A multi-objective optimization design method and system for an aero-engine gear transmission system and a medium

Abstract

The application discloses a kind of multi-objective optimization design method, system and medium of aero-engine gear transmission system, and the method steps are: 1) determine the optimization target of aero-engine gear transmission system, design parameter and constraint condition;2) obtain the feasible scheme of the optimization target of aero-engine gear transmission system to be evaluated and corresponding design parameter;3) the feasible scheme of step 2) is evaluated using feasible scheme evaluation model, whether the design parameter type contained in the feasible scheme satisfies the preset feasible scheme variety diversity index;4) the feasible scheme satisfying the feasible scheme variety diversity index is optimized, and the optimal feasible scheme of aero-engine gear transmission system optimization design variable is obtained.The system includes parameter acquisition module, feasible scheme searching module, feasible scheme evaluation module, feasible scheme optimization module;The application realizes the quick optimization of aero-engine accessory case transmission system structure parameter, and provides technical support for the initiative design of aero-engine transmission system.

Description

Technical Field

[0001] This invention relates to the field of mechanical manufacturing, specifically to a multi-objective optimization design method, system, and medium for an aero-engine gear transmission system. Background Technology

[0002] Aero-engines are highly complex and precise machines that provide power to aircraft, often referred to as the "heart" of the aircraft. As a crucial component of the aero-engine's mechanical system, the accessory housing plays a vital role in transmitting power during the engine's start-up and operation phases, ensuring its safe and reliable operation. Typically, the accessory housing accounts for approximately 3-6% of the total weight of an aero-engine. Due to its complex structure, limited space, and harsh operating conditions such as high speed, high temperature, and heavy load, optimizing the design of the accessory housing has long been challenging. With the development of aero-engine equipment towards higher reliability, higher power density, and lighter weight, the design difficulty of advanced accessory housings has further increased. Traditional aero-engine accessory housing transmission system design methods based on conventional design manuals are no longer sufficient to fully balance these challenges.

[0003] For aero-engine accessory gearbox transmission systems, there is currently relatively little literature on related optimization design. However, in other fields such as vehicles, machine tools, ships, and wind power, research on single-objective optimization design for the dynamic characteristics or lightweighting of transmission systems is relatively mature, and is currently developing towards global multi-objective optimization design for dynamic service life and structural parameters. However, in the field of aero-engine transmissions, due to its requirements for high mobility, high reliability, lightweighting, and complex operating conditions, existing multi-objective optimization techniques still need improvement.

[0004] Currently, multi-objective optimization methods are mainly based on Pareto dominance and decompositional multi-objective optimization frameworks. The former demonstrates superior performance in terms of applicability and solution quality, but suffers from lower solution efficiency, often at the cost of increased complexity and computational cost to provide comprehensive results. The latter, on the other hand, offers the opposite advantage. Therefore, for aero-engine accessory drive systems, achieving efficient design and optimization of accessory drives is a critical issue that urgently needs to be addressed in the design of high-performance aero-engines. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-objective optimization design method for an aero-engine gear transmission system, comprising the following steps:

[0006] 1) Determine the optimization objectives, design parameters, and constraints of the aero-engine gear transmission system;

[0007] 2) Construct a feasible solution search model, and use the feasible solution search model to obtain feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated;

[0008] 3) Construct a feasible solution evaluation model based on TSNE and K-means algorithm, and use the feasible solution evaluation model to evaluate the feasible solution in step 2). Determine whether the types of design parameters contained in the feasible solution meet the preset feasible solution type diversity index. If yes, proceed to step 4); otherwise, return to step 2.

[0009] 4) Optimize the feasible schemes that meet the diversity index of feasible schemes to obtain the optimal feasible scheme of the optimized design variables of the aero-engine gear transmission system.

[0010] Furthermore, the constraints of the optimization model for the aero-engine gear transmission system include basic constraints, structural constraints, and strength constraints;

[0011] The basic constraints include module constraints, number of teeth constraints, transmission ratio constraints, and face width coefficient constraints.

[0012] Structural constraints include fixed center distance constraints, displacement coefficient constraints, slip ratio constraints, undercut prevention, tooth tip thickness interference constraints, and interference prevention constraints.

[0013] Strength constraints include contact safety factor, bending safety factor, and bonding safety factor.

[0014] Furthermore, in step 2), the steps of obtaining feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated using the feasible solution search model include:

[0015] 2.1) Construct an n-layer feasible solution search model using constraints as key nodes;

[0016] 2.2) Use a heuristic search algorithm to perform a hierarchical progressive search on each level of the feasible solution search model to obtain feasible solutions.

[0017] Furthermore, in step 2.2), the search criteria include the finite difference method and the golden section method.

[0018] Furthermore, in the n-level feasible solution search model, the key nodes of the i-th level are the constraints related to the i-th optimization design variables; i = 1, 2, ..., n. n is a positive integer.

[0019] Furthermore, the feasible solution search model is a three-layer feasible solution search model;

[0020] Among them, the key nodes of the first level of hierarchical layering are the constraints related to a single optimization design variable;

[0021] The key nodes of the second level of layering are the constraints related to the two optimization design variables;

[0022] The key nodes of the third level of layering are constraints related to three or more optimization design variables.

[0023] Furthermore, in step 3), the steps of evaluating the feasible solutions in step 2) using the feasible solution evaluation model include:

[0024] 3.1) Use the TSNE algorithm to reduce the dimensionality of feasible solutions;

[0025] 3.2) Use the K-means algorithm to perform cluster analysis on the dimensionality-reduced feasible solutions and calculate the number of design parameter types for the current feasible solutions;

[0026] 3.3) Determine whether the types of design parameters included in the feasible solution meet the preset feasible solution type diversity index.

[0027] Furthermore, in step 4), the steps for optimizing feasible solutions that meet the feasible solution diversity index include:

[0028] 4.1) Based on the optimization objectives, design parameters, constraints, and feasible solutions of the aero-engine gear transmission system, establish an optimization model for the aero-engine gear transmission system;

[0029] 4.2) The improved NSGA-Ⅱ algorithm is used to solve the optimization model of the aero-engine gear transmission system to obtain the optimal feasible solution for the optimization design variables of the aero-engine gear transmission system. The steps include:

[0030] 4.2.1) The feasible solutions that passed the evaluation were used as the initial population for the optimization model of the aero-engine gear transmission system;

[0031] 4.2.2) Calculate the objective function value for each individual and perform non-dominated sorting to obtain the frontier level and crowding degree;

[0032] The top m individuals with the lowest crowding and the highest frontier rank in the population sequence were selected as the objects of crossover and mutation.

[0033] 4.2.3) Perform crossover and mutation on the objects from step 4.2.2) to obtain a new population, and use an elite selection strategy to ensure that the population size reaches a preset value;

[0034] 4.2.4) Determine if the current iteration number t ≥ tmax is true. If not, set the iteration number t = t + 1 and return to step 4.2.2). If yes, output the current population as the optimal feasible solution. tmax is the maximum number of iterations.

[0035] A system using a multi-objective optimization design method for aero-engine gear transmission systems includes a parameter acquisition module, a feasible solution search module, a feasible solution evaluation module, and a feasible solution optimization module.

[0036] The parameter acquisition module determines the optimization objective, design parameters, and constraints of the aero-engine gear transmission system and transmits them to the feasible solution search module.

[0037] The feasible solution search module constructs a feasible solution search model and uses the feasible solution search model to obtain feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated.

[0038] The feasible solution search module transmits feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated to the feasible solution evaluation module.

[0039] The feasible solution evaluation module constructs a feasible solution evaluation model based on the TSNE and K-means algorithms, and uses the feasible solution evaluation model to evaluate feasible solutions;

[0040] The evaluation process is as follows: determine whether the types of design parameters contained in the feasible solution meet the preset feasible solution type diversity index. If so, the feasible solution is transmitted to the feasible solution optimization module. Otherwise, the feasible solution search module regenerates the feasible solution of the optimization target and corresponding design parameters of the aero-engine gear transmission system.

[0041] The feasible solution optimization module optimizes feasible solutions that meet the feasible solution diversity index to obtain the optimal feasible solution for the optimized design variables of the aero-engine gear transmission system.

[0042] A computer-readable storage medium having a computer program stored thereon;

[0043] When a computer program is invoked, the steps of the above method are executed.

[0044] The technical effects of this invention are undeniable. This invention proposes a multi-objective optimization design method for aero-engine gear transmission systems, which adopts a three-step approach of feasible solution search, feasible solution evaluation, and feasible solution optimization. It addresses the problems of complex constraints, difficulties in optimizing structural parameters, and low optimization efficiency caused by the harsh service environment and stringent performance requirements of aero-engine accessory transmission systems. This method enables rapid optimization of the structural parameters of the aero-engine accessory gearbox transmission system, providing technical support for the proactive design of aero-engine transmission systems. Attached Figure Description

[0045] Figure 1 This is a flowchart of the model of the present invention;

[0046] Figure 2 For the gear transmission system of the engine accessory housing;

[0047] Figure 3 This is a flowchart of the method of the present invention. Detailed Implementation

[0048] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0049] Example 1:

[0050] See Figures 1 to 3 A multi-objective optimization design method for an aero-engine gear transmission system includes the following steps:

[0051] 1) Determine the optimization objectives, design parameters, and constraints of the aero-engine gear transmission system;

[0052] 2) Construct a feasible solution search model, and use the feasible solution search model to obtain feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated;

[0053] 3) Construct a feasible solution evaluation model based on TSNE (t distributed stochastic neighbor embedding) and K-means (k-means) algorithm, and use the feasible solution evaluation model to evaluate the feasible solution in step 2). Determine whether the types of design parameters contained in the feasible solution meet the preset feasible solution type diversity index. If yes, proceed to step 4); otherwise, return to step 2.

[0054] 4) Optimize the feasible schemes that meet the diversity index of feasible schemes to obtain the optimal feasible scheme of the optimized design variables of the aero-engine gear transmission system.

[0055] The constraints of the optimization model for the aero-engine gear transmission system include basic constraints, structural constraints, and strength constraints.

[0056] The basic constraints include module constraints, number of teeth constraints, transmission ratio constraints, and face width coefficient constraints.

[0057] Structural constraints include fixed center distance constraints, displacement coefficient constraints, slip ratio constraints, undercut prevention, tooth tip thickness interference constraints, and interference prevention constraints.

[0058] Strength constraints include contact safety factor, bending safety factor, and bonding safety factor.

[0059] Step 2), the steps for obtaining feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated using the feasible solution search model include:

[0060] 2.1) Construct an n-layer feasible solution search model using constraints as key nodes;

[0061] 2.2) Use a heuristic search algorithm to perform a hierarchical progressive search on each level of the feasible solution search model to obtain feasible solutions.

[0062] In step 2.2), the search criteria include the finite difference method and the golden section method.

[0063] In the n-level feasible solution search model, the key nodes of the i-th level are the constraints related to the i optimization design variables; i = 1, 2, ..., n. n is a positive integer.

[0064] The feasible solution search model is a three-layer feasible solution search model;

[0065] Among them, the key nodes of the first level of hierarchical layering are the constraints related to a single optimization design variable;

[0066] The key nodes of the second level of layering are the constraints related to the two optimization design variables;

[0067] The key nodes of the third level of layering are constraints related to three or more optimization design variables.

[0068] Step 3), which involves evaluating the feasible solutions from step 2) using a feasible solution evaluation model, includes the following steps:

[0069] 3.1) Use the TSNE algorithm to reduce the dimensionality of feasible solutions;

[0070] 3.2) Use the K-means algorithm to perform cluster analysis on the dimensionality-reduced feasible solutions and calculate the number of design parameter types for the current feasible solutions;

[0071] 3.3) Determine whether the types of design parameters included in the feasible solution meet the preset feasible solution type diversity index.

[0072] Step 4) involves optimizing feasible solutions that meet the feasibility diversity index, including the following steps:

[0073] 4.1) Based on the optimization objectives, design parameters, constraints, and feasible solutions of the aero-engine gear transmission system, establish an optimization model for the aero-engine gear transmission system;

[0074] 4.2) The improved NSGA-II algorithm (Non-dominated Sorting Genetic Algorithm II) is used to solve the optimization model of the aero-engine gear transmission system to obtain the optimal feasible solution for the optimization design variables of the aero-engine gear transmission system. The steps include:

[0075] 4.2.1) The feasible solutions that passed the evaluation were used as the initial population for the optimization model of the aero-engine gear transmission system;

[0076] 4.2.2) Calculate the objective function value for each individual and perform non-dominated sorting to obtain the frontier level and crowding degree;

[0077] The top m individuals with the lowest crowding and the highest frontier rank in the population sequence were selected as the objects of crossover and mutation.

[0078] 4.2.3) Perform crossover and mutation on the objects from step 4.2.2) to obtain a new population, and use an elite selection strategy to ensure that the population size reaches a preset value;

[0079] 4.2.4) Determine if the current iteration number t ≥ tmax is true. If not, set the iteration number t = t + 1 and return to step 4.2.2). If yes, output the current population as the optimal feasible solution. tmax is the maximum number of iterations.

[0080] A system using a multi-objective optimization design method for aero-engine gear transmission systems includes a parameter acquisition module, a feasible solution search module, a feasible solution evaluation module, and a feasible solution optimization module.

[0081] The parameter acquisition module determines the optimization objective, design parameters, and constraints of the aero-engine gear transmission system and transmits them to the feasible solution search module.

[0082] The feasible solution search module constructs a feasible solution search model and uses the feasible solution search model to obtain feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated.

[0083] The feasible solution search module transmits feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated to the feasible solution evaluation module.

[0084] The feasible solution evaluation module constructs a feasible solution evaluation model based on the TSNE and K-means algorithms, and uses the feasible solution evaluation model to evaluate feasible solutions;

[0085] The evaluation process is as follows: determine whether the types of design parameters contained in the feasible solution meet the preset feasible solution type diversity index. If so, the feasible solution is transmitted to the feasible solution optimization module. Otherwise, the feasible solution search module regenerates the feasible solution of the optimization target and corresponding design parameters of the aero-engine gear transmission system.

[0086] The feasible solution optimization module optimizes feasible solutions that meet the feasible solution diversity index to obtain the optimal feasible solution for the optimized design variables of the aero-engine gear transmission system.

[0087] A computer-readable storage medium having a computer program stored thereon;

[0088] When a computer program is invoked, the steps of the above method are executed.

[0089] Example 2:

[0090] A multi-objective optimization design method for an aero-engine gear transmission system includes the following steps:

[0091] Step 1: Construct a feasible solution search model for the aero-engine gear transmission system based on a heuristic search algorithm:

[0092] Step 1.1: Based on the aero-engine gear transmission system model, analyze the weak points of the transmission system and compile the design parameters and constraints required for the transmission system;

[0093] Step 1.2: Based on the relationship between design parameters and constraints, divide the number of key nodes. Constraints related to a single factor, two factors, and multiple factors are respectively used as key nodes of each loop. Multi-factor key nodes can be extended.

[0094] Step 1.3: Based on the key nodes defined above, perform a progressive search at each level. If the search at a level is successful, proceed to the next level; if the search at a level fails, restart the search until the initial solution is found. The finite difference method and the golden section method are used as the design parameters for adjustment and as the search criteria.

[0095] Step 2: Build a feasibility evaluation model and conduct a diversity assessment of existing solutions.

[0096] Step 2.1: Determine the evaluation indicators for feasible solutions, i.e., the number of types of feasible solutions;

[0097] Step 2.2: Using the design parameters of the obtained feasible solutions as input, the TSNE algorithm is used to reduce the data dimensionality of the design parameters to obtain the data distribution of feasible solutions. Using this data as input, the K-means algorithm is used to perform cluster analysis on the design parameters to determine the types of feasible solutions.

[0098] Step 2.3: Determine whether the evaluation indicators are met. If the requirements are not met, a restart strategy is adopted to regenerate feasible solutions in the decision space. If the requirements are met, proceed to the next step of design parameter optimization.

[0099] Step 3: Establish an optimization model based on the improved NSGAⅡ engine gear transmission system:

[0100] Step 3.1: Based on the given aero-engine gear transmission system, determine the three elements of the optimization model, namely the objective function, design variables, and constraints, and at the same time give the number of feasible solutions and the number of iterations;

[0101] Step 3.2: Using the successful feasible solutions as the initial population of the optimization model, the non-dominated sorting algorithm and crowding calculation are first applied to them. Based on this, the better individuals are selected as the objects of crossover and mutation. The non-dominated sorting algorithm is a judgment of the excellence level of the solution, while the crowding calculation is a judgment index of whether the solution is concentrated.

[0102] Step 3.3: Select feasible schemes for the population, crossover, and mutation. Then, use an elite selection strategy to ensure that the population enters the next iteration cycle with a given number. The crossover and mutation are changed from the original single-point crossover and mutation to multi-point crossover and mutation, which is more in line with the actual laws of the interrelationship of gear design parameters.

[0103] Step 3.4: After the population has undergone a given number of iterations, the optimization model can be solved, and the curve with a Pareto rank of 1 for the multi-objective optimization model can be obtained.

[0104] Step 3.5: Based on the obtained Pareto curve and the weights of different objective importance, select a suitable solution on the Pareto curve as the final optimization scheme. Generally, the ideal solution is selected as the final optimization scheme. The ideal solution is the point where the objective function weights are consistent.

[0105] Combining the three steps of feasible solution search, feasible solution evaluation, and feasible solution optimization can achieve efficient design and optimization of aero-engine gear transmission. Feasible solution search quickly obtains a given number of feasible solutions, providing data support for optimization. Feasible solution evaluation assesses the diversity of feasible solutions, ensuring data quality for optimization. Based on these two steps, the HS-NSGAⅡ algorithm is used to optimize the feasible solutions, obtaining the final optimized solution.

[0106] Example 3:

[0107] A multi-objective optimization design method for an aero-engine gear transmission system includes the following steps:

[0108] like Figure 1 The flowchart shown is a representation of the method of this invention. First, the operating conditions, transmission structure, and weak points of the acquired transmission system are analyzed to determine the optimization objectives, design parameters, and constraints. Then, based on the above optimization objectives, design parameters, and constraints, a multi-objective optimization model of the transmission system is established, and the HS-NSGAⅡ algorithm is used to solve the optimization model to obtain the final optimization result. The optimization algorithm's solution process consists of three steps: feasible solution search, feasible solution evaluation, and feasible solution optimization.

[0109] Step 1 Figure 2For the transmission system of a certain aero-engine accessory casing, the operating conditions, transmission structure, and weak points of the acquired transmission system were analyzed to determine the number of transmission stages and the location of the weak points. Among them, gear 9 on the left side of the third stage is the weak point of this transmission system. The specific structural parameters of the proposed solution are shown in Table 1.

[0110] Table 1 Original Design Scheme

[0111]

[0112] Step 2: Based on the above data and analysis results, determine the optimization objective, design parameters, and constraints of the transmission system;

[0113] Step 3: Establish a multi-objective optimization model with lightweighting and high reliability as optimization objectives, gear macroscopic parameters as design variables, and considering the basic constraints, structural constraints, and strength constraints of the aero-engine gear transmission system:

[0114] The initial selection of macroscopic design variables for gear transmission uses a total of 30 variables, including gear module m, number of teeth z, tooth width b, and displacement coefficient x, as design parameters to ensure that geometric assembly and strength requirements are met, as shown in equation (1).

[0115]

[0116] To reduce the weight of the transmission system, control the size of the housing, and coordinate the strength of each gear, so as to ensure that the transmission system can operate with better performance, this study selects both lightweighting and the minimum contact safety factor of weak links as objective functions, expressed as Equation (2).

[0117]

[0118] The constraints include basic constraints, structural constraints, and strength constraints. Among these, module constraints, number of teeth constraints, transmission ratio constraints, and face width coefficient constraints are all basic constraints. Structural constraints include fixed center distance constraints, displacement coefficient constraints, slip ratio constraints, undercut prevention constraints, tooth tip thickness interference constraints, and interference prevention constraints. Strength constraints include contact safety factors, bending safety factors, and scuffing safety factors.

[0119] Step 4: Use the HS-NSGAⅡ algorithm to solve the optimization model and obtain the final optimization solution: such as Figure 2 The flowchart shown is a flowchart of the method. The method quickly obtains a given number of feasible solutions through feasible solution search, providing data support for optimization. Based on the feasible solution evaluation, the method judges the diversity of feasible solutions, providing data quality assurance for optimization. Based on the above two steps, the HS-NSGAⅡ algorithm is used to optimize the feasible solutions and obtain the final optimized solution.

[0120] In the feasible solution search phase, considering that some constraints are only related to some parameters and have a certain hierarchical relationship, a heuristic search algorithm is adopted to search each level hierarchically and progressively to quickly find effective initial solutions, ensure solution efficiency, and reduce the efficiency loss caused by random search. Constraints related to a single factor, two factors, and multiple factors are respectively used as key nodes in each loop. The three loops form a cascaded heuristic search decision function St(X) = St1(X1)St2(X2)St3(X3). If any loop satisfies all conditions, then St... i (X) takes the value 1, otherwise it takes the value 0. The number of key nodes depends on the specific constraints and can be extended. The specific decision function is as follows:

[0121]

[0122] In the feasible solution evaluation stage, in order to ensure the diversity of feasible solutions obtained based on heuristic search algorithms, TSNE and K-means algorithms are used to calculate the number of types of feasible solutions obtained.

[0123] The TSNE algorithm is used for dimensionality reduction analysis of feasible design parameters, while the K-means algorithm performs cluster analysis on the dimensionality-reduced data to calculate the number of feasible solutions. If the diversity of the obtained data is less than the given expected value, a restart strategy needs to be adopted to search again to ensure that the given expected value is met. Before adopting the restart strategy, it is necessary to determine whether the population has stagnated in the infeasible region. Once it is detected that the population search time is too long or the similarity between individuals is too high, it can be determined that the population is in the infeasible region. At this time, the restart strategy will be triggered—all solutions in the population will be regenerated from the decision space according to the population initialization strategy. The specific determination conditions are:

[0124]

[0125] Where X represents the set of initial design parameters, D is the feasible region of design parameters required by the design; N and δ represent the types of initial parameters and the predefined thresholds, respectively; T and μ represent the program running time and the predefined thresholds, respectively.

[0126] In the feasible solution optimization phase, a series of design schemes satisfying the constraints are first obtained based on heuristic search, forming an initial population N1, which is used to iteratively obtain the optimal design scheme. The number of individuals in the initial population is set to 1000 (i.e., the number of design schemes covered by the initial population). After calculating the objective function values ​​f1 and f2 of each individual in the initial population, a non-dominated sort is performed to obtain the frontier level and crowding degree.

[0127] Subsequently, binary tournament selection, gear design variable grouped crossover, and grouped mutation are used to transform the initial population N1 into a new population N2 through genetic evolution. At this point, the number of individuals in the new population N2 exceeds the number of individuals in the original population N2, satisfying N2>N1. Through design constraint screening, non-dominated sorting, and dispersion calculation, non-dominated sorting is performed on population N2 to select the best individuals, thus obtaining the next generation population N3.

[0128] At this point, the number of individuals in the next generation population is equal to the number of individuals in the initial population, satisfying N3 = N1. Considering the computational cost of solving this multi-objective optimization model, setting the maximum number of iterations to 200 provides acceptable computational cost and good convergence. That is, the algorithm terminates after 200 genetic iterations, generating an optimal solution set and a Pareto curve, thereby obtaining the optimal structure parameters.

[0129] Table 2. Based on HS-NSGAⅡ

[0130]

[0131] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the invention. The optimization algorithms proposed in this invention include, but are not limited to, heuristic search and NSGA II. Regarding structural parameter optimization, in addition to its application to aero-engine gear structural parameters, it is also applicable to the optimization of structural parameters in gear transmission systems of ships, vehicles, etc.

[0132] Example 4:

[0133] A multi-objective optimization design method for an aero-engine gear transmission system includes the following steps:

[0134] 1) Determine the optimization objectives, design parameters, and constraints of the aero-engine gear transmission system.

[0135] 2) Construct a feasible solution search model, and use the feasible solution search model to obtain feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated;

[0136] 3) Construct a feasible solution evaluation model based on TSNE and K-means algorithm, and use the feasible solution evaluation model to evaluate the feasible solution in step 2). Determine whether the types of design parameters contained in the feasible solution meet the preset feasible solution type diversity index. If yes, proceed to step 4); otherwise, return to step 2.

[0137] 4) Optimize the feasible schemes that meet the diversity index of feasible schemes to obtain the optimal feasible scheme of the optimized design variables of the aero-engine gear transmission system.

[0138] Example 5:

[0139] A multi-objective optimization design method for an aero-engine gear transmission system is described in Example 4. The constraints of the optimization model for the aero-engine gear transmission system include basic constraints, structural constraints, and strength constraints.

[0140] The basic constraints include module constraints, number of teeth constraints, transmission ratio constraints, and face width coefficient constraints.

[0141] Structural constraints include fixed center distance constraints, displacement coefficient constraints, slip ratio constraints, undercut prevention, tooth tip thickness interference constraints, and interference prevention constraints.

[0142] Strength constraints include contact safety factor, bending safety factor, and bonding safety factor.

[0143] Example 6:

[0144] A multi-objective optimization design method for an aero-engine gear transmission system, the main contents of which are described in Example 4, wherein step 2), which involves using a feasible solution search model to obtain feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated, includes the following steps:

[0145] 2.1) Construct an n-layer feasible solution search model using constraints as key nodes;

[0146] 2.2) Use a heuristic search algorithm to perform a hierarchical progressive search on each level of the feasible solution search model to obtain feasible solutions.

[0147] Example 7:

[0148] A multi-objective optimization design method for an aero-engine gear transmission system is described in Example 4. In step 2.2), the search criteria include the finite difference method and the golden section method.

[0149] Example 8:

[0150] A multi-objective optimization design method for an aero-engine gear transmission system, the main contents of which are shown in Example 4, wherein in the n-layer feasible solution search model, the key node of the i-th layer is the constraint condition related to the i-th optimization design variable; i = 1, 2, ..., n. n is a positive integer; Example 9:

[0151] A multi-objective optimization design method for an aero-engine gear transmission system, the main contents of which are shown in Example 4, wherein the feasible solution search model is a three-layer feasible solution search model.

[0152] Among them, the key nodes of the first level of hierarchical layering are the constraints related to a single optimization design variable;

[0153] The key nodes of the second level of layering are the constraints related to the two optimization design variables;

[0154] The key nodes of the third level of layering are constraints related to three or more optimization design variables.

[0155] Example 10:

[0156] A multi-objective optimization design method for an aero-engine gear transmission system, the main contents of which are shown in Example 4, wherein step 3), which evaluates the feasible solutions in step 2) using a feasible solution evaluation model, includes the following steps:

[0157] 3.1) Use the TSNE algorithm to reduce the dimensionality of feasible solutions;

[0158] 3.2) Use the K-means algorithm to perform cluster analysis on the dimensionality-reduced feasible solutions and calculate the number of design parameter types for the current feasible solutions;

[0159] 3.3) Determine whether the types of design parameters included in the feasible solution meet the preset feasible solution type diversity index.

[0160] Example 11:

[0161] A multi-objective optimization design method for an aero-engine gear transmission system, the main contents of which are shown in Example 4, wherein step 4) involves optimizing feasible solutions that satisfy the feasibility diversity index, including:

[0162] 4.1) Based on the optimization objectives, design parameters, constraints, and feasible solutions of the aero-engine gear transmission system, establish an optimization model for the aero-engine gear transmission system;

[0163] 4.2) The improved NSGA-Ⅱ algorithm is used to solve the optimization model of the aero-engine gear transmission system to obtain the optimal feasible solution for the optimization design variables of the aero-engine gear transmission system. The steps include:

[0164] 4.2.1) The feasible solutions that passed the evaluation were used as the initial population for the optimization model of the aero-engine gear transmission system;

[0165] 4.2.2) Calculate the objective function value for each individual and perform non-dominated sorting to obtain the frontier level and crowding degree;

[0166] The top m individuals with the lowest crowding and the highest frontier rank in the population sequence were selected as the objects of crossover and mutation.

[0167] 4.2.3) Perform crossover and mutation on the objects from step 4.2.2) to obtain a new population, and use an elite selection strategy to ensure that the population size reaches a preset value;

[0168] 4.2.4) Determine whether the current iteration number t ≥ tmax is true. If not, let the iteration number t = t + 1 and return to step 4.2.2). If yes, output the current population as the optimal feasible solution.

[0169] Example 12:

[0170] A system using the multi-objective optimization design method for the aero-engine gear transmission system described in Examples 4-11 includes a parameter acquisition module, a feasible solution search module, a feasible solution evaluation module, and a feasible solution optimization module.

[0171] The parameter acquisition module determines the optimization objective, design parameters, and constraints of the aero-engine gear transmission system and transmits them to the feasible solution search module.

[0172] The feasible solution search module constructs a feasible solution search model and uses the feasible solution search model to obtain feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated.

[0173] The feasible solution search module transmits feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated to the feasible solution evaluation module.

[0174] The feasible solution evaluation module constructs a feasible solution evaluation model based on the TSNE and K-means algorithms, and uses the feasible solution evaluation model to evaluate feasible solutions;

[0175] The evaluation process is as follows: determine whether the types of design parameters contained in the feasible solution meet the preset feasible solution type diversity index. If so, the feasible solution is transmitted to the feasible solution optimization module. Otherwise, the feasible solution search module regenerates the feasible solution of the optimization target and corresponding design parameters of the aero-engine gear transmission system.

[0176] The feasible solution optimization module optimizes feasible solutions that meet the feasible solution diversity index to obtain the optimal feasible solution for the optimized design variables of the aero-engine gear transmission system.

[0177] Example 13:

[0178] A computer-readable storage medium having a computer program stored thereon;

[0179] When the computer program is invoked, the steps of the method described in Examples 4-11 are executed.

Claims

1. A multi-objective optimization design method for an aero-engine gear transmission system, characterized in that, Includes the following steps: Step 1) Determine the optimization objectives, design parameters, and constraints of the aero-engine gear transmission system; Step 2) Construct a feasible solution search model and use the feasible solution search model to obtain feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated; Step 3) Construct a feasible solution evaluation model based on TSNE and K-means algorithms, and use the feasible solution evaluation model to evaluate the feasible solution in Step 2). Determine whether the types of design parameters included in the feasible solution meet the preset feasible solution type diversity index. If yes, proceed to Step 4); otherwise, return to Step 2. Step 4) Optimize the feasible schemes that meet the feasible scheme diversity index using the improved NSGA-Ⅱ algorithm to obtain the optimal feasible scheme for the optimized design variables of the aero-engine gear transmission system. The feasible solution search model is a three-layer feasible solution search model; Among them, the key nodes of the first level of hierarchical layering are the constraints related to a single optimization design variable; The key nodes of the second level of layering are the constraints related to the two optimization design variables; The key nodes of the third level of layering are constraints related to three or more optimization design variables; Step 3), which involves evaluating the feasible solutions from step 2) using a feasible solution evaluation model, includes the following steps: Step 3.1) Use the TSNE algorithm to reduce the dimensionality of feasible solutions; Step 3.2) Use the K-means algorithm to perform cluster analysis on the dimensionality-reduced feasible solutions and calculate the number of design parameter types for the current feasible solutions; Step 3.3) Determine whether the types of design parameters included in the feasible solution meet the preset feasible solution variety index.

2. The multi-objective optimization design method for an aero-engine gear transmission system according to claim 1, characterized in that, The constraints of the gear transmission system of an aero-engine include basic constraints, structural constraints, and strength constraints; The basic constraints include module constraints, number of teeth constraints, transmission ratio constraints, and face width coefficient constraints. Structural constraints include fixed center distance constraints, displacement coefficient constraints, slip ratio constraints, undercut prevention, tooth tip thickness interference constraints, and interference prevention constraints. Strength constraints include contact safety factor, bending safety factor, and bonding safety factor.

3. The multi-objective optimization design method for an aero-engine gear transmission system according to claim 1, characterized in that, Step 2), the steps for obtaining feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated using the feasible solution search model include: Step 2.1) Construct a three-layer feasible solution search model using constraints as key nodes; Step 2.2) Use a heuristic search algorithm to perform a hierarchical progressive search on each level of the feasible solution search model to obtain feasible solutions.

4. The multi-objective optimization design method for an aero-engine gear transmission system according to claim 3, characterized in that, In step 2.2), the search criteria include the finite difference method and the golden section method.

5. The multi-objective optimization design method for an aero-engine gear transmission system according to claim 3, characterized in that, In the n-level feasible solution search model, the key nodes of the i-th level are the constraints related to the i-th optimization design variables; i=1,2,...,n.

6. The multi-objective optimization design method for an aero-engine gear transmission system according to claim 1, characterized in that, Step 4) involves optimizing feasible solutions that meet the feasibility diversity index, including the following steps: Step 4.1) Based on the optimization objectives, design parameters, constraints, and feasible solutions of the aero-engine gear transmission system, establish an optimization model for the aero-engine gear transmission system; Step 4.2) Solve the optimization model of the aero-engine gear transmission system using the improved NSGA-II algorithm to obtain the optimal feasible solution for the optimization design variables of the aero-engine gear transmission system. The steps include: Step 4.2.1) Use the feasible solutions that pass the evaluation as the initial population for the optimization model of the aero-engine gear transmission system; Step 4.2.2) Calculate the objective function value for each individual and perform non-dominated sorting to obtain the frontier level and crowding degree; The top m individuals with the lowest crowding and the highest frontier rank in the population sequence were selected as the objects of crossover and mutation. Step 4.2.3) Perform crossover and mutation on the objects from Step 4.2.2) to obtain a new population, and use an elite selection strategy to ensure that the population size reaches a preset value; Step 4.2.4) Determine whether the current iteration number t ≥ tmax is true. If not, let the iteration number t = t + 1 and return to step 4.2.2). If yes, output the current population as the optimal feasible solution; tmax is the maximum number of iterations.

7. A system using a multi-objective optimization design method for aero-engine gear transmission systems, characterized in that, It includes a parameter acquisition module, a feasible solution search module, a feasible solution evaluation module, and a feasible solution optimization module; The parameter acquisition module determines the optimization objective, design parameters, and constraints of the aero-engine gear transmission system and transmits them to the feasible solution search module. The feasible solution search module constructs a feasible solution search model and uses the feasible solution search model to obtain feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated. The feasible solution search module transmits feasible solutions for the optimization objectives and corresponding design parameters of the aero-engine gear transmission system to be evaluated to the feasible solution evaluation module. The feasible solution evaluation module constructs a feasible solution evaluation model based on the TSNE and K-means algorithms, and uses the feasible solution evaluation model to evaluate feasible solutions; The evaluation process is as follows: determine whether the types of design parameters contained in the feasible solution meet the preset feasible solution type diversity index. If so, the feasible solution is transmitted to the feasible solution optimization module. Otherwise, the feasible solution search module regenerates the feasible solution of the optimization target and corresponding design parameters of the aero-engine gear transmission system. The feasible solution optimization module uses the improved NSGA-II algorithm to optimize feasible solutions that meet the feasible solution diversity index, and obtains the optimal feasible solution for the optimized design variables of the aero-engine gear transmission system. The feasible solution search model is a three-layer feasible solution search model; Among them, the key nodes of the first level of hierarchical layering are the constraints related to a single optimization design variable; The key nodes of the second level of layering are the constraints related to the two optimization design variables; The key nodes of the third level of layering are constraints related to three or more optimization design variables; Step 3), which involves evaluating the feasible solutions from step 2) using a feasible solution evaluation model, includes the following steps: Step 3.1) Use the TSNE algorithm to reduce the dimensionality of feasible solutions; Step 3.2) Use the K-means algorithm to perform cluster analysis on the dimensionality-reduced feasible solutions and calculate the number of design parameter types for the current feasible solutions; Step 3.3) Determine whether the types of design parameters included in the feasible solution meet the preset feasible solution variety index.

8. A computer-readable storage medium, characterized in that, It contains computer programs; When the computer program is invoked, the steps of the method according to any one of claims 1-6 are performed.

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