Rotor system parameter intelligent optimization method based on multi-objective genetic algorithm

Abstract

The invention relates to the technical field of rotary machinery dynamics design and optimization, in particular to a rotor system parameter intelligent optimization method based on a multi-objective genetic algorithm, and the method comprises the steps: determining design parameters of a rotor system needing to be optimized, and defining a physically feasible value range for each design parameter; establishing a parameterized rotor system dynamics analysis model based on the target rotor system; according to design requirements, the performance indexes are converted into a target function of multiple optimization targets; a multi-objective genetic algorithm is adopted as an optimization engine, population initialization is carried out based on design parameters and boundaries of the design parameters, after population initialization is completed, iterative circulation of evaluation, selection and reproduction is carried out, and after the preset maximum number of iterations is reached or a preset convergence standard is met, a Pareto optimal solution set is output; according to actual engineering preference, one or more optimal solutions are selected from the Pareto optimal solution set to form an optimal design scheme, and the rotor system is designed based on the optimal design scheme.

Description

Technical Field

[0001] The embodiments of this application relate to the field of rotating machinery dynamics design and optimization technology, and in particular to an intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm. Background Technology

[0002] The rotor system is a core component of high-end equipment such as aero-engines, gas turbines, compressors, and centrifuges. Its dynamic performance, particularly its critical speed, vibration modes, and response characteristics, directly determines the reliability, stability, and lifespan of the entire system. The dynamic characteristics of the rotor system are primarily determined by its mass distribution, support stiffness, and the inertial parameters of its rotating components.

[0003] Traditional rotor system design methods typically rely on engineers' experience and trial-and-error methods. That is, parameters are initially determined based on experience, and then verified using dynamic calculation software (such as SAMCEF, ROTOR, ANSYS, etc.). If the requirements are not met, the parameters are manually adjusted and recalculated.

[0004] This traditional method, which relies on manual labor, has the following significant drawbacks.

[0005] First, it is inefficient. Traditional methods have a long design cycle, and repeated manual adjustments and verifications consume a lot of time and computing resources.

[0006] Second, it is difficult to find the globally optimal solution. Due to the complex coupling relationships between parameters, manual adjustment is very likely to get stuck in local optima, failing to fully realize the design potential.

[0007] Third, it is difficult to coordinate multiple objectives. In practical engineering, it is often necessary to simultaneously meet multiple conflicting objectives (such as avoiding the critical speed range while minimizing vibration and weight). Traditional methods are difficult to effectively balance and compromise on these objectives.

[0008] In recent years, some research teams have introduced optimization algorithms into engineering design, but there has been no reliable research on the deep integration of optimization algorithms with professional rotor dynamics analysis software. Summary of the Invention

[0009] In view of this, embodiments of this application propose an intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm. This method aims to comprehensively consider the actual operating conditions and coupling characteristics of the rotor system, automatically and efficiently perform multi-parameter collaborative optimization, and improve the dynamic performance and reliability of the rotor system from the design source.

[0010] To achieve the above objectives, embodiments of this application provide an intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm, applicable to the intelligent design of rotor systems. The method includes: determining the design parameters of the rotor system to be optimized and defining a physically feasible range for each design parameter; establishing a parameterized rotor system dynamics analysis model based on the target rotor system and solving it, with the input being a vector of design parameter variables and the output being the dynamic response result of the target rotor system; transforming performance indicators into objective functions with multiple optimization objectives according to design requirements; using a multi-objective genetic algorithm as the optimization engine, initializing the population based on the design parameters and their boundaries, and after population initialization, performing iterative cycles of evaluation, selection, and reproduction until a preset maximum number of iterations is reached or a preset convergence criterion is met, outputting a Pareto optimal solution set; and selecting one or more optimal solutions from the Pareto optimal solution set according to actual engineering preferences to form an optimal design scheme, and designing the rotor system based on the optimal design scheme.

[0011] To achieve the above objectives, embodiments of this application also provide an intelligent optimization device for rotor system parameters based on a multi-objective genetic algorithm, suitable for the intelligent design of rotor systems. The system includes: a design variable and constraint boundary module, used to determine the design parameters of the rotor system to be optimized and define a physically feasible value range for each design parameter; a rotor system dynamic analysis model construction module, used to establish a parameterized rotor system dynamic analysis model based on the target rotor system and solve it, with the input being a variable vector of design parameters and the output being the dynamic response result of the target rotor system; a multi-optimization objective definition module, used to transform performance indicators into objective functions of multiple optimization objectives according to design requirements; an optimization execution module, used to use a multi-objective genetic algorithm as the optimization engine, perform population initialization based on the design parameters and their boundaries, and after completing population initialization, perform iterative cycles of evaluation, selection, and reproduction until a preset maximum number of iterations is reached or a preset convergence criterion is met, and output a Pareto optimal solution set; and a final design module, used to select one or more optimal solutions from the Pareto optimal solution set according to actual engineering preferences to form an optimal design scheme, and design the rotor system based on the optimal design scheme.

[0012] To achieve the above objectives, embodiments of this application also propose an electronic device comprising: a processor and a memory, wherein the memory stores instructions executable by the processor, and the processor is configured to execute the instructions such that the electronic device can implement the intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm as described above.

[0013] To achieve the above objectives, embodiments of this application also provide a computer-readable storage medium storing a computer program that, when executed by a processor, enables the implementation of a rotor system parameter intelligent optimization method based on a multi-objective genetic algorithm as described above.

[0014] Optionally, the rotor system includes a support unit, a mass block unit, and a rotating shaft segment unit, and the design parameters include support stiffness parameters, lumped mass parameters, and rotational inertia parameters. Support stiffness parameters Here are the stiffness parameters for each support element. , This represents the total number of support units. For the first Stiffness parameters of each support element; Lumped mass parameters The mass parameters of each mass block unit. , This represents the total number of mass block units. For the first Mass parameters of each mass block unit; rotational inertia parameters The rotational inertia parameters of each rotating shaft segment unit, , This represents the total number of rotating shaft segment units. For the first Rotational inertia parameters of a single rotating shaft segment unit.

[0015] Optionally, a parameterized rotor system dynamic analysis model is established based on the target rotor system, including: Based on the stiffness parameters of each support unit and support. Establish a motion model for the support unit; Based on each mass block element and lumped mass parameters Establish a motion model for the mass block unit; Based on each rotating shaft segment unit and rotational inertia parameters Establish a motion model for the rotating shaft segment unit; Based on the number of nodes in the rotor system, the motion models of the support unit, the mass block unit, and the rotating shaft segment unit are assembled using a system matrix to obtain the dynamic analysis model of the rotor system. No. The motion model of a support element is expressed by the formula: ; Among them, the upper right corner mark Indicates the support unit. Indicates the first Damping matrix of each support element and They represent the first Displacement vector and velocity vector of each support element Indicates the first The stiffness matrix of the nth support element, which is the nth support element's stiffness matrix. Stiffness parameters of each support element Indicates the first External force vector of each support unit; No. The motion model of a mass block element is expressed by the formula: ; Among them, the upper right corner mark Represents a mass block element. Indicates the first The mass matrix of the nth mass block unit, which is the nth mass matrix. Lumped mass parameters of each mass block element. and They represent the first The velocity vector and acceleration vector of each mass element Indicates the rotational speed of the rotor system. Indicates the first The gyro effect matrix of each mass block unit Indicates the first External force vector of each mass block element; No. The motion model of a rotating shaft segment unit is expressed by the formula: ; Among them, the upper right corner mark Indicates a rotating shaft segment unit. Indicates the first Mass matrix of each rotating shaft segment element , and They represent the first The displacement vector, velocity vector, and acceleration vector of each rotating shaft segment element. Indicates the first The gyroscopic effect matrix of the nth rotating shaft segment unit, i.e. the nth Rotational inertia parameters of a single rotating shaft segment unit. Indicates the first Stiffness matrix of a rotating shaft segment element Indicates the first The external force vector of a rotating shaft segment unit.

[0016] Optionally, let the number of nodes in the rotor system be... , If the integer is greater than 1, then the size of the system matrix of the rotor system is Based on the finite element method, the motion models of the support unit, the mass block unit, and the rotating shaft segment unit are assembled to obtain the rotor system dynamic analysis model, including: For a motion unit with 4 degrees of freedom concentrated at a single node, let it be... The matrix is ​​directly written into the corresponding position in the system matrix; among them, the support unit and the mass block unit are both motion units with 4 degrees of freedom lumped together at a single node; For a beam element with 8 degrees of freedom and two nodes, let it be... The matrix is ​​written at the corresponding position in the system matrix, but the matrix at the common node of the adjacent beam element is superimposed; where the rotation axis segment element is a beam element; The dynamic analysis model of the rotor system is expressed by the following formula: ; Among them, the upper right corner mark Indicates a rotor system. Represents the mass matrix of the rotor system. , and Let these represent the displacement vector, velocity vector, and acceleration vector of the rotor system, respectively. Indicates the rotational speed of the rotor system. This represents the damping matrix of the rotor system. This represents the gyroscopic effect matrix of the rotor system. Represents the stiffness matrix of the rotor system. This represents the external force vector of the rotor system.

[0017] Optionally, the dynamic analysis model of the rotor system is solved, including: The modal shapes of the rotor system are solved using the state vector method and the following formula: (5-1); (5-2); in, , , , These are the stiffness matrix, mass matrix, gyroscopic effect matrix, and damping matrix of the target rotor system, respectively. For state vectors, for The derivative, and These are the displacement vector and velocity vector of the target rotor system, respectively. Indicates the rotational speed of the target rotor system; set up Solving equation (5-1) is transformed into solving for the following eigenvalues ​​and eigenvectors: (5-3); in, The eigenvalues ​​characterize the dynamic properties of the rotor system; the eigenvectors are the mode shapes. Solve equation (5-3) by letting , Depends on , actual part Indicates damping, imaginary part Represents the natural frequency, when and When the speeds are equal, the rotor system resonates, and the corresponding speed is the critical speed. This can be controlled by changing... The value and observe The changes in the value were used to determine the critical speed, and a Campbell's diagram was plotted.

[0018] Optionally, the objective function for multiple optimization objectives includes: an objective based on critical rotational speed, an objective based on vibration response, and an objective based on mass. Objectives based on critical speed include minimizing the absolute value of the difference between the critical speed and the target operating speed; objectives based on vibration response include minimizing the maximum vibration amplitude at a specific location; and objectives based on mass include minimizing the total mass of the rotor system.

[0019] Optionally, a multi-objective genetic algorithm is used as the optimization engine. Population initialization is performed based on design parameters and their boundaries. After initialization, an iterative cycle of evaluation, selection, and reproduction is conducted until a preset maximum number of iterations is reached or a preset convergence criterion is met. The Pareto optimal solution set is then output, including: During the initialization phase, a set of initial individuals is randomly generated to form the initial population; In the evaluation phase, the objective function is used to calculate the objective function value for each individual. In the selection phase, based on the non-dominated ranking principle and the crowding principle, excellent individuals are selected. The non-dominated ranking principle selects individuals that are no worse than other individuals in all objectives and are better in at least one objective, i.e., individuals on the Pareto front. The crowding principle encourages the selection of individuals distributed on the periphery of the Pareto front to ensure the diversity of solutions and avoid all being concentrated in one solution. During the breeding phase, based on the selected superior individuals, a new generation of individuals is bred through crossover and mutation operations to form a new generation of population. The evaluation, selection, and reproduction phases are repeated until the preset maximum number of iterations is reached or the preset convergence criterion is met. The latest generation of the population is then used as the Pareto optimal solution set.

[0020] The intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm proposed in this application can bring the following significant benefits compared with traditional rotor system design methods.

[0021] First, automation and high efficiency. This application achieves full automation from parameter adjustment and dynamic analysis to result judgment, which greatly shortens the design cycle, reduces manual intervention, and improves design efficiency.

[0022] Second, it possesses global optimization capabilities. This application uses a multi-objective genetic algorithm, which has powerful global search capabilities, can avoid getting trapped in local optima, find truly excellent parameter combinations, and fully realize the design potential.

[0023] Third, multi-objective collaborative optimization. This application is the first to comprehensively consider support stiffness, concentrated mass and rotational inertia, and can simultaneously handle multiple conflicting design objectives, providing a series of optimal trade-off solutions for designers to make decisions based on final requirements, resulting in greater design flexibility.

[0024] Fourth, it has strong versatility. The framework built in this application is decoupled from the rotor dynamics analysis tool and can be integrated with various commercial software or self-developed programs through a simulation adapter interface, which has good versatility and portability.

[0025] Fifth, it effectively improves product performance. The rotor system designed in this application can precisely avoid the operating range at its critical speed and effectively suppress vibration, thereby significantly improving the operational reliability, stability, and service life of rotating machinery. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies of this application will be briefly introduced below. Obviously, the following drawings are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. The drawings described herein are only used to explain this application and are not intended to limit this application.

[0027] Figure 1 This is a flowchart of an intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm, provided in one embodiment of this application; Figure 2This is a detailed schematic diagram of an intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm provided in one embodiment of this application; Figure 3 This is a schematic diagram of a parameterized model of a rotor system provided in one embodiment of this application; Figure 4 This is a schematic diagram of a multi-objective genetic algorithm provided in one embodiment of this application; Figure 5 This is a schematic diagram of the critical speed of the target rotor system provided in one embodiment of this application; Figure 6 This is a schematic diagram of the Pareto optimal front output after optimization by a multi-objective genetic algorithm, provided in one embodiment of this application. Figure 7 This is a schematic diagram of genetic iteration convergence provided in one embodiment of this application; Figure 8 This is a characterization parameter for the overall deviation of the critical speed provided in one embodiment of this application. A schematic diagram; Figure 9 This is a schematic diagram of the structure of a rotor system parameter intelligent optimization device based on a multi-objective genetic algorithm provided in another embodiment of this application; Figure 10 This is a schematic diagram of the structure of an electronic device provided in another embodiment of this application. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the various embodiments of this application will be described in detail below with reference to the accompanying drawings. Those skilled in the art will understand that many technical details have been presented in the embodiments of this application to facilitate better understanding. However, the technical solutions claimed in this application can be implemented even without these technical details and various variations and modifications based on the following embodiments. The division of the following embodiments is for ease of description and should not constitute any limitation on the specific implementation of this application. The following embodiments can be combined with and referenced by each other without contradiction.

[0029] One embodiment of this application proposes an intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm, which is applicable to the intelligent design of rotor systems. The implementation details of the intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm proposed in this embodiment are described below. The following implementation details are provided for ease of understanding and are not necessary for implementing this solution.

[0030] The specific process of the intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm proposed in this embodiment can be described as follows: Figure 1 As shown, its visual details are as follows Figure 2 As shown, the method includes: Step 11: Determine the design parameters of the rotor system that need to be optimized, and define the physically feasible range of values ​​for each design parameter.

[0031] In the specific implementation, we first need to determine the design parameters of the target rotor system. These design parameters include at least two of the following three parameters: support stiffness parameter, lumped mass parameter, and rotational inertia parameter (the following explanation will use all three as examples). We also need to define the physically feasible range of values ​​for each design parameter.

[0032] In one example, the characteristic parameters of the target rotor system include support units, mass block units, and rotating shaft segment units, and the design parameters include support stiffness parameters, lumped mass parameters, and rotational inertia parameters.

[0033] Support stiffness parameters Here are the stiffness parameters for each support element. , This represents the total number of support units. For the first The stiffness parameters of each support unit. Each support unit includes a bearing housing and a thrust surface.

[0034] Lumped mass parameters The mass parameters of each mass block unit. , This represents the total number of mass block units. For the first The mass parameters of each mass block unit.

[0035] rotational inertia parameters The rotational inertia parameters of each rotating shaft segment unit, , This represents the total number of rotating shaft segment units. For the first Rotational inertia parameters of a single rotating shaft segment unit.

[0036] Step 12: Establish a parameterized rotor system dynamic analysis model based on the target rotor system and solve it. The input is the variable vector of design parameters and the output is the dynamic response result of the target rotor system.

[0037] In practical implementation, after determining the design parameters of the target rotor system, a parameterized rotor system dynamics analysis model can be established and solved. The input is a vector of design parameters, and the output is the dynamic response result of the target rotor system. This dynamic response result includes at least one of the following: critical speeds, mode shapes, and vibration response amplitudes. The rotor system dynamics analysis model will serve as the computational basis for subsequent analysis and optimization.

[0038] In one example, a parameterized rotor system dynamics analysis model can be as follows: Figure 3 As shown.

[0039] In one example, when establishing a parameterized rotor system dynamics analysis model based on the target rotor system, the first step is to establish the model based on the stiffness parameters of each support element and the support. A motion model of the support unit is established, and then based on each mass block element and lumped mass parameters... A motion model of the mass block element is established, and then based on the rotational axis segment elements and rotational inertia parameters... A motion model of the rotating shaft segment unit is established. Finally, based on the finite element method, the motion models of the support unit, the mass block unit, and the rotating shaft segment unit are assembled to obtain the dynamic analysis model of the rotor system.

[0040] No. The motion model of a support element is expressed by the formula: ; Among them, the upper right corner mark Indicates the support unit. Indicates the first Damping matrix of each support element and They represent the first Displacement vector and velocity vector of each support element Indicates the first The stiffness matrix of the nth support element, which is the nth support element's stiffness matrix. Stiffness parameters of each support element Indicates the first External force vector of each support unit.

[0041] No. The motion model of a mass block element is expressed by the formula: ; Among them, the upper right corner mark Represents a mass block element. Indicates the first The mass matrix of the nth mass block unit, which is the nth mass matrix. Lumped mass parameters of each mass block element. and They represent the first The velocity vector and acceleration vector of each mass element Indicates the rotational speed of the rotor system. Indicates the first The gyro effect matrix of each mass block unit Indicates the first The external force vector of each mass block element.

[0042] No. The motion model of a rotating shaft segment unit is expressed by the formula: ; Among them, the upper right corner mark Indicates a rotating shaft segment unit. Indicates the first Mass matrix of each rotating shaft segment element , and They represent the first The displacement vector, velocity vector, and acceleration vector of each rotating shaft segment element. Indicates the first The gyroscopic effect matrix of the nth rotating shaft segment unit, i.e. the nth Rotational inertia parameters of a single rotating shaft segment unit. Indicates the first Stiffness matrix of a rotating shaft segment element Indicates the first The external force vector of a rotating shaft segment unit.

[0043] In one example, the dynamic analysis model of the rotor system can be obtained by assembling the motion models of each support unit, each mass block unit, and each rotating shaft segment unit. Let the number of nodes in the rotor system be... , If the integer is greater than 1, then the rotor system dynamic analysis model can be based on the number of nodes. Determined to be a size of The system matrix. For a motion unit with 4 degrees of freedom aggregated at a single node, let it be... The matrix is ​​directly written into the corresponding position in the system matrix. The support element and the mass block element are both 4-DOF motion elements lumped together at one node. For a beam element with 8 DDOF and two nodes, let it be... The matrix is ​​written at the corresponding position in the system matrix, but the matrix at the common node of the adjacent beam element is superimposed, where the rotating shaft segment element is a beam element.

[0044] The dynamic analysis model of the rotor system is expressed by the following formula: ; Among them, the upper right corner mark Indicates a rotor system. Represents the mass matrix of the rotor system. , and Let these represent the displacement vector, velocity vector, and acceleration vector of the rotor system, respectively. Indicates the rotational speed of the rotor system. This represents the damping matrix of the rotor system. This represents the gyroscopic effect matrix of the rotor system. Represents the stiffness matrix of the rotor system. This represents the external force vector of the rotor system.

[0045] In one example, the modal shapes of the rotor system are solved using the following formula: (5-1); (5-2); in, , , , These are the stiffness matrix, mass matrix, gyroscopic effect matrix, and damping matrix of the target rotor system, respectively. For state vectors, for The derivative, and These are the displacement vector and velocity vector of the target rotor system, respectively. This indicates the rotational speed of the target rotor system.

[0046] set up Solving equation (5-1) is transformed into solving for the following eigenvalues ​​and eigenvectors: (5-3); in, The eigenvalues ​​characterize the dynamic characteristics of the rotor system, and the eigenvectors are the mode shapes.

[0047] Solve equation (5-3) by letting , Depends on , actual part Indicates damping, imaginary part Represents the natural frequency, when and When the speeds are equal, the rotor system resonates, and the corresponding speed is the critical speed. This can be controlled by changing... The value and observe The changes in the value were used to determine the critical speed, and a Campbell's diagram was plotted.

[0048] Step 13: Based on the design requirements, transform the performance indicators into an objective function with multiple optimization objectives.

[0049] In practical implementation, after establishing the dynamic analysis model of the rotor system, the performance indicators can be transformed into objective functions with multiple optimization objectives according to the design requirements. These objectives include objectives based on critical speed, objectives based on vibration response, and objectives based on mass.

[0050] In rotor system dynamics, mass distribution and support stiffness are two core parameters that determine the vibration characteristics of the system, and their influence is crucial. Mass distribution directly determines the rotor's inertial characteristics and natural frequencies. Uneven mass distribution will produce significant unbalanced responses, excite synchronous vibrations, and may affect the precession behavior of the system due to gyroscopic effects. Its distribution pattern further affects the location of the critical speed and the mode shape, and is the basis for rotor dynamic design and balancing correction.

[0051] Support stiffness defines the boundary conditions of the system and directly affects the dynamic characteristics of the support. Insufficient stiffness will lower the system's natural frequency, leading to a lower critical speed and increasing the risk of resonance. Anisotropy of stiffness will induce anisotropic vibrations in the system, and may even induce unstable vibrations, such as oil film oscillations. Furthermore, support stiffness and rotor mass together constitute the support modes of the system, and their matching relationship is crucial for vibration transmission and stability.

[0052] In other words, the mass distribution and the support stiffness are coupled together, which determine the inherent characteristics, critical speed, dynamic response and stability boundary of the rotor system. They are the core elements for rotor system dynamic analysis, optimization design and fault diagnosis.

[0053] Based on this, we can establish multiple optimization objectives. Objectives based on critical speed include minimizing the absolute value of the difference between the critical speed and the target operating speed; objectives based on vibration response include minimizing the maximum vibration amplitude at a specific location; and objectives based on mass include minimizing the total mass of the rotor system. These objectives are often conflicting (e.g., increasing stiffness may increase the critical speed but will increase weight).

[0054] Step 14: Use a multi-objective genetic algorithm as the optimization engine to initialize the population based on the design parameters and their boundaries. After the population initialization is completed, iterate through evaluation, selection and reproduction until the preset maximum number of iterations is reached or the preset convergence criterion is met, and then output the Pareto optimal solution set.

[0055] A schematic diagram of a multi-objective genetic algorithm is shown below. Figure 4 As shown.

[0056] In practical implementation, after establishing the objective function for multiple optimization objectives, a multi-objective genetic algorithm can be used as the optimization engine. Based on the design parameters and their boundaries, the population is initialized. After initialization, an iterative cycle of evaluation, selection, and reproduction is performed until the preset maximum number of iterations is reached or the preset convergence criterion is met, at which point a Pareto optimal solution set is output. The optimization idea of ​​the multi-objective genetic algorithm can be summarized as "simulating biological evolution to find the optimal trade-off." This algorithm does not seek a single optimal solution, but rather a set of "Pareto optimal solutions" representing the best trade-offs.

[0057] Multi-objective genetic algorithms can be divided into five parts: initialization phase, evaluation phase, selection phase, reproduction phase, and iteration phase.

[0058] During the initialization phase, a set of initial individuals is randomly generated to form the initial population.

[0059] In the evaluation phase, the objective function is used to calculate the objective function value for each individual.

[0060] In the selection phase, superior individuals are chosen based on the non-dominated ranking principle and the crowding principle. The non-dominated ranking principle selects individuals that are no worse than other individuals in all objectives and are better in at least one objective, i.e., individuals on the Pareto front. The crowding principle encourages the selection of individuals distributed on the periphery of the Pareto front to ensure the diversity of solutions and avoid concentration in a single solution.

[0061] During the breeding phase, based on the selected superior individuals, a new generation of individuals is bred to form a new generation of population through crossover (gene recombination) and mutation (introducing random minimization).

[0062] The iteration phase involves repeated evaluation, selection, and reproduction phases (i.e., generation after generation evolution) until the preset maximum number of iterations is reached or the preset convergence criterion is met. The latest generation of the population is then used as the Pareto optimal solution set (Pareto optimal front).

[0063] Step 15: Based on actual engineering preferences, select one or more optimal solutions from the Pareto optimal solution set to form the optimal design scheme, and design the rotor system based on the optimal design scheme.

[0064] In practical implementation, after the multi-objective genetic algorithm completes, we obtain a series of solutions (e.g., Solution A: critical speed is well avoided but slightly heavier, Solution B: very lightweight but critical speed is slightly worse avoided). We can make a final decision from this set of optimal solutions based on actual, possibly unquantified, preferences (such as cost, process constraints, also known as practical engineering preferences). Based on practical engineering preferences, one or more optimal solutions are selected from the Pareto optimal solution set to form the optimal design scheme, and the rotor system is designed based on the optimal design scheme.

[0065] In one example, a schematic diagram of the critical speed of the target rotor system is shown below. Figure 5 As shown, Figure 5 The critical speeds shown are first-order / 2504.9 rpm and second-order / 4932.1 rpm. Figure 5 The red curve in the middle is the synchronous excitation line, the blue line with an upward slope is the rotor's forward precession curve, and the blue line with a downward slope is the rotor's reverse precession curve. The intersection of the excitation line and the rotor's forward precession curve is the correct rotor critical speed.

[0066] The Pareto optimal front output by the multi-objective genetic algorithm after optimization is as follows: Figure 6 As shown in the figure. During the evaluation phase, the fitness value changes with the number of iterations as follows. Figure 7 As shown.

[0067] In one example, to quantify the degree to which the dynamic characteristics of the target rotor corresponding to the Pareto solution set obtained by the optimization algorithm conform to the design target, a characterization parameter called "critical speed comprehensive deviation" is defined. This parameter It is a dimensionless scalar, and its core idea is to measure the normalized total degree of deviation of each critical speed of the rotor from the center point of its respective target interval. Its schematic diagram is shown below. Figure 8 As shown, its mathematical expression is as follows: ; in, It is the first rotor system The actual calculated value of the first critical speed. It is the first The center value of the target range for the critical speed, i.e. (target upper limit + target lower limit) / 2. It is the first The width of the target range for the critical speed, i.e., the upper limit of the target range minus the lower limit of the target range.

[0068] Ideally, this means that the critical speeds of all orders are precisely located at the center of their target range, with the maximum safety margin.

[0069] An excellent state means that all critical speeds fall within the target range, but not at the center. The smaller the value, the closer the critical speed is to the center of the range, the better the system dynamics characteristics, and the higher the safety margin.

[0070] An unacceptable state indicates that at least one critical speed has deviated from the target range (falls outside the range). The larger the value, the more severe the deviation, and the higher the risk of system resonance.

[0071] In one example, the optimal combination of design parameters obtained from the optimization algorithm, i.e., the Pareto solution set, is substituted into the parameterized dynamic analysis model of the target rotor for calculation, using the critical speed to comprehensively measure the deviation. The specific numerical values ​​and their alignment with the design goals are shown in Table 1.

[0072] Table 1: Overall Deviation of Optimized Critical Speed value

[0073] The intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm proposed in this embodiment can bring the following significant benefits compared with traditional rotor system design methods.

[0074] First, automation and high efficiency. This embodiment automates the entire process from parameter adjustment and dynamic analysis to result judgment, greatly shortening the design cycle, reducing manual intervention, and improving design efficiency.

[0075] Second, it possesses global optimization capabilities. This embodiment uses a multi-objective genetic algorithm, which has powerful global search capabilities, can avoid getting trapped in local optima, find truly excellent parameter combinations, and fully realize the design potential.

[0076] Third, multi-objective collaborative optimization. This embodiment is the first to comprehensively consider support stiffness, concentrated mass, and rotational inertia, and can simultaneously handle multiple conflicting design objectives, providing a series of optimal trade-off solutions for designers to make decisions based on final requirements, resulting in greater design flexibility.

[0077] Fourth, it has strong versatility. The framework built in this embodiment is decoupled from the rotor dynamics analysis tool and can be integrated with various commercial software or self-developed programs through the simulation adapter interface, which has good versatility and portability.

[0078] Fifth, it effectively improves product performance. The rotor system designed in this embodiment can precisely avoid the operating range at its critical speed and effectively suppress vibration, thereby significantly improving the operational reliability, stability, and service life of rotating machinery.

[0079] The steps described above are for clarity only. In implementation, they can be combined into one step, or some steps can be broken down into multiple steps, as long as they involve the same logical relationship, they are all within the scope of protection of this application. Adding insignificant modifications or introducing insignificant designs to the algorithm or process, without changing the core design of the algorithm and process, are also within the scope of protection of this application.

[0080] Another embodiment of this application proposes an intelligent optimization device for rotor system parameters based on a multi-objective genetic algorithm, which is suitable for the intelligent design of rotor systems. The details of the intelligent optimization device for rotor system parameters based on a multi-objective genetic algorithm proposed in this embodiment are described below. The following content is only for the convenience of understanding and is not necessary for implementing this example. Figure 9 This is a schematic diagram of the structure of an intelligent optimization device for rotor system parameters based on a multi-objective genetic algorithm proposed in this embodiment, including: a design variable and constraint boundary module 21, a rotor system dynamic analysis model construction module 22, a multi-optimization objective definition module 23, an optimization execution module 24, and a final design module 25.

[0081] The design variable and constraint boundary module 21 is used to determine the design parameters of the rotor system that needs to be optimized, and to define the physically feasible range of values ​​for each design parameter.

[0082] The rotor system dynamics analysis model construction module 22 is used to establish a parameterized rotor system dynamics analysis model based on the target rotor system and solve it. Its input is the variable vector of design parameters and its output is the dynamic response result of the target rotor system.

[0083] The multi-optimization objective definition module 23 is used to transform performance indicators into objective functions with multiple optimization objectives according to design requirements.

[0084] The optimization execution module 24 is used to use a multi-objective genetic algorithm as the optimization engine to initialize the population based on the design parameters and their boundaries. After the population initialization is completed, iterative loops of evaluation, selection and reproduction are performed until the preset maximum number of iterations is reached or the preset convergence criterion is met, and then the Pareto optimal solution set is output.

[0085] The final design module 25 is used to select one or more optimal solutions from the Pareto optimal solution set according to actual engineering preferences, form an optimal design scheme, and design the rotor system based on the optimal design scheme.

[0086] It is not difficult to see that this embodiment is a system embodiment corresponding to the above method embodiments, and this embodiment can be implemented in conjunction with the above method embodiments. The relevant technical details and technical effects mentioned in the above method embodiments are still valid in this embodiment, and will not be repeated here to reduce repetition. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above method embodiments.

[0087] It is worth mentioning that all modules and units involved in this embodiment are logical modules. In practical applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. Furthermore, to highlight the innovative aspects of this application, this embodiment does not introduce units that are not closely related to solving the technical problems proposed in this application; however, this does not mean that other units do not exist in this embodiment.

[0088] Another embodiment of this application provides an electronic device, such as Figure 10 As shown, it includes a processor 31 and a memory 32. The memory 32 stores instructions that the processor 31 can execute. When the processor 31 is configured to execute the instructions, the electronic device can realize a rotor system parameter intelligent optimization method based on a multi-objective genetic algorithm as described in the above method embodiment.

[0089] The memory and processor are connected via a bus, which includes any number of interconnecting buses and bridges, connecting various circuits of one or more processors and the memory. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single component or multiple components, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0090] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0091] Another embodiment of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, enables intelligent optimization of rotor system parameters based on a multi-objective genetic algorithm as described in the above method embodiments.

[0092] That is, those skilled in the art will understand that all or part of the steps in the above method embodiments can be implemented by a program instructing related hardware. The program is stored in a storage medium and includes several instructions to cause a device (such as a microcontroller, chip, etc.) or processor to execute all or part of the steps of the method described in the method embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory, random access memory, magnetic disks, or optical disks.

[0093] Those skilled in the art will understand that the above embodiments are specific implementations of this application, and in practical applications, various changes can be made in form and detail without departing from the spirit and scope of this application. For those skilled in the art, several improvements and modifications can be made without departing from the principles of this application, and these improvements and modifications are also considered to be within the scope of protection of this application.

Claims

1. A method for intelligent optimization of rotor system parameters based on a multi-objective genetic algorithm, applicable to the intelligent design of rotor systems, characterized in that, The method includes: Determine the design parameters of the rotor system that needs to be optimized, and define the physically feasible range of values ​​for each design parameter; A parameterized rotor system dynamic analysis model is established based on the target rotor system and solved. The input is the variable vector of design parameters, and the output is the dynamic response result of the target rotor system. Based on design requirements, performance metrics are transformed into objective functions with multiple optimization objectives; A multi-objective genetic algorithm is used as the optimization engine. The population is initialized based on the design parameters and their boundaries. After the population initialization is completed, the evaluation, selection and reproduction are iteratively cycled until the preset maximum number of iterations is reached or the preset convergence criterion is met, and then the Pareto optimal solution set is output. Based on actual engineering preferences, one or more optimal solutions are selected from the Pareto optimal solution set to form the optimal design scheme, and the rotor system is designed based on the optimal design scheme.

2. The intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm as described in claim 1, characterized in that, The rotor system includes support units, mass block units, and rotating shaft segment units. The design parameters include support stiffness parameters, lumped mass parameters, and rotational inertia parameters. Support stiffness parameters Here are the stiffness parameters for each support element. , This represents the total number of support units. For the first Stiffness parameters of each support element; Lumped mass parameters The mass parameters of each mass block unit. , This represents the total number of mass block units. For the first Mass parameters of each mass block unit; rotational inertia parameters Here are the rotational inertia parameters for each rotating shaft segment unit. , This represents the total number of rotating shaft segment units. For the first Rotational inertia parameters of a single rotating shaft segment unit.

3. The intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm as described in claim 2, characterized in that, A parameterized rotor system dynamic analysis model is established based on the target rotor system, including: Based on the stiffness parameters of each support unit and support. Establish a motion model for the support unit; Based on each mass block element and lumped mass parameters Establish a motion model for the mass block unit; Based on each rotating shaft segment unit and rotational inertia parameters Establish a motion model for the rotating shaft segment unit; Based on the finite element method, the motion models of the support unit, the mass block unit, and the rotating shaft segment unit are assembled to obtain the dynamic analysis model of the rotor system. No. The motion model of a support element is expressed by the formula: ； Among them, the upper right corner mark Indicates the support unit. Indicates the first Damping matrix of each support element and They represent the first Displacement vector and velocity vector of each support element Indicates the first The stiffness matrix of the nth support element, which is the nth support element's stiffness matrix. Stiffness parameters of each support element Indicates the first External force vector of each support unit; No. The motion model of a mass block element is expressed by the formula: ； Among them, the upper right corner mark Represents a mass block element. Indicates the first The mass matrix of the nth mass block unit, which is the nth mass matrix. Lumped mass parameters of each mass block element. and They represent the first The velocity vector and acceleration vector of each mass element Indicates the rotational speed of the rotor system. Indicates the first The gyro effect matrix of each mass block unit Indicates the first External force vector of each mass block element; No. The motion model of a rotating shaft segment unit is expressed by the formula: ； Among them, the upper right corner mark Indicates a rotating shaft segment unit. Indicates the first Mass matrix of each rotating shaft segment element , and They represent the first The displacement vector, velocity vector, and acceleration vector of each rotating shaft segment element. Indicates the first The gyroscopic effect matrix of the nth rotating shaft segment unit, i.e. the nth Rotational inertia parameters of a single rotating shaft segment unit. Indicates the first Stiffness matrix of a rotating shaft segment element Indicates the first The external force vector of a rotating shaft segment unit.

4. The intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm as described in claim 3, characterized in that, let... The number of nodes in the rotor system is , If the integer is greater than 1, then the size of the system matrix of the rotor system is Based on the finite element method, the motion models of the support unit, the mass block unit, and the rotating shaft segment unit are assembled to obtain the rotor system dynamic analysis model, including: For a motion unit with 4 degrees of freedom concentrated at a single node, let it be... The matrix is ​​directly written into the corresponding position in the system matrix; among them, the support unit and the mass block unit are both motion units with 4 degrees of freedom lumped together at a single node; For a beam element with 8 degrees of freedom and two nodes, let it be... The matrix is ​​written at the corresponding position in the system matrix, but the matrix at the common node of the adjacent beam element is superimposed; where the rotation axis segment element is a beam element; The dynamic analysis model of the rotor system is expressed by the following formula: ； Among them, the upper right corner mark Indicates a rotor system. Represents the mass matrix of the rotor system. , and These represent the displacement vector, velocity vector, and acceleration vector of the rotor system, respectively. Indicates the rotational speed of the rotor system. This represents the damping matrix of the rotor system. This represents the gyroscopic effect matrix of the rotor system. Represents the stiffness matrix of the rotor system. This represents the external force vector of the rotor system.

5. The intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm as described in claim 4, characterized in that, Solving the dynamic analysis model of the rotor system includes: The modal shapes of the rotor system are solved using the state vector method and the following formula: （5-1）； （5-2）； in, , , , These are the stiffness matrix, mass matrix, gyroscopic effect matrix, and damping matrix of the target rotor system, respectively. For state vectors, for The derivative, and These are the displacement vector and velocity vector of the target rotor system, respectively. Indicates the rotational speed of the target rotor system; set up Solving equation (5-1) is transformed into solving for the following eigenvalues ​​and eigenvectors: （5-3）； in, The eigenvalues ​​characterize the dynamic properties of the rotor system; the eigenvectors are the mode shapes. Solve equation (5-3) by letting , Depends on , actual part Indicates damping, imaginary part Represents the natural frequency, when and When the speeds are equal, the rotor system resonates, and the corresponding speed is the critical speed. This can be controlled by changing... The value and observe The changes in the value were used to determine the critical speed, and a Campbell's diagram was plotted.

6. The intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm as described in claim 5, characterized in that, Objective functions for multiple optimization objectives include: objectives based on critical rotational speed, objectives based on vibration response, and objectives based on mass. Objectives based on critical speed include minimizing the absolute value of the difference between the critical speed and the target operating speed; objectives based on vibration response include minimizing the maximum vibration amplitude at a specific location; and objectives based on mass include minimizing the total mass of the rotor system.

7. The intelligent optimization method for rotor system parameters based on a multi-objective genetic algorithm as described in claim 1, characterized in that, A multi-objective genetic algorithm is used as the optimization engine. Population initialization is performed based on design parameters and their boundaries. After initialization, an iterative cycle of evaluation, selection, and reproduction is conducted until a preset maximum number of iterations is reached or a preset convergence criterion is met. The Pareto optimal solution set is then output, including: During the initialization phase, a set of initial individuals is randomly generated to form the initial population; In the evaluation phase, the objective function is used to calculate the objective function value for each individual. In the selection phase, based on the non-dominated ranking principle and the crowding principle, excellent individuals are selected. The non-dominated ranking principle selects individuals that are no worse than other individuals in all objectives and are better in at least one objective, i.e., individuals on the Pareto front. The crowding principle encourages the selection of individuals distributed on the periphery of the Pareto front to ensure the diversity of solutions and avoid all being concentrated in one solution. During the breeding phase, based on the selected superior individuals, a new generation of individuals is bred through crossover and mutation operations to form a new generation of population. The evaluation, selection, and reproduction phases are repeated until the preset maximum number of iterations is reached or the preset convergence criterion is met. The latest generation of the population is then used as the Pareto optimal solution set.

8. A rotor system parameter intelligent optimization device based on a multi-objective genetic algorithm, suitable for the intelligent design of rotor systems, characterized in that, The device includes: The design variable and constraint boundary module is used to determine the design parameters of the rotor system that needs to be optimized, and to define the physically feasible range of values ​​for each design parameter. The rotor system dynamics analysis model construction module is used to build a parameterized rotor system dynamics analysis model based on the target rotor system and solve it. Its input is the variable vector of design parameters and its output is the dynamic response result of the target rotor system. The multi-optimization objective definition module is used to transform performance indicators into objective functions with multiple optimization objectives based on design requirements. The optimization execution module is used to use a multi-objective genetic algorithm as the optimization engine. Based on the design parameters and their boundaries, it initializes the population. After the population initialization is completed, it performs an iterative loop of evaluation, selection and reproduction until the preset maximum number of iterations is reached or the preset convergence criterion is met, and then outputs the Pareto optimal solution set. The final design module is used to select one or more optimal solutions from the Pareto optimal solution set according to actual engineering preferences, form the optimal design scheme, and design the rotor system based on the optimal design scheme.

9. An electronic device, characterized in that, include: The processor and memory, wherein the memory stores instructions executable by the processor, and the processor is configured to, when executing the instructions, enable the electronic device to implement a rotor system parameter intelligent optimization method based on a multi-objective genetic algorithm as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it can implement a method for intelligent optimization of rotor system parameters based on a multi-objective genetic algorithm as described in any one of claims 1 to 7.

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