Robust optimization method and device for low-frequency sound absorption metamaterial

Abstract

The invention provides a robust optimization method and device for a low-frequency sound absorption metamaterial, and relates to the technical field of punching, and the method comprises the steps: obtaining a response function of a target metamaterial through employing a linear one-dimensional rheological model; determining a target coupling region by using an imaginary part of a transfer function zero point corresponding to the response function or a size relationship between inherent loss and radiation loss as a coupling criterion, and determining a closed coupling region where a preset parameter point is located as an initial robust region; the target coupling region comprises a closed coupling region; the preset parameter point meets the one-dimensional frequency domain response of the target metamaterial; and determining the size of the initial robust region by using the Lexberg measure of the Euclidean space, and optimizing the robust region by maximizing the Lexberg measure of the initial robust region in the Euclidean space to obtain a target robust region. According to the method, the maximum robust region in the parameter space is found through maximum measurement, so that the response characteristics of the viscoelastic damping material under the actual working condition can be accurately described.

Description

Technical Field

[0001] The present invention relates to the field of pulse technology, and in particular to a method and device for robust optimization of low-frequency sound-absorbing metamaterials. Background Art

[0002] In underwater sound absorption, the use of viscoelastic damping materials to enhance sound absorption is a common practice. While significant progress has been made in acoustic tiles reinforced with viscoelastic damping materials, the mechanical properties of viscoelastic damping materials are often extremely unstable, affecting their actual sound absorption performance. The mechanical properties of viscoelastic damping materials are affected by numerous factors, such as pre-deformation, temperature, aging, and excitation frequency. If only a few influencing factors are considered, dynamic mechanical analysis can be used to accurately predict material parameters and conduct inverse design. When linear assumptions hold, more sophisticated models are often employed to describe these factors. However, accurately characterizing the response characteristics of viscoelastic damping materials under actual operating conditions remains a significant challenge. For one thing, accurately measuring the impact of various factors is difficult. This process involves selecting an appropriate fitting model and determining the relevant parameters through dynamic mechanical analysis. Furthermore, due to the complex and variable operating conditions, the models often fail to accurately reflect the actual response. Existing design approaches are primarily based on traditional robust optimization methods, which introduce random parameters and rely on topology optimization and other complex configurations to optimize the statistics of acoustic parameters. This design approach has high computational costs, the designed configuration is too complex and therefore difficult to manufacture, and has too many statistical assumptions about random parameters, thus limiting its applicability. Summary of the Invention

[0003] In view of this, the present invention proposes a method and device for robust optimization of low-frequency sound-absorbing metamaterials.

[0004] The technical solution of the present invention is implemented as follows: In a first aspect, the present invention provides a robust optimization method for low-frequency sound-absorbing metamaterials, comprising:

[0005] A linear one-dimensional rheological model is used to obtain a response function of the target metamaterial; the response function includes a mechanical response and a frequency domain response;

[0006] The target coupling region is determined by using the imaginary part of the transfer function zero point corresponding to the response function or the magnitude relationship between the intrinsic loss and the radiation loss as a coupling criterion, and the closed coupling region where the preset parameter point is located is determined as the initial robust region; the target coupling region includes the closed coupling region; the preset parameter point satisfies the one-dimensional frequency domain response of the target metamaterial;

[0007] The size of the initial robust region is determined by using the Lebesgue measure of the Euclidean space, and the robust region is optimized by maximizing the Lebesgue measure of the initial robust region in the Euclidean space to obtain a target robust region.

[0008] Based on the above technical solution, preferably, the step of obtaining the response function of the target metamaterial using a linear one-dimensional rheological model includes:

[0009] The mechanical response is obtained using the following formula: Where ω is the circular frequency, and are strain and stress, respectively, is the one-dimensional frequency domain response of the target metamaterial, i.e., Young’s modulus;

[0010] The frequency domain response is obtained using the following formula: Among them, φ(ω)={φ1(ω), φ2(ω),..φ n (ω)} is the spectral function basis given by the model, e={e1,e2,..e n} are the parameters of the linear one-dimensional rheological model.

[0011] Based on the above technical solution, preferably, the coupling criterion includes an impedance criterion and an energy criterion; the target coupling region is determined by using the imaginary part of the transfer function zero point corresponding to the response function or the magnitude relationship between the intrinsic loss and the radiation loss as the coupling criterion, and the closed coupling region where the preset parameter point is located is determined as the initial robust region, including:

[0012] The dynamic parameter variation range is determined by the parameter coordinates, and is set as D(e): e={e1,e2,...,e n}∈D(e);

[0013] The dynamic parameters corresponding to the preset parameter points are satisfy

[0014] The over-coupling domain defined by the impedance criterion is: f is the frequency parameter, f T is the frequency range of the over-coupling domain, e0 is the coordinate of the preset parameter point, and n is the total number of parameter points;

[0015] Wherein, Δ is the imaginary part of the zero point of the transfer function corresponding to the response function, that is,

[0016] Among them, Z w =ρ w c w is the characteristic impedance of water, ρ w , c ware the density of water and the speed of sound respectively, Im represents the imaginary part of the complex number, is the oscillation frequency.

[0017] Based on the above technical solution, preferably, the method of using the imaginary part of the transfer function zero point corresponding to the response function or the magnitude relationship between the intrinsic loss and the radiation loss as a coupling criterion to determine the target coupling region, and determining the closed coupling region where the preset parameter point is located as the initial robust region includes:

[0018] The energy criterion is determined based on the response function:

[0019] Where ξ is the damping ratio, defined as C leak (ω) and C loss (ω) are intrinsic loss and radiation loss respectively;

[0020] For an axisymmetric 2D system:

[0021] C leak (ω)=βS inc Z w

[0022]

[0023] in, Characterize the scattering parameters, a, d and s are the length, inner diameter and depth of the two-dimensional system, j is the imaginary unit, k is the wave number, β is the radiation area correction factor, specifically the ratio of the incident area to the radiation area, S inc is the incident domain area.

[0024] Based on the above technical solution, preferably, the method of using the imaginary part of the transfer function zero point corresponding to the response function or the magnitude relationship between the intrinsic loss and the radiation loss as a coupling criterion to determine the target coupling region, and determining the closed coupling region where the preset parameter point is located as the initial robust region includes:

[0025] By solving the critical coupling equation ξ(ω res )=1 or Δ=0, and the target coupling area X is obtained. c.c :

[0026] X c.c. ={e|f i (e) = 0, i = 1, 2, ... n};

[0027] Among them, f i (e) is each non-overlapping subset of the target coupling region; the over-coupling region is the interior of the target coupling region, i.e.

[0028] X o.c. ={e|fi (e)<0,i=1,2,…n};

[0029] Substitute the preset parameter point e0 into the target coupling region X c.c Every subset f i (e), if f i (e)<0, determine the initial robust region.

[0030] On the basis of the above technical solution, preferably, the determining the size of the initial robust region by using the Lebesgue measure of the Euclidean space includes determining the size of the initial robust region by using the following formula:

[0031]

[0032] in, is an n-dimensional Hilbert space, S is Any measurable closed subset in , μ(S) is the measure result, vol represents the n-dimensional volume of the set, and T represents the isomorphism transformation.

[0033] On the basis of the above technical solution, preferably, optimizing the robust region by maximizing the Lebesgue measure of the initial robust region in the Euclidean space to obtain a target robust region includes:

[0034] A target robust region is obtained by tuning the target metamaterial to maximize the robust region.

[0035] More preferably, the second aspect of the present invention provides a low-frequency sound-absorbing metamaterial robust optimization device, comprising: a function acquisition module, a region determination module and a region optimization module; wherein,

[0036] The function acquisition module is configured to acquire a response function of the target metamaterial using a linear one-dimensional rheological model; the response function includes a mechanical response and a frequency domain response;

[0037] The region determination module is configured to use the imaginary part of the transfer function zero point corresponding to the response function or the relationship between the intrinsic loss and the radiation loss as a coupling criterion to determine the target coupling region, and determine the closed coupling region where the preset parameter point is located as the initial robust region; the target coupling region includes the closed coupling region; the preset parameter point satisfies the one-dimensional frequency domain response of the target metamaterial;

[0038] The region optimization module is configured to determine the size of the initial robust region using the Lebesgue measure of the Euclidean space, and optimize the robust region by maximizing the Lebesgue measure of the initial robust region in the Euclidean space to obtain a target robust region.

[0039] More preferably, the third aspect of the present invention provides an electronic device, comprising a processor and a memory; the memory stores a computer program, wherein the computer program, when executed by the processor, implements the robust optimization method for low-frequency sound-absorbing metamaterials described in the first aspect.

[0040] More preferably, the fourth aspect of the present invention provides a computer storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the robust optimization method for low-frequency sound-absorbing metamaterials described in the first aspect is implemented.

[0041] The robust optimization method for low-frequency sound-absorbing metamaterials of the present invention has the following beneficial effects compared to the prior art:

[0042] 1. By establishing the metamaterial acoustic impedance response function, the dynamic behavior of the system under specific conditions can be more accurately described, thereby more accurately determining the robust region. The acoustic impedance response function is solved using the finite element method. Based on the robust sound absorption performance of the passive system in the over-coupled state, the tunable characteristics of the metamaterial are used to make the initial preset parameter points fall as far as possible into the over-coupled region, thereby maximizing the robust region and accurately characterizing the response characteristics of the viscoelastic damping material under actual working conditions.

[0043] 2. By considering the imaginary part of the transfer function zero, the system's oscillation characteristics and stability can be accurately reflected, allowing for more precise determination of the coupling region. Furthermore, the relationship between intrinsic and radiation losses provides an intuitive assessment of coupling efficiency. By comparing intrinsic and radiation losses, the coupling efficiency can be intuitively determined, thereby determining the target coupling region. The flexibility of selecting the appropriate coupling criterion based on system stability or coupling efficiency requirements enhances selection flexibility.

[0044] 3. Maximize the robust area by maximizing the Lebesgue measure, use mathematical optimization methods and simulation technology to predict the behavior of the system, maximize the robust area on the basis of simplifying the design and debugging process, and ensure that the system can still operate reliably under these changes, thereby improving the accuracy and reliability of the design. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0046] Figure 1 A schematic flow chart of a robust optimization method for low-frequency sound-absorbing metamaterials provided by an embodiment of the present invention;

[0047] Figure 2 A schematic diagram of a robust optimization process provided by an embodiment of the present invention;

[0048] Figure 3 A schematic structural diagram of a Helmholtz resonance cavity reinforced with viscoelastic material according to an embodiment of the present invention;

[0049] Figure 4 A schematic diagram of the robustness of the low-frequency sound absorption spectrum provided by an embodiment of the present invention;

[0050] Figure 5 A schematic structural diagram of a low-frequency sound-absorbing metamaterial robust optimization device provided by an embodiment of the present invention;

[0051] Figure 6 A schematic structural diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0053] In some embodiments, as Figure 1 As shown, Figure 1 A schematic flow chart of a robust optimization method for low-frequency sound-absorbing metamaterials provided by an embodiment of the present invention; a robust optimization method for low-frequency sound-absorbing metamaterials provided by the present invention includes:

[0054] S110, using a linear one-dimensional rheological model to obtain a response function of the target metamaterial; the response function includes a mechanical response and a frequency domain response.

[0055] In this embodiment, the target metamaterial may be a viscoelastic damping material. The linear one-dimensional rheological model mainly considers the relationship between strain and stress of the target metamaterial in one-dimensional direction, and this relationship is assumed to be linear.

[0056] In some embodiments, S110, using a linear one-dimensional rheological model to obtain a response function of a target metamaterial includes:

[0057] The mechanical response is obtained using the following formula: Where ω is the circular frequency, and are strain and stress, respectively, is the one-dimensional frequency domain response of the target metamaterial, i.e., Young’s modulus;

[0058] The frequency domain response is obtained using the following formula: Among them, φ(ω)={φ1(ω),φ2(ω),..φ n (ω)} is the spectral function basis given by the model, e={e1,e2,..e n} are the parameters of the linear one-dimensional rheological model. Combined with the finite element method, the impedance response function of the metamaterial can be calculated.

[0059] S120, using the imaginary part of the transfer function zero point corresponding to the response function or the relationship between the intrinsic loss and the radiation loss as a coupling criterion to determine the target coupling region, and determining the closed coupling region where the preset parameter point is located as the initial robust region; the target coupling region includes the closed coupling region; the preset parameter point satisfies the one-dimensional frequency domain response of the target metamaterial.

[0060] A transfer function is a mathematical relationship between a system's input and output. By solving for the zeros of the transfer function, the resonant characteristics of the system at certain frequencies can be determined. Intrinsic loss is typically associated with energy dissipation within the material, while radiation loss is associated with the outward radiation of energy in the form of electromagnetic waves. Using the imaginary part of the transfer function zeros or the relationship between intrinsic loss and radiation loss as coupling criteria, regions in parameter space that meet specific coupling conditions—the target coupling region—can be identified. This region may include multiple closed coupling regions corresponding to different combinations of system parameters.

[0061] In an optional embodiment, the coupling region can be determined by the sound absorption spectrum. The specific principle is as follows. The evaluation indexes of the sound absorption spectrum include α1 and α2. Assuming that the target frequency domain segment is [f1, f2], α1 and α2 can be expressed as:

[0062]

[0063] Where α1 is the average sound absorption coefficient and α2 is the total reflection intensity of the real wavelength under the logarithmic scale. For passive acoustic systems, α2 is used to measure whether the thickness of the sound absorber reaches the lower limit given by the causal law, so it is also called the causal integral. If the cutoff frequency f c If the frequency is not higher than the lower bound f1 of the target frequency, the contribution of the extremely low frequency band can be ignored, that is, In this case, the two indices are approximately equivalent. Specifically, a sound absorption spectrum with high quality in the sense of α1 also has high quality in the sense of α2, and vice versa.

[0064] According to the definition of the coupling state, the causal integral maintains a static value in the over-coupling region, so the sound absorption spectrum in this region is insensitive to parameter changes.

[0065]

[0066] Where L is the effective propagation length of the sound absorber, specifically the sound propagation volume divided by the incident area. w is the bulk modulus of water, B eff is the static effective bulk modulus of the sound absorber, that is For underwater sound absorbers reinforced with viscoelastic damping materials, this limit is the weighted average of the bulk moduli of each part of the sound absorber under static conditions, i.e., B eff =mB r,0 +(1-m)B w . Among them B r,0 and B w are the static bulk moduli of the viscoelastic damping material and water, respectively, and m is the ratio of the rubber volume to the total volume. Combined with the equivalence of the indicators, the above formula shows the robustness of the average sound absorption coefficient α1 in the overcoupled region.

[0067] In some embodiments, the coupling criterion includes an impedance criterion and an energy criterion. S120, using the imaginary part of the transfer function zero point corresponding to the response function or the relationship between the intrinsic loss and the radiation loss as the coupling criterion to determine the target coupling region, and determining the closed coupling region where the preset parameter point is located as the initial robust region, including:

[0068] The dynamic parameter variation range is determined by the parameter coordinates, and is set as D(e): e={e1,e2,...,e n}∈D(e);

[0069] The dynamic parameters corresponding to the preset parameter points are satisfy

[0070] The over-coupling domain defined by the impedance criterion is: f is the frequency parameter, f T is the frequency range of the over-coupling domain, e0 is the coordinate of the preset parameter point, and n is the total number of parameter points;

[0071] Where Δ is the imaginary part of the transfer function zero corresponding to the response function, that is,

[0072] Among them, Z w =ρ w c w is the characteristic impedance of water, ρ w , c w are the density of water and the speed of sound respectively, Im represents the imaginary part of the complex number, is the oscillation frequency.

[0073] In some embodiments, S120, determining a target coupling region using the imaginary part of the transfer function zero point corresponding to the response function or the relationship between the intrinsic loss and the radiation loss as a coupling criterion, and determining the closed coupling region where the preset parameter point is located as the initial robust region includes:

[0074] Determine the energy criterion based on the response function:

[0075] Where ξ is the damping ratio, defined as C leak (ω) and C loss (ω) are intrinsic loss and radiation loss respectively;

[0076] For an axisymmetric 2D system:

[0077] C leak (ω)=βS inc Z w

[0078]

[0079] in, Characterize the scattering parameters, a, d and s are the length, inner diameter and depth of the two-dimensional system, j is the imaginary unit, k is the wave number, β is the radiation area correction factor, specifically the ratio of the incident area to the radiation area, S inc is the incident domain area.

[0080] In some embodiments, S120, determining a target coupling region using the imaginary part of the transfer function zero point corresponding to the response function or the relationship between the intrinsic loss and the radiation loss as a coupling criterion, and determining the closed coupling region where the preset parameter point is located as the initial robust region includes:

[0081] By solving the critical coupling equation ξ(ω res )=1 or Δ=0, and the target coupling area X is obtained. c.c :

[0082] X c.c. ={e|f i (e) = 0, i = 1, 2, ... n};

[0083] Among them, f i (e) is each non-overlapping subset of the target coupling region; the over-coupling region is the interior of the target coupling region, i.e.

[0084] X o.c. ={e|f i (e)<0,i=1,2,...n};

[0085] Substitute the preset parameter point e0 into the target coupling region Xc.c Every subset f i (e), if f i (e)<0, determine the initial robust region.

[0086] S130 , determining the size of the initial robust region using the Lebesgue measure in the Euclidean space, and optimizing the robust region by maximizing the Lebesgue measure of the initial robust region in the Euclidean space to obtain a target robust region.

[0087] Here, the given viscoelastic model gives an n-dimensional Hilbert space Therefore, there is To n-dimensional Euclidean space Isomorphic transformation of : The size of the robust region can be determined by The Lebesgue measure in is given by .

[0088] In some embodiments, S130, determining the size of the initial robust region using the Lebesgue measure of the Euclidean space includes determining the size of the initial robust region using the following formula:

[0089]

[0090] in, is an n-dimensional Hilbert space, S is Any measurable closed subset in , μ(S) is the measure result, vol represents the n-dimensional volume of the set, and T represents the isomorphism transformation.

[0091] In some embodiments, S130, optimizing the robust region by maximizing the Lebesgue measure of the initial robust region in Euclidean space to obtain a target robust region includes:

[0092] By tuning the target metamaterial to maximize the robust area, a target robust area is obtained.

[0093] In this embodiment, the optimal solution that maximizes the robust region is found by adjusting the metamaterial's structural parameters and material properties. An optimization algorithm is then used to tune and optimize the metamaterial. This process requires multiple iterations and parameter adjustments to gradually approach the optimal solution. Furthermore, the results of each iteration must be evaluated and verified to ensure the effectiveness and accuracy of the optimization process.

[0094] In an alternative embodiment, see Figure 2 , Figure 2Schematic diagram of the robust optimization process provided by an embodiment of the present invention; using the acoustic response Z(ω, ζ) and the viscoelastic model to solve the algebraic equation, using the imaginary part of the transfer function zero point or the relationship between the intrinsic loss and the radiation loss as the coupling criterion, the over-coupling region can be identified in the parameter space. On this basis, it is determined whether the initial viscoelastic design parameters are located inside the over-coupling region, and then the maximized robust region is calculated. Here, an optimization algorithm can be used to search the parameter space to find the parameter combination that maximizes the robustness of the system. This process involves multiple iterations and calculations. Conversely, if the initial viscoelastic design parameters are not located inside the over-coupling region, random design values are generated, the acoustic response is adjusted, and the above steps are repeated until the maximized robust region is determined. The final result can be evaluated by calculating the frequency response of the transfer function, observing the stability of the system and other indicators.

[0095] In an alternative embodiment, see Figure 3 , Figure 3 A schematic diagram of the structure of a viscoelastic material-reinforced Helmholtz resonant cavity provided by an embodiment of the present invention is provided. This example illustrates a rigid-backed, viscoelastic damping material-reinforced Helmholtz resonant sound-absorbing structure. The tunable parameters are ζ = {t, d}. Here, t is the thickness of the viscoelastic damping material substrate of the unit, and d is the inner diameter of the unit tube. Optimization is performed for a six-unit parallel sound-absorbing unit, with d = {d1, d2, d3, d4, d5, d6} and t = {t1, t2, t3, t4, t5, t6}.

[0096] The acoustic impedance response function of the metamaterial is established. The viscoelastic damping material is described by a four-branch generalized Maxwell model, where the parameter coordinates are the relaxation time and storage modulus of each branch, i.e.

[0097]

[0098] Among them, E r，i is the Young's modulus of each branch, τ i is the viscosity of each branch.

[0099] D(e) is determined by the storage modulus E r The upper and lower bounds of ′ and loss factor η are given. The upper and lower bounds are set to E r ′∈[10MPa, 30MPa] and η∈[0.1, 1]. The corresponding research range is:

[0100]

[0101] D(e)={e|10MPa<E r '<30MPa,0.1<η<1}.

[0102] At the same time, the initial design parameter coordinate e0 is selected, as shown in Table 1. It should be noted that this initial parameter coordinate makes the dynamic parameter range basically maintain a constant value E in the 100 Hz frequency range. r ′=20MPa,η=0.2。

[0103] Table 1 Coordinates of initial viscoelastic design parameters

[0104]

[0105] The surface impedance response function of the element is calculated using the lumped element method. The impedance transfer function of a Helmholtz resonator reinforced with viscoelastic damping material contains nonlinearities arising from solving the governing acoustic equations. Here, a partial polynomial approximation is employed to replace these nonlinearities. In the low-frequency region, partial polynomial fitting allows the analytical impedance to be approximated using a polynomial impedance. This results in an expression for the lumped system.

[0106] Under the two-end impedance boundary conditions, the analytical impedance of the micro-perforated plate is:

[0107]

[0108] Among them, J i is the i-th order Bessel function, η w is the dynamic viscosity of water, is the shear number, σ=π(d / 2)^ 2 / S inc is the perforation rate.

[0109] Approximate impedance: Z en =R en +jωL

[0110] The acoustic resistance part is:

[0111] The sound sense part is:

[0112] At low frequencies in the hundreds of hertz range, this expression can be further simplified to a polynomial form using rational approximations and linearization:

[0113]

[0114] Here, y0 is the constant shear factor: y0 = (y(f1) + y(f2)) / 2. To further simplify the shear factor y, a constant approximation is used, treating the shear factor as a constant in the low-frequency range. Note that this approximation only holds for high shear factors, generally requiring y > 10. Once the shear factor is too low, the nonlinear impedance introduced by the Poiseuille flow becomes non-negligible.

[0115] In the low-frequency range, since the transverse modes are almost negligible, a one-dimensional approximation can be used for both the water cavity and the viscoelastic damping material substrate:

[0116]

[0117] Among them, Z w and Z r are the impedances of the water cavity and the viscoelastic damping material substrate, ρ r is the density of the viscoelastic damping material, and are the complex sound velocity and complex wave number of the viscoelastic damping material substrate, respectively, where B r，0 =E r，0 (1-v) / (1+v) / (1-2v), where v is Poisson's ratio.

[0118] Similarly, the water cavity and the viscoelastic damping material substrate have a linear approximation cot(kL)=(kL) -1 , we can get the rational impedance of the Helmholtz resonator enhanced by viscoelastic damping material:

[0119]

[0120] Among them, C w =L w / ρ w 2 is the acoustic capacity of the water cavity, is the complex acoustic capacitance of the viscoelastic damping material substrate, L w and L r are the effective propagation lengths of the water cavity and the viscoelastic damping material, respectively.

[0121] Here the frequency range is f1 = 300 Hz, f2 = 900 Hz, and the water parameter is ρ w =1500kg / m 3 ,c w =1000kg / m 3 To save computational cost, the critical coupling equation can be solved by substituting the surface impedance function obtained by the lumped mass method in step 1. For this highly nonlinear optimization problem, a gradient-free direct search algorithm is used. Here, the direct Nelder-Mead simplex method is selected, and the step size tolerance and optimization tolerance are selected as 1×10 -8 and 1×10 -6 The solver converged to 63660 after 334 iterations, and the optimized parameters are shown in Table 2.

[0122] Table 2 Coordinates of initial viscoelastic design parameters

[0123]

[0124] Based on this, a sensitivity analysis of viscoelasticity is performed to demonstrate the stability of the optimized design value. Specifically, the variation of the average sound absorption coefficient α1 with the storage modulus in the e0 branch is analyzed. Since different relaxation times correspond to different time scales, each coordinate corresponds to a branch with different dynamic characteristics. In the studied excitation frequency range, E r，1 Mainly affects the elasticity, while E r，2 Mainly affects damping; E r，3 and E r，4 belongs to the viscoelastic coordinates, where E r，3 More emphasis on flexibility, E r，4 focuses more on damping. Figure 4 , Figure 4 A schematic diagram of the robustness of the low-frequency sound absorption spectrum provided by an embodiment of the present invention; Figure 4 The isosurface of the average sound absorption coefficient α1 = 0.9 is shown as it varies with the three parameters. In a large frequency range, α1 is always greater than 0.9, which fully confirms the stability of the design point. At the same time, compared with the elastic coordinate, it can be seen that the design point has a good relationship with the damping coordinate E. r，3 and E r，4 It shows more stable robustness.

[0125] In some embodiments, see Figure 5 , Figure 5 The present invention provides a low-frequency sound absorption metamaterial robust optimization device 500, comprising: a function acquisition module 510, a region determination module 520 and a region optimization module 530; wherein,

[0126] Function acquisition module 510 is configured to acquire the response function of the target metamaterial using a linear one-dimensional rheological model; the response function includes a mechanical response and a frequency domain response;

[0127] The region determination module 520 is configured to determine a target coupling region using the imaginary part of the transfer function zero point corresponding to the response function or the relationship between the intrinsic loss and the radiation loss as a coupling criterion, and determine the closed coupling region where the preset parameter point is located as the initial robust region; the target coupling region includes the closed coupling region; the preset parameter point satisfies the one-dimensional frequency domain response of the target metamaterial;

[0128] The region optimization module 530 is configured to determine the size of the initial robust region using the Lebesgue measure in the Euclidean space, and optimize the robust region by maximizing the Lebesgue measure of the initial robust region in the Euclidean space to obtain a target robust region.

[0129] In some embodiments, the function acquisition module 510 is specifically configured as follows:

[0130] The mechanical response is obtained using the following formula: Where ω is the circular frequency, and are strain and stress, respectively, is the one-dimensional frequency domain response of the target metamaterial, i.e., Young’s modulus;

[0131] The frequency domain response is obtained using the following formula: Among them, φ(ω)={φ1(ω), φ2(ω),..φ n (ω)} is the spectral function basis given by the model, e={e1,e2,..e n} are the parameters of the linear one-dimensional rheological model.

[0132] In some embodiments, the coupling criterion includes an impedance criterion and an energy criterion; the region determination module 520 is specifically configured as follows:

[0133] The dynamic parameter variation range is determined by the parameter coordinates, and is set as D(e): e={e1,e2,…,e n}∈D(e);

[0134] The dynamic parameters corresponding to the preset parameter points are satisfy

[0135] The over-coupling domain defined by the impedance criterion is: f is the frequency parameter, f T is the frequency range of the over-coupling domain, e0 is the coordinate of the preset parameter point, and n is the total number of parameter points;

[0136] Where Δ is the imaginary part of the transfer function zero corresponding to the response function, that is,

[0137] Among them, Z w =ρ w c w is the characteristic impedance of water, ρ w , c w are the density of water and the speed of sound respectively, Im represents the imaginary part of the complex number, is the oscillation frequency.

[0138] In some embodiments, the region determination module 520 is specifically configured to:

[0139] Determine the energy criterion based on the response function:

[0140] Where ξ is the damping ratio, defined as C leak (ω) and C loss (ω) are intrinsic loss and radiation loss respectively;

[0141] For an axisymmetric 2D system:

[0142] C leak (ω)=βS inc Z w

[0143]

[0144] in, Characterize the scattering parameters, a, d and s are the length, inner diameter and depth of the two-dimensional system, j is the imaginary unit, k is the wave number, β is the radiation area correction factor, specifically the ratio of the incident area to the radiation area, S inc is the incident domain area.

[0145] In some embodiments, the region determination module 520 is specifically configured to:

[0146] By solving the critical coupling equation ξ(ω res )=1 or Δ=0, and the target coupling area X is obtained. c.c :

[0147] X c.c. ={e|f i (e) = 0, i = 1, 2, ... n};

[0148] Among them, f i (e) is each non-overlapping subset of the target coupling region; the over-coupling region is the interior of the target coupling region, i.e.

[0149] X o.c. ={e|f i (e)<0,i=1,2,...n};

[0150] Substitute the preset parameter point e0 into the target coupling region X c.c Every subset f i (e), if f i (e)<0, determine the initial robust region.

[0151] In some embodiments, the region optimization module 530 is specifically configured to determine the size of the initial robust region using the following formula:

[0152]

[0153] in, is an n-dimensional Hilbert space, S is Any measurable closed subset in , μ(s) is the measure result, vol represents the n-dimensional volume of the set, and T represents the isomorphism transformation.

[0154] In some embodiments, the region optimization module 530 is specifically configured to:

[0155] By tuning the target metamaterial to maximize the robust area, a target robust area is obtained.

[0156] It should be noted that the low-frequency sound-absorbing metamaterial robust optimization device provided in the embodiment of the present application and the low-frequency sound-absorbing metamaterial robust optimization method provided in the embodiment of the present application are based on the same application concept. Therefore, the specific implementation of this embodiment can refer to the implementation of the aforementioned low-frequency sound-absorbing metamaterial robust optimization method, and the repeated parts will not be repeated.

[0157] In some embodiments, see Figure 6 , Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application. The electronic device 600 provided in an embodiment of the present application includes a processor 610 and a memory 620; the memory 620 stores a computer program, wherein the computer program, when executed by the processor, implements the above-mentioned robust optimization method for low-frequency sound-absorbing metamaterials.

[0158] Specifically, the processor 610 may include, for example, a general-purpose microprocessor, an instruction set processor and / or a related chipset and / or a dedicated microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor 610 may also include onboard memory for caching purposes. The processor 610 may be a single processing unit or multiple processing units for executing different actions of the method flow according to the embodiments of the present application.

[0159] Memory 620 can be, for example, any medium capable of containing, storing, conveying, disseminating, or transmitting instructions. For example, memory 620 can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, components, or propagation media. Specific examples of memory 620 include: magnetic storage devices, such as magnetic tape or hard disk drives (HDDs); optical storage devices, such as compact discs (CD-ROMs); random access memory (RAM) or flash memory; and / or wired or wireless communication links.

[0160] This application also provides a computer-readable medium storing a computer program that, when executed by a processor, implements the aforementioned robust optimization method for low-frequency sound-absorbing metamaterials. This computer-readable medium may be included in the device / apparatus / system described in the aforementioned embodiments, or it may exist independently and not incorporated into the device / apparatus / system. The computer-readable medium carries one or more programs that, when executed, implement the methods according to the embodiments of this application.

[0161] According to an embodiment of the present application, a computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium or any combination thereof. A computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or component, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In the present application, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device, or component. In the present application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, which carries computer-readable program code. Such a propagated data signal may take a variety of forms, including but not limited to an electromagnetic signal, an optical signal, or any suitable combination thereof. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium that can transmit, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code embodied on a computer-readable medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical cable, radio frequency signals, or any suitable combination thereof.

[0162] Those skilled in the art will understand that the features described in the various embodiments and / or claims of the present application may be combined and / or combined in a variety of ways, even if such combinations or combinations are not explicitly described in the present application. In particular, without departing from the spirit and teachings of the present application, the features described in the various embodiments and / or claims of the present application may be combined and / or combined in a variety of ways. All of these combinations and / or combinations fall within the scope of the present application. Therefore, the scope of the present application should not be limited to the above-mentioned embodiments, but should be determined not only by the attached claims, but also by the equivalents of the attached claims. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A robust optimization method for low-frequency sound-absorbing metamaterials, characterized in that: include: A linear one-dimensional rheological model is used to obtain a response function of the target metamaterial; the response function includes a mechanical response and a frequency domain response; The target coupling region is determined by using the imaginary part of the transfer function zero point corresponding to the response function or the magnitude relationship between the intrinsic loss and the radiation loss as a coupling criterion, and the closed coupling region where the preset parameter point is located is determined as the initial robust region; The target coupling region includes a closed coupling region; The preset parameter points satisfy the one-dimensional frequency domain response of the target metamaterial; The size of the initial robust region is determined by using the Lebesgue measure of the Euclidean space, and the robust region is optimized by maximizing the Lebesgue measure of the initial robust region in the Euclidean space to obtain a target robust region.

2. The robust optimization method for low-frequency sound-absorbing metamaterials according to claim 1, characterized in that: The method of obtaining the response function of the target metamaterial by adopting a linear one-dimensional rheological model includes: The mechanical response is obtained using the following formula: Where ω is the circular frequency, and are strain and stress, respectively, is the one-dimensional frequency domain response of the target metamaterial, i.e., Young’s modulus; The frequency domain response is obtained using the following formula: Among them, φ(ω)={φ1(ω), φ2(ω),..φ n (ω)} is the spectral function basis given by the model, e={e1,e2,..e n } are the parameters of the linear one-dimensional rheological model.

3. The robust optimization method for low-frequency sound-absorbing metamaterials according to claim 2, characterized in that: The coupling criterion includes an impedance criterion and an energy criterion; the target coupling region is determined by using the imaginary part of the transfer function zero point corresponding to the response function or the magnitude relationship between the intrinsic loss and the radiation loss as the coupling criterion, and the closed coupling region where the preset parameter point is located is determined as the initial robust region, including: The dynamic parameter variation range is determined by the parameter coordinates, and is set as D(e): e={e1,e2,…,e n }∈D(e); The dynamic parameters corresponding to the preset parameter points are satisfy The over-coupling domain defined by the impedance criterion is: f is the frequency parameter, f T is the frequency range of the over-coupling domain, e0 is the coordinate of the preset parameter point, and n is the total number of parameter points; Wherein, Δ is the imaginary part of the zero point of the transfer function corresponding to the response function, that is, Among them, Z w =ρ w c w is the characteristic impedance of water, ρ w , c w are the density of water and the speed of sound, I m Represents the imaginary part of a complex number, is the resonant frequency.

4. The robust optimization method for low-frequency sound-absorbing metamaterials according to claim 3, characterized in that: The method of determining a target coupling region by using the imaginary part of the transfer function zero point corresponding to the response function or the magnitude relationship between the intrinsic loss and the radiation loss as a coupling criterion, and determining the closed coupling region where the preset parameter point is located as the initial robust region, includes: The energy criterion is determined based on the response function: Where ξ is the damping ratio, defined as C leak (ω) and C loss (ω) are intrinsic loss and radiation loss respectively; For an axisymmetric 2D system: C leak (ω)=βS inc Z w in, Characterize the scattering parameters, d and s are the length, inner diameter and depth of the two-dimensional system, j is the imaginary unit, k is the wave number, β is the radiation area correction factor, specifically the ratio of the incident area to the radiation area, S inc is the incident domain area.

5. The robust optimization method for low-frequency sound-absorbing metamaterials according to claim 4, characterized in that: The method of determining a target coupling region by using the imaginary part of the transfer function zero point corresponding to the response function or the magnitude relationship between the intrinsic loss and the radiation loss as a coupling criterion, and determining the closed coupling region where the preset parameter point is located as the initial robust region, includes: By solving the critical coupling equation ξ(ω res )=1 or Δ=0, and the target coupling area X is obtained. c.c : X c.c. ={e|f i (e)=0,i=1,2,…n}; Among them, f i (e) is each non-overlapping subset of the target coupling region; the over-coupling region is the interior of the target coupling region, i.e. X o.c. ={e|f i (e)<0,i=1,2,…n}; Substitute the preset parameter point e0 into the target coupling region X c.c Every subset f i (e), if f i (e)<0, determine the initial robust region.

6. The robust optimization method for low-frequency sound-absorbing metamaterials according to claim 2, characterized in that: The determining the size of the initial robust region by using the Lebesgue measure of the Euclidean space includes determining the size of the initial robust region by using the following formula: Where H′ is the n-dimensional Hilbert space, S is any measurable closed subset in H′, μ(S) is the measure result, vol represents the n-dimensional volume of the set, and T represents the isomorphism transformation.

7. The robust optimization method for low-frequency sound-absorbing metamaterials according to claim 1, wherein: Optimizing the robust region by maximizing the Lebesgue measure of the initial robust region in the Euclidean space to obtain a target robust region includes: A target robust region is obtained by tuning the target metamaterial to maximize the robust region.

8. A low-frequency sound-absorbing metamaterial robust optimization device, characterized in that: include: Function acquisition module, region determination module and region optimization module; among them, The function acquisition module is configured to acquire a response function of the target metamaterial using a linear one-dimensional rheological model; the response function includes a mechanical response and a frequency domain response; The region determination module is configured to use the imaginary part of the transfer function zero point corresponding to the response function or the relationship between the intrinsic loss and the radiation loss as a coupling criterion to determine the target coupling region, and determine the closed coupling region where the preset parameter point is located as the initial robust region; the target coupling region includes the closed coupling region; the preset parameter point satisfies the one-dimensional frequency domain response of the target metamaterial; The region optimization module is configured to determine the size of the initial robust region using the Lebesgue measure of the Euclidean space, and optimize the robust region by maximizing the Lebesgue measure of the initial robust region in the Euclidean space to obtain a target robust region.

9. An electronic device comprising a processor and a memory; the memory stores a computer program, wherein: When the computer program is executed by the processor, the computer program implements the robust optimization method for low-frequency sound-absorbing metamaterials according to any one of claims 1 to 7.

10. A computer storage medium, characterized in that A computer program is stored thereon, wherein when the computer program is executed by a processor, the robust optimization method for low-frequency sound-absorbing metamaterials according to any one of claims 1 to 7 is implemented.

Images