference point, and select the second-class subpopulation from the candidate offspring individual vectors generated by the second-step dimensional perturbation mutation operation; The ideal reference point and the nadir reference point are determined by the following two equations: , , In the above formula, Indicates the ideal reference point j The value of a target, Indicates the nadir reference point at j The value of a target, DB For the database, OP To optimize the population, Indicates the first j target value, Represents the first j target value, m is the number of targets; The Chebyshev aggregation function based on the ideal reference point and the nadir reference point is determined by the following two equations: , , In the above formula, is a Chebyshev aggregation function based on an ideal reference point. is a Chebyshev aggregation function based on the nadir reference point. is the reference vector in i The weight of the target, is the target value of the current individual, Indicates that the ideal reference point in the database is i target value, Indicates the position of the nadir reference point in the database. i target value, m is the target number.

[0009] Furthermore, the specific steps of step (4) are as follows: In the first step, for each type of subpopulation, in the inner evolution, the maximum number of approximate evaluations based on the radial basis function machine learning model is set. Within the maximum number of approximate evaluations, the adaptive differential evolution operation is used to generate the candidate offspring individual vector formula as follows: , In the above formula, Indicates that from the previous p % randomly selects an individual vector, represents the current individual vector, and represents two individual vectors randomly selected from the current subpopulation and the set consisting of the replaced individual vector, and the scaling factor F Control the magnitude of individual vector variation; In the second step, a two-layer screening strategy is designed for the generated candidate offspring individual vectors, which respectively combines the distance between the candidate offspring individual vectors and the aggregation value information calculated by the two Chebyshev aggregation functions constructed by the reference point types corresponding to the two types of subpopulations to obtain the optimal candidate offspring individual vectors and the optimal candidate subpopulations for the first type of subpopulation and the second type of subpopulation. The specific steps of the two-layer screening strategy are as follows: According to the reference point type of the generated candidate offspring individual vector, 3 are selected based on the Chebyshev aggregation value. N A vector of candidate offspring individuals; Calculate the distance between the closest candidate offspring individual vectors, and perform non-dominated sorting with distance and Chebyshev aggregation value as two targets to obtain the ranking level; According to the ascending order of the ranking level, the Chebyshev aggregation value is used as the screening indicator to select N candidate offspring individual vectors 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; Constructing a Chebyshev aggregation function according to an ideal reference point, and screening the optimal candidate offspring individual vector for the first type of subpopulation from the offspring individual set; A Chebyshev aggregation function is constructed according to the nadir reference point, and the optimal candidate offspring individual vector for the second type of subpopulation is screened from the offspring individual set.

[0010] Furthermore, the step of updating the precise population in step (5) is specifically as follows: In the first step, static analysis is performed on each optimal candidate offspring individual vector in ANSYS Workbench and the weight of the azimuth propeller drive shaft is read. The static analysis results and the time series load borne by the azimuth propeller drive shaft are 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 stored in the database. The optimal candidate offspring individual vectors saved in the database are uniformly named as individual vectors in subsequent steps. In the second step, the precise population is updated according to the non-dominated sorting method.

[0011] Furthermore, the specific steps of step (6) are as follows: The first step is to find the individual vectors related to the reference vector according to the vertical distance in each subinterval, in the updated precise population and the first subpopulation obtained by the inner evolution; The second step is to calculate the Chebyshev aggregation value of the precise population individual vector associated with the reference vector, and select the individual vector with the minimum Chebyshev aggregation value as the optimal candidate offspring individual vector; The third step is to calculate the Chebyshev aggregation value of the first type of subpopulation individual vector associated with the reference vector, and select the individual vector with the minimum Chebyshev aggregation value as the optimal candidate offspring individual vector; Step 4: When the reference vector is not associated with an individual in the precise population, the optimal candidate offspring individual vector for the reference vector in the first subpopulation is used as the updated optimized population individual vector; Step 5: When the reference vector is associated with the individual in the precise population, the Chebyshev aggregation value of the optimal candidate offspring individual vector for the reference vector in the first subpopulation is compared with the optimal candidate offspring individual vector for the reference vector in the precise population, and the optimal candidate offspring individual vector with the minimum Chebyshev aggregation value is selected as the updated optimized population individual vector; The sixth step is to obtain the Pareto set of individual vectors in the database according to non-dominated sorting, and determine the satisfaction relationship between the service life and weight values ​​corresponding to all individual vectors in the Pareto set and the service life and lightweight design indicators of the full-rotation propeller drive shaft under actual working conditions. If the design indicators are met, the optimized structure of the full-rotation propeller drive shaft corresponding to all individual vectors in the current Pareto set is output; otherwise, the next iterative cycle is entered until the design indicators are met.

[0012] 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 when the processor executes the computer program, the steps of the ML-based full-rotation propeller drive shaft service life and lightweight design method described in the aforementioned embodiment are implemented.

[0013] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the ML-based full-rotation propeller drive shaft service life and lightweight design method described in the aforementioned embodiment.

[0014] In summary, compared with the prior art, the service life and lightweight design method of the azimuth propeller drive shaft based on ML provided by the present invention has the following improvements over the limitations of the prior art: Considering the problem that the two target values ​​of service life and weight obtained by simulation of the optimized population generated by the uniform sampling method are unevenly distributed in the target space, a method for constructing an evolutionary starting point set based on the distribution state of the simulation results of the optimized population in the target space is designed to ensure that the two target values ​​of service life and weight are uniformly considered in the subspace divided by the reference vector; an initial individual vector is randomly selected from the evolutionary starting point set to implement a two-step progressive evolution strategy, and the optimal individual vector obtained by the first step of evolution is used as the starting point of the second step, which improves the quality of the optimized individuals in a targeted manner; at the same time, the Chebyshev aggregation functions constructed with different reference point types are respectively used for screening in the two-step evolution, and two types of sub-populations with different convergence characteristics are obtained in a targeted manner; the Chebyshev aggregation functions constructed based on the two types of reference point types are respectively screened out to select the optimal candidate offspring individual vectors for service life and quality simulation; in the optimization process, only the service life and quality simulation are performed on the best candidate offspring individual vectors, and the service life and target values ​​of the remaining candidate individual vectors are predicted by the radial basis function machine learning model, which effectively speeds up the optimization efficiency, so that the structural design parameters that meet the structural design requirements of the full-rotation propeller drive shaft can be obtained within a limited design cycle; an optimization population update strategy is designed, and the optimization population is updated with the best candidate sub-population, and the individual vectors that have been simulated and the individual vectors generated during the evolution process are comprehensively considered, which helps to provide a better starting point in the evolution process, thereby improving the optimization quality; the present invention can optimize multi-objective problems involving complex simulations, improves the optimization efficiency of complex simulations, and can optimize multiple objectives at the same time to achieve the overall optimum, which is beneficial to the optimization application of various complex structures and is practical. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 A simplified flow chart of the service life and lightweight design method of an azimuth propeller drive shaft based on ML provided by the present invention. DETAILED DESCRIPTION

[0015] In order to more clearly illustrate the purpose, technical solutions and advantages of the present invention, we will describe it in detail with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit it. In addition, as long as the technical features in the following embodiments do not conflict with each other, they can be combined with each other.

[0016] See also Figure 1 The present invention provides a method for designing the service life and lightweight of a full-revolving propeller drive shaft based on ML, which is applicable to the two-objective optimization problem of the service life and lightweight of the full-revolving propeller drive shaft structure. Specifically, the method includes steps (1) to (6).

[0017] Step (1): According to the static load on the azimuth propeller drive shaft, a geometric model of the azimuth propeller drive shaft is constructed in Pro / E and force decomposition is performed. The geometric model is imported into ANSYS Workbench for static analysis and the weight of the azimuth propeller drive shaft is read. The static analysis results and the sequential loads borne by the azimuth propeller drive shaft are imported into ANSYS nCode DesignLife together, wherein the static load is the support load borne by the azimuth propeller drive shaft when it is fixed, and the sequential load is the dynamic load that changes with time when the azimuth propeller drive shaft is working. According to the material properties of the azimuth propeller drive shaft, the service life SN curve in the ANSYS nCode DesignLife software is corrected by the Goodman method, and the service life of the azimuth propeller drive shaft is obtained by simulation in ANSYS nCode DesignLife. The radius of each shaft segment, the length of each shaft segment and the number of shaft segments are used as structural design parameters, and the service life and weight of the azimuth propeller drive shaft are used as two optimization targets. The mathematical optimization model of the service life and lightweight design problem of the azimuth propeller drive shaft is derived.

[0018] In step (1), the service life SN curve in the ANSYS nCodeDesignLife software is corrected by using the Goodman method according to the material properties of the azimuth propeller drive shaft, and the service life of the azimuth propeller drive shaft is obtained by simulation in ANSYS nCode DesignLife. The radius of each shaft segment, the length of each shaft segment and the number of shaft segments are used as structural design parameters, and the service life and weight of the azimuth propeller drive shaft are used as two optimization targets. The mathematical optimization model of the service life and lightweight design problem of the azimuth propeller drive shaft is derived. The specific steps are as follows: The first step is to use the Goodman method to correct the service life SN curve in the ANSYS nCodeDesignLife software according to the material properties of the azimuth propeller drive shaft. The Goodman method specifically includes the following steps: ‌The stress range corresponding to the material is used as the horizontal axis, and the average stress corresponding to the material is used as the vertical axis to draw a Goodman diagram, where 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; ‌According to the various load conditions borne by the azimuth propeller drive shaft in actual operation, the actual stress range and average stress of the azimuth propeller drive shaft are calculated; ‌The actual stress points are plotted on the Goodman diagram and the service life SN curve of the azimuth propeller drive shaft is corrected by comparing it with the allowable stress line; Based on the modified service life SN curve, the service life of the azimuth propeller drive shaft is obtained by simulation in ANSYS nCode DesignLife. In the second step, the radius of each shaft segment, the length of each shaft segment and the number of shaft segments are used as structural design parameters, and the service life and weight of the azimuth propeller drive shaft are used as two optimization targets to derive the mathematical optimization model for the service life and lightweight design of the azimuth propeller drive shaft. The specific expression is as follows: , In the above formula, X represents the structural design parameters of the azimuth propeller drive shaft, represents the radius of the first axis segment, Indicates M The radius of the shaft segment, Indicates the length of the first axis segment, Indicates M The length of the shaft segment, Indicates the number of shaft segments, Indicates the weight of the azimuth propeller drive shaft, represents the density of the azimuth propeller drive shaft, Indicates the structural design parameters X The volume of the azimuth propeller drive shaft corresponding to Indicates that the structural design parameters are X The corresponding azimuth propeller drive shaft shape function is The service life of the azimuth propeller drive shaft under the Goodman method is represented by the constant C that matches the material, which ranges from 2.56 to 3.85. Indicates the yield strength load of the material used in the azimuth propeller drive shaft, Indicates the yield stress of the material used in the azimuth propeller drive shaft, represents the yield strain of the material used in the azimuth propeller drive shaft, 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 azimuth propeller drive shaft, respectively. It represents the multidimensional design space formed by the structural design parameters of the azimuth propeller drive shaft, Find represents the optimal solution of the structural optimization parameters, Min represents minimizing the weight of the azimuth propeller drive shaft and maximizing the service life of the azimuth propeller drive shaft, and St represents the constraints that need to be met.

[0019] Step (2): Considering the material strength, manufacturing process and space constraints, determine the range of values ​​of each shaft segment radius, each shaft segment length and the number of shaft segments, and construct a multidimensional design space consisting of each shaft segment radius, each shaft segment length and the number of shaft segments, where one dimension represents a structural design parameter; determine the number of individual vectors that need to be sampled based on the dimensions of the multidimensional design space and computing resources. N , in the multidimensional design space, the simplex method generates N uniformly distributed reference vectors; in the multidimensional design space, the uniform sampling method is used to generate N Each of these individual vectors contains the values ​​of the radius, length, and number of segments of each axis. N Individual vectors form an optimized population; ANSYS nCodeDesignLife is used to simulate the service life and weight of each individual vector in the optimized population to obtain the two target values ​​of service life and weight, and all individual vector information is stored in the database.

[0020] Step (3): Based on the optimization population simulation results, an evolutionary starting point set is constructed in the distribution state of the target space composed of the two optimization objectives of the service life and weight of the full-rotation propeller drive shaft. For each evolutionary starting point set, an initial individual vector is randomly selected from the evolutionary starting point set within the multidimensional design space composed of the structural design parameters of the radius of each shaft segment, the length of each shaft segment and the number of shaft segments to implement a two-step progressive evolution operation to generate a candidate offspring individual vector. In the two-step progressive evolution operation, the first type of sub-population and the best first type of candidate offspring individual vector are screened 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, and the second step dimensional perturbation mutation operation is performed using the best first type of candidate offspring individual vector as the starting point of the second step dimensional perturbation mutation operation, and the second type of sub-population is screened 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.

[0021] The specific steps of step (3) are as follows: In the first step, a normalization operation based on the maximum and minimum values ​​is performed according to the two target values ​​of service life and weight obtained in the ANSYS nCode DesignLife simulation; The second step is to calculate the minimum vertical distance between the normalized target value and each reference vector, and connect each individual vector in the optimized population with the reference vector with the minimum vertical distance: The third step is, for the reference vectors that are associated with individual vectors, all the corresponding individual vectors are used as the evolutionary starting points of the reference vectors; Step 4: For reference vectors that have no individual vectors connected to them, select the neighboring reference vectors that are closest to the reference vectors according to the vertical distance from small to large, and use all individual vectors connected to the neighboring reference vectors as the evolutionary starting point set of the reference vectors; The fifth step is to randomly select an initial individual vector for each reference vector evolution starting point set, perform the first dimensional perturbation mutation operation in the multidimensional design space composed of the axis segment radius, the axis segment length and the axis segment number structural design parameters, and construct a Chebyshev aggregation function based on the ideal reference point, and select the first-class subpopulation and the best first-class candidate offspring individual vector from the candidate offspring individual vectors generated by the first dimensional perturbation mutation operation; The sixth step is to use the best first-class candidate offspring individual vectors selected based on the ideal reference point as the starting point, perform the second-step dimensional perturbation mutation operation within the multidimensional design space composed of the design parameters of the axis segment radius, the axis segment length, and the number of axis segments, and construct a Chebyshev aggregation function based on the nadir reference point, and select the second-class subpopulation from the candidate offspring individual vectors generated by the second-step dimensional perturbation mutation operation; The ideal reference point and the nadir reference point are determined by the following two equations: , , In the above formula, Indicates the ideal reference point j The value of a target, Indicates the nadir reference point at j The value of a target, DB For the database, OP To optimize the population, Indicates the first j target value, Represents the first j target value, m is the number of targets; The Chebyshev aggregation function based on the ideal reference point and the nadir reference point is determined by the following two equations: , , In the above formula, is a Chebyshev aggregation function based on an ideal reference point. is a Chebyshev aggregation function based on the nadir reference point. is the reference vector in i The weight of the target, is the target value of the current individual, Indicates that the ideal reference point in the database is i target value, Indicates the position of the nadir reference point in the database. i target value, m is the target number.

[0022] Step (4): For each type of subpopulation, the inner evolution based on the radial basis function machine learning model is used to obtain the optimal candidate subpopulation, and two Chebyshev aggregation functions are constructed according to the two types of reference points. Based on each Chebyshev aggregation value, the corresponding optimal candidate offspring individual vector is selected from the optimal candidate subpopulation.

[0023] The specific steps of step (4) are as follows: In the first step, for each type of subpopulation, in the inner evolution, the maximum number of approximate evaluations based on the radial basis function machine learning model is set. Within the maximum number of approximate evaluations, the adaptive differential evolution operation is used to generate the candidate offspring individual vector formula as follows: , In the above formula, Indicates that from the previous p % randomly selects an individual vector, represents the current individual vector, and represents two individual vectors randomly selected from the current subpopulation and the set consisting of the replaced individual vector, and the scaling factor F Control the magnitude of individual vector variation; In the second step, a two-layer screening strategy is designed for the generated candidate offspring individual vectors, which respectively combines the distance between the candidate offspring individual vectors and the aggregation value information calculated by the two Chebyshev aggregation functions constructed by the reference point types corresponding to the two types of subpopulations to obtain the optimal candidate offspring individual vectors and the optimal candidate subpopulations for the first type of subpopulation and the second type of subpopulation. The specific steps of the two-layer screening strategy are as follows: According to the reference point type of the generated candidate offspring individual vector, 3 are selected based on the Chebyshev aggregation value. N A vector of candidate offspring individuals; Calculate the distance between the closest candidate offspring individual vectors, and perform non-dominated sorting with distance and Chebyshev aggregation value as two targets to obtain the ranking level; According to the ascending order of the ranking level, the Chebyshev aggregation value is used as the screening indicator to select N candidate offspring individual vectors 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; Constructing a Chebyshev aggregation function according to an ideal reference point, and screening the optimal candidate offspring individual vector for the first type of subpopulation from the offspring individual set; A Chebyshev aggregation function is constructed according to the nadir reference point, and the optimal candidate offspring individual vector for the second type of subpopulation is screened from the offspring individual set. Step (5): Use the service life and weight simulation model of the azimuth propeller drive shaft structure to simulate and evaluate the optimal candidate offspring individual vectors, and update the precise population and database.

[0024] The steps for updating the precise population in step (5) are as follows: In the first step, static analysis is performed on each optimal candidate offspring individual vector in ANSYS Workbench and the weight of the azimuth propeller drive shaft is read. The static analysis results and the time series load borne by the azimuth propeller drive shaft are 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 stored in the database. The optimal candidate offspring individual vectors saved in the database are uniformly named as individual vectors in subsequent steps. In the second step, the precise population is updated according to the non-dominated sorting method.

[0025] Step (6): Design an optimization population update strategy, use the best candidate subpopulation obtained for the first type of subpopulation in step (4) to update the optimization population, and judge the simulation evaluation results in step (5). If the service life and weight meet the design requirements, output the optimized structure of the full-rotation propeller drive shaft corresponding to all individual vectors in the Pareto set screened by the database; otherwise, go to step (3) until the optimized structure meets the design requirements.

[0026] The specific steps of step (6) are as follows: The first step is to find the individual vectors related to the reference vector according to the vertical distance in each subinterval, in the updated precise population and the first subpopulation obtained by the inner evolution; The second step is to calculate the Chebyshev aggregation value of the precise population individual vector associated with the reference vector, and select the individual vector with the minimum Chebyshev aggregation value as the optimal candidate offspring individual vector; The third step is to calculate the Chebyshev aggregation value of the first type of subpopulation individual vector associated with the reference vector, and select the individual vector with the minimum Chebyshev aggregation value as the optimal candidate offspring individual vector; Step 4: When the reference vector is not associated with an individual in the precise population, the optimal candidate offspring individual vector for the reference vector in the first subpopulation is used as the updated optimized population individual vector; Step 5: When the reference vector is associated with the individual in the precise population, the Chebyshev aggregation value of the optimal candidate offspring individual vector for the reference vector in the first subpopulation is compared with the optimal candidate offspring individual vector for the reference vector in the precise population, and the optimal candidate offspring individual vector with the minimum Chebyshev aggregation value is selected as the updated optimized population individual vector; The sixth step is to obtain the Pareto set of individual vectors in the database according to non-dominated sorting, and determine the satisfaction relationship between the service life and weight values ​​corresponding to all individual vectors in the Pareto set and the service life and lightweight design indicators of the full-rotation propeller drive shaft under actual working conditions. If the design indicators are met, the optimized structure of the full-rotation propeller drive shaft corresponding to all individual vectors in the current Pareto set is output; otherwise, the next iterative cycle is entered until the design indicators are met.

[0027] Example This embodiment uses the benchmark test function ZDT1 to illustrate the optimization performance of the service life and lightweight design method of the azimuth propeller drive shaft based on ML provided in this embodiment. The expression of the benchmark test function ZDT1 with two objectives is as follows: , In this embodiment, and are two objective function expressions, represents the first design variable, are the remaining design variables in the multidimensional design space except the first design variable, is an auxiliary constructor, f 1 is the first objective function value, is the i-th design variable among the other remaining design variables, and n is the dimension, i.e., the number of design variables.

[0028] The benchmark test function ZDT1 is processed through steps (1) to (6) of the ML-based service life and lightweight design method for an azimuth propeller drive shaft provided by the present invention to obtain experimental results.

[0029] In order to illustrate this embodiment in more detail, the service life and lightweight design method of the azimuth propeller drive shaft based on ML in this embodiment is compared with another excellent Kriging-assisted reference vector guided evolutionary algorithm (K-RVEA), and the maximum number of simulation evaluations in this embodiment is set to 300 times, and the number of design variables is set to 30. The experimental results are shown in Table 1. The comparison method adopted is the average IGD value of 25 independent runs. Under the same number of simulations, the method of this embodiment is significantly better than the Kriging-assisted reference vector guided evolutionary algorithm (K-RVEA). It can be considered that the method of this embodiment can excellently solve the service life and lightweight optimization design problems of the azimuth propeller drive shaft structure.

[0030] Table 1 Comparison of optimization results of different algorithms

[0031] The ML-based service life and lightweight design method for the azimuth propeller drive shaft provided by the present invention constructs different evolutionary starting point sets for the distribution state of the target information obtained by simulation in the target space, adopts a two-step progressive evolution, and a selection strategy of the Chebyshev aggregation function constructed with two types of reference points, thereby providing a systematic solution for the two-objective design of the service life and lightweight of the azimuth propeller drive shaft structure.

[0032] In a second aspect, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the ML-based full-rotation propeller drive shaft service life and lightweight design method of the aforementioned embodiment are implemented.

[0033] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the ML-based service life and lightweight design method for an omni-rotation propeller drive shaft of the aforementioned embodiment.

[0034] 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 ML-based service life and lightweight design method for an azimuth propeller drive shaft, characterized in that: The method comprises: Step (1): According to the static load on the azimuth propeller drive shaft, a geometric model of the azimuth propeller drive shaft is constructed in Pro / E and force decomposition is performed. The geometric model is imported into ANSYS Workbench for static analysis and the weight of the azimuth propeller drive shaft is read. The static analysis results and the sequential loads borne by the azimuth propeller drive shaft are imported into ANSYS nCode DesignLife together, wherein the static load is the support load borne by the azimuth propeller drive shaft when it is fixed, and the sequential load is the dynamic load that changes with time when the azimuth propeller drive shaft is working. According to the material properties of the azimuth propeller drive shaft, the service life SN curve in the ANSYS nCode DesignLife software is corrected by the Goodman method, and the service life of the azimuth propeller drive shaft is obtained by simulation in ANSYS nCode DesignLife. The radius of each shaft segment, the length of each shaft segment and the number of shaft segments are used as structural design parameters, and the service life and weight of the azimuth propeller drive shaft are used as two optimization targets. The mathematical optimization model of the service life and lightweight design problem of the azimuth propeller drive shaft is derived. Step (2): Considering the material strength, manufacturing process and space constraints, determine the range of values ​​of each shaft segment radius, each shaft segment length and the number of shaft segments, and construct a multidimensional design space consisting of each shaft segment radius, each shaft segment length and the number of shaft segments, where one dimension represents a structural design parameter; determine the number of individual vectors that need to be sampled based on the dimensions of the multidimensional design space and computing resources. N , in the multidimensional design space, the simplex method generates N uniformly distributed reference vectors; in the multidimensional design space, the uniform sampling method is used to generate N Each of these individual vectors contains the values ​​of the radius of each axis segment, the length of each axis segment, and the number of axis segments. N Individual vectors form an optimized population; ANSYS nCode DesignLife is used to simulate the service life and weight of each individual vector in the optimized population to obtain the two target values ​​of service life and weight, and all individual vector information is stored in the database; Step (3): Based on the optimization population simulation results, an evolutionary starting point set is constructed in the distribution state of the target space composed of the two optimization objectives of the service life and weight of the full-rotation propeller drive shaft. For each evolutionary starting point set, an initial individual vector is randomly selected from the evolutionary starting point set within the multidimensional design space composed of the structural design parameters of the radius of each shaft segment, the length of each shaft segment and the number of shaft segments to implement a two-step progressive evolution operation to generate a candidate offspring individual vector. In the two-step progressive evolution operation, a first-class subpopulation and the best first-class candidate offspring individual vector are screened 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, and the second-step dimensional perturbation mutation operation is performed using the best first-class candidate offspring individual vector as the starting point of the second-step dimensional perturbation mutation operation, and the second-step dimensional perturbation mutation operation is performed according to the Chebyshev aggregation function constructed based on the nadir reference point. Step (4): For each type of subpopulation, the inner evolution based on the radial basis function machine learning model is used to obtain the optimal candidate subpopulation, and two Chebyshev aggregation functions are constructed according to the two types of 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 service life and weight simulation model of the azimuth propeller drive shaft structure to simulate and evaluate the optimal candidate offspring individual vectors, and update the precise population and database; Step (6): Design an optimization population update strategy, use the best candidate subpopulation obtained for the first type of subpopulation in step (4) to update the optimization population, and judge the simulation evaluation results in step (5). If the service life and weight meet the design requirements, output the optimized structure of the full-rotation propeller drive shaft corresponding to all individual vectors in the Pareto set screened by the database; otherwise, go to step (3) until the optimized structure meets the design requirements.

2. The method according to claim 1, characterized in that In the step (1), the service life SN curve in the ANSYS nCode DesignLife software is corrected by using the Goodman method according to the material properties of the azimuth propeller drive shaft, and the service life of the azimuth propeller drive shaft is obtained by simulation in the ANSYS nCode DesignLife. The radius of each shaft segment, the length of each shaft segment and the number of shaft segments are used as structural design parameters, and the service life and weight of the azimuth propeller drive shaft are used as two optimization targets. The mathematical optimization model of the service life and lightweight design problem of the azimuth propeller drive shaft is derived. The specific steps are as follows: The first step is to use the Goodman method to correct the service life SN curve in the ANSYS nCodeDesignLife software according to the material properties of the azimuth propeller drive shaft. The Goodman method specifically includes the following steps: ‌The stress range corresponding to the material is used as the horizontal axis, and the average stress corresponding to the material is used as the vertical axis to draw a Goodman diagram, where 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; ‌According to the various load conditions borne by the azimuth propeller drive shaft in actual operation, the actual stress range and average stress of the azimuth propeller drive shaft are calculated; ‌The actual stress points are plotted on the Goodman diagram and the service life SN curve of the azimuth propeller drive shaft is corrected by comparing it with the allowable stress line; Based on the modified service life SN curve, the service life of the azimuth propeller drive shaft is obtained by simulation in ANSYS nCode DesignLife. In the second step, the radius of each shaft segment, the length of each shaft segment and the number of shaft segments are used as structural design parameters, and the service life and weight of the azimuth propeller drive shaft are used as two optimization targets to derive the mathematical optimization model for the service life and lightweight design of the azimuth propeller drive shaft. The specific expression is as follows: ， In the above formula, X represents the structural design parameters of the azimuth propeller drive shaft, represents the radius of the first axis segment, Indicates M The radius of the shaft segment, Indicates the length of the first axis segment, Indicates M The length of the shaft segment, Indicates the number of shaft segments, Indicates the weight of the azimuth propeller drive shaft, represents the density of the azimuth propeller drive shaft, Indicates the structural design parameters X The volume of the azimuth propeller drive shaft corresponding to Indicates that the structural design parameters are X The corresponding azimuth propeller drive shaft shape function is The service life of the azimuth propeller drive shaft under the Goodman method is represented by the constant C that matches the material, which ranges from 2.56 to 3.

85. Indicates the yield strength load of the material used in the azimuth propeller drive shaft, Indicates the yield stress of the material used in the azimuth propeller drive shaft, represents the yield strain of the material used in the azimuth propeller drive shaft, 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 azimuth propeller drive shaft, respectively. It represents the multidimensional design space formed by the structural design parameters of the azimuth propeller drive shaft, Find represents the optimal solution of the structural optimization parameters, Min represents minimizing the weight of the azimuth propeller drive shaft and maximizing the service life of the azimuth propeller drive shaft, and St represents the constraints that need to be met.

3. The method according to claim 1, characterized in that The specific steps of step (3) are as follows: In the first step, a normalization operation based on the maximum and minimum values ​​is performed according to the two target values ​​of service life and weight obtained in the ANSYS nCode DesignLife simulation; The second step is to calculate the minimum vertical distance between the normalized target value and each reference vector, and connect each individual vector in the optimized population with the reference vector with the minimum vertical distance: The third step is, for the reference vectors that are associated with individual vectors, all the corresponding individual vectors are used as the evolutionary starting points of the reference vectors; Step 4: For reference vectors that have no individual vectors connected to them, select the neighboring reference vectors that are closest to the reference vectors according to the vertical distance from small to large, and use all individual vectors connected to the neighboring reference vectors as the evolutionary starting point set of the reference vectors; The fifth step is to randomly select an initial individual vector for each reference vector evolution starting point set, perform the first dimensional perturbation mutation operation in the multidimensional design space composed of the axis segment radius, the axis segment length and the axis segment number structural design parameters, and construct a Chebyshev aggregation function based on the ideal reference point, and select the first-class subpopulation and the best first-class candidate offspring individual vector from the candidate offspring individual vectors generated by the first dimensional perturbation mutation operation; The sixth step is to use the best first-class candidate offspring individual vectors selected based on the ideal reference point as the starting point, perform the second-step dimensional perturbation mutation operation within the multidimensional design space composed of the design parameters of the axis segment radius, the axis segment length, and the number of axis segments, and construct a Chebyshev aggregation function based on the nadir reference point, and select the second-class subpopulation from the candidate offspring individual vectors generated by the second-step dimensional perturbation mutation operation; The ideal reference point and the nadir reference point are determined by the following two equations: ， ， In the above formula, Indicates the ideal reference point j The value of a target, Indicates the nadir reference point at j The value of a target, DB For the database, OP To optimize the population, Indicates the first j target value, Represents the first j target value, m is the number of targets; The Chebyshev aggregation function based on the ideal reference point and the nadir reference point is determined by the following two equations: ， ， In the above formula, is a Chebyshev aggregation function based on an ideal reference point. is a Chebyshev aggregation function based on the nadir reference point. is the reference vector in i The weight of the target, is the target value of the current individual, Indicates that the ideal reference point in the database is i target value, Indicates the position of the nadir reference point in the database. i target value, m is the target number.

4. The method according to claim 1, characterized in that The specific steps of step (4) are as follows: In the first step, for each type of subpopulation, in the inner evolution, the maximum number of approximate evaluations based on the radial basis function machine learning model is set. Within the maximum number of approximate evaluations, the adaptive differential evolution operation is used to generate the candidate offspring individual vector formula as follows: ， In the above formula, Indicates that from the previous p % randomly selects an individual vector, represents the current individual vector, and represents two individual vectors randomly selected from the current subpopulation and the set consisting of the replaced individual vector, and the scaling factor F Control the magnitude of individual vector variation; In the second step, a two-layer screening strategy is designed for the generated candidate offspring individual vectors, which respectively combines the distance between the candidate offspring individual vectors and the aggregation value information calculated by the two Chebyshev aggregation functions constructed by the reference point types corresponding to the two types of subpopulations to obtain the optimal candidate offspring individual vectors and the optimal candidate subpopulations for the first type of subpopulation and the second type of subpopulation. The specific steps of the two-layer screening strategy are as follows: According to the reference point type of the generated candidate offspring individual vector, 3 are selected based on the Chebyshev aggregation value. N A vector of candidate offspring individuals; Calculate the distance between the closest candidate offspring individual vectors, and perform non-dominated sorting with distance and Chebyshev aggregation value as two targets to obtain the ranking level; According to the ascending order of the ranking level, the Chebyshev aggregation value is used as the screening indicator to select N candidate offspring individual vectors 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; Constructing a Chebyshev aggregation function according to an ideal reference point, and screening the optimal candidate offspring individual vector for the first type of subpopulation from the offspring individual set; A Chebyshev aggregation function is constructed according to the nadir reference point, and the optimal candidate offspring individual vector for the second type of subpopulation is screened from the offspring individual set.

5. The method according to claim 1, characterized in that The steps of updating the precise population in step (5) are as follows: In the first step, static analysis is performed on each optimal candidate offspring individual vector in ANSYS Workbench and the weight of the azimuth propeller drive shaft is read. The static analysis results and the time series load borne by the azimuth propeller drive shaft are 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 stored in the database. The optimal candidate offspring individual vectors saved in the database are uniformly named as individual vectors in subsequent steps. In the second step, the precise population is updated according to the non-dominated sorting method.

6. The method according to claim 1, characterized in that The specific steps of step (6) are as follows: The first step is to find the individual vectors related to the reference vector according to the vertical distance in each subinterval, in the updated precise population and the first subpopulation obtained by the inner evolution; The second step is to calculate the Chebyshev aggregation value of the precise population individual vector associated with the reference vector, and select the individual vector with the minimum Chebyshev aggregation value as the optimal candidate offspring individual vector; The third step is to calculate the Chebyshev aggregation value of the first type of subpopulation individual vector associated with the reference vector, and select the individual vector with the minimum Chebyshev aggregation value as the optimal candidate offspring individual vector; Step 4: When the reference vector is not associated with an individual in the precise population, the optimal candidate offspring individual vector for the reference vector in the first subpopulation is used as the updated optimized population individual vector; Step 5: When the reference vector is associated with the individual in the precise population, the Chebyshev aggregation value of the optimal candidate offspring individual vector for the reference vector in the first subpopulation is compared with the optimal candidate offspring individual vector for the reference vector in the precise population, and the optimal candidate offspring individual vector with the minimum Chebyshev aggregation value is selected as the updated optimized population individual vector; The sixth step is to obtain the Pareto set of individual vectors in the database according to non-dominated sorting, and determine the satisfaction relationship between the service life and weight values ​​corresponding to all individual vectors in the Pareto set and the service life and lightweight design indicators of the full-rotation propeller drive shaft under actual working conditions. If the design indicators are met, the optimized structure of the full-rotation propeller drive shaft corresponding to all individual vectors in the current Pareto set is output; otherwise, the next iterative cycle is entered until the design indicators are 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, the steps of the method according to any one of claims 1 to 6 are implemented.

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

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