High-dimensional metamaterial acoustic performance prediction method and system based on space mapping multi-fidelity modeling

Abstract

The invention belongs to but is not limited to the technical field of acoustic metamaterial performance prediction, and discloses a high-dimensional metamaterial acoustic performance prediction method based on space mapping multi-fidelity modeling, and the method comprises the steps: obtaining high / low-fidelity training sample points through combining acoustic metamaterial finite element models with different calculation costs and precisions; a low-fidelity proxy model is constructed based on a Cut-HDMR model to capture the overall trend of the performance change of the high-dimensional acoustic metamaterial, a high-dimensional problem is decomposed into superposition of one-dimensional and two-dimensional component functions, and low-fidelity model prediction is used as priori and mapped to a high-fidelity output space to construct a multi-fidelity model. And high-dimensional many-to-one mapping is converted into easy-to-process one-to-one mapping, so that the high-dimensional dilemma in multi-fidelity modeling is eliminated, and the performance prediction of the high-dimensional acoustic metamaterial is accurately and efficiently performed.

Description

Technical Field

[0001] The present invention belongs to but is not limited to the technical field of acoustic metamaterial performance prediction, and in particular relates to a high-dimensional metamaterial acoustic performance prediction method and system based on spatial mapping multi-fidelity modeling. Background Art

[0002] Acoustic metamaterials are a type of artificial layered structure composed of subwavelength microstructure units. Based on the generalized Snell's law, the geometric arrangement and physical parameters of the microstructure are designed to control acoustic / elastic waves and achieve extraordinary physical properties such as negative mass, negative elastic modulus, and subwavelength band gap. Its macroscopic properties depend on the special structure designed inside, rather than the intrinsic properties of the material. Compared with traditional metamaterials that are large in size, high in production cost, and have a narrow working bandwidth, acoustic metamaterials have the advantages of being ultra-thin and flexible in controlling sound waves. By utilizing the abnormal reflection and refraction characteristics of acoustic metamaterials to sound waves, it has broad application prospects in wavefront control, acoustic imaging, acoustic stealth, and other aspects.

[0003] In order to achieve free control of sound waves, a specific metasurface structure needs to be designed. However, acoustic metamaterials are composed of many unit cells, and their performance prediction often involves many design parameters, such as the material properties and geometric shapes of each unit cell. These high-dimensional parameters greatly increase the computational cost of the traditional metamaterial design process based on numerical simulation, and may cause the design process to fall into the "curse of dimensionality" disaster. Some dimensionality reduction strategies and auxiliary information-based proxy modeling techniques have been proposed to solve the dilemma of high-dimensional modeling, but these methods are still limited by sparse and expensive high-fidelity sample points in terms of sample collection and fusion mode. Although the method based on high-dimensional model representation (HDMR) can effectively decompose high-dimensional problems to achieve efficient modeling, it still has gaps in processing multi-fidelity data.

[0004] In the field of acoustic metamaterial performance prediction, existing technologies mainly rely on high-fidelity numerical simulation models for performance analysis. However, although high-fidelity models are accurate, they have extremely high computational costs. Especially when dealing with complex multi-physics field interactions and high-dimensional design variables, the simulation speed is slow and it is difficult to meet industrial design and optimization needs. In addition, although low-fidelity models have fast computational speeds, their prediction accuracy is insufficient and cannot meet the requirements of performance evaluation alone. Existing technologies lack a method to effectively integrate high-fidelity and low-fidelity models, resulting in low efficiency in acoustic metamaterial performance prediction in industrial applications and difficulty in large-scale promotion. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention provides a method and system for predicting the acoustic performance of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling.

[0006] The present invention is implemented as follows: a method for predicting the acoustic performance of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling, comprising the following steps:

[0007] Step 1: Determine the prediction target according to the design requirements of acoustic metamaterials;

[0008] Step 2: Divide the acoustic metamaterial structure into sub-units to determine the high-dimensional design variables contained in its inherent physical property combination;

[0009] Step 3: Perform multi-physics modeling of acoustic metamaterials based on COMSOL software and construct high / low fidelity numerical simulation models with different computational costs and accuracies;

[0010] Step 4: Use the maximum and minimum distance sequential sampling to obtain the grid sample points x of each component function l , calling the low-fidelity simulation model to obtain the response value f of the sample point l (x l ), building a low-fidelity proxy model of acoustic metamaterials based on the Cut-HDMR model

[0011] Step 5: Use optimized Latin hypercube sampling to obtain high-fidelity sample points x h , calling the high-fidelity simulation model to calculate the response value f of the sample point h (x h ), calculate the low-fidelity prediction value through the low-fidelity proxy model A SM-HDMR multi-fidelity model was constructed based on the spatial mapping method;

[0012] Step 6: Output the acoustic metamaterial SM-HDMR model and the nonlinear first-order terms and coupled second-order terms, and evaluate the prediction error of the model.

[0013] Furthermore, according to the design requirements of acoustic metamaterials, the prediction targets are determined, including:

[0014] According to the design requirement of designing a combination of inherent physical properties of acoustic metamaterials to modulate the far-field sound pressure level, the far-field sound pressure level at 90° is determined to characterize the influence of metamaterials on sound waves, which is the prediction target.

[0015] Furthermore, the acoustic metamaterial structure is divided into sub-units to determine the design variables x contained in its inherent physical property combination, including:

[0016] The acoustic metamaterial structure is divided into m subunits along the length direction. The physical properties of each subunit are characterized by the two indicators of density ρ and Young's modulus E. The 2m design variables contained in the combination of inherent physical properties of the acoustic metamaterial are determined. Let dimension D = 2m, then x = [x 1,x 2 ,…,x D ] T , where x 1 , x 2 , …, x m represents the density of m subunits, x m+1 , x m+2 , …, x 2m represents the Young's modulus of m subunits.

[0017] Furthermore, the maximum and minimum distance sequential sampling is adopted to obtain the grid sample points x of each component function. l , calling the low-fidelity simulation model to obtain the response value f of the sample point l (x l ), building a low-fidelity proxy model of acoustic metamaterials based on the Cut-HDMR model include:

[0018] (1) Determine the cutting center; select the midpoint of the design domain as the cutting center of the Cut-HDMR model And based on the coarse grid low-fidelity simulation model to obtain the corresponding low-fidelity response

[0019] (2) Construct a first-order component function; for variable x i (i=1,2,…,D), select the upper and lower boundary points x i - and is the initial sample point, and the corresponding function value is obtained from the low-fidelity simulation model to obtain the training point Constructing the initial first-order component function based on the Kriging model

[0020] (3) Check the linearity of the first-order component function; if the constructed surrogate model By cutting center x 0 ,Right now but is a linear function consisting of only two sample points; conversely, more sample points are obtained through maximum and minimum distance sampling until the accuracy requirement is met; D first-order component functions are completed in sequence The low-fidelity proxy model containing only the first-order component function is constructed as follows:

[0021]

[0022] in, is the 0th order constant, i.e. the low fidelity response value at the cut point, and the first order component function The variable is x i , the training sample points of the i-th component Build, Indicates that all variables except the i-th dimension variable are related to x 0 The value of is the same, s i is the number of sample points used for the corresponding component.

[0023] (4) Check the second-order existence; if the corner point The predicted value of If it is similar to its low-fidelity simulation response value, the influence of the high-order term is considered to be negligible, otherwise, continue to construct the second-order component function;

[0024] (5) Check and construct the second-order component function; evaluate any two variables x i and x j If the relative error is greater than the threshold ε 2 ,Right now: Then on the cutting surface x i -x j Based on the maximum and minimum distance sampling, more low-fidelity second-order sample points are obtained to construct the second-order component function The construction of all second-order component functions is completed in sequence, and a more refined low-fidelity proxy model is obtained:

[0025]

[0026] Among them, the second-order term with coupling effect Contains two-dimensional variables x i and x j , by the corresponding training sample points Build, Indicates that except for the i-th and j-th dimension variables, all other variables are related to x 0 The value of is the same, s ij is the number of sample points used for the corresponding component.

[0027] Furthermore, optimized Latin hypercube sampling is used to obtain high-fidelity sample points x h , calling the high-fidelity simulation model to calculate the response value f of the sample point h (x h ), calculate the low-fidelity prediction value through the low-fidelity proxy model The SM-HDMR multi-fidelity model is constructed based on the spatial mapping method, including:

[0028] Perform optimized Latin hypercube sampling in the entire design domain, call the high-fidelity simulation model to calculate the corresponding response value, and obtain high-fidelity sample points [x h ,f h (x h)]; the corresponding low-fidelity prediction value is calculated by the constructed Cut-HDMR model Will As training sample points, the Kriging model is constructed. As input variable, f h (x h ) as the corresponding output data, thereby mapping the low-fidelity output information to the high-fidelity output space, and transforming the "many-to-one" mapping into an easy-to-handle "one-to-one" mapping relationship to eliminate the high-dimensional dilemma in multi-fidelity modeling. The final multi-fidelity model is:

[0029]

[0030] in, is a random process, representing the local fluctuation or error of the objective function. is a regression term, and the overall behavior of the target is represented by a linear combination of p regression functions:

[0031]

[0032] where h(·) consists of the regression function and β is the regression coefficient.

[0033] Further, the acoustic metamaterial SM-HDMR model and the nonlinear first-order terms and coupled second-order terms are output, and the prediction error of the model is evaluated, including:

[0034] The prediction error of the constructed SM-HDMR model is evaluated using the global error index relative mean absolute error (RAAE) and the local error index relative root mean square error (RRMSE), where:

[0035]

[0036] Among them, n is the number of test sample points, y i Represents the actual response value of the test sample point, is the corresponding SM-HDMR model prediction value, and STD represents the standard deviation.

[0037] Furthermore, the prediction error of the constructed SM-HDMR model is evaluated, the nonlinear first-order terms and coupled second-order terms are derived, and guidance is provided for adding high / low-fidelity samples of acoustic metamaterials. When only the first-order component function and the second-order component function are constructed in step 4, the prediction accuracy of the SM-HDMR model in the corresponding cases is evaluated using error indicators, the accuracy improvement ratio and the number of sample points are obtained, and the corresponding nonlinear first-order terms and second-order terms with non-negligible coupling effects are provided, providing guidance for adding high / low-fidelity samples of acoustic metamaterials.

[0038] Another object of the present invention is to provide a high-dimensional metamaterial acoustic performance prediction method based on spatial mapping multi-fidelity modeling and a high-dimensional metamaterial acoustic performance prediction system based on spatial mapping multi-fidelity modeling, comprising:

[0039] Prediction target determination module: determines the prediction target according to the design requirements of acoustic metamaterials;

[0040] Subunit division module: divide the acoustic metamaterial structure into subunits to determine the high-dimensional design variables contained in its inherent physical property combination;

[0041] Numerical simulation model building module: Based on COMSOL software, multi-physics modeling of acoustic metamaterials is carried out to build high / low fidelity numerical simulation models with different computational costs and accuracies;

[0042] Low-fidelity proxy model construction module: Use maximum and minimum distance sequential sampling to obtain the grid sample points x of each component function l , calling the low-fidelity simulation model to obtain the response value of the sample point, and constructing the acoustic metamaterial low-fidelity proxy model based on the Cut-HDMR model

[0043] SM-HDMR multi-fidelity model building module: Use optimized Latin hypercube sampling to obtain high-fidelity sample points x h , calling the high-fidelity simulation model to calculate the response value f of the sample point h (x h ), calculate the low-fidelity prediction value through the low-fidelity proxy model A SM-HDMR multi-fidelity model was constructed based on the spatial mapping method;

[0044] Model prediction error evaluation module: outputs the acoustic metamaterial SM-HDMR model and nonlinear first-order terms and coupled second-order terms, and evaluates the model prediction error.

[0045] Another object of the present invention is to provide a computer device, the computer device comprising a memory and a processor, the memory storing a computer program, and when the computer program is executed by the processor, the processor executes the steps of the method for predicting the acoustic performance of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling.

[0046] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to execute the steps of the method for predicting the acoustic performance of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling.

[0047] Another object of the present invention is to provide an information data processing terminal, which includes the high-dimensional metamaterial acoustic performance prediction system based on spatial mapping multi-fidelity modeling.

[0048] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0049] First, the present invention is a high-dimensional acoustic metamaterial performance prediction method based on spatial mapping multi-fidelity proxy modeling, which combines acoustic metamaterial finite element models with different computational costs and accuracies to obtain high / low fidelity training sample points, and constructs a low-fidelity proxy model based on the Cut-HDMR model to capture the overall trend of high-dimensional acoustic metamaterial performance changes, decomposes the high-dimensional problem into a superposition of one-dimensional and two-dimensional component functions, and uses the low-fidelity model prediction as a priori to map it to the high-fidelity output space to construct a multi-fidelity model, which converts the high-dimensional "many-to-one" mapping into an easy-to-handle "one-to-one" mapping, so as to eliminate the high-dimensional dilemma in multi-fidelity modeling and accurately and efficiently predict the performance of high-dimensional acoustic metamaterials.

[0050] Second, as auxiliary evidence of the inventiveness of the present invention, it is also reflected in the following important aspects:

[0051] (1) The expected benefits and commercial value of the technical solution of the present invention after transformation are:

[0052] The acoustic metamaterials studied in the present invention have extraordinary physical properties such as negative mass, negative elastic modulus, and subwavelength band gap, which make them play an important role in wavefront control, acoustic imaging, acoustic stealth, etc., and have significant military application value. Developing and researching multi-fidelity proxy modeling methods that effectively predict the performance of high-dimensional acoustic metamaterials can significantly reduce the number of calls to expensive numerical simulations while accurately characterizing their performance changes, greatly alleviating the computational cost of the acoustic metamaterial design process that relies on repeated performance calculations, and is an important basis for optimizing the design of acoustic metamaterial structures.

[0053] (2) The technical solution of the present invention fills the technical gap in the industry at home and abroad:

[0054] The present invention utilizes high-dimensional proxy modeling technology to construct a prediction model that characterizes the relationship between high-dimensional design variables contained in the combination of acoustic metamaterial performance and its physical properties. The decomposition strategy based on HDMR effectively avoids the metamaterial design process from falling into the dilemma of "dimensionality curse". Based on the multi-fidelity modeling method, a large number of low-fidelity sample points are used to capture the overall trend of high-dimensional acoustic metamaterial performance changes, and a small number of high-fidelity sample points are used to ensure the prediction accuracy of the proxy model. Based on the idea of ​​spatial mapping, while alleviating the burden of high-dimensional modeling, high / low-fidelity sample information with different precision and time costs is integrated. Compared with the single-precision proxy modeling method, the modeling accuracy and modeling efficiency are further effectively balanced, and the accurate and efficient prediction of the acoustic performance of metamaterials is achieved.

[0055] Third, the present invention introduces multi-fidelity modeling technology based on spatial mapping, cleverly combining the accuracy advantage of high-fidelity models and the computational efficiency of low-fidelity models to solve the problem of difficult balance between computational cost and prediction accuracy in the prior art. By constructing the SM-HDMR (spatial mapping high-dimensional model representation) multi-fidelity model, the present invention significantly reduces the computational cost of complex acoustic metamaterials while maintaining high-precision prediction capabilities. This method can quickly analyze the contribution of multi-dimensional design variables to acoustic performance, providing a more economical and efficient solution for industrial design.

[0056] Compared with the prior art, the present invention has demonstrated significant technological progress in industrial applications. First, by optimizing Latin hypercube sampling and spatial mapping technology, the demand for high-fidelity data is greatly reduced, and the calculation time is shortened by more than 50%, which significantly improves the industrial applicability of the model. Secondly, the SM-HDMR model can simultaneously output nonlinear first-order and second-order coupling terms, allowing designers to intuitively analyze the impact of design variables on performance, thereby more efficiently adjusting parameters and optimizing structures. In addition, the present invention solves the problem of performance prediction under high-dimensional design variables and complex physical field coupling conditions, and expands the application scope of acoustic metamaterials in precision industries.

[0057] The present invention provides a fast, accurate and low-cost solution for the performance prediction and optimization of acoustic metamaterials, significantly improving the feasibility of complex design solutions. Its application in the fields of noise reduction equipment, sound wave control, and medical acoustic imaging will accelerate the development and industrialization of related technologies. At the same time, based on the high efficiency of the multi-fidelity modeling method, the present invention can be widely used in industries such as aerospace, automobile manufacturing and architectural acoustics, providing technical support for the intelligent design and industrial upgrading of acoustic materials, and injecting new impetus into the efficient development of modern industry. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a flow chart of a high-dimensional acoustic metamaterial performance prediction method based on spatial mapping multi-fidelity proxy modeling provided by an embodiment of the present invention;

[0059] Figure 2 A schematic diagram of an acoustic metamaterial structure and modeling in one embodiment;

[0060] Figure 3 A schematic diagram of mesh division of an acoustic metamaterial simulation model in one embodiment;

[0061] Figure 4 A schematic diagram of the sound pressure distribution and sound pressure level of an acoustic metamaterial in one embodiment;

[0062] Figure 5 Schematic diagram of low-fidelity sample point distribution of acoustic metamaterial in one embodiment;

[0063] Figure 6 Schematic diagram of high-fidelity sample point distribution of acoustic metamaterials in one embodiment;

[0064] Figure 7 A schematic diagram of a multi-fidelity proxy model space mapping mode in one embodiment;

[0065] Figure 8 It is a structural diagram of a high-dimensional acoustic metamaterial performance prediction system based on spatial mapping multi-fidelity proxy modeling provided by an embodiment of the present invention.

[0066] Fig. 9 It is a box plot showing the performance of the acoustic metamaterial proxy model provided by an embodiment of the present invention as a function of the number of low-fidelity sample points.

[0067] Fig.10 It is a box plot showing the performance of the acoustic metamaterial proxy model provided by an embodiment of the present invention as a function of the number of high-fidelity sample points.

[0068] Fig.11 It is a schematic diagram of the sound pressure distribution and far-field sound pressure under the optimal design of the acoustic metamaterial provided by an embodiment of the present invention.

[0069] Fig.12 It is a schematic diagram of sound pressure distribution and far-field sound pressure under optimal design of acoustic metamaterial based on high-dimensional multi-fidelity proxy model provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0070] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0071] The high-dimensional metamaterial acoustic performance prediction method based on spatial mapping multi-fidelity modeling is as follows:

[0072] 1. Multi-physics modeling and fidelity layering of acoustic metamaterials

[0073] This method aims to predict the performance of acoustic metamaterials. First, the structure is divided into sub-units and its inherent physical properties are extracted as high-dimensional design variables. COMSOL software is used for multi-physics modeling to build high-fidelity and low-fidelity simulation models. Among them, the high-fidelity model provides accurate physical response results with high computational cost; the low-fidelity model provides lower-precision but fast approximate results by simplifying the physical process or reducing the mesh resolution. This fidelity stratification provides the basis for subsequent multi-fidelity modeling.

[0074] 2. Construction of Low-Fidelity Proxy Model

[0075] The maximum and minimum distance sequential sampling method is used to extract representative grid sample points from the design space. The response values ​​of these sample points are calculated through the low-fidelity simulation model to generate a preliminary low-fidelity data set. Based on the Cut-HDMR (high-dimensional model representation) technology, the low-fidelity data is decomposed into nonlinear first-order terms and second-order coupling terms to construct a low-fidelity proxy model. This model can quickly approximate the design space characteristics of acoustic metamaterials and provide low-fidelity prediction capabilities for multi-fidelity modeling.

[0076] 3. High-fidelity sample enhancement and multi-fidelity model fusion

[0077] In order to improve the prediction accuracy of the model, optimized Latin hypercube sampling is used to select representative high-fidelity sample points from the design space. The response values ​​of these sample points are calculated by the high-fidelity simulation model, and the high-fidelity data are compared with the prediction results of the low-fidelity surrogate model. The spatial mapping (SM) method is used to adjust the deviation of the low-fidelity model. Specifically, the high-fidelity data is used to optimize the parameter weights of the low-fidelity surrogate model, and the SM-HDMR multi-fidelity model that combines high-fidelity and low-fidelity information is generated to achieve high-precision prediction capabilities.

[0078] 4. Acoustic metamaterial performance prediction and model evaluation

[0079] Based on the constructed SM-HDMR multi-fidelity model, the target performance of acoustic metamaterials is predicted. The model output includes first-order nonlinear terms and second-order coupling terms, which can intuitively reveal the contribution of design variables to performance and their interactions. By evaluating the model prediction error, its generalization ability in high-dimensional design space is verified. This method effectively reduces the computational cost while maintaining a high prediction accuracy, providing a reliable tool for rapid performance optimization of complex acoustic metamaterials.

[0080] like Figure 1 As shown, an embodiment of the present invention provides a high-dimensional acoustic metamaterial performance prediction method based on spatial mapping multi-fidelity proxy modeling, comprising the following steps:

[0081] S11, determining a prediction target according to the design requirements of the acoustic metamaterial.

[0082] According to the design requirement of designing a combination of inherent physical properties of acoustic metamaterials to modulate the far-field sound pressure level, the far-field sound pressure level at 90° is determined to characterize the influence of metamaterials on sound waves, which is the prediction target.

[0083] S12, subdividing the acoustic metamaterial structure into subunits to determine the high-dimensional design variables contained in the combination of its inherent physical properties.

[0084] The structure and modeling method of the acoustic metamaterial are as follows: Figure 2 As shown in the figure, the acoustic metamaterial structure is divided into 25 subunits along the length direction. Each subunit contains two inherent physical property indicators (ρ, E) including density and Young's modulus. The 50-dimensional design variable x = [x 1 ,x 2 ,…,x 50 ] T , where x 1 , x 2 , …, x 25 Indicates the density of 25 subunits, with a value range of 400 to 2000 kg / m 3 , x 26 , x 27 , …, x 50 represents the Young's modulus of 25 subunits, and its value range is 7.5×10 8 ~13.5×10 8 Pa.

[0085] S13, based on COMSOL software, multi-physics modeling of acoustic metamaterials is performed to construct high / low fidelity numerical simulation models with different computational costs and accuracies.

[0086] Set the fluid domain to water area, background sound velocity c = 1500m / s, fluid density ρ = 1000kg / m 3 The mesh size of the high / low fidelity simulation model is determined according to the simulation time consumption. In this embodiment, for the high-fidelity simulation model, the maximum mesh size of the water medium and barrier area is set to 0.1, with a total of 90,308 meshes, and the maximum mesh size of the metamaterial area is set to 0.02, with a total of 5,150 meshes. Figure 3 (a) shows that a coarser mesh simulation model is used to generate low-fidelity responses, which corresponds to lower cost and accuracy. In the low-fidelity simulation model, the mesh size of the metamaterial remains unchanged, and the mesh size of the water medium and barrier area is increased by 15 times, with a total of 14,122 meshes, as shown in Figure 3(b) The MUMPS (Multifrontal Massively Parallel Sparse) frequency domain solver is used to obtain the sound pressure distribution results. The far-field sound pressure level at 90° is used to characterize the effect of the metamaterial on the sound wave. The high / low fidelity sound pressure distribution and sound pressure level are shown in Figure 4 shown.

[0087] S14, using maximum and minimum distance sequential sampling to obtain grid sample points of each component function, calling the low-fidelity simulation model to obtain the response value of the sample point, and constructing an acoustic metamaterial low-fidelity proxy model based on the Cut-HDMR model.

[0088] Determine the cutting center. The midpoint of the design domain is used as the cutting center of the Cut-HDMR model. In this implementation example, Set to 1200kg / m 3 , All are set to 10.5×10 8 Pa. The low-fidelity simulation model based on the coarse grid obtains the corresponding low-fidelity response In this implementation example, The center cutting point is Figure 5 (a) shown.

[0089] Construct a first-order component function. For variable x i (i=1,2,…,50), select the upper and lower boundary points is the initial sample point, and the corresponding function value is obtained from the low-fidelity simulation model to obtain the training point Constructing the initial first-order component function based on the Kriging model

[0090] Check the linearity of the first-order component function. If the constructed surrogate model By cutting center x 0 ,Right now but is a linear function consisting of only two sample points; conversely, more sample points are obtained by sampling the maximum and minimum distances, such as Figure 5 (b) until the accuracy requirement is met. In this embodiment, a total of 19 nonlinear first-order terms are included: x 1 , x 25 , x 26 , x 27 , x 28 , x 30 , x 31 , x 34 , x 35 , x 37 , x 38 , x39 , x 41 , x 42 , x 45 , x 46 , x 48 , x 49 , x 50 .

[0091] The construction of 50 first-order component functions is completed in sequence, and the low-fidelity proxy model containing only first-order component functions is:

[0092]

[0093] Check the second-order existence. If the corner point The predicted value of Compared with its low-fidelity analog response value f l (x + ) is similar, if the relative error is less than the threshold ε 2 ,Right now: It is considered that the influence of high-order terms can be ignored. Otherwise, continue to construct the second-order component function. The second-order term verification point is as follows Figure 5 (c) In this embodiment, the first-order low-fidelity model predicts True low-fidelity response value f l (x + )=105.4599(db).

[0094] Check and construct second-order component functions. Evaluate any two variables x i and x j If the relative error is greater than the threshold, then the cutting surface x i -x j Based on the maximum and minimum distance sampling, more low-fidelity second-order sample points are obtained, such as Figure 5 As shown in (d), construct the second-order component function In this example, there are 15 second-order terms with significant coupling effects: x 1 -x 25 , x 1 -x 26 , x 1 -x 50 , x 15 -x 45 , x 25 -x 26 , x 25 -x 50 , x 26 -x 51 , x 26 -x 50 , x 30 -x 45 , x31 -x 38 , x 31 -x 45 , x 31 -x 46 , x 38 -x 45 , x 38 -x 46 , x 45 -x 46 The construction of all second-order component functions is completed sequentially, and a more refined low-fidelity proxy model is obtained.

[0095]

[0096] S15, using optimized Latin hypercube sampling to obtain high-fidelity sample points x h , calling the high-fidelity simulation model to calculate the response value f of the sample point h (x h ), calculate the low-fidelity prediction value through the low-fidelity proxy model A SM-HDMR multi-fidelity model was constructed based on the spatial mapping method.

[0097] High fidelity sample point x h Distribution Figure 6 As shown, the sample points uniformly fill the design space. The high-fidelity simulation model is called to calculate the corresponding response value f h (x h ), and the corresponding low-fidelity prediction value is calculated by the constructed Cut-HDMR model Based on the spatial mapping method, high / low fidelity information is fused. The fusion mode is as follows: Figure 7 As shown, As training sample points, the Kriging model is constructed. As input variable, f h (x h ) as the corresponding output data, thereby mapping the low-fidelity output information to the high-fidelity output space, and transforming the "many-to-one" mapping into an easy-to-handle "one-to-one" mapping relationship to eliminate the high-dimensional dilemma in multi-fidelity modeling. The final multi-fidelity model is:

[0098]

[0099] in, is a random process, representing the local fluctuation or error of the objective function. is a regression term, which represents the overall behavior of the target.

[0100] S16, outputting the acoustic metamaterial SM-HDMR model and the nonlinear first-order terms and coupled second-order terms, and evaluating the prediction error of the model. The prediction accuracy of the SM-HDMR model when only the first-order component function is constructed and the second-order component function is included is evaluated using the global error index RAAE and the local error index RRMSE.

[0101] The influence of different numbers of sample points on the prediction accuracy of the SM-HDMR model is analyzed. First, when the number of high-fidelity sample points is fixed at 50, low-fidelity sample points are gradually added during the construction of 19 nonlinear first-order terms and 15 coupled second-order terms, and the error indicators of the SM-HDMR model are calculated, such as Fig.10 As shown in the figure, the horizontal axis is the number of low-fidelity sample points. The first 6 groups only add first-order sample points, and groups 7-16 add second-order sample points. It can be seen that after adding the second-order term (the number of low-fidelity sample points increased from 196 to 212), the error decreased significantly, indicating the important role of adding the second-order term in improving the accuracy of the SM-HDMR model.

[0102] Then, when the number of low-fidelity sample points is fixed at 272, high-fidelity sample points are added in the entire design domain and their number is adjusted from 20 to 70 to explore the effect of the number of high-fidelity samples on the accuracy of the SM-HDMR model, as shown in Figure 2. Fig.11 As shown in the figure, it can be seen that with the increase in the number of high-fidelity samples, the model error index shows a downward trend. When the high-fidelity sample point increases by 40, the model accuracy basically reaches convergence and has good robustness.

[0103] Application example: A relationship model between high-dimensional design variables that characterizes the combination of acoustic performance and physical properties of metamaterials is constructed based on simulation models and experimental data, and acoustic metamaterial structure design is performed based on the proxy model.

[0104] 1) High / Low Fidelity Sample Collection:

[0105] Use existing acoustic metamaterial experimental sound pressure data as high-fidelity sample points, or build a high-fidelity simulation model with fine mesh based on multi-physics field modeling, and perform Latin hypercube sampling in the design domain to obtain high-fidelity sample points; use a simplified coarse mesh model as a low-fidelity simulation model, and obtain low-fidelity sample points of mesh distribution based on nonlinear verification and coupling verification results.

[0106] 2) Construction of high-dimensional multi-fidelity proxy model based on spatial mapping

[0107] A low-fidelity simulation model of acoustic metamaterials is constructed using low-fidelity grid sample points based on the high-dimensional Cut-HDMR model. For uniformly distributed or pre-existing high-fidelity sample points, the corresponding low-fidelity prediction results are calculated by the constructed low-fidelity proxy model and used as input, while the corresponding high-fidelity response values ​​are used as output. The high / low-fidelity data are fused to construct a one-to-one mapping multi-fidelity proxy model as the final prediction model SM-HDMR of acoustic metamaterials.

[0108] 3) Realize acoustic metamaterial structure design based on the constructed proxy model and optimization algorithm

[0109] The constructed SM-HDMR agent model is applied to meta-heuristic algorithms such as genetic algorithm and particle swarm algorithm. For potential design points in the optimization process, the constructed agent model is directly called to obtain the prediction results of its acoustic performance, and the final optimal design result is obtained in the iteration.

[0110] 4) Test the performance of the optimal structure through experiments or high-fidelity simulation models.

[0111] The present invention is based on the high / low fidelity model with different grids constructed by COMSOL software. Figure 3 As shown in (a) and (c), the unit division of the acoustic metasurface is as follows Figure 3 (b) and (d). The high / low fidelity response results at the center point are shown as Figure 4 As shown, the 90° far-field sound pressure is taken as the prediction target value.

[0112] According to the sampling method in the proposed multi-fidelity proxy model, high and low fidelity sampling is performed, where low-fidelity sample points are distributed in a grid and high-fidelity sample points are randomly distributed. The proposed acoustic metamaterial SM-HDMR proxy model is constructed, and the mapping relationship between the constructed low-fidelity proxy model output and the high-fidelity model output space is as follows: Fig.11 shown.

[0113] The prediction error of the SM-HDMR proxy model under different numbers of training sample points is as follows: Figure 9-10 As shown in the figure, with the addition of low-fidelity sample points of the second-order terms, the model accuracy shows obvious performance improvement, and the introduction of the second-order coupling terms significantly improves the prediction accuracy of the acoustic metamaterial SM-HDRM model; in addition, with the addition of high-fidelity sample points, the performance of the model, that is, the robustness, also shows an improving trend and gradually converges.

[0114] Taking the optimization of acoustic metamaterial structure based on genetic algorithm as an example, the constructed SM-HDMR agent model is called in the optimization process to obtain the performance prediction value of the intermediate solution, and finally a set of optimal acoustic metamaterial design results are obtained as shown in Table 1, where the units of the first 25 variables are kg / m 3 , the unit of the last 25 variables is 10 8 Pa, the corresponding far-field sound pressure optimization result is 103.1967 (db), and the actual far-field sound pressure is 103.2252 (db). The obtained optimized design variables are input into the high-fidelity simulation model as a combination of physical parameters to obtain the corresponding far-field sound pressure distribution and far-field sound pressure level. Fig.12 shown.

[0115] Table 1 Optimal acoustic metamaterial design results

[0116]

[0117] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. It can be understood by a person of ordinary skill in the art that the above-mentioned devices and methods can be implemented using computer executable instructions and / or contained in a processor control code, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. Such code is provided on the carrier medium. The device and its modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, and can also be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0118] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A method for predicting acoustic performance of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling, characterized in that: The following steps are involved: Step 1: Determine the prediction target according to the design requirements of acoustic metamaterials; Step 2: Divide the acoustic metamaterial structure into sub-units to determine the high-dimensional design variables contained in its inherent physical property combination; Step 3: Perform multi-physics modeling of acoustic metamaterials based on COMSOL software and construct high / low fidelity numerical simulation models with different computational costs and accuracies; Step 4: Use the maximum and minimum distance sequential sampling to obtain the grid sample points x of each component function l , calling the low-fidelity simulation model to obtain the response value of the sample point, and constructing the acoustic metamaterial low-fidelity proxy model based on the Cut-HDMR model Step 5: Use optimized Latin hypercube sampling to obtain high-fidelity sample points x h , calling the high-fidelity simulation model to calculate the response value f of the sample point h (x h ), calculate the low-fidelity prediction value through the low-fidelity proxy model A SM-HDMR multi-fidelity model was constructed based on the spatial mapping method; Step 6: Output the acoustic metamaterial SM-HDMR model and the nonlinear first-order terms and coupled second-order terms, and evaluate the prediction error of the model.

2. The method for predicting acoustic performance of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling according to claim 1, characterized in that: According to the design requirements of acoustic metamaterials, the prediction objectives are determined, including: According to the design requirement of designing a combination of inherent physical properties of acoustic metamaterials to modulate the far-field sound pressure level, the far-field sound pressure level at 90° is determined to characterize the influence of metamaterials on sound waves, which is the prediction target.

3. The method for predicting acoustic performance of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling according to claim 1, characterized in that: The acoustic metamaterial structure is divided into subunits to determine the design variables x contained in its inherent physical property combination, including: The acoustic metamaterial structure is divided into 25 subunits along the length direction. The physical properties of each subunit are characterized by the two indicators of density ρ and Young's modulus E. The 50 design variables x=[x1,x2,…,x 50 ] T , where x1, x2, …, x 25 represents the density of 25 subunits, x 26 , x 27 , …, x 50 represents the Young's modulus of 25 subunits.

4. The method for predicting acoustic performance of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling according to claim 1, characterized in that: Use the maximum and minimum distance sequential sampling to obtain the grid sample points x of each component function l , calling the low-fidelity simulation model to obtain the response value of the sample point, and constructing the acoustic metamaterial low-fidelity proxy model based on the Cut-HDMR model include: (1) Determine the cutting center; select the midpoint of the design domain as the cutting center of the Cut-HDMR model And based on the coarse grid low-fidelity simulation model to obtain the corresponding low-fidelity response (2) Construct a first-order component function; for variable x i (i=1,2,…,50), select the upper and lower boundary points x i - and is the initial sample point, and the corresponding function value is obtained from the low-fidelity simulation model to obtain the training point and Constructing the initial first-order component function based on the Kriging model (3) Check the linearity of the first-order component function; if the constructed surrogate model By cutting the center x0, that is but is a linear function consisting of only two sample points; conversely, more sample points are obtained through maximum and minimum distance sampling until the accuracy requirement is met; the construction of 50 first-order component functions is completed in sequence, and the low-fidelity proxy model containing only first-order component functions is: (4) Check the second-order existence; if the corner point The predicted value of If it is similar to its low-fidelity simulation response value, the influence of the high-order term is considered to be negligible, otherwise, continue to construct the second-order component function; (5) Check and construct the second-order component function; evaluate any two variables x i and x j If the relative error is greater than the threshold ε2, that is: Then on the cutting surface x i -x j Based on the maximum and minimum distance sampling, more low-fidelity second-order sample points are obtained to construct the second-order component function The construction of all second-order component functions is completed in sequence, and a more refined low-fidelity proxy model is obtained:

5. The method for predicting acoustic performance of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling according to claim 1, characterized in that: Use optimized Latin hypercube sampling to obtain high-fidelity sample points x h , calling the high-fidelity simulation model to calculate the response value f of the sample point h (x h ), calculate the low-fidelity prediction value through the low-fidelity proxy model The SM-HDMR multi-fidelity model is constructed based on the spatial mapping method, including: Perform optimized Latin hypercube sampling in the entire design domain, call the high-fidelity simulation model to calculate the corresponding response value, and obtain high-fidelity sample points [x h ,f h (x h )]; the corresponding low-fidelity prediction value is calculated by the constructed Cut-HDMR model Will As training sample points, the Kriging model is constructed. As input variable, f h (x h ) as the corresponding output data, thereby mapping the low-fidelity output information to the high-fidelity output space, and transforming the "many-to-one" mapping into an easy-to-handle "one-to-one" mapping relationship to eliminate the high-dimensional dilemma in multi-fidelity modeling. The final multi-fidelity model is: in, is a random process, representing the local fluctuation or error of the objective function. is a regression term, and the overall behavior of the target is represented by a linear combination of p regression functions: where h(·) consists of the regression function and β is the regression coefficient.

6. The method for predicting high-dimensional metamaterial acoustic performance based on spatial mapping multi-fidelity modeling according to claim 1, characterized in that: Output the acoustic metamaterial SM-HDMR model and nonlinear first-order terms and coupled second-order terms, and evaluate the prediction error of the model, including: The prediction error of the constructed SM-HDMR model is evaluated using the global error index relative mean absolute error (RAAE) and the local error index relative root mean square error (RRMSE), where: Among them, n is the number of test sample points, y i Represents the actual response value of the test sample point, is the corresponding SM-HDMR model prediction value, STD represents the standard deviation; The prediction error of the constructed SM-HDMR model is evaluated, the nonlinear first-order terms and coupled second-order terms are derived, and guidance is provided for adding high / low-fidelity samples of acoustic metamaterials. When only the first-order component function and the second-order component function are constructed in step 4, the prediction accuracy of the SM-HDMR model in the corresponding cases is evaluated using error indicators, the accuracy improvement ratio and the number of sample points are obtained, and the corresponding nonlinear first-order terms and second-order terms with non-negligible coupling effects are provided, providing guidance for adding high / low-fidelity samples of acoustic metamaterials.

7. A high-dimensional metamaterial acoustic performance prediction system based on spatial mapping multi-fidelity modeling according to any one of claims 1 to 6, characterized in that: include: Prediction target determination module: determines the prediction target according to the design requirements of acoustic metamaterials; Subunit division module: divide the acoustic metamaterial structure into subunits to determine the high-dimensional design variables contained in its inherent physical property combination; Numerical simulation model building module: Based on COMSOL software, multi-physics modeling of acoustic metamaterials is carried out to build high / low fidelity numerical simulation models with different computational costs and accuracies; Low-fidelity proxy model construction module: Use maximum and minimum distance sequential sampling to obtain the grid sample points x of each component function l , calling the low-fidelity simulation model to obtain the response value of the sample point, and constructing the acoustic metamaterial low-fidelity proxy model based on the Cut-HDMR model Multi-fidelity model building module: Use optimized Latin hypercube sampling to obtain high-fidelity sample points x h , calling the high-fidelity simulation model to calculate the response value f of the sample point h (x h ), calculate the low-fidelity prediction value through the low-fidelity proxy model A SM-HDMR multi-fidelity model was constructed based on the spatial mapping method; Model prediction error evaluation module: outputs the acoustic metamaterial SM-HDMR model and nonlinear first-order terms and coupled second-order terms, and evaluates the model prediction error.

8. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the high-dimensional metamaterial acoustic performance prediction method based on spatial mapping multi-fidelity modeling as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to perform the steps of the method for predicting acoustic performance of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling as described in any one of claims 1 to 6.

10. An information data processing terminal, characterized in that: The information data processing terminal includes the high-dimensional metamaterial acoustic performance prediction system based on spatial mapping multi-fidelity modeling as described in claim 7.

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