A multi-stage vibration isolation system integrated optimization design method based on genetic algorithm

Abstract

This invention relates to an integrated optimization design method for a multi-level vibration isolation system based on a genetic algorithm, comprising: establishing an integrated simulation model; determining the initial parameter values ​​of each design variable based on the simulation model and the search space, and determining the objective function of the vibration isolation system; transforming the design variable combinations into chromosomes based on the initial parameter values ​​of each design variable and the objective function, wherein each design variable combination includes each design variable; setting mutation operators, mutation amounts, mutation order, and selection operators; eliminating unreasonable design variable combinations based on a first fitness function; determining, based on a second fitness function, that the chromosome corresponding to the smallest second fitness value greater than 0 is used as a high-quality gene to continue breeding until the genetic algorithm terminates and obtains the optimal design parameter combination; the mutation order is: vibration isolation foundation platform thickness, vibration isolation foundation hanging dimensions, vibration isolator internal pressure, vibration isolator diameter, number of dampers, damper parameters, and the thickness of the base plate and sidewalls of the enclosure auxiliary structure.

Description

[0001] This application is a divisional application of the parent application, filed on September 25, 2023, with application number 202311245067.7 and invention title "An Integrated Optimization Design Method for Multi-Level Vibration Isolation System Considering Vibration Sources". Technical Field

[0002] This invention relates to the field of vibration isolation technology, and in particular to an integrated optimization design method for multi-level vibration isolation systems based on genetic algorithms. Background Technology

[0003] In the design of air-floating vibration isolation systems for large vibration-generating equipment, existing technologies typically only perform parametric design on the isolation system itself. For example... Figure 1 The large-scale vibration-generating equipment multi-stage vibration isolation system shown consists of three levels: the upper first level is the vibration source, i.e., the vibration-generating equipment; the middle second level is the vibration-generating foundation, i.e., the vibration-generating system; and the lower third level is the enclosure auxiliary structure. Existing technologies typically ignore the shape of the upper vibration source, simplifying its weight as a static load acting on the top surface of the vibration isolation foundation, while neglecting the vibration isolation effect of the enclosure auxiliary structure. When parametrically designing the vibration isolation foundation itself, manual empirical calculations are usually used, with multiple schemes optimized and compared based on indicators such as vibration isolation performance and cost control.

[0004] Analysis revealed that the existing technical solutions only design the vibration isolation system separately and do not design the vibration isolation performance of the auxiliary enclosure structure. This makes it impossible to fully utilize the optimal vibration isolation performance under the synergistic effect of the two. At the same time, it cannot solve the problem that it is difficult to use the general dynamic foundation half-space theory to calculate the load of large vibration-generating equipment after it has passed through a multi-stage vibration isolation system. It also fails to accurately assess the vibration impact of large thrust vibration on the surrounding environment.

[0005] Existing technical solutions use large mass points to model the upper vibration-generating equipment, effectively ignoring the stiffness matrix of the upper vibration-generating equipment, thus leading to distortion in the calculation of system vibration characteristics. Furthermore, the parametric design of vibration isolation foundations typically relies on manual calculations. Due to the large number of design parameters and the difficulty in converting multiple optimization objectives into a single control optimization objective (e.g., vibration isolation performance and cost), manually calculated design parameters cannot efficiently and accurately optimize the design scheme. Especially in recent years, the rapid rise in the prices of commodities such as steel has increased the time cost of manual calculations, preventing vibration isolation system developers from adjusting their bids based on real-time market prices, thereby limiting effective cost control and increasing the risk of losses. Summary of the Invention

[0006] In view of the above analysis, the present invention aims to provide an integrated optimization design method for multi-level vibration isolation systems based on genetic algorithms, in order to solve the problems of vibration calculation distortion caused by ignoring the vibration source stiffness matrix when designing multi-level vibration isolation systems for large vibrating equipment, and the difficulty in performance optimization and ineffective cost control caused by ignoring the synergistic effect between the vibration isolation system and the enclosure auxiliary structure.

[0007] To achieve the above objectives, this invention proposes an integrated optimization design method for a multi-stage vibration isolation system based on a genetic algorithm, comprising the following steps: Step S1: Establish an integrated simulation model of the multi-level vibration isolation system; determine the initial parameter values ​​of each design variable based on the design variables and search space of the integrated simulation model of the multi-level vibration isolation system, and determine the objective function of the multi-level vibration isolation system. Step S2: Based on the initial parameter values ​​of each design variable and the objective function, the design variable combination is transformed into a chromosome, where the design variable combination includes each design variable; a mutation operator, mutation amount, mutation order, and selection operator are set; unreasonable design variable combinations are eliminated based on the first fitness function; based on the second fitness function, the chromosome corresponding to the smallest second fitness value greater than 0 is selected as a high-quality gene and continues to reproduce until the genetic algorithm terminates when the termination condition is met, thus obtaining the optimal design variable combination parameters as the optimal design parameter combination for the vibration isolation system; The order of variation is as follows: thickness of the vibration isolation foundation platform, hanging dimensions of the vibration isolation foundation, internal pressure of the vibration isolator, diameter of the vibration isolator, number of dampers, damper parameters, thickness of the base plate of the enclosure auxiliary structure, and thickness of the side wall of the enclosure auxiliary structure.

[0008] Furthermore, the design variables of the multi-stage vibration isolation system include: Vibration isolation foundation platform thickness, vibration isolation foundation hanging dimensions, vibration isolator parameters, quantity and location, damper quantity and parameters, enclosure auxiliary structure base plate thickness and side wall thickness; The design variables are combined and transformed into a chromosome representation, with each chromosome containing the design variables as genes. The search space is determined based on the value range of each of the design variables.

[0009] Furthermore, an integrated simulation model of a multi-level vibration isolation system is established, including: The multi-level vibration isolation system is a three-level vibration isolation system; The first stage is the vibration source, which is the vibration generating equipment; The second level is the vibration isolation foundation, which includes a vibration isolation foundation platform and vibration isolators. The vibration isolation foundation platform includes a vibration isolation foundation platform and a vibration isolation foundation underpinning arranged rigidly at the top and bottom. The vibration isolators are evenly arranged along the outer edge of the vibration isolation foundation platform. The vibration isolation foundation underpinning is used to lower the center of gravity of the vibration isolation foundation platform, increase the counterweight of the vibration isolation foundation platform, and improve the vibration isolation performance. The third level is the retaining auxiliary structure, which is bound to the bottom of the vibration isolation system; soil elements multiple times the length of the retaining auxiliary structure are built around the retaining auxiliary structure, and rigid boundary conditions are set at the boundaries of the soil elements. The vibration isolator includes multiple air springs, with dampers installed in the gaps between the air springs. The dampers are not connected to the vibration isolator but are bolted between the vibration isolation foundation platform and the enclosure auxiliary structure. The vibration source, vibration isolation foundation, and enclosure auxiliary structure are designed as a whole and together form a mass and stiffness matrix in the calculation, reflecting the true dynamic characteristics of the vibration isolation system.

[0010] Further, step S2 includes: Step S21: Initialize the population and convert the design variable combination into chromosomes, wherein the design variable combination includes each of the design variables; Step S22: Set the mutation operator, mutation amount and mutation order of the chromosome, set the selection operator, and eliminate unreasonable combinations of design variables based on the first fitness function to obtain a chromosome with a reasonable vibration isolator diameter; Step S23: Based on the combination of design variables that conform to the first fitness function, the vibration response amplitude acc in the 1-100Hz frequency domain at 1m from the edge of the auxiliary structure of the enclosure under the most unfavorable working state of the vibration generating equipment is obtained by solving the finite element model. Based on the vibration response amplitude acc, the second fitness value of each individual is calculated one by one. Genes with a second fitness value greater than 0 and a second fitness value of minimum value are used as high-quality genes to continue to reproduce. Step S24: Based on the Python language, multiple model calculation codes are generated, and the numerical results of multiple gene combinations are calculated in parallel. When the genetic algorithm terminates, the genetic algorithm terminates, and the optimal design variable combination parameters of the vibration isolation system are obtained. The termination conditions of the genetic algorithm include having at least 500 iterations and a second fitness value greater than zero.

[0011] Further, step S22 includes: The thickness of the vibration isolation foundation platform, the hanging dimensions of the vibration isolation foundation, the diameter of the vibration isolator, the internal pressure of the vibration isolator, the number and parameters of the dampers, the thickness of the bottom plate of the enclosure auxiliary structure, and the thickness of the side wall of the enclosure auxiliary structure are set as mutation operators in the chromosome. Set the mutation amount and mutation order of the mutation operator; The vibration isolator position spacing is obtained based on the vibration isolator position, and the vibration isolator position spacing is set as the selection operator; A first fitness function is set for screening, and the design variable combinations corresponding to genes that satisfy the first fitness function are used for further breeding.

[0012] Furthermore, the spacing between the vibration isolators is calculated as follows: The spacing between vibration isolators = (circumference of the vibration isolation base platform - 4d - sum of the diameters of all vibration isolators) / number of vibration isolators; The perimeter of the vibration isolator platform is calculated based on the length and width of the vibration isolation foundation platform.

[0013] Furthermore, the first fitness function is: Fitness1 = Sum of diameters of all vibration isolators - (Circumference of vibration isolation base platform - 4d). If the first adaptive fitness value Fitness1 < 0, the gene is eliminated and will not be included in subsequent calculations; if the first adaptive fitness value Fitness1 ≥ 0, the gene can continue to reproduce. The design combinations corresponding to genes that meet the first fitness function are used as high-quality genes for continued reproduction; The first fitness function screens the engineering feasibility of the parameters of gene mutation.

[0014] Further, step S23 includes: Based on the high-quality genes of the design variable combination that conforms to the first fitness function, the finite element model is automatically generated using Python language to calculate acc. The acc is the vibration response amplitude in the 1-100Hz frequency domain at 1m from the edge of the enclosure auxiliary structure under the most unfavorable working state of the vibration generating equipment under the design variable combination represented by the chromosome. Calculate the cost control price of the design variable combination; Based on the vibration response amplitude acc and the cost control price, the second fitness value of each high-quality gene is calculated, and the gene corresponding to the smallest second fitness value greater than 0 is taken as a high-quality gene and continues to reproduce. Furthermore, the calculation of the second fitness value for each individual is as follows: The second fitness value is obtained by calculating the second fitness function for screening high-quality genes; Genes with minimum second fitness function values ​​greater than 0 are used as high-quality genes for further propagation.

[0015] Furthermore, the second fitness function is:

[0016] Where target1 is the vibration performance objective function, and target2 is the cost control objective function. and Here, is the weighting coefficient for the vibration performance objective function and the cost control objective function; acc is the vibration response amplitude in the 1-100Hz frequency domain at a distance of 1m from the edge of the auxiliary structure of the enclosure, under the most unfavorable working state of the vibration generating equipment under the design variable combination represented by chromosome; and price is the cost control amount.

[0017] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: 1. This invention employs an integrated modeling and design method, encompassing the vibration-generating equipment, vibration-isolation foundation, and enclosure auxiliary structures, and performs solid modeling of the vibration-generating equipment above the vibration isolation system. This design method enables the accurate calculation of the system's vibration characteristics and ensures full utilization of the synergistic effect of the vibration isolation system and enclosure auxiliary structures, achieving optimal vibration isolation performance under certain cost control conditions; 2. To meet the construction feasibility requirements of air-floating vibration isolation systems for large-scale vibration-generating equipment, this invention uses a search space range derived from extensive engineering experience. The scope and variation of the variable optimization search must be within the range specified in this invention to ensure that it does not deviate from the actual engineering application. The variation operators include: vibration isolation foundation platform thickness, vibration isolation foundation hanging dimensions, vibration isolator diameter, vibration isolator internal pressure, number and parameters of dampers, thickness of the base plate of the enclosure auxiliary structure, and thickness of the sidewall of the enclosure auxiliary structure. 3. In genetic algorithm design, the design of the fitness function is the core criterion for evaluating the optimization algorithm. This invention designs a first fitness function, Fitness1, to screen the engineering feasibility of gene mutation parameters. Subsequently, a second fitness function, Fitness2, is further designed, which can effectively determine the weight relationship between the two objectives of vibration isolation performance and price control, performing multi-objective screening to obtain high-quality genes. The calculation of the cost control price includes a steel content coefficient, which is an empirically estimated coefficient. This coefficient value of 0.3-0.35 is derived from a large amount of practical experience. 4. This invention uses a genetic algorithm for optimization search, continuously updates and optimizes the gene combination of each individual, and automatically generates finite element models for different gene combinations based on Python language to calculate the best combination of vibration isolation parameters, thereby improving vibration isolation performance and reducing costs.

[0018] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0019] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0020] Figure 1 is a schematic diagram of the multi-stage vibration isolation system for a large vibration-generating device; Figure 2 Flowchart of integrated optimization design method for multi-stage vibration isolation system considering vibration source; Figure 3 Design a flowchart for the genetic optimization algorithm; 1-Vibration generating equipment; 2-Vibration isolation foundation platform; 3-Vibration isolation foundation underlay; 4-Vibration isolator; 5-Enclosure auxiliary structure. Detailed Implementation

[0021] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0022] This invention proposes an integrated optimization design method for a multi-stage vibration isolation system based on a genetic algorithm. The multi-stage vibration isolation system is an air-floating multi-stage vibration isolation system for large vibration-generating equipment. The integrated design refers to the integrated optimization design method for the "vibration isolation equipment - vibration isolation foundation - enclosure auxiliary structure" of the vibration isolation system.

[0023] This method designs large vibration-generating equipment, vibration isolation devices, and enclosure auxiliary structures as a whole. For example... Figure 1 As shown, the large vibration generating equipment is used as the vibration source and is added to the simulation model according to its actual size and material properties. The large vibration generating equipment and the vibration isolation foundation are connected by a binding method so that the two together form the mass and stiffness matrix in the calculation, reflecting the real dynamic characteristics of the vibration isolation system. like Figure 1As shown, the vibration isolation foundation pedestal and the vibration isolator 4 constitute the vibration isolation foundation. The vibration isolation foundation pedestal consists of two parts: the vibration isolation foundation platform 2 and the vibration isolation foundation underpinning 3. The two parts are rigidly connected vertically, with the vibration isolation foundation platform 2 on top and the vibration isolation foundation underpinning 3 on the bottom. The function of the vibration isolation foundation underpinning 3 is to lower the center of gravity of the entire vibration isolation foundation pedestal, increase the counterweight of the pedestal, and improve the vibration isolation performance. The vibration isolator 4 includes multiple air springs, which are evenly arranged along the outer edge of the vibration isolation foundation platform 2. Dampers are installed in the gaps between the air springs. The dampers are not connected to the vibration isolator 4 but are bolted between the vibration isolation foundation platform 2 and the auxiliary enclosure structure 5, which is not shown in the figure.

[0024] The retaining auxiliary structure 5 is bonded to the bottom of the vibration isolation system. Soil elements, 3-5 times the length of the retaining auxiliary structure, are then established around it. Rigid boundary conditions are set at the boundaries of these soil elements to effectively assess the vibration impact on the surrounding environment after the load from the large vibration-generating equipment passes through the vibration isolation system. Preferably, a multi-objective genetic optimization algorithm is used to determine the design parameters of the multi-stage vibration isolation system that best balances vibration isolation effectiveness and economic cost.

[0025] like Figure 2 As shown, the integrated optimization design method for a multi-stage vibration isolation system considering the vibration source includes steps S1-S2.

[0026] Step S1: Determine the initial parameter values ​​of each design variable based on the design variables and search space of the multi-stage vibration isolation system, and determine the objective function of the multi-stage vibration isolation system. Step S2: Based on the initial parameter values ​​of each design variable and the objective function, the design variable combination is transformed into a chromosome, wherein the design variable combination includes each design variable; a mutation operator, mutation amount, mutation order, and selection operator are set; unreasonable design variable combinations are eliminated based on the first fitness function; based on the second fitness function, the chromosome corresponding to the smallest second fitness value greater than 0 is selected as a high-quality gene and continues to reproduce until the genetic algorithm terminates when the termination condition is met, thus obtaining the optimal design variable combination parameters as the optimal design parameter combination.

[0027] Step S1, including steps S11-S14, specifically: Step S11: Determine the design variables for the multi-stage vibration isolation system; Determine the design variables, including: the thickness of the vibration isolation foundation platform, the dimensions of the vibration isolation foundation under the structure, the parameters, quantity and location of the vibration isolators, the quantity and parameters of the dampers, and the thickness of the base plate and sidewalls of the enclosure auxiliary structure.

[0028] The parameters of the vibration isolator include the diameter range and the load-bearing capacity range of the vibration isolator, wherein the load-bearing capacity range of the vibration isolator is calculated from the internal pressure of the vibration isolator and the effective diameter of the air spring; the parameters of the damper include the horizontal damping ratio and the vertical damping ratio.

[0029] Step S12: Determine the search space for design variables; The search space for design variables is the range of values ​​that the design variables can take. The ranges of values ​​for each design variable are derived from extensive practical experience, as follows: (1) The thickness of the vibration isolation foundation platform ranges from 800 to 1600 mm.

[0030] (2) The dimensions of the vibration isolation foundation underlayment include: the length, width, and thickness of the vibration isolation foundation underlayment, with the search space as follows: a) The hanging length of the vibration isolation foundation is in the range of (vibration isolation foundation platform length - 2000mm) to (vibration isolation foundation platform length - 1000mm). b) The width range of the underlayment of the vibration isolation foundation is: (width of vibration isolation foundation platform - 2000mm) to (width of vibration isolation foundation platform - 1000mm); c) The thickness range of the vibration isolation foundation is 200mm to (elevation of the top surface of the auxiliary structure bottom plate of the enclosure - 300mm).

[0031] (3) The vibration isolator is an air spring vibration isolator. The vibration isolator parameters include: the effective diameter of the vibration isolator and the load-bearing capacity of the vibration isolator. The search spaces are as follows: a) Effective diameter range of vibration isolators: 600mm to 1000mm; b) Vibration isolator load-bearing capacity range: Where d is the effective diameter of the air spring, and p is the internal pressure range of the vibration isolator. to .

[0032] (4) The number of vibration isolators is: the total weight of the upper part of the vibration isolators / the bearing capacity of the vibration isolators; (5) Vibration isolator position: evenly arranged along the outer edge of the vibration isolation foundation platform, the distance between the centroids of the vibration isolators is not less than the effective diameter d of the air spring, the maximum position spacing between vibration isolators = (circumference of the vibration isolation foundation platform - 4d - sum of the diameters of all vibration isolators) / number of vibration isolators, where d is the effective diameter of the air spring; (6) Number of dampers: 2 to 4; (7) Damper parameters: horizontal damping ratio 0.05 to 0.4, vertical damping ratio 0.05 to 0.4; the larger the damping ratio, the higher the damping degree of the vibration isolation system, the smaller the vibration amplitude, and the longer the vibration period.

[0033] (8) Thickness of the base plate of the enclosure auxiliary structure: 1000mm to 1500mm; (9) Thickness of the sidewall of the enclosure auxiliary structure: 200mm to 500mm.

[0034] Step S13: Determine the initial parameter values ​​for each design variable; Specifically, the initial parameter values ​​of each design variable should be determined based on the actual situation.

[0035] For example, (1) The initial thickness of the vibration isolation foundation platform is 800 mm; (2) Dimensions of the vibration isolation foundation under the structure: a) The initial value of the hanging length of the vibration isolation foundation is: the length of the vibration isolation foundation platform - 2000mm; b) The initial value of the under-suspension width of the vibration isolation foundation is: the width of the vibration isolation foundation platform - 2000mm; c) The initial thickness of the vibration isolation foundation under the suspension is 200mm; (3) Vibration isolator parameters, including the effective diameter range and initial values ​​of the vibration isolator bearing capacity range, are as follows: a) The initial effective diameter of the vibration isolator is 600 mm; b) The initial load-bearing capacity of the vibration isolator is: ; (4) The initial value of the number of vibration isolators is: the total weight of the upper part of the vibration isolators / the bearing capacity of the vibration isolators, wherein the sum of the weight of the upper part of the vibration isolators is set according to specific requirements; (5) The vibration isolators are evenly arranged along the lower part of the outer edge of the vibration isolation platform. The initial spacing between the vibration isolators is (circumference of the vibration isolation platform - 4d - sum of the diameters of all vibration isolators) / number of vibration isolators, where d is the diameter of the air spring. (6) Initial number of dampers: 2; (7) Initial values ​​of damper parameters: horizontal damping ratio 0.05, vertical damping ratio 0.05; (8) Initial thickness of the base plate of the enclosure auxiliary structure: 1000mm; (9) Initial thickness of the sidewall of the enclosure auxiliary structure: 200mm.

[0036] Step S14: Determine the objective function of the multi-stage vibration isolation system.

[0037] The objective functions of a multi-stage vibration isolation system include: a vibration performance objective function and a cost control objective function, which are as follows: (1) The objective function for vibration performance is: under the most unfavorable working condition of the vibration generating equipment, the vibration response in the 1-100Hz frequency range at a distance of 1m from the edge of the auxiliary structure of the enclosure is less than 0.05g; If the vibration response is less than 0.05g, the objective function value for vibration performance is 1; otherwise, it is 0.

[0038] (2) The objective function of cost control is: the cost control price is not greater than the bidding control price.

[0039] If the cost control price is less than or equal to the bidding control price, the cost control objective function value is 1; otherwise, it is 0. The bidding control price is set according to specific requirements.

[0040] Step S2, specifically.

[0041] like Figure 3 As shown, this step includes S21-S24.

[0042] In genetic algorithms, an individual contains chromosomes, a chromosome contains genes, and a gene is a component of a chromosome. In this application, a chromosome is an abstract representation of an individual, including all combinations of design variables.

[0043] Step S21: Initialize the population and convert the design variable combination into chromosomes, wherein the design variable combination includes each of the design variables.

[0044] The design variables are transformed into a chromosome representation, with each chromosome containing the genetic information of: the thickness of the vibration isolation foundation platform, the dimensions of the vibration isolation foundation hanging, the parameters, quantity and location of the vibration isolators, the quantity and parameters of the dampers, and the thickness of the base plate and sidewalls of the enclosure auxiliary structure.

[0045] Step S22: Set the mutation operator, mutation amount and mutation order of the chromosome, set the selection operator, and eliminate unreasonable combinations of design variables based on the first fitness function to obtain a chromosome with a reasonable vibration isolator diameter.

[0046] Selecting some design variables from a combination of design variables as mutation operators; selecting some design variables from a combination of design variables as selection operators. Mutation operators and selection operators are different design variables.

[0047] The first step is to set the mutation operator for the chromosome; Set mutation operators, which include: vibration isolation foundation platform thickness, vibration isolation foundation hanging dimensions, vibration isolator diameter, vibration isolator internal pressure, number and parameters of dampers, thickness of the base plate of the enclosure auxiliary structure, and thickness of the side wall of the enclosure auxiliary structure.

[0048] The internal pressure of the vibration isolator is calculated from the vibration isolator bearing capacity in the design variables, as shown in formula (1): (1) Where P is the internal pressure of the vibration isolator, in MPa; F is the load-bearing capacity of the vibration isolator, in N; and d is the effective diameter of the air spring, in mm. .

[0049] The second step is to set the mutation amount and mutation order of the mutation operator; a) The thickness of the vibration isolation foundation platform varies by 100mm; b) The dimensions of the vibration isolation foundation under the suspension can vary by 100mm; c) The internal pressure variation of the vibration isolator is 0.1 kg / cm². 2 ; d) The diameter of the vibration isolator varies by 100 mm; e) Number of dampers, with a variation of 2; f) Damper parameters: the variation of both horizontal damping ratio and vertical damping ratio is 0.01; g) The thickness of the base plate of the auxiliary enclosure structure varies by 100 mm; h) The thickness of the sidewalls of the enclosure auxiliary structure varies by 100 mm.

[0050] The order of mutation is a)-g).

[0051] The third step is to set the selection operator; The operator is selected as the vibration isolator position spacing, as shown in formula (2).

[0052] The spacing between vibration isolators = (circumference of the vibration isolation foundation platform - 4d - sum of the diameters of all vibration isolators) / number of vibration isolators (2) Where d is the effective diameter of the air spring, and the perimeter of the vibration isolation base platform is calculated from the length and width of the vibration isolation base platform.

[0053] Selection is the fundamental operator in genetic algorithms. It selects a certain number of superior individuals from the current population to serve as parents for the next generation, giving them the opportunity to reproduce and embodying the natural selection principle of "survival of the fittest." Individual selection is based on fitness values; individuals with fitness values ​​greater than the standard are retained, while those with fitness values ​​less than the standard are eliminated.

[0054] The fourth step is to set the first fitness function, Fitness1, to perform screening, and genes that meet the conditions will continue to reproduce; The first fitness function, Fitness1, is shown in formula (3).

[0055] Fitness1 = Sum of diameters of all vibration isolators - (Circumference of vibration isolation base platform - 4d) (3) Based on the first fitness function, the extreme first fitness value is Fitness1.

[0056] If the first fitness value Fitness1 < 0, then the gene is eliminated and will not be included in subsequent calculations; If the first fitness value Fitness1 ≥ 0, then the gene can continue to reproduce.

[0057] The sum of all vibration isolator diameters is calculated, and the perimeter of the vibration isolation foundation platform is subtracted by four times the diameter of the air spring. The purpose is to eliminate unreasonable vibration isolator diameters during the design process, avoiding situations that do not conform to engineering realities. Design combinations corresponding to genes that meet the first fitness function are considered superior genes and continue to be propagated.

[0058] The first fitness function filters out design variable combinations that do not conform to the design criteria for the diameter of the vibration isolator, which helps to speed up the search process of the genetic algorithm and enable the genetic algorithm to find the optimal solution that meets the design goal more quickly.

[0059] Step S23: Based on the combination of design variables that conform to the first fitness function, the vibration response amplitude acc in the 1-100Hz frequency domain at a distance of 1m from the edge of the auxiliary structure of the enclosure is calculated by solving the finite element model under the most unfavorable working state of the vibration generating equipment. Based on the vibration response amplitude acc, the second fitness value of each individual is calculated one by one. Genes with a second fitness value greater than 0 and a second fitness value of minimum value are selected as high-quality genes for continued reproduction.

[0060] The first step is to automatically generate a finite element model based on the high-quality genes that meet the design variable combination of the first fitness function, using Python to calculate the acc.

[0061] acc represents the vibration response amplitude in the 1-100Hz frequency range at a distance of 1m from the edge of the enclosure auxiliary structure under the most unfavorable working condition of the vibration generating equipment, represented by the combination of design variables (chromosomes).

[0062] Using Python, a finite element model is automatically generated for calculation to obtain the accuracy.

[0063] The second step is to calculate the cost control price of the design variable combination.

[0064] The price is the cost control price calculated by combining design variables, as shown in formula (4).

[0065] price = (volume of vibration isolation foundation platform + volume of vibration isolation foundation underlay) × market price of concrete + (mass of vibration isolation foundation platform + mass of vibration isolation foundation underlay) × steel content coefficient × market price of steel + number of vibration isolators × market price of vibration isolators + number of dampers × market price of dampers + volume of enclosure auxiliary structure × market price of reinforced concrete (4) In formula (4), the volume of the vibration isolation foundation platform is obtained by multiplying the thickness of the vibration isolation foundation platform by the area of ​​the vibration isolation foundation platform (platform length × platform width); the volume of the vibration isolation foundation underlay is obtained by multiplying the length of the vibration isolation foundation underlay, the width of the vibration isolation foundation underlay, and the thickness of the vibration isolation foundation underlay; the market price of concrete, the mass of the vibration isolation foundation platform, the mass of the vibration isolation foundation underlay, the market price of steel, the market price of vibration isolators, the market price of dampers, and the market price of reinforced concrete are constants, set according to actual needs; and the steel content coefficient is a constant parameter set empirically, with a value range of 0.3-0.35.

[0066] The third step is to calculate the second fitness value (Fitness2) of each high-quality gene based on the vibration response amplitude (acc) and the cost control price. Genes with the smallest second fitness value greater than 0 are then used as high-quality genes for further propagation.

[0067] After modeling and calculating several genes, the second fitness function Fitness2 is used to screen high-quality genes, as shown in formula (5).

[0068] (5) Among them, target1 is the vibration performance objective function, that is, the vibration response in the 1-100Hz frequency domain at a distance of 1m from the edge of the auxiliary structure is less than 0.05g; target2 is the cost control objective function, that is, the cost control price is not greater than the bidding control price. and These are the weighting coefficients for the vibration performance objective function and the cost control objective function, used to balance the importance of the two objective functions. They are set according to actual needs to meet [the requirements]. ; acc represents the vibration response amplitude in the 1-100Hz frequency range at a distance of 1m from the edge of the auxiliary structure of the enclosure, under the most unfavorable working state of the vibration generating equipment under the design variable combination represented by chromosomes; price represents the cost control price.

[0069] For target1, calculate the vibration response value in the 1-100Hz frequency domain at a distance of 1m from the edge of the auxiliary structure of the enclosure under the most unfavorable working state of the vibration generating equipment under the design variable combination represented by the chromosome; if the vibration response is less than 0.05g, then target1 is 1, otherwise it is 0.

[0070] For target2, the cost control price is calculated based on the combination of design variables and compared with the tender control price. If the cost control price is less than or equal to the tender control price, target2 is set to 1; otherwise, it is set to 0. The tender control price is set according to specific requirements.

[0071] Based on the set weight coefficients and the values ​​of the objective function, the second fitness function for screening high-quality genes is calculated one by one to obtain the fitness value Fitness2 of each individual. Individuals with a fitness value Fitness2 greater than 0 and Fitness2 being the minimum value (i.e., a set of parameters) are selected, and they have a greater chance of continuing to reproduce in the selection operation of the genetic algorithm.

[0072] Step S24: When the number of iterations is reached and the second fitness value is greater than zero, the genetic algorithm terminates, and the optimal combination of design variables is obtained.

[0073] The stopping criterion for genetic algorithms is: the number of iterations should be no less than 500 and the fitness value Fitness2 should be greater than zero. The number of iterations can be increased or changed according to the complexity of the problem.

[0074] By using a fitness function, the genetic algorithm can continuously improve the combination of chromosome design parameters to find a balance among multiple objectives and ultimately find the optimal solution. The weighting coefficients can adjust the algorithm's emphasis on both vibration performance and cost control.

[0075] The genetic algorithm is used for optimization search, continuously updating and optimizing the gene combination of each individual. Multiple model calculation codes are developed using Python, and the numerical results of multiple gene combinations are calculated in parallel until the optimal combination of design variables is obtained, which is the best combination of vibration isolation parameters. This achieves the goal of improving vibration isolation effect and reducing cost. Typically, 500 generations of genetic iteration are set to output the optimal combination of vibration isolation parameters. The number of iterations can be set according to actual needs and does not have to be 500.

[0076] This invention integrates the vibration generating equipment, vibration isolation foundation, and surrounding auxiliary structures into a unified modeling design. By using a genetic algorithm to optimize the parameters of the vibration isolation foundation and surrounding auxiliary structures, the overall vibration isolation effect is optimized under certain cost control conditions, thus saving design time and engineering costs.

[0077] Implemented using Python scripts, this method performs parallel calculations of numerical results for multiple gene combinations, accelerating optimization and effectively improving the inefficiency of previous manual calculations based on experience.

[0078] This invention performs solid modeling of the upper vibration generating equipment of the vibration isolation system, which solves the problem of system vibration characteristic calculation distortion caused by the previous method of replacing the upper vibration table with a large mass point for solid modeling.

[0079] 1. This invention employs an integrated modeling and design method, encompassing the vibration-generating equipment, vibration-isolation foundation, and enclosure auxiliary structures, and performs solid modeling of the vibration-generating equipment above the vibration isolation system. This design method enables the accurate calculation of the system's vibration characteristics and ensures full utilization of the synergistic effect of the vibration isolation system and enclosure auxiliary structures, achieving optimal vibration isolation performance under certain cost control conditions; 2. To meet the construction feasibility requirements of air-floating vibration isolation systems for large-scale vibration-generating equipment, this invention uses a search space range derived from extensive engineering experience. The scope and variability of the variable optimization search must be within the range specified in this invention to ensure that it does not deviate from the actual engineering application. This includes: the thickness of the vibration isolation foundation platform, the dimensions of the vibration isolation foundation underlayment, the diameter of the vibration isolator, the internal pressure of the vibration isolator, the number and parameters of the dampers, the thickness of the base plate of the enclosure auxiliary structure, and the thickness of the sidewalls of the enclosure auxiliary structure. 3. In genetic algorithm design, the design of the fitness function is the core criterion for evaluating the optimization algorithm. This invention designs a fitness function, Fitness1, to perform an initial screening of the engineering feasibility of gene mutation parameters. Subsequently, a fitness function, Fitness2, is further designed, which can effectively determine the weight relationship between the two objectives of vibration isolation performance and price control, performing multi-objective screening to obtain high-quality genes. The price calculation formula includes a steel content coefficient, which is an empirically estimated coefficient term. This coefficient value of 0.3-0.35 is derived from a large amount of practical experience. 4. This invention uses a genetic algorithm for optimization search, continuously updates and optimizes the gene combination of each individual, and automatically generates finite element models for different gene combinations based on Python language to calculate the optimal combination of vibration isolation parameters, thereby improving the vibration isolation effect and reducing costs.

[0080] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0081] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. An integrated optimization design method for a multi-stage vibration isolation system based on a genetic algorithm, characterized in that, Includes the following steps: Step S1: Establish an integrated simulation model of the multi-level vibration isolation system; determine the initial parameter values ​​of each design variable based on the design variables and search space of the integrated simulation model of the multi-level vibration isolation system, and determine the objective function of the multi-level vibration isolation system. Step S2: Based on the initial parameter values ​​of each design variable and the objective function, the design variable combination is transformed into a chromosome, wherein the design variable combination includes each of the design variables; Set mutation operators, mutation amounts, mutation order, and selection operators; eliminate unreasonable combinations of design variables based on the first fitness function; based on the second fitness function, select chromosomes corresponding to the smallest second fitness value greater than 0 as high-quality genes to continue breeding until the genetic algorithm terminates when the termination condition is met, and obtain the optimal combination of design variable parameters as the optimal design parameter combination of the vibration isolation system; The order of variation is as follows: thickness of the vibration isolation foundation platform, hanging dimensions of the vibration isolation foundation, internal pressure of the vibration isolator, diameter of the vibration isolator, number of dampers, damper parameters, thickness of the base plate of the enclosure auxiliary structure, and thickness of the side wall of the enclosure auxiliary structure.

2. The integrated optimization design method for a multi-stage vibration isolation system based on a genetic algorithm according to claim 1, characterized in that, The design variables of the multi-stage vibration isolation system include: Vibration isolation foundation platform thickness, vibration isolation foundation hanging dimensions, vibration isolator parameters, quantity and location, damper quantity and parameters, enclosure auxiliary structure base plate thickness and side wall thickness; The design variables are combined and transformed into a chromosome representation, with each chromosome containing the design variables as genes. The search space is determined based on the value range of each of the design variables.

3. The integrated optimization design method for a multi-stage vibration isolation system based on a genetic algorithm according to claim 1 or 2, characterized in that, Establish an integrated simulation model for a multi-stage vibration isolation system, including: The multi-level vibration isolation system is a three-level vibration isolation system; The first stage is the vibration source, which is the vibration generating equipment; The second level is the vibration isolation foundation, which includes a vibration isolation foundation platform and vibration isolators. The vibration isolation foundation platform includes a vibration isolation foundation platform and a vibration isolation foundation underpinning arranged rigidly at the top and bottom. The vibration isolators are evenly arranged along the outer edge of the vibration isolation foundation platform. The vibration isolation foundation underpinning is used to lower the center of gravity of the vibration isolation foundation platform, increase the counterweight of the vibration isolation foundation platform, and improve the vibration isolation performance. The third level is the retaining auxiliary structure, which is bound to the bottom of the vibration isolation system; soil elements multiple times the length of the retaining auxiliary structure are built around the retaining auxiliary structure, and rigid boundary conditions are set at the boundaries of the soil elements. The vibration isolator includes multiple air springs, with dampers installed in the gaps between the air springs. The dampers are not connected to the vibration isolator but are bolted between the vibration isolation foundation platform and the enclosure auxiliary structure. The vibration source, vibration isolation foundation, and enclosure auxiliary structure are designed as a whole and together form a mass and stiffness matrix in the calculation, reflecting the true dynamic characteristics of the vibration isolation system.

4. The integrated optimization design method for a multi-stage vibration isolation system based on a genetic algorithm according to claim 2, characterized in that, Step S2 includes: Step S21: Initialize the population and convert the design variable combination into chromosomes, wherein the design variable combination includes each of the design variables; Step S22: Set the mutation operator, mutation amount and mutation order of the chromosome, set the selection operator, and eliminate unreasonable combinations of design variables based on the first fitness function to obtain a chromosome with a reasonable vibration isolator diameter; Step S23: Based on the combination of design variables that conform to the first fitness function, the vibration response amplitude acc in the 1-100Hz frequency domain at 1m from the edge of the auxiliary structure of the enclosure under the most unfavorable working state of the vibration generating equipment is calculated by solving the finite element model. Based on the vibration response amplitude acc, the second fitness value of each individual is calculated one by one. Genes with a second fitness value greater than 0 and a second fitness value of minimum value are used as high-quality genes to continue to reproduce. Step S24: Generate multiple model calculation programs based on Python language, use parallel computing to process the numerical results of multiple gene combinations, and terminate the genetic algorithm when the termination condition is met, thus obtaining the optimal design variable combination parameters of the vibration isolation system. The termination conditions of the genetic algorithm include having at least 500 iterations and a second fitness value greater than zero.

5. The integrated optimization design method for a multi-stage vibration isolation system based on a genetic algorithm according to claim 4, characterized in that, Step S22 includes: The thickness of the vibration isolation foundation platform, the hanging dimensions of the vibration isolation foundation, the diameter of the vibration isolator, the internal pressure of the vibration isolator, the number and parameters of the dampers, the thickness of the bottom plate of the enclosure auxiliary structure, and the thickness of the side wall of the enclosure auxiliary structure are set as mutation operators in the chromosome. Set the mutation amount and mutation order of the mutation operator; The vibration isolator position spacing is obtained based on the vibration isolator position, and the vibration isolator position spacing is set as the selection operator; A first fitness function is set for screening, and the design variable combinations corresponding to genes that satisfy the first fitness function are used for further breeding.

6. The integrated optimization design method for a multi-stage vibration isolation system based on a genetic algorithm according to claim 5, characterized in that, The spacing between the vibration isolators is calculated as follows: The spacing between vibration isolators = (circumference of the vibration isolation base platform - 4d - sum of the diameters of all vibration isolators) / number of vibration isolators; The perimeter of the vibration isolator platform is calculated based on the length and width of the vibration isolation foundation platform.

7. The integrated optimization design method for a multi-stage vibration isolation system based on a genetic algorithm according to claim 5, characterized in that, The first fitness function is: Fitness1 = Sum of diameters of all vibration isolators - (Circumference of vibration isolation base platform - 4d). If the first adaptive fitness value Fitness1 < 0, the gene is eliminated and will not be included in subsequent calculations; if the first adaptive fitness value Fitness1 ≥ 0, the gene can continue to reproduce. The design combinations corresponding to genes that meet the first fitness function are used as high-quality genes for continued reproduction; The first fitness function screens the engineering feasibility of the parameters of gene mutation.

8. The integrated optimization design method for a multi-stage vibration isolation system based on a genetic algorithm according to claim 7, characterized in that, Step S23 includes: Based on the high-quality genes of the design variable combination that conforms to the first fitness function, the finite element model is automatically generated using Python language to calculate acc. The acc is the vibration response amplitude in the 1-100Hz frequency domain at 1m from the edge of the enclosure auxiliary structure under the most unfavorable working state of the vibration generating equipment under the design variable combination represented by the chromosome. Calculate the cost control price of the design variable combination; Based on the vibration response amplitude acc and the cost control price, the second fitness value of each high-quality gene is calculated, and the gene corresponding to the smallest second fitness value greater than 0 is taken as a high-quality gene and continues to reproduce.

9. The integrated optimization design method for a multi-stage vibration isolation system based on a genetic algorithm according to claim 8, characterized in that, The second fitness value for each individual is calculated as follows: The second fitness value is obtained by calculating the second fitness function for screening high-quality genes; Genes with minimum second fitness function values ​​greater than 0 are used as high-quality genes for further propagation.

10. The integrated optimization design method for a multi-stage vibration isolation system based on genetic algorithms according to any one of claims 1-9, characterized in that, The second fitness function is: Where target1 is the vibration performance objective function, and target2 is the cost control objective function. and Here, is the weighting coefficient for the vibration performance objective function and the cost control objective function; acc is the vibration response amplitude in the 1-100Hz frequency domain at a distance of 1m from the edge of the auxiliary structure of the enclosure, under the most unfavorable working state of the vibration generating equipment under the design variable combination represented by chromosome; and price is the cost control amount.

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