A structural parameter optimization method for elastic wave metamaterials based on dynamic Kriging and DQN

Abstract

This application relates to a method for optimizing the structural parameters of elastic wave metamaterials based on dynamic Kriging and DQN. This method constructs a high-precision dynamic Kriging proxy model and integrates it into the DQN optimization algorithm framework. This method eliminates the need for unnecessary searches within the design space and can quickly discover the approximate optimal structural parameters of the elastic wave metamaterial. The inexpensive, high-precision dynamic Kriging proxy model replaces the time-consuming finite element analysis process to accurately predict the real world and guide the optimization algorithm's search direction, ultimately achieving an optimal solution. This method improves the efficiency of the entire optimization process while ensuring the bandwidth optimization requirements of the elastic wave metamaterial, significantly reducing computational costs.

Description

Technical Field

[0001] The present application relates to the field of elastic wave metamaterial bandgap optimization, and specifically to a method for optimizing elastic wave metamaterial structural parameters based on dynamic Kriging and DQN. Background Art

[0002] Acoustic metamaterials (AMs) refer to artificial composite structures / materials with extraordinary physical properties. Through their microstructure or arrangement, they can control, regulate or change the way and properties (i.e., bandgap characteristics) of sound waves or elastic waves propagating in them. Elastic metamaterials (EMs) are a subcategory of acoustic metamaterials that can open sound insulation band gaps in the low-frequency range, which makes them have broad application prospects in the field of low-frequency vibration / noise reduction. From a practical point of view, it is hoped that the band gap generated by the designed EMs is in the low-frequency range and the wider the better. The bandgap range of elastic waves depends largely on the structural parameters of the EMs. Selecting different design parameter combinations to ensure that the EMs exhibit a bandgap response that meets the expected operating frequency range is a very challenging task.

[0003] As the performance of EMs is integrated and upgraded, its configuration becomes more and more complex. At present, in the face of such complex, multi-parameter EMs parameter optimization problems, related fields at home and abroad widely use non-gradient optimization algorithms such as genetic algorithms (GAs). However, such algorithms have the problems of high computational cost and low iteration efficiency. The main reason is that when the dimensions of the design variables increase and the feasible domain of the problem to be solved becomes larger, the number of iterations of the population increases exponentially, and each iteration requires a high-density search in the design space and calculation of the fitness value of each individual, which seriously restricts the solution speed of the EMs structural parameter optimization model. At the same time, as the structure of EMs becomes more and more complex, its frequency bandgap performance often needs to be evaluated through high-precision complex models, which makes the numerical simulation process of the optimization model quite expensive. Summary of the Invention

[0004] In order to overcome at least one deficiency in the prior art, the present application provides a method for optimizing elastic wave metamaterial structure parameters based on dynamic Kriging and DQN.

[0005] In a first aspect, a method for optimizing elastic wave metamaterial structural parameters based on dynamic Kriging and DQN is provided, comprising:

[0006] Step S1, establishing an elastic wave metamaterial structural parameter optimization model, the model including design variables, objective functions and constraints;

[0007] Step S2: construct the framework structure of the DQN optimization algorithm and determine the state space, action space, and reward function of the DQN optimization algorithm based on the model;

[0008] Step S3, obtaining a data set for constructing a Kriging proxy model, and constructing a Kriging proxy model based on the data set;

[0009] Step S4, initializing the structural parameters of the elastic wave metamaterial to obtain initial structural parameters, i.e., an initial state; based on the initial state, a DQN optimization algorithm is used to determine the optimal structural parameters and the corresponding reward value; the environment in the DQN optimization algorithm is a Kriging agent model;

[0010] Step S5: The optimal structural parameters and the corresponding reward values constitute new data points, which are added to the data set to obtain a new data set;

[0011] In step S6, it is determined whether the number of data points in the new data set reaches the set number. If so, the current optimal structural parameters are the optimal structural parameters of the elastic wave metamaterial finally determined. If not, return to step S3 and use the new data set to rebuild the Kriging proxy model.

[0012] In one embodiment, the objective function is:

[0013]

[0014] Where f(x) is the objective function value, m(x) is the total mass of the structure of the optimized solution, x is the design variable, m0 is the upper limit of the total mass of the structure of the optimized solution, δ is the set value to prevent the denominator from being 0, Δb(x) is the default value, ω n+1 (k,x) is the band gap frequency corresponding to the kth sampling point on the n+1th energy band, ω n (k,x) is the band gap frequency corresponding to the kth sampling point on the nth energy band, Δω n is the band gap width between the nth energy band and the n+1th energy band, Δω n =minω n+1 (k,x)-maxω n (k,x).

[0015] In one embodiment, the framework structure of the constructed DQN optimization algorithm includes a trained Q network.

[0016] In one embodiment, determining the state space, action space, and reward function of the DQN optimization algorithm based on the model includes:

[0017] The state space includes multiple states, where a state is a set of values of design variables, and the upper and lower limits of the design variables constitute the boundaries of the state space;

[0018] Actions in the action space are used to change the state;

[0019] The reward function is the objective function.

[0020] In one embodiment, obtaining a data set for constructing a Kriging proxy model includes:

[0021] The design variable data set is obtained by experimental method, and the finite element numerical simulation is performed on the design variable data set to obtain the target response data set;

[0022] The design variable dataset and the target response dataset constitute the dataset used to build the Kriging surrogate model.

[0023] In one embodiment, the DQN optimization algorithm is used to determine the optimal structural parameters and corresponding reward values based on the initial state, including:

[0024] Step S41: The initial state is used as the current state, and the current state interacts with the environment to obtain the current reward value;

[0025] Step S42: Use the absolute ε-greed strategy to select an action and obtain the next state, interact with the environment again, and obtain the next reward value;

[0026] Step S43, determine whether the termination condition is met. If so, compare the next reward value and the current reward value, and select the state corresponding to the larger reward value as the optimal structural parameter. If not, select the state corresponding to the larger reward value as the current state and return to step S41.

[0027] In a second aspect, a device for optimizing elastic wave metamaterial structural parameters based on dynamic Kriging and DQN is provided, comprising:

[0028] Parameter optimization model building module, used to establish elastic wave metamaterial structure parameter optimization model, the model includes design variables, objective function and constraint conditions;

[0029] The framework building module is used to build the framework structure of the DQN optimization algorithm and determine the state space, action space and reward function of the DQN optimization algorithm based on the model;

[0030] The proxy model building module is used to obtain a data set for building a Kriging proxy model and build a Kriging proxy model based on the data set;

[0031] The optimization module is used to initialize the structural parameters of the elastic wave metamaterial and obtain the initial structural parameters, that is, the initial state. Based on the initial state, the DQN optimization algorithm is used to determine the optimal structural parameters and the corresponding reward value. The environment in the DQN optimization algorithm is the Kriging agent model.

[0032] Dynamic update module, which is used to construct new data points based on the optimal structural parameters and corresponding reward values, and add the new data points to the data set to obtain a new data set;

[0033] The judgment module is used to determine whether the number of data points in the new data set reaches the set number. If so, the current optimal structural parameters are the optimal structural parameters of the elastic wave metamaterial finally determined. If not, the proxy model construction module is entered to reconstruct the Kriging proxy model using the new data set.

[0034] In a third aspect, a computer-readable storage medium is provided, which stores a computer program. When the computer program is executed by a processor, it implements the above-mentioned elastic wave metamaterial structure parameter optimization method based on dynamic Kriging and DQN.

[0035] In a fourth aspect, a computer program product is provided, comprising a computer program / instruction, which, when executed by a processor, implements the above-mentioned elastic wave metamaterial structure parameter optimization method based on dynamic Kriging and DQN.

[0036] Compared to the prior art, the present application has the following beneficial effects: The present application's dynamic Kriging and DQN-based elastic wave metamaterial structural parameter optimization method constructs a high-precision dynamic Kriging proxy model and integrates it into the DQN optimization algorithm framework. The trained DQN algorithm eliminates the need for unnecessary searches within the design space and can quickly discover the approximate optimal structural parameters of the elastic wave metamaterial. The inexpensive, high-precision dynamic Kriging proxy model replaces the time-consuming finite element analysis process to accurately predict the real world and guide the optimization algorithm's search direction, ultimately achieving an optimal solution. While ensuring the bandwidth optimization requirements of the elastic wave metamaterial, the present application's method improves the optimization efficiency of the entire optimization process and significantly reduces computational costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The present application may be better understood by referring to the following description in conjunction with the accompanying drawings, which together with the following detailed description are incorporated into and form a part of this specification. In the drawings:

[0038] Figure 1 A flowchart of a method for optimizing elastic wave metamaterial structure parameters based on dynamic Kriging and DQN according to an embodiment of the present application is shown;

[0039] Figure 2 A schematic diagram of the unit cell structure of elastic wave metamaterial is shown;

[0040] Figure 3 shows a schematic diagram of the elastic wave metamaterial structure;

[0041] Figure 4 The historical convergence curve of the objective function based on the method of the present application is shown;

[0042] Figure 5 The energy band diagram of the optimal elastic wave metamaterial structure after optimization based on the method of the present application is shown;

[0043] Figure 6 shows the band diagram of the initial configuration of the elastic wave metamaterial;

[0044] Figure 7 The figure shows a structural block diagram of an elastic wave metamaterial structural parameter optimization device based on dynamic Kriging and DQN according to an embodiment of the present application. DETAILED DESCRIPTION

[0045] Exemplary embodiments of the present application are described below with reference to the accompanying drawings. For the sake of clarity and conciseness, not all features of actual embodiments are described in this specification. However, it should be understood that in the process of developing any such actual embodiment, many implementation-specific decisions may be made to achieve the developer's specific goals, and these decisions may vary from one implementation to another.

[0046] It is also necessary to explain here that, in order to avoid obscuring the present application due to unnecessary details, the accompanying drawings only show the device structure closely related to the solution according to the present application, while other details that are not closely related to the present application are omitted.

[0047] It should be understood that the present application is not limited to the described embodiments due to the following description with reference to the accompanying drawings. In this document, where feasible, the embodiments may be combined with each other, features between different embodiments may be replaced or borrowed, and one or more features may be omitted in one embodiment.

[0048] In the field of structural optimization of electromechanical systems (EMs), non-gradient algorithms face computational bottlenecks when faced with high-precision, complex EM configurations. Traditional reinforcement learning methods, such as Q-learning, suffer from excessive states, resulting in slow search processes. Furthermore, numerical simulation of high-precision, complex EMs is also a costly problem. Due to the significant computational cost reduction of the dynamic Kriging surrogate model for complex structural optimization problems, and the efficient perception and decision-making capabilities of the DQN (deep Q-network) algorithm for high-dimensional, complex problems, an elastic wave metamaterial design framework combining the dynamic Kriging surrogate model with the DQN algorithm can efficiently and cost-effectively solve complex metamaterial bandgap optimization problems.

[0049] The present invention provides a method for optimizing elastic wave metamaterial structure parameters based on dynamic Kriging and DQN. Figure 1 A flowchart of a method for optimizing elastic wave metamaterial structure parameters based on dynamic Kriging and DQN according to an embodiment of the present application is shown. Figure 1 , methods include:

[0050] Step S1: Establishing an elastic wave metamaterial structural parameter optimization model, the model includes design variables, objective functions and constraints.

[0051] Here, the design variables are the main structural parameters that affect the bandgap performance of elastic wave metamaterials:

[0052] x=[x1,x2,…x i …,x a ],u=1,2,…,α

[0053] x i ∈[x min ,x max ]

[0054] Among them, x is the design variable, x i is the i-th structural parameter, α is the number of structural parameters, x min is x l The lower limit of x max is x i upper limit.

[0055] The objective function with added constraints can be expressed as follows:

[0056]

[0057] Where f(x) is the objective function value, m(x) is the total mass of the structure of the optimized solution, x is the design variable, m0 is the upper limit of the total mass of the structure of the optimized solution, m(x)≤m0, δ is the set value to prevent the denominator from being 0, Δb(x) is the default value, ωn+1 (k,x) is the band gap frequency corresponding to the kth sampling point on the n+1th energy band, ω n (k,x) is the band gap frequency corresponding to the kth sampling point on the nth energy band, Δω n is the band gap width between the nth energy band and the n+1th energy band, Δω n =minω n+1 (k,x)-maxω n (k,x).

[0058] Step S2: construct the framework structure of the DQN optimization algorithm and determine the state space, action space, and reward function of the DQN optimization algorithm based on the model.

[0059] To achieve high-precision bandgap optimization for complex EMs, the DQN optimization algorithm, with its perception and decision-making capabilities, was applied to the EMs structural parameter optimization framework. The DQN optimization algorithm framework includes a Q network, and the DQN optimization algorithm framework constructed here includes a trained Q network.

[0060] During the network training process, based on the target network and the experience replay data pool, the Q network is the intelligent agent itself that has been trained to produce the optimal state-action value, which is used to predict the Q value; the target network generates the target Q value and is used to calculate the loss function to update the Q network; the experience replay data pool is used to store sample data obtained by the continuous interaction between the intelligent agent and the environment. These data are used to train the Q network. A set of sample data includes: the current state, the action to be performed, the reward value obtained, and the next state reached after the action is performed.

[0061] Specifically, the number of state divisions should be appropriate and the expression should be reasonable. Too many states will make the algorithm converge too slowly and difficult to reach the optimal solution; too few states will miss the optimal solution. Here, the state space includes multiple states, and the state is the value of the design variable. The upper and lower limits of the design variable constitute the boundaries of the state space.

[0062] In parameter optimization problems, an action refers to a change in a design variable, thereby altering the agent's state. In this paper, the increase or decrease value of the design variable is d. Actions in the action space are used to change the state. If a variable is out of bounds after an action, the variable remains unchanged.

[0063] In the parameter optimization problem of elastic wave metamaterials, the reward function is directly defined as the size of the objective function. Therefore, the agent's learning always tends to find a state with a larger reward value; the reward function is the objective function.

[0064] Step S3: Acquire a data set for constructing a Kriging proxy model, and construct the Kriging proxy model based on the data set.

[0065] Specifically, the LHS experimental method is used to obtain the design variable data set, and the finite element numerical simulation is performed on the design variable data set to obtain the target response data set; the design variable data set and the target response data set constitute the data set for constructing the Kriging surrogate model.

[0066] Here, the LHS experimental design method adopts Iman's method: the distribution with the smallest correlation between variables is used as the final result to improve the uneven spatial distribution of sampling points and effectively avoid the LHS sampling instability phenomenon. This experimental design method provides a set of feasible design variable data sets for the construction of the surrogate model:

[0067]

[0068] Among them, X s is the design variable data set, N dv is the design variable dimension, N sp is the number of sampling points.

[0069] When performing finite element analysis on these sampling points, we use the solid mechanics module in the multi-physics coupling software COMSOL. According to the requirements of the problem, we conduct secondary development of its script language and obtain the program code in the MATLAB environment. Then, we start COMSOL with MATLAB and perform the finite element analysis on the input design variable data set X. s Perform finite element numerical simulation to obtain the target response data set The two constitute the data set (X s ,Y s ).

[0070] It should be noted that building a Kriging proxy model based on a data set is an existing technology and will not be described in detail.

[0071] Step S4: Initialize the structural parameters of the elastic wave metamaterial to obtain the initial structural parameters, i.e., the initial state; based on the initial state, use the DQN optimization algorithm to determine the optimal structural parameters and the corresponding reward value; the environment in the DQN optimization algorithm is the Kriging agent model.

[0072] Here, the Kriging agent model is used as the environment in the DQN optimization algorithm, replacing the traditional complex and time-consuming finite element analysis process.

[0073] In step S5, the optimal structural parameters and the corresponding reward values constitute new data points, which are added to the data set to obtain a new data set.

[0074] In step S6, it is determined whether the number of data points in the new data set reaches the set number. If so, the current optimal structural parameters are the optimal structural parameters of the elastic wave metamaterial finally determined. If not, return to step S3 and use the new data set to rebuild the Kriging proxy model.

[0075] To improve the prediction accuracy and robustness of the Kriging surrogate model, a high-precision dynamic Kriging surrogate model is constructed based on the initial Kriging surrogate model using the point addition criterion. The point addition criterion (MP criterion) is used to improve the accuracy of the Kriging surrogate model, significantly improving the model's prediction accuracy near the optimal solution.

[0076] The method of this embodiment constructs a high-precision dynamic Kriging proxy model and integrates it into the DQN optimization algorithm framework. This eliminates the need for unnecessary searches within the design space for the trained DQN algorithm, allowing it to quickly discover the approximate optimal structural parameters of the elastic wave metamaterial. The inexpensive, high-precision dynamic Kriging proxy model replaces the time-consuming finite element analysis process to accurately predict the real world and guide the optimization algorithm's search direction, ultimately achieving an optimal solution. While ensuring the bandwidth optimization requirements of the elastic wave metamaterial, this method improves the efficiency of the entire optimization process and significantly reduces computational costs.

[0077] In one embodiment, in step S4, the optimal structural parameters and corresponding reward values are determined based on the initial state using the DQN optimization algorithm, including:

[0078] Step S41: The initial state is used as the current state, and the current state interacts with the environment to obtain the current reward value;

[0079] Step S42: Use the absolute ε-greed strategy to select an action and obtain the next state, interact with the environment again, and obtain the next reward value;

[0080] Step S43 determines whether the termination condition is met. If so, the next reward value is compared with the current reward value, and the state corresponding to the larger reward value is selected as the optimal structural parameter. If not, the state corresponding to the larger reward value is selected as the current state, and the process returns to step S41. Here, the termination condition can be, for example, reaching the maximum number of iteration steps, which can be set to 1000.

[0081] In one embodiment, Figure 2 Figure 2 shows a schematic diagram of the unit cell structure of elastic wave metamaterials. Figure 3A schematic diagram of the elastic wave metamaterial structure is shown. This example investigates a localized resonant elastic wave metamaterial with multiple resonators, constructed from a two-dimensional hexagonal lattice composed of aluminum, lead, and silicone rubber. The lattice constant is a = 50 mm. Aluminum serves as the matrix; silicone rubber serves as the elastic medium; and lead serves as the localized resonator counterweight between the scatterer and the interlayer. The material properties are shown in Table 1 below:

[0082] Table 1 Material properties

[0083] Material composition Elastic modulus / MPa <![CDATA[Density / (kg / m 3 )]]> Poisson's ratio Material A: Aluminum 71000 2700 0.33 Material B: Silicone rubber 0.4 1340 0.47 Material C: Lead 1600000 11340 0.44

[0084] The elastic wave metamaterial structural parameters that need to be optimized in this embodiment are: the three diameters of the inclusion scatterer, d0 = 6mm, d1 = 4mm, d2 = 4mm, and the two thicknesses of the multilayer coating, t1 = 6mm, t2 = 6mm. The specific parameters correspond to the position of Figure 2 .

[0085] In step S1, the initial design variables are [6, 4, 4, 6, 6], and the upper and lower limits of the design variables are [10, 8, 8, 7.5, 7.5] and [6, 4, 4, 3.5, 3.5] respectively; m0 takes the middle value of the design variable value range, that is, m0 = 10.8706 kg; the objective function is to maximize the relative band gap width between the first 12 energy bands, and the objective function value is: 0.5428.

[0086] In step S2, consider a set of design variables, such as [6, 4, 4, 6, 6], as a state. The upper and lower limits of this state (a set of design variables) are [10, 8, 8, 7.5, 7.5] and [6, 4, 4, 3.5, 3.5], respectively. Each design variable has an increment or decrement value of d = 0.05. As shown in Table 2, each state has 10 actions to choose from. After the actions are discretized, the total number of states is 81 × 81 × 81 × 81 × 81 = 3486784401. The reward function is the objective function value.

[0087] Table 2 Action division of Kriging-DQN optimization algorithm

[0088]

[0089]

[0090] The Q network is a neural network with six hidden nodes, trained using a gradient descent algorithm. The neural network training parameters are set as follows: a learning rate of 0.1, a learning decay of 0.01, and a training period of 1. 500 sets of sample data are prepared to train the neural network, generating a Q network with initialized weights. This Q network is then replicated to the target network. Initially, 3000 sets of sample data are initialized and populated into the experience replay data pool. During the Q network training process, the pool is continuously updated with sample data, with 30 sets of samples randomly selected from the experience replay data pool each time for training the Q network.

[0091] Step S3, the implementation process of LHS is: dv = N is sampled in the 5-dimensional design space sp = 15 sampling points, these 15 initial sampling points are in the range of [0, 1], and then the generated initial sampling points are converted to the design variable parameter space range. The 15 sampling points X obtained from LHS are converted to 15 Bring it into the finite element software for analysis and obtain the objective function response value Y corresponding to the 15 sampling points 15 All sampling points and corresponding function response values constitute the I / O data set (X 15 ,Y 15 ), which is the dataset used to build the Kriging surrogate model.

[0092] First, according to the data set (X 15 ,Y 15 ) constructs an initial Kriging proxy model, but the prediction accuracy of the initial proxy model is relatively low. Therefore, based on the initial model, the subsequent process uses the optimization point addition criterion to purposefully add points to the "interesting" area within the design domain to update the Kriging proxy model and improve model accuracy. In this embodiment, the points are added based on the MP point addition criterion, and the ratio of the number of initial points to the number of points added later is 1:2, that is, 30 sampling points are added later.

[0093] In step S4, the Kriging agent model is embedded into the DQN optimization algorithm and replaces the finite analysis process to become the new environment space.

[0094] Substitute the initial state Initial-State = [6, 4, 4, 6, 6] into the environment built by the Kriging agent model to interact, obtain the reward value Reward, select the best action according to the absolute ε-greed strategy and enter the new state New-State.

[0095] The new state is introduced into the environment again for interaction, obtaining a new reward value (New-Reward). The reward and New-Reward are compared, and the state with the larger value is retained to replace the initial state (Initial-state). The search continues until the maximum number of iteration steps is met. The maximum number of steps is set to 1000.

[0096] Step S5: Output the optimal structural parameter x found by the DQN optimization algorithm. (new) and the corresponding objective function y(x new ), generate new input / output sampling points, and add the results as new sample data to the existing dataset (X 15 ,Y 15 ), a new data set (X 15+t ,Y 15+t ), where t=1, 2...30 is the current number of added points.

[0097] Step S6, determine whether the maximum number of sampling points (45) is reached (initial sampling points 15 + optimization points 30). If yes, accept the optimization solution, and the current optimal structural parameters are the optimal structural parameters of the elastic wave metamaterial determined in the end; otherwise, use the data set (X 15+t ,Y 15+t ) to rebuild the Kriging surrogate model.

[0098] In order to further verify the effectiveness of the method of this application, the method of this application (Kriging-DQN) was used to solve the mathematical model, and the optimization converged after 24 iterations. Figure 4 The historical convergence curve of the objective function based on the method of the present application is shown. Table 3 shows the optimization results of the elastic wave metamaterial using the method of the present application. It can be seen that the optimized design variables are: d0 = 8.15mm, d1 = 4.30mm, d2 = 7.2mm, t1 = 5.45mm and t2 = 4.35mm. Compared with the initial structure, the circular scatterer diameter d0 and the inner and outer layer inclusion diameters d1 and d2 of the optimized structure increase, and the thicknesses t1 and t2 of the elastic coating decrease. The optimized objective function value is 0.8879, which is 63.58% higher than the initial design target value of 0.5428.

[0099] Table 3 Kriging-DQN optimization algorithm optimization results

[0100]

[0101] Figure 5 The energy band diagram of the optimal elastic wave metamaterial structure after optimization based on the method of the present application is shown. Figure 6 The energy band diagram of the initial configuration of elastic wave metamaterial is shown in Figure 2. Figure 5 It can be seen that the frequency ranges of the three complete band gaps are [327.69-398.65] Hz, [502.53-746.10] Hz, and [857.99-1172.32] Hz, respectively. Compared to the initial elastic wave metamaterial, the width of the first relative band gap decreases slightly, while the second and third band gaps increase significantly, ultimately leading to an increase in the target value of the function.

[0102] To illustrate the effectiveness of the proposed method, Table 4 compares the results using the proposed method and the FEA-GA method. The table shows that the objective function values optimized by the proposed method and the FEA-GA method are 0.8879 and 0.8814, respectively, representing improvements of 63.58% and 62.38% relative to the initial structural parameter configuration, respectively. The difference between the two is minimal. However, under the same computer configuration (same optimization environment), the optimal solution calculation times for the proposed method and the FEA-GA method are 58 and 186 hours, respectively.

[0103] Table 4 Comparison of optimization results between Kriging-DQN and FEA-GA

[0104]

[0105] Results show that optimizing the structural parameters of elastic wave metamaterials using this method significantly increases the total band gap of the first 12 energy bands, achieving the optimization goal. This method also overcomes the computational complexity and time-consuming nature of the FEA-GA optimization method, significantly improving optimization efficiency.

[0106] Based on the same inventive concept as the elastic wave metamaterial structure parameter optimization method based on dynamic Kriging and DQN, this embodiment also provides a corresponding elastic wave metamaterial structure parameter optimization device based on dynamic Kriging and DQN. Figure 7 The structure block diagram of the elastic wave metamaterial structure parameter optimization device based on dynamic Kriging and DQN according to an embodiment of the present application is shown, including:

[0107] A parameter optimization model building module 71 is used to build an elastic wave metamaterial structure parameter optimization model, the model including design variables, objective functions and constraints;

[0108] A framework construction module 72 is used to construct a framework structure of the DQN optimization algorithm and determine the state space, action space, and reward function of the DQN optimization algorithm based on the model;

[0109] The proxy model construction module 73 is used to obtain a data set for constructing a Kriging proxy model and construct the Kriging proxy model based on the data set;

[0110] The optimization module 74 is used to initialize the structural parameters of the elastic wave metamaterial to obtain the initial structural parameters, i.e., the initial state; based on the initial state, the DQN optimization algorithm is used to determine the optimal structural parameters and the corresponding reward value; the environment in the DQN optimization algorithm is the Kriging agent model;

[0111] Dynamic update module 75, for forming new data points based on the optimal structural parameters and the corresponding reward values, and adding the new data points to the data set to obtain a new data set;

[0112] The judgment module 76 is used to determine whether the number of data points in the new data set reaches the set number. If so, the current optimal structural parameters are the optimal structural parameters of the elastic wave metamaterial finally determined. If not, enter the proxy model construction module and use the new data set to rebuild the Kriging proxy model.

[0113] The elastic wave metamaterial structure parameter optimization device based on dynamic Kriging and DQN in this embodiment has the same inventive concept as the elastic wave metamaterial structure parameter optimization method based on dynamic Kriging and DQN mentioned above. Therefore, the specific implementation method of the device can be seen in the embodiment part of the elastic wave metamaterial structure parameter optimization method based on dynamic Kriging and DQN in the above text, and its technical effects correspond to the technical effects of the above method, which will not be repeated here.

[0114] An embodiment of the present application provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the method for optimizing elastic wave metamaterial structure parameters based on dynamic Kriging and DQN is implemented.

[0115] An embodiment of the present application provides a computer program product, including a computer program / instruction. When the computer program / instruction is executed by a processor, it implements the above-mentioned elastic wave metamaterial structure parameter optimization method based on dynamic Kriging and DQN.

[0116] The above descriptions are merely examples of various embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any modifications or substitutions that can be readily conceived by a person skilled in the art within the technical scope disclosed in the present application should be included within the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for optimizing elastic wave metamaterial structural parameters based on dynamic Kriging and DQN, characterized in that: include: Step S1, establishing an elastic wave metamaterial structural parameter optimization model, wherein the model includes design variables, objective functions, and constraints; Step S2, constructing a framework structure of the DQN optimization algorithm, and determining the state space, action space, and reward function of the DQN optimization algorithm based on the model; Step S3, obtaining a data set for constructing a Kriging proxy model, and constructing a Kriging proxy model based on the data set; Step S4, initializing the structural parameters of the elastic wave metamaterial to obtain initial structural parameters, i.e., initial state; Based on the initial state, a DQN optimization algorithm is used to determine the optimal structural parameters and the corresponding reward value; the environment in the DQN optimization algorithm is the Kriging agent model; Step S5, the optimal structural parameters and the corresponding reward values constitute a new data point, and the new data point is added to the data set to obtain a new data set; Step S6, determining whether the number of data points in the new data set reaches a set number; if so, the current optimal structural parameters are the optimal structural parameters of the elastic wave metamaterial finally determined; if not, returning to step S3, and reconstructing the Kriging proxy model using the new data set; The objective function is: in, is the objective function value, is the total mass of the structure of the optimized solution, is the design variable, is the upper limit of the total mass of the structure of the optimal solution, To prevent the denominator from being set to 0, is the default value, is the band gap frequency corresponding to the kth sampling point on the n+1th energy band, The nth energy band corresponds to the kth sampling point , is the band gap width between the nth energy band and the n+1th energy band, .

2. The method according to claim 1, wherein The framework structure of the constructed DQN optimization algorithm includes the trained Q network.

3. The method according to claim 1, wherein in, Determining the state space, action space, and reward function of the DQN optimization algorithm based on the model includes: The state space includes a plurality of states, each of which is a set of values of design variables, and the upper and lower limits of the design variables constitute the boundaries of the state space; The actions in the action space are used to change the state; The reward function is the objective function.

4. The method according to claim 1, wherein in, Get the dataset used to build the Kriging surrogate model, including: A design variable data set is obtained by an experimental method, and a finite element numerical simulation is performed on the design variable data set to obtain a target response data set; The design variable data set and the target response data set constitute a data set for constructing a Kriging surrogate model.

5. The method according to claim 1, wherein in, Based on the initial state, the DQN optimization algorithm is used to determine the optimal structural parameters and the corresponding reward value, including: Step S41, taking the initial state as the current state, and interacting with the environment to obtain a current reward value; Step S42, using absolute -greed strategy selects an action and obtains the next state, interacts with the environment again, and obtains the next reward value; Step S43, determine whether the termination condition is met. If so, compare the next reward value and the current reward value, and select the state corresponding to the larger reward value as the optimal structural parameter. If not, select the state corresponding to the larger reward value as the current state, and return to step S41.

6. An elastic wave metamaterial structural parameter optimization device based on dynamic Kriging and DQN, characterized in that: include: A parameter optimization model building module is used to build an elastic wave metamaterial structure parameter optimization model, wherein the model includes design variables, objective functions and constraint conditions; A framework construction module, configured to construct a framework structure of the DQN optimization algorithm and determine the state space, action space, and reward function of the DQN optimization algorithm based on the model; A proxy model construction module is used to obtain a data set for constructing a Kriging proxy model and construct the Kriging proxy model based on the data set; An optimization module is used to initialize the structural parameters of the elastic wave metamaterial and obtain the initial structural parameters, i.e., the initial state; Based on the initial state, a DQN optimization algorithm is used to determine the optimal structural parameters and the corresponding reward value; the environment in the DQN optimization algorithm is the Kriging agent model; A dynamic update module, configured to construct a new data point from the optimal structural parameters and the corresponding reward value, and add the new data point to the data set to obtain a new data set; a judgment module for judging whether the number of data points in the new data set reaches a set number; if so, the current optimal structural parameters are the optimal structural parameters of the elastic wave metamaterial finally determined; if not, entering the proxy model construction module and reconstructing the Kriging proxy model using the new data set; The objective function is: in, is the objective function value, is the total mass of the structure of the optimized solution, is the design variable, is the upper limit of the total mass of the structure of the optimal solution, To prevent the denominator from being set to 0, is the default value, is the band gap frequency corresponding to the kth sampling point on the n+1th energy band, The nth energy band corresponds to the kth sampling point , is the band gap width between the nth energy band and the n+1th energy band, .

7. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the elastic wave metamaterial structure parameter optimization method based on dynamic Kriging and DQN according to any one of claims 1 to 5.

8. A computer program product, characterized in that The method comprises a computer program / instruction, which, when executed by a processor, implements the elastic wave metamaterial structure parameter optimization method based on dynamic Kriging and DQN according to any one of claims 1 to 5.

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