A robust optimization method and apparatus for low-frequency sound-absorbing metamaterials

Abstract

This invention proposes a robust optimization method and apparatus for low-frequency sound-absorbing metamaterials, relating to the field of pulse technology. The method includes: obtaining the response function of the target metamaterial using a linear one-dimensional rheological model; determining the target coupling region using the relationship between the imaginary part or intrinsic loss of the transfer function zero corresponding to the response function and the radiation loss as a coupling criterion, and defining 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; determining the size of the initial robust region using the Lebesgue measure in Euclidean space, and optimizing the robust region by maximizing the Lebesgue measure of the initial robust region in Euclidean space to obtain the target robust region. This invention finds the largest robust region in the parameter space by maximizing the measure, thereby accurately characterizing the response properties of viscoelastic damping materials under actual operating conditions.

Description

Technical Field

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

[0002] In underwater sound absorption, enhancing sound absorption performance using viscoelastic damping materials is a common practice. While significant progress has been made in viscoelastic damping material-reinforced sound-absorbing tiles, the mechanical properties of these materials are often extremely unstable, affecting their actual sound absorption performance. The mechanical properties of viscoelastic damping materials are influenced by various factors, such as pre-deformation, temperature, aging, and excitation frequency. If only a few influencing factors are considered, accurate material parameter prediction and reverse design can be achieved through dynamic mechanical analysis. Under the assumption of linearity, more refined models are typically used to describe these factors. However, accurately characterizing the response of viscoelastic damping materials under actual operating conditions remains a considerable challenge. On the one hand, accurately measuring the impact of various factors is extremely difficult. This process involves selecting a suitable fitting model and determining relevant parameters through dynamic mechanical analysis. On the other hand, due to the complexity and variability of actual operating conditions, the models used often fail to accurately reflect the true response. Existing design approaches are mainly based on traditional robust optimization methods, which optimize the statistics of acoustic parameters by introducing random parameters and relying on topology optimization and other complex configurations. This design method is computationally expensive, the design configuration is too complex to manufacture, and there are too many statistical assumptions about the random parameters, thus limiting its applicability. Summary of the Invention

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

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

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

[0006] The target coupling region is determined by using the relationship between the imaginary part of the zero point of the transfer function corresponding to the response function or 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 using the Lebesgue measure in Euclidean space, and the target robust region is obtained by optimizing the robust region by maximizing the Lebesgue measure of the initial robust region in Euclidean space.

[0008] Based on the above technical solutions, 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 angular frequency. and Strain and stress, respectively. The one-dimensional frequency domain response of the target metamaterial is defined as 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 given spectral function basis for the model, e = {e1, e2, ..., e} n} represents the parameters of a linear one-dimensional rheological model.

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

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

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

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

[0015] Where Δ is the imaginary part of the zero of the transfer function corresponding to the response function, i.e.

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

[0017] Based on the above technical solutions, preferably, the step of using the relationship between the imaginary part or intrinsic loss of the transfer function zero corresponding to the response function 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) represent inherent loss and radiation loss, respectively;

[0020] For axisymmetric two-dimensional systems:

[0021] C leak (ω)=βS inc Z w

[0022]

[0023] in, The scattering parameters are characterized by a, d, and s, which are the length, inner diameter, and depth of the two-dimensional system, respectively; j is the imaginary unit; k is the wavenumber; β is the radiation area correction factor, specifically the ratio of the incident area to the radiating area; and S... inc Let be the area of ​​the incident region.

[0024] Based on the above technical solutions, preferably, the step of using the relationship between the imaginary part or intrinsic loss of the transfer function zero corresponding to the response function 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 If Δ = 1 or Δ = 0, the target coupling region X is obtained. c.c :

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

[0027] Among them, f i (e) represents each disjoint closed subset of the target coupling region; the overcoupled 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 Each subset f i (e), if f is satisfied i (e) < 0, determine the initial robust region.

[0030] Based on the above technical solutions, preferably, determining the size of the initial robust region using the Lebesgue measure of Euclidean space includes determining the size of the initial robust region using the following formula:

[0031]

[0032] in, Let S be an n-dimensional Hilbert space. Let S be any measurable closed subset, μ(S) be the measure result, vol be the n-dimensional volume of the set, and T be the isomorphic transformation.

[0033] Based on the above technical solutions, preferably, the step of optimizing the robust region by maximizing the Lebesgue measure of the initial robust region in Euclidean space to obtain the target robust region includes:

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

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

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

[0037] The region determination module is configured to use the relationship between the imaginary part of the zero point of the transfer function corresponding to the response function or the magnitude of the intrinsic loss and the radiation loss as a coupling criterion to determine the target coupling region, and to 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 in Euclidean space, and optimize the robust region by maximizing the initial robust region in the Lebesgue measure in Euclidean space to obtain the target robust region.

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

[0041] The robust optimization method for low-frequency sound-absorbing metamaterials of the present invention has the following advantages over the prior art:

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

[0043] 2. By considering the imaginary part of the zeros of the transfer function, the oscillation characteristics and stability of the system can be accurately reflected, thus allowing for a more precise determination of the coupling region. Simultaneously, the relationship between inherent loss and radiation loss provides an intuitive assessment of coupling efficiency. By comparing inherent loss and radiation loss, the level of coupling efficiency can be intuitively judged, thereby determining the target coupling region. The ability to flexibly select appropriate coupling criteria based on system stability or coupling efficiency requirements enhances the flexibility of choice.

[0044] 3. By maximizing the Lebesgue measure to maximize the robust region, mathematical optimization methods and simulation techniques are used to predict the system's behavior. This simplifies the design and debugging process, maximizes the robust region, and ensures that the system can still operate reliably under these changes, thus improving the accuracy and reliability of the design. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 A flowchart illustrating a robust optimization method for low-frequency sound-absorbing metamaterials provided in an embodiment of the present invention;

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

[0048] Figure 3 A schematic diagram of the structure of a viscoelastic material-reinforced Helmholtz resonant cavity provided in an embodiment of the present invention;

[0049] Figure 4 This is a schematic diagram illustrating the robustness of the low-frequency absorption spectrum provided in an embodiment of the present invention.

[0050] Figure 5 This is a schematic diagram of a robust optimization device for low-frequency sound-absorbing metamaterials provided in an embodiment of the present invention;

[0051] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0052] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0053] In some embodiments, such as Figure 1 As shown, Figure 1 This is a flowchart illustrating a robust optimization method for low-frequency sound-absorbing metamaterials provided in an embodiment of the present invention; the robust optimization method for low-frequency sound-absorbing metamaterials provided by the present invention includes:

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

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

[0056] In some embodiments, S110, the response function of the target metamaterial is obtained using a linear one-dimensional rheological model, including:

[0057] The mechanical response is obtained using the following formula: Where ω is the angular frequency. and Strain and stress, respectively. The one-dimensional frequency domain response of the target metamaterial is defined as 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 given spectral function basis for the model, e = {e1, e2, ..., e} n} represents the parameters of a linear one-dimensional rheological model. Using the finite element method, the impedance response function of the metamaterial can be calculated.

[0059] S120, the imaginary part of the zero of the transfer function corresponding to the response function or the relationship between the magnitude of the intrinsic loss and the radiation loss is used as the coupling criterion to determine the target coupling region, 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.

[0060] The transfer function is the mathematical relationship between the system's input and output. By solving for the zeros of the transfer function, the resonance characteristics of the system at certain frequencies can be obtained. Inherent losses are usually related to energy dissipation within the material, while radiation losses are related to energy radiated outward in the form of electromagnetic waves. Using the imaginary part of the transfer function's zeros or the relationship between inherent losses and radiation losses as coupling criteria, regions satisfying specific coupling conditions, i.e., target coupling regions, can be identified in the parameter space. This region may include multiple closed coupling regions, corresponding to different combinations of system parameters.

[0061] In an alternative embodiment, the coupling region can be determined by the sound absorption spectrum, as follows. The evaluation metrics for the sound absorption spectrum include α1 and α2. Assuming the target frequency band is [f1, f2], α1 and α2 can be expressed as:

[0062]

[0063] Where α1 is the average absorption coefficient and α2 is the total reflection intensity at the real wavelength under logarithmic scale. For passive acoustic systems, α2 is used to measure whether the thickness of the absorber reaches the lower limit given by the causality law, and is therefore 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. In this case, the two indicators are approximately equivalent. Specifically, an absorption spectrum with high quality in the α1 sense also has high quality in the α2 sense, and vice versa.

[0064] According to the definition of coupling state, the causal integral remains static in the overcoupled region; therefore, the absorption spectrum is insensitive to parameter changes in this region.

[0065]

[0066] Where L is the effective propagation length of the sound absorber, specifically the sound propagation volume divided by the area of ​​the incident region. B w B is the bulk modulus of water. eff The static effective bulk modulus of the sound absorber, i.e. p represents the normal stress. For underwater sound absorbers reinforced with viscoelastic damping materials, this limiting value is the weighted average of the bulk moduli of all parts 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 Let be the static bulk modulus of the viscoelastic damping material and water, respectively, and m be the ratio of the rubber volume to the total volume. Considering the equivalence of the indices, the above equation demonstrates the robustness of the average sound absorption coefficient α1 within the overcoupling region.

[0067] In some embodiments, the coupling criterion includes an impedance criterion and an energy criterion; S120, using the relationship between the imaginary part of the transfer function zero corresponding to the response function or 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 range of dynamic parameter variation is determined by the parameter coordinates, denoted as D(e): e={e1,e2,...,e...} n}∈D(e);

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

[0070] The overcoupling region defined by the impedance criterion is: f is the frequency parameter, f T For the frequency range of the over-coupled 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 zeros of the transfer function corresponding to the response function, i.e.

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

[0073] In some embodiments, S120, the target coupling region is determined by using the relationship between the imaginary part of the zero of the transfer function corresponding to the response function or 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, including:

[0074] Determining energy criteria based on response function:

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

[0076] For axisymmetric two-dimensional systems:

[0077] C leak (ω)=βS inc Z w

[0078]

[0079] in, The scattering parameters are characterized by a, d, and s, which are the length, inner diameter, and depth of the two-dimensional system, respectively; j is the imaginary unit; k is the wavenumber; β is the radiation area correction factor, specifically the ratio of the incident area to the radiating area; and S... inc Let be the area of ​​the incident region.

[0080] In some embodiments, S120, the target coupling region is determined by using the relationship between the imaginary part of the zero of the transfer function corresponding to the response function or 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, including:

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

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

[0083] Among them, f i (e) represents each disjoint closed subset of the target coupling region; the overcoupled 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 X.c.c Each subset f i (e), if f is satisfied i (e) < 0, determine the initial robust region.

[0086] S130: The size of the initial robust region is determined using the Lebesgue measure in Euclidean space, and the robust region is optimized by maximizing the Lebesgue measure of the initial robust region in Euclidean space to obtain the target robust region.

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

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

[0089]

[0090] in, Let S be an n-dimensional Hilbert space. Let S be any measurable closed subset, μ(S) be the measure result, vol be the n-dimensional volume of the set, and T be the isomorphic transformation.

[0091] In some embodiments, S130, the target robust region is obtained by optimizing the robust region by maximizing the Lebesgue measure of the initial robust region in Euclidean space, including:

[0092] The target robust region is obtained by tuning the target metamaterial to maximize the robust region.

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

[0094] In an alternative embodiment, please refer to Figure 2 , Figure 2This diagram illustrates the robust optimization process provided in this embodiment of the invention. It utilizes the acoustic response Z(ω, ζ) and a viscoelastic model to solve algebraic equations. By using the relationship between the imaginary part of the transfer function zeros or the intrinsic loss and the radiation loss as a coupling criterion, over-coupling regions can be identified in the parameter space. Based on this, it is determined whether the initial viscoelastic design parameters are located within the over-coupling region, and then the robust region is calculated to maximize it. Here, an optimization algorithm can be used to search the parameter space to find the parameter combination that maximizes the system's robustness. This process involves multiple iterations and calculations. Conversely, if the initial viscoelastic design parameters are not located within the over-coupling region, random design values ​​are generated, the acoustic response is adjusted, and the above steps are repeated until the robust region is maximized. The final result can be evaluated by calculating the frequency response of the transfer function and observing the system's stability.

[0095] In an alternative embodiment, please refer to Figure 3 , Figure 3 This is a schematic diagram of a viscoelastic material-reinforced Helmholtz resonant cavity provided in an embodiment of the present invention. An example is a Helmholtz resonant sound-absorbing structure with a rigid backing and viscoelastic damping material reinforcement. The tunable parameter is ζ = {t, d}, where t is the thickness of the unit's viscoelastic damping material substrate and d is the inner diameter of the unit's tube. Optimization is performed on a six-unit parallel sound-absorbing unit, resulting in 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 using a four-branch generalized Maxwell model, with the parameter coordinates being the relaxation time and storage modulus of each branch.

[0097]

[0098] Among them, E r，i The Young's modulus τ for each branch i Viscosity for each branch.

[0099] D(e) is defined by the storage modulus E r The upper and lower bounds of ′ and the 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 scope is:

[0100]

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

[0102] Simultaneously, the initial design parameter coordinates e0 were selected, as shown in Table 1. It should be noted that these initial parameter coordinates ensure that the dynamic parameters remain essentially constant within the 100Hz frequency range. r ′=20MPa, η=0.2.

[0103] Table 1 Initial viscoelastic design parameter coordinates

[0104]

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

[0106] Under the boundary condition of impedance at both ends, the analytical impedance of the microperforated plate is:

[0107]

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

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

[0110] The acoustic impedance part is:

[0111] The sound sensor part is:

[0112] In the low-frequency range of 100 Hz, this expression can be further simplified to a polynomial form through rational approximation and linearization:

[0113]

[0114] Where y0 is the constant shear number y0 = (y(f1) + y(f2)) / 2. Here, to further simplify the shear number y, a constant approximation is used, treating the shear number in the low-frequency range as a constant. It should be noted that this approximation only holds for high shear numbers, generally requiring y > 10. Once the shear number is too low, the nonlinear impedance introduced by the Poiseuille flow will become 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 The impedances ρ of the water cavity and the viscoelastic damping material substrate are respectively. r The density of the viscoelastic damping material. and These represent the complex sound velocity and complex wave number of the viscoelastic damping material substrate, respectively. 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 Substituting the values, we obtain the rational form impedance of the Helmholtz resonator reinforced with viscoelastic damping material:

[0119]

[0120] Among them, C w =L w / ρ w 2 For the acoustic volume of the water cavity. For a complex acoustic-capacitor with a viscoelastic damping material substrate, L w and L r These represent the effective propagation lengths of the water cavity and the viscoelastic damping material, respectively.

[0121] Here, the frequency range is taken as f1 = 300Hz, f2 = 900Hz, and the water parameter is taken as 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 from the lumped mass method in step one. For this highly nonlinear optimization problem, a gradient-free direct search algorithm is adopted. Here, the direct Nelder-Mead simplex method is selected, with the step size tolerance and optimization tolerance both chosen to be 1×10⁻⁶. -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 Initial viscoelastic design parameter coordinates

[0123]

[0124] Based on this, a sensitivity analysis of viscoelasticity is conducted to demonstrate the stability of the optimized design values. Specifically, the variation of the average sound absorption coefficient α1 with the storage modulus in the e0 branch is analyzed. Given that different relaxation times correspond to different time scales, each coordinate corresponds to a branch exhibiting different dynamic characteristics. Within the studied excitation frequency range, E r，1 It mainly affects elasticity, while E r，2 Mainly affects damping; E r，3 and E r，4 This belongs to the viscoelastic coordinate system, where E r，3 More emphasis is placed on flexibility, E r，4 This places greater emphasis on damping. Please refer to [link / reference]. Figure 4 , Figure 4 This is a schematic diagram illustrating the robustness of the low-frequency absorption spectrum provided in an embodiment of the present invention. Figure 4 The isosurface of the average sound absorption coefficient α1 = 0.9 is presented, showing its variation with three parameters. Over a large frequency range, α1 is consistently greater than 0.9, fully demonstrating the stability of the design point. Furthermore, compared to the elastic coordinates, it can be seen that the design point's stability relative to the damped coordinate E... r，3 and E r，4 It exhibits more stable robustness.

[0125] In some embodiments, please refer to Figure 5 , Figure 5 This is a schematic diagram of a robust optimization device for low-frequency sound-absorbing metamaterials provided in an embodiment of the present invention. The present invention provides a robust optimization device 500 for low-frequency sound-absorbing metamaterials, comprising: a function acquisition module 510, a region determination module 520, and a region optimization module 530; wherein,

[0126] The 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 mechanical response and frequency domain response.

[0127] The region determination module 520 is configured to use the relationship between the imaginary part of the zero of the transfer function corresponding to the response function or the magnitude of the intrinsic loss and the radiation loss as the coupling criterion to determine the target coupling region, and to 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 Euclidean space, and optimize the robust region by maximizing the Lebesgue measure of the initial robust region in Euclidean space to obtain the 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 angular frequency. and Strain and stress, respectively. The one-dimensional frequency domain response of the target metamaterial is defined as 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 given spectral function basis for the model, e = {e1, e2, ..., e} n} represents the parameters of a 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 range of dynamic parameter variation is determined by the parameter coordinates, denoted as D(e): e={e1,e2,…,e…} n}∈D(e);

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

[0135] The overcoupling region defined by the impedance criterion is: f is the frequency parameter, f T For the frequency range of the over-coupled 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 zeros of the transfer function corresponding to the response function, i.e.

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

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

[0139] Determining energy criteria based on response function:

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

[0141] For axisymmetric two-dimensional systems:

[0142] C leak (ω)=βS inc Z w

[0143]

[0144] in, The scattering parameters are characterized by a, d, and s, which are the length, inner diameter, and depth of the two-dimensional system, respectively; j is the imaginary unit; k is the wavenumber; β is the radiation area correction factor, specifically the ratio of the incident area to the radiating area; and S... inc Let be the area of ​​the incident region.

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

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

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

[0148] Among them, f i (e) represents each disjoint closed subset of the target coupling region; the overcoupled 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 Each subset f i (e), if f is satisfied 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, Let S be an n-dimensional Hilbert space. Let μ(s) be any measurable closed subset of the set, vol be the n-dimensional volume of the set, and T be the isomorphic transformation.

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

[0155] The target robust region is obtained by tuning the target metamaterial to maximize the robust region.

[0156] It should be noted that the low-frequency sound-absorbing metamaterial robust optimization device provided in this application embodiment and the low-frequency sound-absorbing metamaterial robust optimization method provided in this application embodiment 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 described again.

[0157] In some embodiments, please refer to Figure 6 , Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device 600 provided in this 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 aforementioned robust optimization method for low-frequency sound-absorbing metamaterials.

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

[0159] Memory 620 may be any medium capable of containing, storing, transmitting, propagating, or transmitting instructions. For example, memory 620 may include, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, instruments, 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 optical discs (CD-ROMs); and may also be random access memory (RAM) or flash memory; and / or wired / wireless communication links.

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

[0161] According to embodiments of this 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, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this 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, apparatus, or device. In this application, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media can also be any computer-readable medium other than computer-readable storage media, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wireless, wired, optical fiber, radio frequency signals, etc., 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 this application can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in this application. In particular, the features described in the various embodiments and / or claims of this application can be combined and / or combined in various ways without departing from the spirit and teachings of this application. All such combinations and / or combinations fall within the scope of this application. Therefore, the scope of this application should not be limited to the above embodiments, but should be defined not only by the appended claims, but also by their equivalents. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the protection scope of this invention.

Claims

1. A method of robust optimization of low-frequency sound absorbing metamaterials, characterized in that, The method comprises the following steps: obtaining a response function of the target metamaterial by using a linear one-dimensional rheological model; the response function comprises a mechanical response and a frequency domain response; The response function of the target metamaterial is obtained by using a linear one-dimensional rheological model, comprising: obtaining the mechanical response by using the following formula: ; wherein, is a circular frequency, and are strain and stress respectively, is a one-dimensional frequency domain response of the target metamaterial, that is, Young's modulus; the frequency domain response is obtained by using the following formula: ; wherein, is a frequency spectrum function base given by the model, is a parameter of the linear one-dimensional rheological model; determining a target coupling region by using a size relationship between an imaginary part of a zero point of a transfer function corresponding to the response function or inherent loss and radiation loss as a coupling criterion, and determining a closed coupling region in which a preset parameter point is located as an initial robust region; the target coupling region comprises the closed coupling region; the preset parameter point satisfies a one-dimensional frequency domain response of the target metamaterial; the coupling criterion comprises an impedance criterion and an energy criterion; determining a target coupling region by using a size relationship between an imaginary part of a zero point of a transfer function corresponding to the response function or inherent loss and radiation loss as a coupling criterion, and determining a closed coupling region in which a preset parameter point is located as an initial robust region, comprising: The dynamic parameter variation range is determined by the parameter coordinates, and is set as D(e): ; The dynamic parameter corresponding to the preset parameter point is satisfies ; a over-coupling domain defined by the impedance criterion is: ; is a frequency parameter, is a frequency range interval of the overcoupling domain, is a coordinate of a preset parameter point, and n is a total number of parameter points. wherein is the imaginary part of the zero of the transfer function corresponding to the response function, i.e. wherein Z0is the characteristic impedance of water, , respectively the density and the sound speed of water, characterizes the imaginary part of the complex number, is the resonance frequency; determining an energy criterion based on the response function: ; wherein is the damping ratio, defined as ; and are the intrinsic and radiative losses, respectively; for an axisymmetric two-dimensional system: ； wherein , a scattering parameter, , and is the length, inner diameter and depth of the two-dimensional system, is the imaginary unit, is the wave number, is a radiation area correction factor, in particular the ratio of the incident area and the radiation area, is the incident area; determining a size of the initial robust region by using a Lebesgue measure of a 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.

2. The low-frequency sound absorbing metamaterial robust optimization method of claim 1, wherein, the method of determining a target coupling region by using a size relationship between an imaginary part of a zero point of a transfer function corresponding to the response function or inherent loss and radiation loss as a coupling criterion, and determining a closed coupling region in which a preset parameter point is located as an initial robust region, comprising: By solving the decoupled equations or , the target coupling region is obtained. ； wherein, is each disjoint closed subset of the target coupling region; the over-coupling region is the interior of the target coupling region, i.e. ； substitute the preset parameter point into each subset of the target coupling region , and determine the initial robust region if the preset parameter point satisfies the preset condition.

3. The low-frequency sound absorbing metamaterial robust optimization method of claim 1, wherein, the method of determining a size of the initial robust region by using a Lebesgue measure of a Euclidean space, comprising: ； wherein, is an n-dimensional Hilbert space, is any measurable closed subset of is a measure, denotes the n-dimensional volume of a set, denotes an isomorphic transformation.

4. The low-frequency sound absorbing metamaterial robust optimization method of claim 1, wherein, the method of optimizing the robust region by maximizing the Lebesgue measure of the initial robust region in the Euclidean space to obtain a target robust region, comprising: obtaining a target robust region by tuning the target metamaterial to maximize the robust region.

5. A low-frequency sound absorbing metamaterial robust optimization apparatus, characterized by, The method comprises the following steps: a function obtaining module, a region determining module and a region optimizing module; wherein The function acquisition module is configured to acquire a response function of the target metamaterial by using a linear one-dimensional rheological model; the response function comprises a mechanical response and a frequency domain response; specifically, the mechanical response is acquired by using the following formula: ; wherein, is a circular frequency, and are strain and stress respectively, is a one-dimensional frequency domain response of the target metamaterial, i.e., a Young's modulus; the frequency domain response is acquired by using the following formula: ; wherein, is a spectrum function base given by the model, is a parameter of the linear one-dimensional rheological model. the region determining module is configured to determine a target coupling region by using a size relationship between an imaginary part of a zero point of a transfer function corresponding to the response function or inherent loss and radiation loss as a coupling criterion, and determine a closed coupling region in which a preset parameter point is located as an initial robust region; the target coupling region comprises the closed coupling region; the preset parameter point satisfies a one-dimensional frequency domain response of the target metamaterial; specifically comprising: The dynamic parameter variation range is determined by the parameter coordinates, and is set as D(e): ; The dynamic parameter corresponding to the preset parameter point is satisfies ; a over-coupling domain defined by the impedance criterion is: ; is a frequency parameter, is a frequency range interval of the overcoupling domain, is a coordinate of a preset parameter point, and n is a total number of parameter points. wherein is the imaginary part of the zero of the transfer function corresponding to the response function, i.e. wherein, is the characteristic impedance of water, , are the density and sound speed of water, respectively, characterizes the imaginary part of the complex number, is the resonance frequency; determining an energy criterion based on the response function: ; wherein is the damping ratio, defined as ; and are the intrinsic and radiative losses, respectively; for an axisymmetric two-dimensional system: ； wherein , a scattering parameter, , and is the length, inner diameter and depth of the two-dimensional system, is the imaginary unit, is the wave number, is a radiation area correction factor, in particular the ratio of the incident area and the radiation area, is the incident area; the region optimizing module is configured to determine a size of the initial robust region by using a Lebesgue measure of a 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.

6. An electronic device comprising a processor and a memory; said memory having stored a computer program, wherein, The computer program, when executed by the processor, implements the low-frequency sound-absorbing metamaterial robust optimization method of any one of claims 1 to 4.

7. A computer storage medium, characterized in that A computer program is stored thereon, wherein the computer program is executed by a processor to implement the low-frequency sound-absorbing metamaterial robust optimization method of any one of claims 1 to 4.

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