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

Abstract

This invention belongs to, but is not limited to, the field of acoustic metamaterial performance prediction technology. It discloses a method for predicting the acoustic performance of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling. It obtains high / low fidelity training sample points by combining acoustic metamaterial finite element models with different computational costs and accuracies. Based on the Cut-HDMR model, a low-fidelity surrogate model is constructed to capture the overall trend of high-dimensional acoustic metamaterial performance changes. The high-dimensional problem is decomposed into the superposition of one-dimensional and two-dimensional component functions. The prediction of the low-fidelity model is used as a priori and mapped to the high-fidelity output space to construct a multi-fidelity model. The high-dimensional "many-to-one" mapping is transformed into an easily processed "one-to-one" mapping to eliminate the high-dimensional dilemma in multi-fidelity modeling and to accurately and efficiently predict the performance of high-dimensional acoustic metamaterials.

Description

Technical Field

[0001] This invention belongs to, but is not limited to, the field of acoustic metamaterial performance prediction technology, and particularly relates to a method and system for predicting the acoustic performance of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling. Background Technology

[0002] Acoustic metamaterials are a class of artificial layered structures composed of subwavelength microstructural units. Based on the generalized Snell's law, the geometric arrangement and physical properties of these microstructures are designed to control acoustic / elastic waves, achieving extraordinary physical properties such as negative mass, negative elastic modulus, and subwavelength bandgap. Their macroscopic properties depend on the specially designed internal structure, rather than the intrinsic properties of the material. Compared to traditional metamaterials, which are large in size, expensive to manufacture, and have narrow operating bandwidths, acoustic metamaterials offer advantages such as ultrathinness and flexible control over sound waves. Utilizing the anomalous reflection and refraction characteristics of acoustic metamaterials for sound waves, they hold broad application prospects in wavefront manipulation, acoustic imaging, and acoustic cloaking.

[0003] To achieve free control of sound waves, specific metasurface structures need to be designed. However, acoustic metamaterials are composed of numerous unit cells, and their performance prediction often involves many design parameters, such as the material properties and geometry of each unit cell. These high-dimensional parameters significantly increase the computational cost of traditional numerical simulation-based metamaterial design processes and may lead to the "curse of dimensionality." Some dimensionality reduction strategies and surrogate modeling techniques based on auxiliary information have been proposed to address the dilemma of high-dimensional modeling. However, these methods are still limited by sparse and expensive high-fidelity sample points in terms of sample collection and pattern fusion. Although high-dimensional model representation (HDMR) methods can effectively decompose high-dimensional problems and achieve efficient modeling, there are still gaps in handling multi-fidelity data.

[0004] In the field of acoustic metamaterial performance prediction, existing technologies primarily rely on high-fidelity numerical simulation models for performance analysis. However, while high-fidelity models are accurate, they are computationally extremely expensive, especially when dealing with complex multiphysics interactions and high-dimensional design variables, resulting in slow simulation speeds that fail to meet the needs of industrial design and optimization. Furthermore, while low-fidelity models are computationally fast, their predictive accuracy is insufficient to meet the requirements of performance evaluation on its own. The lack of an effective method to integrate high-fidelity and low-fidelity models in current technologies leads to inefficiencies in acoustic metamaterial performance prediction in industrial applications, hindering its large-scale deployment. Summary of the Invention

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

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

[0007] Step 1: Determine the prediction target based on the design requirements of the acoustic metamaterial;

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

[0009] Step 3: Multiphysics modeling of acoustic metamaterials using COMSOL software to construct high / low fidelity numerical simulation models with different computational costs and accuracies;

[0010] Step 4: Use maximum-minimum distance sequential sampling to obtain grid sample points x for each component function. l The response value f of the sample point is obtained by calling the low-fidelity simulation model. l (x l A low-fidelity surrogate model for acoustic metamaterials was constructed based on the Cut-HDMR model.

[0011] Step 5: Obtain high-fidelity sample points x using optimized Latin hypercube sampling. h The high-fidelity simulation model is invoked to calculate the response value f of the sample points. h (x h The low-fidelity predicted value is calculated using the low-fidelity proxy model. Constructing a multi-fidelity SM-HDMR model based on spatial mapping method;

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

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

[0014] Based on the design requirements of modulating far-field sound pressure level by combining the inherent physical properties of acoustic metamaterials, the influence of metamaterials on sound waves is characterized by the far-field sound pressure level at 90°, which is the prediction target.

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

[0016] The acoustic metamaterial structure is divided into m sub-units along its length. The physical properties of each sub-unit are characterized by two indices: density ρ and Young's modulus E. The 2m design variables included in the combination of inherent physical properties of the acoustic metamaterial are determined. Let dimension D = 2m, then x = [x1, x2, ..., xm].D ] T Where x1, x2, ..., x m Let x represent the density of m sub-units. m+1 x m+2 , ..., x 2m This represents the Young's modulus of m sub-units.

[0017] Furthermore, by employing maximum-minimum distance sequential sampling, grid sample points x for each component function are obtained. l The response value f of the sample point is obtained by calling the low-fidelity simulation model. l (x l A low-fidelity surrogate model for acoustic metamaterials was constructed 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. The corresponding low-fidelity response was obtained based on the low-fidelity simulation model with a coarse mesh.

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

[0020] (3) Check the linearity of the first-order component functions; if the constructed surrogate model By cutting through the center x0, that is but For a linear function consisting of only two sample points, the method proceeds by sampling with maximum and minimum distances to obtain more sample points until the accuracy requirement is met; this process is repeated for D first-order component functions. The construction thus yields a low-fidelity surrogate model containing only first-order component functions:

[0021]

[0022] in, The zeroth-order constant, i.e., the low-fidelity response value at the cut-off point, is the first-order component function. The variable is x i The training sample points of the i-th component Build, This means that all variables except the i-th dimension have the same value as x0. s i The number of sample points used for the corresponding component.

[0023] (4) Check for second-order existence; if the corner point Predicted value If the response value is similar to that of the low-fidelity simulation, the influence of higher-order terms is considered negligible; otherwise, the second-order component function is constructed.

[0024] (5) Examine and construct the second-order component functions; evaluate any two variables x i and x j The coupling effect, if the relative error is greater than the threshold ε2, that is: Then on the cutting surface x i -x j The inner part obtains more low-fidelity second-order sample points based on maximum and minimum distance sampling, and constructs a second-order component function. The construction of all second-order component functions is completed sequentially, resulting in a more refined low-fidelity proxy model:

[0025]

[0026] Among them, the second-order terms with coupling effects Includes two-dimensional variable x i and x j From the corresponding training sample points Build, This means that all variables except for the i-th and j-th dimensions have the same value as x0. s ij The number of sample points used for the corresponding component.

[0027] Furthermore, optimized Latin hypercube sampling is employed to obtain high-fidelity sample points x. h The high-fidelity simulation model is invoked to calculate the response value f of the sample points. h (x h The low-fidelity predicted value is calculated using the low-fidelity proxy model. A multi-fidelity SM-HDMR model is constructed based on the spatial mapping method, including:

[0028] Optimized Latin hypercube sampling was performed across the entire design domain, and the corresponding response values ​​were calculated using a high-fidelity simulation model to obtain high-fidelity sample points [x]. h ,f h (x h The corresponding low-fidelity predicted values ​​are calculated using the constructed Cut-HDMR model. Will The Kriging model is constructed using the training sample points, where As an input variable, fh (x h This data serves as the corresponding output data, mapping low-fidelity output information to a high-fidelity output space. This transforms the "many-to-one" mapping into a more easily processed "one-to-one" mapping, thus eliminating the high-dimensionality dilemma in multi-fidelity modeling. The final multi-fidelity model is:

[0029]

[0030] in, For stochastic processes, it represents local fluctuations or errors in the objective function. As the regression term, the overall behavior of the target is represented by a linear combination of p regression functions:

[0031]

[0032] Where h(·) is composed of regression functions, and β is the regression coefficient.

[0033] Furthermore, the acoustic metamaterial SM-HDMR model, along with its nonlinear first-order and coupled second-order terms, is 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 to the mean absolute error (RAAE) and the local error index relative to the root mean square error (RRMSE), where:

[0035]

[0036] Where n is the number of test sample points, y i This 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, and nonlinear first-order terms and coupled second-order terms are derived to provide guidance for adding high / low fidelity samples for acoustic metamaterials. When only first-order component functions are constructed in step four, and when second-order component functions are included, the prediction accuracy of the SM-HDMR model under the corresponding conditions is evaluated using error indices to obtain the accuracy improvement ratio and the number of sample points. The corresponding nonlinear first-order terms and second-order terms with non-negligible coupling effects are also provided to guide the addition of high / low fidelity samples for acoustic metamaterials.

[0038] Another objective of this invention is to provide 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 based on the design requirements of the acoustic metamaterial;

[0040] Sub-unit partitioning module: Divides the acoustic metamaterial structure into sub-units to determine the high-dimensional design variables contained in the combination of its inherent physical properties;

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

[0042] Low-fidelity surrogate model construction module: Employs maximum-minimum distance sequential sampling to obtain grid sample points x for each component function. l The response values ​​of the sample points are obtained by calling the low-fidelity simulation model, and a low-fidelity surrogate model of the acoustic metamaterial is constructed based on the Cut-HDMR model.

[0043] SM-HDMR multi-fidelity model construction module: High-fidelity sample points x are obtained by optimizing Latin hypercube sampling. h The high-fidelity simulation model is invoked to calculate the response value f of the sample points. h (x h The low-fidelity predicted value is calculated using the low-fidelity proxy model. Constructing a multi-fidelity SM-HDMR model based on 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 prediction error of the model.

[0045] Another object of the present invention is to provide a computer device, the computer device including a memory and a processor, the memory storing a computer program, and when the computer program is executed by the processor, causing the processor to perform the steps of the high-dimensional metamaterial acoustic performance prediction method 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, causes the processor to perform the steps of the high-dimensional metamaterial acoustic performance prediction method based on spatial mapping multi-fidelity modeling.

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

[0048] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0049] First, this invention provides a method for predicting the performance of high-dimensional acoustic metamaterials based on spatial mapping multi-fidelity proxy modeling. It combines acoustic metamaterial finite element models with different computational costs and accuracies to obtain high / low fidelity training sample points. Based on the Cut-HDMR model, a low-fidelity proxy model is constructed to capture the overall trend of high-dimensional acoustic metamaterial performance changes. The high-dimensional problem is decomposed into the superposition of one-dimensional and two-dimensional component functions. The prediction of the low-fidelity model is used as a priori and mapped to the high-fidelity output space to construct a multi-fidelity model. This transforms the high-dimensional "many-to-one" mapping into an easily processed "one-to-one" mapping, thereby eliminating the high-dimensional dilemma in multi-fidelity modeling and accurately and efficiently predicting the performance of high-dimensional acoustic metamaterials.

[0050] Secondly, as supporting evidence of the inventiveness of this invention, it is also reflected in the following important aspects:

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

[0052] The acoustic metamaterials studied in this invention possess extraordinary physical properties such as negative mass, negative elastic modulus, and subwavelength bandgap, making them crucial for wavefront manipulation, acoustic imaging, and acoustic stealth, and thus possessing significant military application value. Developing and researching multi-fidelity surrogate modeling methods to effectively predict the performance of high-dimensional acoustic metamaterials can significantly reduce the number of expensive numerical simulations required while accurately characterizing performance changes. This greatly alleviates the computational cost of acoustic metamaterial design processes that rely on repetitive performance calculations, and forms an important foundation for optimizing acoustic metamaterial structural design.

[0053] (2) The technical solution of this invention fills a technical gap in the industry both domestically and internationally:

[0054] This invention utilizes high-dimensional surrogate modeling technology to construct a predictive model that characterizes the relationship between high-dimensional design variables, including combinations of acoustic metamaterial properties and their physical properties. The HDMR-based decomposition strategy effectively avoids the "curse of dimensionality" in the metamaterial design process. Based on a multi-fidelity modeling method, it uses a large number of low-fidelity sample points to capture the overall trend of high-dimensional acoustic metamaterial performance changes, while using a small number of high-fidelity sample points to ensure the prediction accuracy of the surrogate model. Furthermore, based on the concept of spatial mapping, it alleviates the burden of high-dimensional modeling while integrating high / low-fidelity sample information with different accuracies and time costs. Compared to single-precision surrogate modeling methods, this further effectively balances modeling accuracy and efficiency, achieving accurate and efficient prediction of metamaterial acoustic properties.

[0055] Third, this invention cleverly combines the accuracy advantages of high-fidelity models with the computational efficiency of low-fidelity models by introducing a spatial mapping-based multi-fidelity modeling technique, thus solving the problem of balancing computational cost and prediction accuracy in existing technologies. By constructing an SM-HDMR (Spatial Mapping High-Dimensional Model Representation) multi-fidelity model, this invention significantly reduces the computational cost of complex acoustic metamaterials while maintaining high-precision prediction capabilities. This method can quickly analyze the contribution of multidimensional design variables to acoustic performance, providing a more economical and efficient solution for industrial design.

[0056] Compared to existing technologies, this invention demonstrates significant technological advancements in industrial applications. First, by optimizing Latin hypercube sampling and spatial mapping techniques, the demand for high-fidelity data is drastically reduced, and computation time is shortened by over 50%, significantly improving the model's industrial applicability. Second, 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 enabling more efficient parameter tuning and structural optimization. Furthermore, this invention solves the performance prediction problem under high-dimensional design variables and complex physical field coupling conditions, expanding the application scope of acoustic metamaterials in precision industries.

[0057] This invention provides a rapid, accurate, and low-cost solution for predicting and optimizing the performance of acoustic metamaterials, significantly improving the feasibility of complex design schemes. Its applications in noise reduction devices, sound wave control, and medical acoustic imaging will accelerate the development and industrialization of related technologies. Furthermore, based on the efficiency of its multi-fidelity modeling method, this invention can be widely applied to industries such as aerospace, automotive manufacturing, and architectural acoustics, providing technical support for the intelligent design and industrial upgrading of acoustic materials, and injecting new momentum into the efficient development of modern industry. Attached Figure Description

[0058] Figure 1 This is a flowchart of the high-dimensional acoustic metamaterial performance prediction method based on spatial mapping multi-fidelity proxy modeling provided in the embodiments of the present invention;

[0059] Figure 2 This is a schematic diagram of the acoustic metamaterial structure and modeling in one embodiment;

[0060] Figure 3 This is a schematic diagram of the mesh generation of an acoustic metamaterial simulation model in one embodiment;

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

[0062] Figure 5 This is a schematic diagram of the low-fidelity sample point distribution of an acoustic metamaterial in one embodiment.

[0063] Figure 6 This is a schematic diagram of the high-fidelity sample point distribution of acoustic metamaterials in one embodiment.

[0064] Figure 7 This is a schematic diagram of the spatial mapping pattern of a multi-fidelity proxy model in one embodiment;

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

[0066] Figure 9 This is a box plot showing the performance of the acoustic metamaterial surrogate model provided in this embodiment of the invention as a function of the number of low-fidelity sample points.

[0067] Figure 10 This is a box plot showing the performance of the acoustic metamaterial surrogate model provided in this embodiment of the invention as a function of the number of high-fidelity sample points.

[0068] Figure 11 This is a schematic diagram of the sound pressure distribution and far-field sound pressure under the optimal design of acoustic metamaterials provided in the embodiments of the present invention.

[0069] Figure 12 This is a schematic diagram of sound pressure distribution and far-field sound pressure under the optimal design of acoustic metamaterials based on a high-dimensional multi-fidelity proxy model, provided in an embodiment of the present invention. Detailed Implementation

[0070] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0071] The specific method for predicting the acoustic performance of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling is as follows:

[0072] 1. Multiphysics Modeling and Fidelity Layering of Acoustic Metamaterials

[0073] This method aims to predict the performance of acoustic metamaterials. First, it divides the structure into sub-units and extracts the inherent physical properties as high-dimensional design variables. Multiphysics modeling is then performed using COMSOL software, constructing both high-fidelity and low-fidelity simulation models. The high-fidelity model provides accurate physical response results but has higher computational costs; the low-fidelity model, by simplifying the physical processes or reducing mesh resolution, provides lower-precision but faster approximations. This hierarchical approach to fidelity provides the foundation for subsequent multi-fidelity modeling.

[0074] 2. Construction of a low-fidelity proxy model

[0075] A maximum-minimum distance sequential sampling method is employed to extract representative grid sample points from the design space. The response values ​​of these sample points are then calculated using a low-fidelity simulation model to generate a preliminary low-fidelity dataset. Based on 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 surrogate model. This model can quickly approximate the design space characteristics of acoustic metamaterials, providing low-fidelity prediction capabilities for multi-fidelity modeling.

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

[0077] To improve the prediction accuracy of the model, optimized Latin hypercube sampling is employed, selecting representative high-fidelity sample points from the design space. The response values ​​of these sample points are calculated using a high-fidelity simulation model. The prediction results of the high-fidelity data are compared with those of the low-fidelity surrogate model, and the spatial mapping (SM) method is used to adjust the bias of the low-fidelity model. Specifically, the parameter weights of the low-fidelity surrogate model are optimized using high-fidelity data to generate an SM-HDMR multi-fidelity model that combines high- and low-fidelity information, achieving high-precision prediction capabilities.

[0078] 4. Prediction and Model Evaluation of Acoustic Metamaterial Properties

[0079] Based on the constructed SM-HDMR multifidelity 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 interaction. By evaluating the model's prediction error, its generalization ability in high-dimensional design spaces is verified. This method effectively reduces computational costs while maintaining high prediction accuracy, providing a reliable tool for rapid performance optimization of complex acoustic metamaterials.

[0080] like Figure 1 As shown, this embodiment of the invention provides a method for predicting the properties of high-dimensional acoustic metamaterials based on spatial mapping multi-fidelity proxy modeling, comprising the following steps:

[0081] S11, determine the prediction target based on the design requirements of the acoustic metamaterial.

[0082] Based on the design requirements of modulating far-field sound pressure level by combining the inherent physical properties of acoustic metamaterials, the influence of metamaterials on sound waves is characterized by the far-field sound pressure level at 90°, which is the prediction target.

[0083] S12, divide the acoustic metamaterial structure into sub-units and 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 2As shown, the acoustic metamaterial structure is divided into 25 sub-units along its length. Each sub-unit contains two inherent physical properties (ρ, E) including density and Young's modulus. A 50-dimensional design variable x = [x1, x2, ..., x] is then determined. 50 ] T Where x1, x2, ..., x 25 This represents the density of 25 sub-units, with values ​​ranging from 400 to 2000 kg / m³. 3 x 26 x 27 , ..., x 50 This represents the Young's modulus of 25 sub-units, with a value range of 7.5 × 10⁻⁶. 8 ~13.5×10 8 Pa.

[0085] S13 uses COMSOL software to perform multiphysics modeling of acoustic metamaterials, constructing high / low fidelity numerical simulation models with different computational costs and accuracies.

[0086] The fluid domain is set as a body of water, the background sound velocity is c = 1500 m / s, and the fluid density is ρ = 1000 kg / m³. 3 The mesh size for high / low fidelity simulation models is determined based on the simulation time consumption. In this implementation example, for the high-fidelity simulation model, the maximum mesh size for the water medium and barrier regions is set to 0.1, totaling 90,308 meshes, while the maximum mesh size for the metamaterial region is set to 0.02, totaling 5,150 meshes. Figure 3 As shown in (a), a coarser mesh simulation model is used to generate a low-fidelity response, corresponding to lower cost and accuracy. In the low-fidelity simulation model, the mesh size of the metamaterial remains unchanged, while the mesh size of the aqueous medium and barrier regions is increased by 15 times, resulting in a total of 14,122 meshes, as shown in (a). Figure 3 As shown in (b), the sound pressure distribution results were obtained using the MUMPS (Multifrontal Massively Parallel Sparse) frequency domain solver. The far-field sound pressure level at 90° was used to characterize the influence of the metamaterial on the sound waves. The high / low fidelity sound pressure distribution and sound pressure level are shown in Figure 1. Figure 4 As shown.

[0087] S14. Using maximum and minimum distance sequential sampling, grid sample points of each component function are obtained. The response values ​​of the sample points are obtained by calling the low-fidelity simulation model. An acoustic metamaterial low-fidelity proxy model is constructed based on the Cut-HDMR model.

[0088] Determine the cutting center. Use the midpoint of the design domain as the cutting center for the Cut-HDMR model. In this implementation example Set to 1200kg / m3 , All are set to 10.5×10 8 Pa. The corresponding low-fidelity response is obtained based on a low-fidelity simulation model with a coarse mesh. In this implementation example Center cutting point as Figure 5 As shown in (a).

[0089] Construct first-order component functions for the variable x. i (i = 1, 2, ..., 50), select the upper and lower boundary points. Using the initial sample points, the corresponding function values ​​are obtained from the low-fidelity simulation model to obtain training points. Constructing initial first-order component functions based on the Kriging model

[0090] Check the linearity of the first-order component functions. If the constructed surrogate model... By cutting through the center x0, that is but A linear function consisting of only two sample points; conversely, more sample points are obtained through maximum and minimum distance sampling, such as... Figure 5 As shown in (b), this continues until the accuracy requirement is met. In this embodiment, a total of 19 nonlinear first-order terms are included: x1, x... 25 x 26 x 27 x 28 x 30 x 31 x 34 x 35 x 37 x 38 x 39 x 41 x 42 x 45 x 46 x 48 x 49 x 50 .

[0091] After constructing 50 first-order component functions sequentially, the low-fidelity surrogate model containing only first-order component functions is as follows:

[0092]

[0093] Check for second-order existence. If the corner point... Predicted value Its low-fidelity simulated response value f l (x + If the relative error is similar to the threshold ε2, that is: If the influence of higher-order terms is considered negligible, then the second-order component functions are constructed. The verification points for the second-order terms are as follows: Figure 5 As shown in (c). In this embodiment, the first-order low-fidelity model predicts... True low-fidelity response value f l (x + = 105.4599 (db).

[0094] Examine and construct the second-order component functions. Evaluate any two variables x. i and x j The coupling effect, if the relative error is greater than the threshold, then on the cutting surface x i -x j Internally, more low-fidelity second-order sample points are obtained based on maximum-minimum distance sampling, such as... Figure 5 As shown in (d), construct the second-order component function. In this embodiment, there are a total of 15 second-order terms with significant coupling effects: x1-x 25 ,x1-x 26 ,x1-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 x 31 -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, resulting in a more refined low-fidelity proxy model.

[0095]

[0096] S15, high-fidelity sample points x are obtained by using optimized Latin hypercube sampling. h The high-fidelity simulation model is invoked to calculate the response value f of the sample points. h (x h The low-fidelity predicted value is calculated using the low-fidelity proxy model. A multi-fidelity SM-HDMR model is constructed based on the spatial mapping method.

[0097] High-fidelity sample points x h Distribution as Figure 6 As shown, the sample points uniformly fill the design space. The corresponding response value f is calculated using a high-fidelity simulation model. h (x h The corresponding low-fidelity predicted values ​​are calculated using the constructed Cut-HDMR model. Based on the spatial mapping method, high / low fidelity information is fused, and the fusion mode is as follows: Figure 7 As shown, it is about to The Kriging model is constructed using the training sample points, where As an input variable, f h (x h This data serves as the corresponding output data, mapping low-fidelity output information to a high-fidelity output space. This transforms the "many-to-one" mapping into a more easily processed "one-to-one" mapping, thus eliminating the high-dimensionality dilemma in multi-fidelity modeling. The final multi-fidelity model is:

[0098]

[0099] in, For stochastic processes, it represents local fluctuations or errors in the objective function. The regression term represents the overall behavior of the target.

[0100] S16 outputs the acoustic metamaterial SM-HDMR model, along with its nonlinear first-order and coupled second-order terms, and evaluates the model's prediction error. The prediction accuracy of the SM-HDMR model is evaluated using the global error index RAAE and the local error index RRMSE, with and without first-order component functions.

[0101] The impact of different sample point numbers on the prediction accuracy of the SM-HDMR model was analyzed. First, with a fixed number of high-fidelity sample points of 50, low-fidelity sample points were gradually added during the construction of 19 nonlinear first-order terms and 15 coupled second-order terms. The error index of the SM-HDMR model was then calculated. Figure 10 As shown, the horizontal axis represents the number of low-fidelity sample points. The first 6 groups only added first-order term sample points, while groups 7-16 show the results with second-order term sample points added. 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, with the low-fidelity sample points fixed at 272, high-fidelity sample points were added across the entire design domain, increasing their number from 20 to 70, to investigate the impact of the number of high-fidelity samples on the accuracy of the SM-HDMR model. Figure 11 As shown, the model error index decreases as the number of high-fidelity samples increases. When the number of high-fidelity sample points increases to 40, the model accuracy basically converges and exhibits good robustness.

[0103] Application Example: Based on simulation models and experimental data, a high-dimensional design variable relationship model is constructed to characterize the combination of acoustic properties and physical properties of metamaterials, and acoustic metamaterial structure design is carried out based on the surrogate model.

[0104] 1) High / low fidelity sample collection:

[0105] Existing acoustic metamaterial experimental sound pressure data can be used as high-fidelity sample points, or a high-fidelity simulation model with a fine mesh can be constructed based on multiphysics modeling, and high-fidelity sample points can be obtained by Latin hypercube sampling within the design domain; a simplified coarse mesh model can be used as a low-fidelity simulation model, and low-fidelity sample points with mesh distribution can be obtained based on the results of nonlinear verification and coupling verification.

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

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

[0108] 3) Design of acoustic metamaterial structures based on the constructed surrogate model and optimization algorithm.

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

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

[0111] This invention is based on high / low fidelity models with different meshes constructed using COMSOL software, such as... Figure 3As shown in (a) and (c), the unit cell division of the acoustic metasurface is as follows: Figure 3 As shown in (b) and (d), the high / low fidelity response results at the center point are as follows. Figure 4 As shown, the 90° far-field sound pressure is used as the prediction target value.

[0112] High- and low-fidelity sampling is performed according to the sampling method in the proposed multi-fidelity surrogate model. Low-fidelity sample points are distributed in a grid pattern, while high-fidelity sample points are randomly distributed. The proposed acoustic metamaterial SM-HDMR surrogate model is constructed, and the mapping relationship between the output of the constructed low-fidelity surrogate model and the output space of the high-fidelity model is as follows: Figure 11 As shown.

[0113] The prediction errors of the SM-HDMR surrogate model under different numbers of training sample points are as follows: Figures 9-10 As shown, with the addition of low-fidelity sample points of the second-order term, the model accuracy shows a significant performance improvement, and the introduction of the second-order coupling term significantly improves the prediction accuracy of the acoustic metamaterial SM-HDRM model; in addition, with the addition of high-fidelity sample points, the model's performance, i.e., robustness, also shows an improving trend and gradually converges.

[0114] Taking the optimization of acoustic metamaterial structures based on genetic algorithms as an example, the constructed SM-HDMR surrogate model is called during the optimization process to obtain the performance prediction values ​​of intermediate solutions. Finally, a set of optimal acoustic metamaterial design results are obtained, as shown in Table 1. The unit of the first 25 variables is kg / m³. 3 The units for the last 25 variables are 10. 8 The corresponding far-field sound pressure level (SPL) is 103.1967 dB, while the actual far-field SPL is 103.2252 dB. The obtained optimized design variables are input as physical parameter combinations into a high-fidelity simulation model to obtain the corresponding far-field SPL distribution and far-field SPL level, as shown below. Figure 12 As shown.

[0115] Table 1 Optimal acoustic metamaterial design results

[0116]

[0117] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0118] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the acoustic properties of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling, characterized in that, Includes the following steps: Step 1: Determine the prediction target based on the design requirements of the acoustic metamaterial; Step 2: Divide the acoustic metamaterial structure into sub-units and determine the high-dimensional design variables contained in the combination of its inherent physical properties; Step 3: Multiphysics modeling of acoustic metamaterials using COMSOL software to construct high / low fidelity numerical simulation models with different computational costs and accuracies; Step 4: Use maximum-minimum distance sequential sampling to obtain grid sample points x for each component function. l The response values ​​of the sample points are obtained by calling the low-fidelity numerical simulation model, and a low-fidelity surrogate model of the acoustic metamaterial is constructed based on the Cut-HDMR model. Step 5: Obtain high-fidelity sample points x using optimized Latin hypercube sampling. h The high-fidelity numerical simulation model is invoked to calculate the response value f of the sample point. h (x h The low-fidelity predicted value is calculated using the low-fidelity proxy model. Constructing a multi-fidelity SM-HDMR model based on spatial mapping method; Step 6: Output the acoustic metamaterial SM-HDMR model, along with the nonlinear first-order term and coupled second-order term, and evaluate the prediction error of the SM-HDMR model; The grid sample points x for each component function are obtained by using maximum-minimum distance sequential sampling. l The response values ​​of the sample points are obtained by calling the low-fidelity numerical simulation model, and a low-fidelity surrogate model of the acoustic metamaterial is constructed 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. The corresponding low-fidelity response was obtained based on the low-fidelity simulation model with a coarse mesh. (2) Construct first-order component functions; for variable x i Let i = 1, 2, ..., 50, and select the upper and lower boundary points x. i - and Using the initial sample points, the corresponding function values ​​are obtained from the low-fidelity numerical simulation model to obtain training points. and Constructing initial first-order component functions based on the Kriging model (3) Check the linearity of the first-order component functions; if the constructed surrogate model By cutting through the center x0, that is but For a linear function consisting of only two sample points, more sample points are obtained through maximum and minimum distance sampling until the accuracy requirement is met; this process is repeated to construct 50 first-order component functions. Thus, the low-fidelity surrogate model containing only first-order component functions is: (4) Check for second-order existence; if the corner point Predicted value If the response value is similar to that of the low-fidelity simulation, the influence of higher-order terms is considered negligible; otherwise, the second-order component function is constructed. (5) Examine and construct the second-order component functions; evaluate any two variables x i and x j The coupling effect, if the relative error is greater than the threshold ε2, that is: Then on the cutting surface x i -x j The inner part obtains more low-fidelity second-order sample points based on maximum and minimum distance sampling, and constructs a second-order component function. The construction of all second-order component functions is completed sequentially, resulting in a more refined low-fidelity proxy model: High-fidelity sample points x are obtained by using optimized Latin hypercube sampling. h The high-fidelity simulation model is invoked to calculate the response value f of the sample points. h (x h The low-fidelity predicted value is calculated using the low-fidelity proxy model. A multi-fidelity SM-HDMR model is constructed based on the spatial mapping method, including: Optimized Latin hypercube sampling was performed across the entire design domain, and the corresponding response values ​​were calculated using a high-fidelity simulation model to obtain high-fidelity sample points [x]. h ,f h (x h The corresponding low-fidelity predicted values ​​are calculated using the constructed Cut-HDMR model. Will The Kriging model is constructed using the training sample points, where As an input variable, f h (x h This data serves as the corresponding output data, mapping low-fidelity output information to a high-fidelity output space. This transforms the "many-to-one" mapping into a more easily processed "one-to-one" mapping, thus eliminating the high-dimensionality dilemma in multi-fidelity modeling. The final multi-fidelity model is: in, For stochastic processes, this represents local fluctuations or errors in the objective function. As the regression term, the overall behavior of the target is represented by a linear combination of p regression functions: Where h(·) is composed of regression functions, and β is the regression coefficient.

2. The method for predicting the acoustic properties of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling as described in claim 1, characterized in that, Based on the design requirements of acoustic metamaterials, the prediction targets are determined, including: Based on the design requirements of modulating far-field sound pressure level by combining the inherent physical properties of acoustic metamaterials, the influence of metamaterials on sound waves is characterized by the far-field sound pressure level at 90°, which is the prediction target.

3. The method for predicting the acoustic properties of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling as described in claim 1, characterized in that, The acoustic metamaterial structure is divided into sub-units to determine the design variable x included in the combination of its inherent physical properties, including: The acoustic metamaterial structure was divided into 25 sub-units along its length. The physical properties of each sub-unit were characterized by two indices: density ρ and Young's modulus E. Fifty design variables x = [x1, x2, ..., x] were determined to account for the inherent physical properties of the acoustic metamaterial. 50 ] T Where x1, x2, ..., x 25 x represents the density of 25 sub-units. 26 x 27 , ..., x 50 This represents the Young's modulus of 25 sub-units.

4. The method for predicting the acoustic properties of high-dimensional metamaterials based on spatial mapping multi-fidelity modeling as described in claim 1, characterized in that, Output the acoustic metamaterial SM-HDMR model, including its first-order nonlinear term and coupled second-order term, and evaluate the model's prediction error, including: The prediction error of the constructed SM-HDMR model is evaluated using the global error index relative to the mean absolute error (RAAE) and the local error index relative to the root mean square error (RRMSE), where: Where n is the number of test sample points, y t This represents the actual response value of the test sample point. The values ​​are the corresponding SM-HDMR model predictions, where STD represents the standard deviation. The prediction error of the constructed SM-HDMR model is evaluated, and the nonlinear first-order term and coupled second-order term are derived to provide guidance for adding high / low fidelity samples for acoustic metamaterials. When only the first-order component function is constructed in step four, and when the second-order component function is included, the prediction accuracy of the SM-HDMR model under the corresponding conditions is evaluated using error indices to obtain the accuracy improvement ratio and the number of sample points. The corresponding nonlinear first-order term and the second-order term with non-negligible coupling effect are also provided to guide the addition of high / low fidelity samples for acoustic metamaterials.

5. A high-dimensional metamaterial acoustic performance prediction system based on spatial mapping multi-fidelity modeling according to any one of claims 1-4, characterized in that, include: Prediction Target Determination Module: Determines the prediction target based on the design requirements of the acoustic metamaterial; Sub-unit partitioning module: Divides the acoustic metamaterial structure into sub-units to determine the high-dimensional design variables contained in the combination of its inherent physical properties; Numerical simulation model building module: Based on COMSOL software, multiphysics modeling of acoustic metamaterials is performed to build high / low fidelity numerical simulation models with different computational costs and accuracies; Low-fidelity surrogate model construction module: Employs maximum-minimum distance sequential sampling to obtain grid sample points x for each component function. l The response values ​​of the sample points are obtained by calling the low-fidelity simulation model, and a low-fidelity surrogate model of the acoustic metamaterial is constructed based on the Cut-HDMR model. Multi-fidelity model construction module: High-fidelity sample points x are obtained by using optimized Latin hypercube sampling. h The high-fidelity simulation model is invoked to calculate the response value f of the sample points. h (x h The low-fidelity predicted value is calculated using the low-fidelity proxy model. A multi-fidelity SM-HDMR model is constructed based on the spatial mapping method; the 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 prediction error of the model.

6. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, causes the processor to perform the steps of the high-dimensional metamaterial acoustic performance prediction method based on spatial mapping multifidelity modeling as described in any one of claims 1-4.

7. A computer-readable storage medium storing a computer program, wherein when executed by a processor, the computer program causes the processor to perform 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 1-4.

8. 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 5.

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