A multi-level quasi-zero stiffness superstructure design method based on reinforcement learning

Abstract

The present invention discloses a multi-level quasi-zero stiffness superstructure design method based on reinforcement learning, comprising the following steps: step 1, creating a multi-level quasi-zero stiffness superstructure, extracting the geometric parameters of the basic configuration of the multi-level quasi-zero stiffness superstructure, and establishing a database including geometric parameter combinations, maximum force values, standard force value distribution and structural quality through finite element simulation; step 2, using a deep neural network to construct a maximum force value prediction model, a standard force value distribution prediction model and a structural quality prediction model; respectively putting the database data into the three prediction models, training, optimizing and evaluating the prediction models; step 3, extracting the prediction model as an evaluation environment, and obtaining the best superstructure geometric parameter combination based on the reinforcement learning framework. The present invention can efficiently and quickly realize the on-demand design of a multi-level quasi-zero stiffness superstructure, and generate the optimal superstructure geometric parameters that meet the personalized needs of users.

Description

Technical Field

[0001] The invention belongs to the technical field of vibration isolator design, and in particular relates to a multi-level quasi-zero stiffness superstructure design method based on reinforcement learning. Background Art

[0002] With the improvement of people's living standards, higher requirements are put forward for the quality of travel. However, with the increase of the operating speed of transport equipment, the corresponding vibration problem has become more and more prominent. Among them, the isolation of low-frequency vibration is the key to affecting the normal operation of transport equipment and the comfort of passengers. Traditional vibration isolators are difficult to break the contradiction between load-bearing capacity and low-frequency vibration reduction. Quasi-zero stiffness vibration isolators have significant high static and low dynamic stiffness characteristics, which can achieve the purpose of high load-bearing and low-frequency vibration reduction. However, the disadvantage of quasi-zero stiffness vibration isolators is that they have a single vibration isolation load, and their vibration reduction performance decreases significantly with the increase of the distance from the load. In the actual operation process of transport equipment, there are multiple load states such as no load, half load and full load. The stiffness characteristics of multi-level quasi-zero stiffness can achieve the required load-bearing capacity and vibration reduction characteristics under different levels of load conditions, breaking the restriction relationship between high load-bearing-low-frequency vibration reduction-single load of traditional vibration isolators and single-stage quasi-zero stiffness vibration isolators. Therefore, it is necessary to design multi-level quasi-zero stiffness vibration isolators according to different operating conditions and load conditions.

[0003] Traditional multi-stage quasi-zero stiffness vibration isolators are mainly based on mechanism design, forward design and single-target design. Traditional mechanism design mainly uses multi-stage vibration isolation mechanisms such as multi-stage cams and gears, and cooperates with vibration isolation accessories such as inclined beams, rods, and springs to achieve alternating coordination of positive stiffness units and negative stiffness units to achieve adjustable multi-stage quasi-zero stiffness vibration reduction characteristics. This kind of mechanism design has high requirements on the size, geometry and installation accuracy of each component. The processing error exceeding a certain threshold will cause the entire stiffness curve to shift and fail to achieve multi-stage rated load. At the same time, there are problems such as high cost and difficulty in installation and maintenance of mechanism components. The complexity of the mechanism determines the complexity of the installation of the vibration isolator itself. When interacting with the application environment, the damage of some components will cause the entire mechanism to fail unstably, so the difficulty and labor cost of later maintenance will also increase accordingly. Traditional forward design is to extract parameter variables of the design process and realize the design of the target stiffness curve through continuous trial and error and iteration. Due to the complexity of the structure of the multi-stage quasi-zero stiffness vibration isolator, its structural parameters are much higher than those of the single-stage quasi-zero stiffness vibration isolator, so the computational cost of iterative trial and error will increase exponentially. At the same time, this trial-and-error method based on gradient parameters has the risk of losing the local optimal solution and the global optimal solution. When facing different application scenarios, the change of design goals requires repeated iterative trial-and-error processes, and the computational cost increases exponentially. Traditional single-objective design only targets the stiffness curve and pursues quasi-zero stiffness characteristics under different loads. However, in the face of actual engineering applications, in addition to having a beneficial low-frequency vibration reduction effect, multiple performances must also be met, such as deadweight, dimensional requirements, static stiffness, and load point displacement. In the forward design considering multiple objectives, the constraint relationship between the design objectives will lead to a significant increase in the randomness and complexity of iterative trial and error. Therefore, the multi-objective and multi-constrained automated design of integrated multi-stage quasi-zero stiffness isolators is the key to reducing design costs, reducing installation and maintenance difficulties, and realizing engineering applications. Summary of the invention

[0004] The purpose of the present invention is to provide a multi-level quasi-zero stiffness superstructure design method based on reinforcement learning to solve the defects existing in the above-mentioned traditional multi-level quasi-zero stiffness vibration isolator design method proposed in the background technology.

[0005] To achieve the above object, the present invention provides a multi-level quasi-zero stiffness superstructure design method based on reinforcement learning, comprising the following steps:

[0006] Step 1, creating a basic configuration of a multi-level quasi-zero stiffness superstructure, extracting geometric parameters of the basic configuration of the multi-level quasi-zero stiffness superstructure, and establishing a sample database including geometric parameter combinations, maximum force values, standard force value distributions, and structural masses through finite element simulation;

[0007] Step 2: Use deep neural networks to build maximum force prediction models, standard force distribution prediction models, and structural quality prediction models; put sample database data into the three prediction models respectively, and train, optimize, and evaluate the prediction models;

[0008] Step 3: Extract the prediction model as the evaluation environment and obtain the optimal combination of geometric parameters of the superstructure based on the reinforcement learning framework.

[0009] In a specific implementation, in step 1, the multi-level quasi-zero stiffness superstructure created includes a multi-level elliptical superstructure and a unit-cell elliptical superstructure, and the multi-level elliptical superstructure or the unit-cell elliptical superstructure is selected according to application size requirements and surface density requirements.

[0010] In a specific embodiment, the basic configuration of the multi-level quasi-zero stiffness superstructure is in the shape of a rectangular parallelepiped, and the basic configuration of the multi-level quasi-zero stiffness superstructure includes a square matrix, an elliptical matrix and a curved matrix. The rest of the basic configuration of the multi-level quasi-zero stiffness superstructure is a hollowed-out area, and two square matrices are respectively arranged at the top and bottom of the multi-level quasi-zero stiffness superstructure, and the elliptical matrix and the curved matrix are both between the two square matrices. The elliptical matrix is ​​a horizontally arranged tubular structure and the cross-section of the tubular structure is elliptical, and the cross-section of the curved matrix is ​​curved. The elliptical matrix and the curved matrix area are both obtained by the expansion operation of the basic curve boundary, and the top of the curved matrix is ​​connected to the square matrix at the top, and the bottom of the curved matrix is ​​connected to the square matrix at the bottom.

[0011] In a specific embodiment, a plurality of elliptical matrices are arranged in a multi-level elliptical superstructure, the center lines of the tubular structures of the plurality of elliptical matrices are all in the same plane and the plane is perpendicular to the horizontal plane, the cross-section of the curved matrix is ​​a curve and the curve is symmetrically distributed with the plane where the center line of the tubular structure of the elliptical matrix is ​​located as the center, the top of the elliptical matrix at the uppermost end is connected to the square matrix at the top, and the bottom of the elliptical matrix at the lowermost end is connected to the square matrix at the bottom.

[0012] In a specific embodiment, only one elliptical matrix is ​​provided in the basic configuration of the unit-cell elliptical superstructure, the cross-section of the curved matrix is ​​curved and the curve is symmetrically distributed with the vertical plane where the center line of the elliptical matrix tubular structure is located as the center, the top of the elliptical matrix is ​​connected to the square matrix at the top, and the bottom of the elliptical matrix is ​​connected to the square matrix at the bottom.

[0013] In a specific implementation, the geometric parameters of the basic configuration of the multi-level quasi-zero stiffness superstructure include position parameters and size parameters, and the distribution intervals of the position parameters and the size parameters are given; the geometric parameter combination of the final superstructure sample is obtained through the given distribution intervals of the position parameters and the size parameters;

[0014] The acquired geometric parameter combinations are assigned to the quasi-zero stiffness superstructure, and static compression finite element simulation is carried out to obtain the force-displacement curve and structural quality of the sample; the force-displacement curve is divided into maximum force value characteristics and standard force value distribution characteristics, and matched with the geometric parameters and structural quality of the sample to finally form a sample database.

[0015] In a specific implementation, a maximum force prediction model is established based on a deep neural network, an input feature of the maximum force prediction model is set as a geometric parameter combination, and an output feature of the maximum force prediction model is set as a maximum force value;

[0016] A standard force value distribution prediction model is established based on a deep neural network, the input feature of the standard force value distribution prediction model is set as a geometric parameter combination, the output feature of the standard force value distribution prediction model is set as a standard force value distribution, and the range of the standard force value is between 0 and 1;

[0017] A structural quality prediction model is established based on a deep neural network, the input features of the structural quality prediction model are set as a geometric parameter combination, and the output features of the structural quality prediction model are set as structural quality.

[0018] In a specific implementation, the database data is divided into a training set, a validation set, and a test set; the training set data is used as training material when constructing a prediction model; the hyperparameters of the prediction model are optimized based on the validation set data; the prediction model is evaluated using the test set data; and finally, the network parameters of the three prediction models are obtained.

[0019] In a specific implementation, in step 3, the network parameters of the fixed maximum force prediction model, the standard force distribution prediction model and the structural quality prediction model are embedded in the reinforcement learning evaluation environment, and the maximum force and standard force distribution data are converted into quasi-zero stiffness interval force, displacement and static stiffness data; an interactive mechanism of reinforcement learning rewards and actions is established to complete the reinforcement learning training process and obtain the optimized geometric parameter combination of the superstructure.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] (1) The proposed quasi-zero stiffness superstructure containing an elliptical matrix is ​​an integrated vibration isolation system that does not require complex mechanical design. After optimization, the superstructure can be prepared by a variety of simple processes and is easy to manufacture. It is easy to install and has low maintenance costs.

[0022] (2) The established multi-level elliptical superstructure and single-cell elliptical superstructure can give full play to the advantages of the integrated superstructure. They can not only obtain multi-level quasi-zero stiffness characteristics, but also facilitate geometric dimension parameter modeling, facilitate the subsequent construction of superstructure performance prediction models and the design process of reinforcement learning.

[0023] (3) The established reinforcement learning design framework can flexibly respond to different design requirements. Quasi-zero stiffness characteristics, fixed load displacement, structural mass, and structural stiffness can all be dynamically designed through the reward mechanism, and the reward function can also be adjusted in real time according to certain constraints.

[0024] (4) The force-displacement curve of the superstructure is decomposed into maximum force data and standard force distribution data, and the prediction model is established as independent features. This method can effectively avoid the problem of disappearance of values ​​caused by dimensionless conversion.

[0025] In summary, the present invention can efficiently and quickly realize the on-demand design of multi-level quasi-zero stiffness superstructures, generate optimal superstructure geometric parameters that meet the personalized needs of users, and provide a new idea and technical methodology for realizing the integrated intelligent design of quasi-zero stiffness structures.

[0026] The integrated quasi-zero stiffness superstructure including an elliptical matrix and an interpolation curve proposed in the present invention can generate multi-level quasi-zero stiffness that meets the design requirements while ensuring easy processing and installation. The present invention utilizes a combination of reinforcement learning and a performance prediction model based on deep learning to dynamically design a quasi-zero stiffness superstructure that meets multiple objectives.

[0027] The present invention decomposes the force-displacement curve into a maximum force value and a standard force value distribution, and predicts them respectively, which can effectively avoid the problem of data disappearance after standardization.

[0028] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention is further described in detail below. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0030] Figure 1 is a basic configuration diagram of a multi-level elliptical superstructure of the present invention; wherein, a 11 yes Figure 1 The length of the major semi-axis of the uppermost elliptical matrix of the middle multi-level elliptical superstructure; b 11 yes Figure 1 The length of the minor semi-axis of the uppermost elliptical matrix of the middle multi-level elliptical superstructure; a 12 yes Figure 1 The length of the major semi-axis of the elliptical matrix in the middle of the multi-level elliptical superstructure; b12 yes Figure 1 The length of the minor semi-axis of the middle elliptical matrix of the middle multi-level elliptical superstructure; a 13 yes Figure 1 The length of the major semi-axis of the lowest elliptical matrix of the middle multi-level elliptical superstructure; b 13 yes Figure 1 The length of the minor semi-axis of the lowest elliptical matrix of the middle multi-level elliptical superstructure; d 10 yes Figure 1 The matrix width of the curvilinear matrix of the medium multi-level elliptical superstructure; d 11 yes Figure 1 The matrix width of the uppermost elliptical matrix of the middle multi-level elliptical superstructure; d 12 yes Figure 1 The matrix width of the elliptical matrix in the middle of the multi-level elliptical superstructure; d 13 yes Figure 1 The matrix width of the lowest elliptical matrix of the middle multi-level elliptical superstructure; r 10 yes Figure 1 The radius length of the rounded corners between the elliptical matrices of the multi-level elliptical superstructure; r 11 yes Figure 1 The radius length of the rounded corners except those between the elliptical matrices in the multi-level elliptical superstructure; y 11 yes Figure 1 The central ordinate of the uppermost elliptical matrix of the multi-level elliptical superstructure; y 12 yes Figure 1 The central ordinate of the elliptical matrix in the middle of the multi-level elliptical superstructure; y 13 yes Figure 1 The central ordinate of the lowest elliptical matrix in the multi-level elliptical superstructure;

[0031] Figure 2 is a schematic diagram of an interpolation curve corresponding to a curve matrix of a multi-level quasi-zero stiffness superstructure of the present invention; wherein, h 11 , h 12 , h 13 , h 14 , h 15 , h 16They are the sequential ordinates of the interpolation points of the interpolation curve corresponding to the curve matrix;

[0032] Figure 3 is a basic configuration diagram of a unit cell elliptical superstructure of the present invention; wherein, a 20 yes Figure 3 The length of the major semi-axis of the elliptical matrix of the basic configuration of the unit cell elliptical superstructure; b 20 yes Figure 3 The length of the minor semi-axis of the elliptical matrix of the basic configuration of the unit cell elliptical superstructure; d 20 yes Figure 3 The matrix width of the curvilinear matrix of the basic configuration of the unit cell elliptical superstructure; d 21 yes Figure 3 The matrix width of the elliptical matrix of the basic configuration of the unit cell elliptical superstructure; r 20 yes Figure 3 The radius lengths of all rounded corners of the basic configuration of the unit cell elliptical superstructure; y 20 yes Figure 3 The central ordinate of the elliptical matrix of the basic configuration of the unit cell elliptical superstructure;

[0033] Figure 4 It is a schematic diagram of a unit cell elliptical superstructure in the present invention;

[0034] Figure 5 It is a schematic diagram of obtaining the maximum force value and standard force value distribution data of the present invention;

[0035] Figure 6 It is a schematic diagram of the framework of the maximum force value and standard force value distribution prediction model of the present invention;

[0036] Among them, 1. Square matrix; 2. Elliptical matrix; 3. Curved matrix; 4. Unit cell elliptical superstructure. DETAILED DESCRIPTION

[0037] The embodiments of the present invention are described in detail below. The specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0038] A multi-level quasi-zero stiffness superstructure design method based on reinforcement learning of the present invention comprises the following steps:

[0039] (1) Establish a multi-level quasi-zero stiffness basic configuration and establish a sample database based on the finite element simulation model. Create a single elliptical quasi-zero stiffness superstructure and a multi-elliptical quasi-zero stiffness superstructure, extract the geometric parameters of the configuration, including shape parameters and position parameters, and give the distribution range of the above parameters. The obtained parameter group will be assigned to the quasi-zero stiffness superstructure, and static compression finite element simulation will be performed to obtain the force-displacement curve and structural quality of the sample. The force-displacement curve is divided into maximum force value characteristics and standard force value distribution characteristics, and matched with the geometric parameters and structural quality of the sample to finally form a sample database.

[0040] (2) Use deep neural networks to construct maximum force prediction models, standard force distribution prediction models, and structural quality prediction models. The geometric parameters of the superstructure are used as model input variables, and the maximum force, standard force distribution, and structural quality are used as output variables to construct three independently trained prediction models.

[0041] The database data is put into the prediction model for training respectively, and the hyperparameters of the prediction model are optimized according to the validation set data. Finally, the prediction model is evaluated by the test set data. Finally, the network parameters of the three prediction models are obtained.

[0042] (3) Extract the prediction model as the evaluation environment and establish a multi-objective optimization method for geometric parameters based on the reinforcement learning framework. The network parameters of the three independent prediction models are fixed and embedded in the reinforcement learning evaluation environment, and the maximum force and standard force distribution data are converted into quasi-zero stiffness interval force, displacement and static stiffness data. Establish an interactive mechanism between reinforcement learning rewards and actions, complete the reinforcement learning training process and obtain the optimized geometric parameter combination of the superstructure. Network parameters refer to the network training parameters (weights and thresholds) and hyperparameters in the model after the three prediction models are trained. Fixing the network parameters is equivalent to fixing the three models.

[0043] Example 1

[0044] A multi-level quasi-zero stiffness superstructure design method based on reinforcement learning comprises the following steps:

[0045] 1. Establishment of sample database.

[0046] The sample database includes geometric parameter combinations, maximum force values, standard force value distribution and structural quality data of the structure samples.

[0047] First, the basic configuration of the multi-level quasi-zero stiffness superstructure is determined according to the actual working conditions, and then the shape and size of the basic configuration are characterized to obtain the geometric parameters. Then, according to the constraints of the geometric parameters, the geometric parameter combinations of the samples are obtained in batches, and finally a finite element static compression simulation model is established, and the geometric parameters of the samples are assigned to the geometric structure to obtain the force-displacement curve and structural quality of the sample structure.

[0048] The basic configuration of the multi-level quasi-zero stiffness superstructure is established. The basic configuration of the multi-level quasi-zero stiffness superstructure includes a multi-level elliptical superstructure and a unit cell elliptical superstructure.

[0049] like Figure 1 The figure shows a schematic diagram of the basic configuration of a multi-level elliptical superstructure. The basic shape of the configuration is a rectangle, which includes a square matrix 1, an elliptical matrix 2, and a curved matrix 3. The rest is a hollowed-out area. The elliptical matrix and the curved matrix area are both obtained by dilation operation of the basic curve boundary, and the width of the curved matrix is ​​set to d 10 , the width of the ellipse matrix is ​​set to d from top to bottom 11 , d 12 , …, d 1n . According to the target multi-level quasi-zero stiffness characteristic level number N, the number of ellipses in the multi-level elliptical superstructure is set to N, and N=3 in this embodiment. The horizontal coordinates of the ellipse centers corresponding to the ellipse matrix are all 0. Each group of adjacent ellipses is guaranteed to have an overlapping area, and the middle area is solid. The curve boundary corresponding to the curve matrix is ​​an interpolation curve, and the open curve type is selected. The curve is symmetric about the y-axis and connected by interpolation points. Taking the interpolation curve on one side as an example, the half-curve interpolation points are set to 6, and the horizontal coordinates of the points are an arithmetic progression. The horizontal coordinates of the starting point and the end point of the interpolation point are set to the left boundary and 0, respectively. The vertical coordinate of the interpolation point is set to the position parameter. In order to avoid stress concentration, all the sharp-angle areas (i.e. Figure 1 The dotted circle range on the left side of the middle is set to rounded corners, and the rounded corner radius between the elliptical matrices is set to r 10 The other fillet radius is set to r 11 .

[0050] like Figure 3 The figure shows the basic configuration of a unit cell elliptical superstructure. The basic shape of the unit cell structure of this configuration is a rectangle, which includes a square matrix 1, an elliptical matrix 2 and a curved matrix 3, and the rest is a hollow area. The elliptical matrix and the curved matrix area are both obtained by dilation operation of the basic curve boundary, and the width of the matrix is ​​set to d 21 . The horizontal coordinate of the ellipse corresponding to the ellipse matrix is ​​0. The above-mentioned unit cell structure is arrayed to form a unit cell ellipse superstructure 4. According to the number of target multi-level quasi-zero stiffness characteristic levels N, the unit cell array of the unit cell ellipse superstructure is set to M×N. The size of M is determined according to the installation dimensions of the actual working conditions. The geometric parameters of all unit cells in the horizontal direction are set to be consistent, and the geometric parameters in the vertical direction are different. The ellipse matrix and the curve matrix area are both obtained by the expansion operation of the basic curve boundary, and the width of the curve matrix is ​​set to d 20 , the width of the ellipse matrix is ​​set to d 21 . All the sharp corners in this configuration (i.e. Figure 3The left half of the dotted circle is set to rounded corners, and the radius is set to r 20 .

[0051] Extraction of superstructure geometric features.

[0052] The geometric parameters of the multi-level elliptical superstructure include position parameters and size parameters, wherein the design variables of this embodiment are shown in Table 1.

[0053] Table 1 Geometric parameters and descriptions of the multi-level elliptical superstructure.

[0054]

[0055] The length and width of the multi-level elliptical superstructure are determined according to the application size requirements, and the upper and lower square matrices intersect with the uppermost elliptical matrix and the lowermost elliptical matrix, and the intersection height is set to d 10 1 / 3 of.

[0056] The geometric parameters of the unit cell elliptical superstructure include position parameters and size parameters, among which the design variables of this embodiment are shown in Table 2.

[0057] Table 2 Unit cell geometric parameters and their descriptions of the unit cell elliptical superstructure.

[0058]

[0059] The length and width of the unit cell elliptical superstructure are determined according to the application size requirements and the number of arrays, and the upper and lower square matrices intersect with the elliptical matrix, and the intersection height is set to d 20 Since the geometric parameters of the unit cell are different in the vertical direction, the design variables need to be multiplied by N times based on Table 2 when designing the unit cell elliptical superstructure.

[0060] Select a multi-level elliptical superstructure or a unit cell elliptical superstructure according to the application size requirements and surface density requirements, and implement the following steps. Both superstructure configurations are suitable for the following structural design method.

[0061] Set geometric parameter constraints to batch obtain geometric feature combinations.

[0062] First, the basic size range of geometric parameters is obtained according to the length relationship between the matrix part and the length and width boundary of the superstructure. Then, other geometric parameter constraints are determined according to the characteristics of the two basic configurations.

[0063] Set the height of the unit cell of the multi-level elliptical superstructure and the unit cell elliptical superstructure to be L 0 , width is D 0 .

[0064] For a multi-level elliptical superstructure, the three elliptical matrices from top to bottom correspond to the load that increases step by step during the compression process, so their geometric parameters have the following constraints: 1) The fillet radius between the elliptical matrices is smaller than the fillet radius of the other elliptical matrices; 2) The adjacent arcs between the three elliptical matrices need to remain intersecting, that is, there is no gap or separation between the two; 3) The topmost elliptical matrix and the bottommost elliptical matrix do not penetrate the upper and lower boundaries of the superstructure; 4) The interpolation curve does not jump, that is, the function corresponding to the curve is a monotonic function; 5) The elliptical matrix cannot be too close to the left and right boundaries of the superstructure. The specific parameter settings are as follows:

[0065]

[0066] For the unit cell elliptical superstructure, in order to ensure the manufacturability of the superstructure and the stability of the array, its geometric parameters have the following constraints: 1) The top and bottom of the elliptical matrix cannot be too close to the upper and lower boundaries of the unit cell; 2) The left and right sides of the elliptical matrix cannot be too close to the left and right boundaries of the unit cell; 3) The interpolation curve does not jump, that is, the function corresponding to the curve is a monotonic function. The specific parameter settings are as follows:

[0067]

[0068] According to L 0 and D 0 The specific value of is used to define the parameter range for each parameter, and the parameter samples of the super structure formed by the combination of geometric parameters are obtained within the parameter range. The geometric features that do not meet the above constraints are eliminated to obtain the parameter combination data of the final super structure sample.

[0069] Finite element simulation batches to obtain the rest of the database data.

[0070] Since the structure deforms by more than 20% of its height during the compression simulation, a hyperelastic constitutive model is required for simulation. In this embodiment, fluororubber material is selected as the superstructure material type, and the hyperelastic constitutive model is selected as the Neo-Hookean model.

[0071] First, according to the national standard GB / T 528-2009 "Determination of tensile stress-strain properties of vulcanized rubber or thermoplastic rubber", a dog-bone-shaped standard specimen made of selected materials is subjected to tensile tests to obtain strain values ​​under different stresses. The preliminary hyperelastic constitutive parameters are solved for the tensile test results. According to GB / T7757-2009 "Determination of compressive stress relaxation of vulcanized rubber or thermoplastic rubber", the selected materials are made into cylindrical standard specimens, the error of the solved hyperelastic constitutive parameters is measured and calibrated, and the final calibrated hyperelastic constitutive parameters are obtained.

[0072] In the finite element simulation, a steady-state solver and solid mechanics physical field are set up, and the above geometric parameters are extracted using parametric modeling as the size parameters for constructing a two-dimensional superstructure. The lower boundary of the superstructure is set as a fixed constraint, and the upper boundary is given a specified displacement, and the displacement value is set to L 0 25% of the friction contact is set inside each contact surface, and the reaction force probe of the upper boundary is constructed to obtain the force-displacement curve during the compression process. At the same time, the area of ​​the geometric cross section is obtained to calculate the structural mass of the superstructure.

[0073] The acquired data is processed, and first the area of ​​the superstructure is multiplied by the density of the fluororubber to convert it into the structural mass. In order to avoid the disappearance of dimensioning of all force values ​​of the load scatter points when the data group is standardized, resulting in too much force value data being converted into values ​​close to 0, the force-displacement curve of the superstructure is converted into a maximum force value and a standard force value distribution. The entire displacement interval is divided into S equal-length intervals, and S is set to 50 in this embodiment. The average value of the reaction force of each equal-length interval is recorded as the reaction force of the equal-length interval. The maximum reaction force of all equal-length intervals is set to the maximum force value under this combination of geometric parameters. The force scatter points in the force-displacement curve are converted into a standard force value distribution using the maximum force value:

[0074]

[0075] in f i For the i The standard force value of the interval is f i The collection of is recorded as the standard force value distribution. F i For the i The reaction force of the interval, F m is the maximum force value.

[0076] Then the geometric parameter combination, maximum force value and structural mass are standardized according to each column of the data, as shown in the following formula:

[0077]

[0078] in and Represent the data values ​​before and after normalization, μ is the average value of the data in this column, σ is the standard deviation of the data in this column.

[0079] Through the above operations, the database is formed, the data in the database is randomly shuffled, and the database data is horizontally divided into training set, validation set and test set in a ratio of 6:3:1. The training set is used as training material in the subsequent performance prediction model construction, the validation set data is used for the hyperparameter optimization of the performance prediction model, and the test set is used for the final evaluation of the optimized model.

[0080] 2. Establishment of superstructure performance prediction model.

[0081] In order to obtain the vibration reduction performance of the superstructure under a specific geometric parameter combination in real time, it is necessary to fit the relationship between the geometric parameter combination and the superstructure performance through a forward correlation model. First, a mapping relationship between the geometric parameter combination and the maximum force value is established, such as Figure 6 shown.

[0082] A maximum force prediction model is established based on a deep neural network. The input features of the model are geometric parameter combinations, including the geometric parameter types set when the database is established. The output feature is the maximum force, which belongs to a many-to-one regression prediction model. The hidden layer of the model is set to 3 layers, and the regularization option is set. Except for the activation function of the output layer set to Linear (linear activation function), the remaining activation functions are set to ReLU (linear rectification function) activation function. The loss function is set to MSE (mean square error), and ADAM (adaptive matrix estimation algorithm) is selected as the optimizer.

[0083] A standard force value prediction model is established based on a deep neural network, such as Figure 6 As shown in the figure, the input feature of the model is a combination of geometric parameters, and the output feature is a standard force value distribution, which ranges from 0 to 1. Set the number of hidden layers to 3 and set the initial number of neurons. Since the output features of the model are 50, overfitting is prone to occur. Therefore, a regularization option is set in the hidden layer, and a dropout layer is set between the hidden layers to block the neuron connections with too small weights. Except for the output layer whose activation function is set to Linear, the remaining activation functions are set to ReLU activation functions. The loss function is set to MAE (mean absolute error), and ADAM is selected as the optimizer.

[0084] A structural quality prediction model is established based on a deep neural network. The input feature of the model is a combination of geometric parameters, and the output feature is the structural quality. The number of hidden layers is set to 2, and the initial number of neurons is set to less than 50. In order to prevent the model from experiencing neuronal necrosis, except for the output layer whose activation function is set to Linear, the activation functions of other hidden layers all use PRelu (parameterized linear rectifier function). MAE is selected as the loss function and ADAM is set as the optimizer.

[0085] The training of the three networks is independent, and the hyperparameters of the above prediction models are optimized through the validation set data. The hyperparameters to be optimized include: the number of neurons in each hidden layer, the type of regularization options, the probability of discarding the discard layer, and the amount of batch data. The hyperparameters are optimized by the control variable method, and the initial optimization interval of the above hyperparameters is set. The hyperparameters other than a certain parameter to be optimized are fixed, and the interval is traversed in a gradient manner. The value of the parameter to be optimized is obtained through the model training loss. The preliminary values ​​of the remaining hyperparameters are obtained in this way, and finally the final hyperparameters are obtained by fine-tuning the linkage between the hyperparameters. The final hyperparameters are brought into the prediction model, the prediction model is trained, and the model accuracy is evaluated through the test set data, and the model parameters (model architecture and training parameters) of the trained model are saved in the H5 file.

[0086] 3. Establishment of multi-objective design method for superstructure.

[0087] The geometric parameters of the superstructure are dynamically designed through reinforcement learning. First, the reinforcement learning Q-learning (Q-Learning) architecture is established. Reinforcement learning is that the intelligent agent continuously performs actions according to the state in the environment to obtain different rewards. By continuously updating the Q value table, the action is better guided to maximize the rewards obtained in the environment.

[0088] Reinforcement learning action execution:

[0089] In geometric parameter design, the state is the current combination of geometric parameters of the superstructure, and the action is to increase or decrease the value of each geometric parameter. The increase or decrease value unit is set to 1 / 100 of the length of each geometric parameter interval, as shown in the following formula:

[0090]

[0091] in a i For the i The action of the step, p j For the j The value of the parameter, Δ p j The numerical unit for increase or decrease.

[0092] The agent adopts a greedy strategy when making action decisions, that is, it has a probability of increasing and decreasing. P 0 Select the action with the larger Q value in the Q table, and the action with probability (1- P 0 ) chooses another action. P 0 Set to 0.95 to prevent losing the best performing geometry parameter combinations.

[0093] The Q table is updated after each step. The Q table update method is as follows:

[0094]

[0095] in and are the Q tables before and after the update, α is the learning rate, which is set to 0.4 in this embodiment. r Is to perform an action After the reward. It's the next move The expected Q value of γ is the attenuation coefficient of future rewards, which is set to 0.85 in this embodiment.

[0096] Rewards for reinforcement learning:

[0097] In reinforcement learning, the agent obtains rewards in the environment. In the present invention, the environment is the superstructure performance prediction model, and the reward is the degree to which the design requirements are met. Therefore, it is necessary to evaluate the superstructure performance of the current state and obtain the reward by subtracting the superstructure performance corresponding to the state after the action is executed. According to the design requirements, a multi-objective reward mechanism is set. The design requirements set in this embodiment are: 1) Obtain a certain force value in multiple fixed displacement intervals F 0 quasi-zero stiffness platform; 2) the force value is F 1 (no load) and F 2 The displacement difference when fully loaded is as small as possible; 3) The structural mass is as small as possible. Other design requirements are still carried out in this way.

[0098] First, you need to retrieve the parameter H5 file of the local performance prediction model, and use the current state as the input of the three prediction models to directly obtain the output of the model, which are the maximum force value, standard force value distribution, and structural quality. Restore the maximum force value and structural quality according to the denormalization method. Use the restored maximum force value as a scaling factor to expand the standard force value distribution to obtain the force-displacement curve of the current state. Calculate the reward function for the current state based on the scattered force value and structural quality of the force-displacement curve:

[0099]

[0100] in δ 1 , δ 2 and δ 3 is the weighting coefficient among the three objectives, Fi ( p ) is the geometric parameter p The force value scatter points in the quasi-zero stiffness platform corresponding to the design requirements are as follows: x ( p ) is the displacement under a fixed force value, m ( p ) is the geometric parameter p The quality of the structure.

[0101] When designing a specific quasi-zero stiffness superstructure on demand, the workflow of the present invention is as follows:

[0102] Step 1. Select the basic configuration of the superstructure and build a database. Select the basic configuration of the superstructure that can generate multi-level quasi-zero stiffness and extract the geometric parameters of the superstructure. Use finite element simulation to establish a database containing geometric parameter combinations, maximum force values, standard force value distribution, and structural mass.

[0103] Step 2. Train the superstructure performance prediction model. Put the data in the database into the maximum force prediction model, the standard force distribution prediction model and the structural quality prediction model, train and optimize the model, fix the prediction model and save the model parameters.

[0104] Step 3. Use reinforcement learning to design geometric parameters. Initialize the state and Q table, and set the reward function according to the design requirements. Through the Q table, the action execution, reward calculation, and Q table update cycle are continuously performed to finally obtain the best combination of hyperstructure geometric parameters.

[0105] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions and substitutions can be made without departing from the concept of the present invention, which should be regarded as belonging to the protection scope of the present invention.

Claims

1. A multi-level quasi-zero stiffness superstructure design method based on reinforcement learning, characterized in that: The steps include: Step 1, creating a basic configuration of a multi-level quasi-zero stiffness superstructure, extracting geometric parameters of the basic configuration of the multi-level quasi-zero stiffness superstructure, and establishing a sample database including geometric parameter combinations, maximum force values, standard force value distributions, and structural masses through finite element simulation; Step 2: Use deep neural networks to build maximum force prediction models, standard force distribution prediction models, and structural quality prediction models; put sample database data into the three prediction models respectively, and train, optimize, and evaluate the prediction models; Step 3: Extract the prediction model as the evaluation environment and obtain the best combination of geometric parameters of the superstructure based on the reinforcement learning framework; In the step 3, the network parameters of the fixed maximum force prediction model, the standard force distribution prediction model and the structural quality prediction model are embedded in the reinforcement learning evaluation environment, and the maximum force and standard force distribution data are converted into quasi-zero stiffness interval force, displacement and static stiffness data; An interactive mechanism between reinforcement learning rewards and actions is established to complete the reinforcement learning training process and obtain the optimized geometric parameter combination of the superstructure.

2. The multi-level quasi-zero stiffness superstructure design method based on reinforcement learning according to claim 1, characterized in that: In the step 1, the multi-level quasi-zero stiffness superstructure created includes a multi-level elliptical superstructure and a unit cell elliptical superstructure, and the multi-level elliptical superstructure or the unit cell elliptical superstructure is selected according to the application size requirements and surface density requirements.

3. The multi-level quasi-zero stiffness superstructure design method based on reinforcement learning according to claim 2 is characterized in that: The basic configuration of the multi-level quasi-zero stiffness superstructure is in the shape of a rectangular parallelepiped. The basic configuration of the multi-level quasi-zero stiffness superstructure includes a square matrix, an elliptical matrix and a curved matrix. The rest of the basic configuration of the multi-level quasi-zero stiffness superstructure is a hollowed-out area. Two square matrices are respectively arranged at the top and bottom of the multi-level quasi-zero stiffness superstructure. The elliptical matrix and the curved matrix are both located between the two square matrices. The elliptical matrix is ​​a horizontally arranged tubular structure and the cross section of the tubular structure is elliptical. The cross section of the curved matrix is ​​a curve. The elliptical matrix and the curved matrix regions are both obtained by dilation operations on the basic curve boundaries. The top of the curved matrix is ​​connected to the square matrix at the top, and the bottom of the curved matrix is ​​connected to the square matrix at the bottom.

4. The multi-level quasi-zero stiffness superstructure design method based on reinforcement learning according to claim 3 is characterized in that: A plurality of elliptical matrices are arranged in the multi-level elliptical superstructure, the center lines of the tubular structures of the plurality of elliptical matrices are all in the same plane and the plane is perpendicular to the horizontal plane, the cross section of the curved matrix is ​​a curve and the curve is symmetrically distributed with the plane where the center line of the tubular structure of the elliptical matrix is ​​located as the center, the top of the elliptical matrix at the uppermost end is connected to the square matrix at the top, and the bottom of the elliptical matrix at the lowermost end is connected to the square matrix at the bottom.

5. The multi-level quasi-zero stiffness superstructure design method based on reinforcement learning according to claim 3 is characterized in that: In the basic configuration of the unit-cell elliptical superstructure, only one elliptical matrix is ​​provided, the cross-section of the curved matrix is ​​curved, and the curve is symmetrically distributed with the vertical plane where the center line of the elliptical matrix tubular structure is located as the center, the top of the elliptical matrix is ​​connected to the square matrix at the top, and the bottom of the elliptical matrix is ​​connected to the square matrix at the bottom.

6. The multi-level quasi-zero stiffness superstructure design method based on reinforcement learning according to claim 1, characterized in that: The geometric parameters of the basic configuration of the multi-level quasi-zero stiffness superstructure include position parameters and size parameters, and the distribution intervals of the position parameters and the size parameters are given; the geometric parameter combination of the final superstructure sample is obtained through the given distribution intervals of the position parameters and the size parameters; The acquired geometric parameter combinations are assigned to the quasi-zero stiffness superstructure, and static compression finite element simulation is carried out to obtain the force-displacement curve and structural quality of the sample; the force-displacement curve is divided into maximum force value characteristics and standard force value distribution characteristics, and matched with the geometric parameters and structural quality of the sample to finally form a sample database.

7. The multi-level quasi-zero stiffness superstructure design method based on reinforcement learning according to claim 1, characterized in that: A maximum force prediction model is established based on a deep neural network, an input feature of the maximum force prediction model is set as a geometric parameter combination, and an output feature of the maximum force prediction model is set as a maximum force value; A standard force value distribution prediction model is established based on a deep neural network, the input feature of the standard force value distribution prediction model is set as a geometric parameter combination, the output feature of the standard force value distribution prediction model is set as a standard force value distribution, and the range of the standard force value is between 0 and 1; A structural quality prediction model is established based on a deep neural network, the input features of the structural quality prediction model are set as a geometric parameter combination, and the output features of the structural quality prediction model are set as structural quality.

8. The multi-level quasi-zero stiffness superstructure design method based on reinforcement learning according to claim 1, characterized in that: The sample database data is divided into training set, validation set and test set; the training set data is used as training material when building the prediction model; the hyperparameters of the prediction model are optimized according to the validation set data; the prediction model is evaluated through the test set data; and finally the network parameters of the three prediction models are obtained.

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