Smooth domain construction and correction method and system based on hybrid statistical energy model

Abstract

The invention discloses a smooth domain construction and correction method and system based on a hybrid statistical energy model, and belongs to the field of acoustics and vibration analysis, and the method comprises the steps: building a finite element subsystem based on the node information of a finite element model, and building a statistical energy analysis subsystem based on the boundary node information of the finite element subsystem; building a hybrid statistical energy model based on the finite element subsystem and the statistical energy analysis subsystem; a smooth domain is constructed based on a hybrid statistical energy model, and correction is carried out by adopting node smoothing and edge smoothing technologies. According to the method, the problem of insufficient modeling of a complex fluctuation propagation path is solved, the false high-frequency resonance phenomenon caused by discretization in a finite element model is inhibited, and the vibration and acoustic performance of the structure can be predicted and analyzed more accurately.

Description

Technical Field

[0001] The present invention belongs to the field of acoustic and vibration analysis, and in particular relates to a smooth domain construction and correction method and system based on a hybrid statistical energy model. Background Art

[0002] With the rapid development of modern industry, the demand for noise and vibration control is increasing. The hybrid statistical energy analysis (FE-SEA) model, as an effective analytical tool, has been widely used in the fields of acoustic and vibration analysis. FE-SEA is a hybrid analysis method that combines the advantages of the finite element method (FEM) and statistical energy analysis (SEA). By dividing the system into deterministic and stochastic subsystems, it effectively addresses the problem of predicting the mechanical environment in the mid-frequency range. This method is particularly suitable for mid-frequency problems.

[0003] Yu Liangliang and other researchers proposed a FE-SEA theory that integrates finite element analysis and statistical energy analysis for analyzing the noise characteristics of box girder structures. Wang Honglong and Gao Yunkai further developed the fully excited FE-SEA method, improving the accuracy of mid-frequency noise prediction in excavator cabs. Wu Fei and others introduced a hybrid ES-FE-SEA method to optimize the prediction accuracy of mid-frequency acoustic-solid coupling analysis. Chen Shuming's team, through numerical simulation and experimental verification, confirmed the effectiveness and high accuracy of the FE-SEA hybrid method in predicting noise inside acoustic cavities, especially in the mid- and high-frequency bands. Zhang Jin and others studied and developed a Matlab calculation program for the FE-SEA hybrid method for mid-frequency mechanical environment prediction, and verified its accuracy and high computational efficiency by comparison with Monte Carlo simulation. Peng Tao and others focused on predicting broadband sound insulation of stiffened panels. Their research showed that the hybrid FE-SEA method has high prediction accuracy in the mid- and high-frequency bands, making it suitable for aircraft structural acoustic design. In the research field of hybrid statistical energy models (ES-FE-SEA), scholars have discovered a common problem: existing models often do not fully consider the influence of boundary conditions during the construction and correction of smooth domains. This negligence limits the accuracy of model analysis results.

[0004] Therefore, it is necessary to design a smooth domain construction and correction method and system based on a hybrid statistical energy model to address the above problems. Summary of the Invention

[0005] The purpose of the present invention is to address the problems existing in the prior art and provide a smooth domain construction and correction method based on a hybrid statistical energy model. By correcting the constructed smooth domain, the problem of insufficient modeling of complex wave propagation paths by traditional methods is solved, and the false high-frequency resonance phenomenon caused by discretization in the finite element model is suppressed. The vibration and acoustic performance of the structure can be predicted and analyzed more accurately, providing a powerful numerical tool for structural design and noise control.

[0006] According to one aspect of the present disclosure, a method for constructing and correcting a smooth domain based on a hybrid statistical energy model is provided, comprising:

[0007] A finite element (FE) subsystem is established based on the node information of the finite element (FE) model, and a statistical energy analysis (SEA) subsystem is established based on the boundary node information of the finite element subsystem;

[0008] Based on the finite element subsystem and statistical energy analysis subsystem, a hybrid statistical energy (FE-SEA) model is built;

[0009] A smooth domain is constructed based on a hybrid statistical energy model, and node smoothing and edge smoothing techniques are used for correction.

[0010] Furthermore, based on the finite element subsystem and the statistical energy analysis subsystem, a hybrid statistical energy model is built, including:

[0011] The finite element subsystem is used to model the geometry and dynamic characteristics, and the statistical energy analysis subsystem is used to model the acoustic characteristics and vibration behavior.

[0012] Furthermore, node smoothing and edge smoothing techniques are used for correction, including:

[0013] Node smoothing technology is used to adjust the spatial distribution of discrete nodes and eliminate grid distortion;

[0014] Edge smoothing technology is used to optimize the boundary geometry and unit connectivity, and a smooth regularization term is introduced to suppress curvature mutations.

[0015] Furthermore, the method further includes:

[0016] Based on the generalized Langevin equation and dissipative structure theory, the non-equilibrium dynamic equation of energy flow in smooth domain is constructed. Based on the Kolmogorov axiom system, the stochastic differential equation of energy flow in smooth domain is constructed.

[0017] Based on the constructed non-equilibrium dynamics equation and stochastic differential equation, a joint probability density function including correction parameters is obtained.

[0018] Furthermore, a beam element model is used to model the beam connecting the finite element subsystem and the statistical energy analysis subsystem.

[0019] Furthermore, the method further includes: the unit size in each direction of the finite element model does not exceed 1 / 6 of the wavelength of the relevant vibration mode.

[0020] According to one aspect of the present disclosure, a system for constructing and modifying a smooth domain based on a hybrid statistical energy model is provided, comprising:

[0021] A subsystem establishment module is used to establish a finite element subsystem based on the node information of the finite element model, and to establish a statistical energy analysis subsystem based on the boundary node information of the finite element subsystem;

[0022] Hybrid statistical energy model building module, used to build a hybrid statistical energy model based on the finite element subsystem and the statistical energy analysis subsystem;

[0023] The smooth domain construction and correction module is used to construct a smooth domain based on a hybrid statistical energy model and to correct it using node smoothing and edge smoothing techniques.

[0024] According to one aspect of this specification, an electronic device is provided, comprising a memory and a processor, wherein the memory stores a computer program, and wherein the processor implements the steps of the method for constructing and correcting a smooth domain based on a hybrid statistical energy model when executing the computer program.

[0025] According to one aspect of the present specification, a computer-readable storage medium is provided, on which a computer program is stored, characterized in that when the computer program is executed by a processor, the steps of the smooth domain construction and correction method based on the hybrid statistical energy model are implemented.

[0026] According to one aspect of the present invention, a computer program product comprising instructions is provided, which, when executed on a computer, enables the computer to execute the steps of the method for constructing and correcting a smooth domain based on a hybrid statistical energy model.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] 1. By modifying the constructed smooth domain, the present invention solves the problem of insufficient modeling of complex wave propagation paths in traditional methods, suppresses the false high-frequency resonance phenomenon caused by discretization in the finite element model, and can more accurately predict and analyze the vibration and acoustic performance of the structure, providing a powerful numerical tool for structural design and noise control.

[0029] 2. The present invention eliminates grid distortion by adjusting the spatial distribution of discrete nodes and optimizes the geometric shape of the boundary and the unit connection relationship. It is suitable for the analysis of medium and high frequency problems, can effectively solve the mechanical environment prediction problem in the medium frequency band, and provides broad application prospects for engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] 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.

[0031] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0032] Figure 2 Schematic diagram of a hybrid FE-SEA calculation model according to an embodiment of the present invention;

[0033] Figure 3 Schematic diagram of a hybrid FE-SEA acoustic cavity model according to an embodiment of the present invention;

[0034] Figure 4 This is an energy variation diagram of a thin plate 1 with a grid density unit number of 2000 according to an embodiment of the present invention;

[0035] Figure 5 Schematic diagram of the coupling loss factor from thin plate 1 to thin plate 2 when the number of mesh density units is 2000 according to an embodiment of the present invention;

[0036] Figure 6 This is a schematic diagram of the vibration velocity of the thin plate 1 when the number of grid density units is 2000 according to an embodiment of the present invention;

[0037] Figure 7 This is an energy variation diagram of a thin plate 1 with a grid density unit number of 4000 according to an embodiment of the present invention;

[0038] Figure 8 Schematic diagram of the coupling loss factor from thin plate 1 to thin plate 2 when the number of mesh density units is 4000 according to an embodiment of the present invention;

[0039] Figure 9 This is a schematic diagram of the vibration velocity of the thin plate 1 when the number of grid density units is 4000 according to an embodiment of the present invention;

[0040] Figure 10 This is an energy variation diagram of a thin plate 1 with a grid density unit number of 6000 according to an embodiment of the present invention;

[0041] Figure 11 Schematic diagram of the coupling loss factor from thin plate 1 to thin plate 2 when the number of mesh density units is 6000 according to an embodiment of the present invention;

[0042] Figure 12This is a schematic diagram of the vibration velocity of the thin plate 1 when the number of grid density units is 6000 according to an embodiment of the present invention. DETAILED DESCRIPTION

[0043] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments 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.

[0044] An embodiment of the present invention provides specific steps of a method for constructing and correcting a smooth domain based on a hybrid statistical energy model: building a hybrid statistical energy model based on a finite element subsystem and a statistical energy analysis subsystem; constructing a smooth domain based on the hybrid statistical energy model using node smoothing and edge smoothing techniques; constructing a non-equilibrium dynamics equation of energy flow in the smooth domain based on the generalized Langevin equation and dissipative structure theory, and constructing a stochastic differential equation of energy flow in the smooth domain based on the Kolmogorov axiom system; obtaining a joint probability density function containing correction parameters based on the constructed non-equilibrium dynamics equation and stochastic differential equation; and solving the joint probability density function containing the correction parameters using a sparse grid point matching method to achieve correction of the smooth domain.

[0045] Specifically, the present invention also provides a hybrid FE-SEA model in which elastic waves produce a reflection effect at the coupling boundary between the SEA and FE subsystems, which will generate additional reverberation force on the FE subsystem. Therefore, the overall dynamic equation of the FE subsystem can be expressed as:

[0046] (1)

[0047] in, is the number of SEA subsystems; is the degree of freedom vector of the FE subsystem; is the overall dynamic stiffness matrix of the FE subsystem; represents the external excitation vector acting on the FE subsystem; represents the reverberation force vector generated by the kth SEA subsystem on the coupled boundary. It can be expressed as:

[0048] (2)

[0049] in, is the dynamic stiffness matrix of the FE subsystem itself; represents the direct dynamic stiffness matrix generated by the kth SEA subsystem on the FE subsystem.

[0050] Specifically, the degree of freedom vector of the FE subsystem is It can be expressed as:

[0051] (3)

[0052] Specifically, the reverberation force on the coupled boundary can be determined by the following formula:

[0053] (4)

[0054] in, is the cross-spectral matrix of the reverberation force; is the average vibration energy of the kth SEA subsystem; is the modal density of the kth SEA subsystem; Indicates the operation of taking the imaginary part; is the circular frequency. Equation (4) establishes the connection between the vibration energy of the SEA subsystem and the reverberation force on the coupling boundary, which is the key to the FE-SEA coupling theory.

[0055] Specifically, according to the law of conservation of energy, the power balance equation of the FE-SEA coupling system can be expressed as:

[0056] (5)

[0057] in, is the internal loss factor of the jth SEA subsystem; is the additional loss factor generated by the FE subsystem on the jth SEA subsystem; is the coupling loss factor between SEA subsystem j and SEA subsystem k; is the external input power directly applied to the jth SEA subsystem; is the input power generated by the external excitation applied to the FE subsystem on the jth SEA subsystem.

[0058] Specifically, according to equations (3) and (4), the cross-spectral matrix of the FE subsystem degree of freedom q can be obtained:

[0059] (6)

[0060] in, represents the cross-spectral matrix of the external excitation acting on the FE subsystem; the superscripts “*” and “T” represent the conjugate operation and the transpose operation, respectively.

[0061] Specifically, the average vibration energy of each SEA subsystem can be obtained from formula (5), and the degrees of freedom of the FE subsystem can be obtained from formula (6), which can then be used to obtain physical quantities such as the vibration velocity and acceleration of the FE subsystem. On this basis, the sound pressure propagated to any point in space can be calculated through noise radiation theory.

[0062] Specifically, the embodiment of the present invention also provides the basic concept of smooth finite element, which is a numerical modeling technology that enhances the intermediate frequency analysis capability by improving the gradient calculation framework of the traditional finite element method (FEM). The core idea is to reconstruct the spatial distribution of the strain field or stress field by introducing gradient smoothing operations, thereby reducing the numerical hardening effect caused by unit discretization in traditional FEM. Specifically, SFE divides the computational domain into several smooth subdomains, and performs weighted averaging of the unit gradients in each subdomain to form a continuous and smooth field variable distribution. For any smooth subdomain , its smooth strain It can be expressed as:

[0063] (7)

[0064] in, is a smooth kernel function, x represents the position of the degree of freedom node 1, represents the position of the degree of freedom node 2, To represent the smooth domain, piecewise polynomials or Gaussian functions are typically chosen to balance computational efficiency and accuracy. Through the smoothing operation, the system's stiffness matrix is ​​explicitly softened, thereby more realistically simulating the energy dissipation characteristics of mid-frequency wave propagation. Compared with traditional FEM, SFE significantly reduces numerical dispersion errors in the mid-frequency range (100 Hz to 1 kHz) while retaining the ability to resolve local geometric details. Furthermore, the weak form equations of SFE avoid the discontinuities of higher-order derivatives of shape functions in traditional FEM by reconstructing the shape function derivatives, thereby improving the robustness of dynamic response predictions.

[0065] Specifically, an embodiment of the present invention also provides the application of smooth finite elements in hybrid statistical energy models. In the medium-frequency acoustic-solid coupling system, the coordinated application of SFE and FE-SEA effectively solves the problem of insufficient modeling of complex wave propagation paths by traditional methods. Through the gradient smoothing technology of SFE, the stiffness matrix of the structural subsystem is corrected to a continuous form that is closer to physical reality, suppressing the false high-frequency resonance phenomenon caused by discretization in the finite element model. For example, in the analysis of aircraft cabin wall-acoustic cavity coupling, the SFE-FE-SEA model can accurately capture the energy exchange mechanism between the bending wave of the thin-walled structure and the standing wave of the acoustic cavity. Its dynamic response cross-spectral matrix can be expressed as:

[0066] (8)

[0067] in, is the overall dynamic stiffness matrix after SFE correction, and the superscript “-H” indicates the conjugate transformation of the matrix.

[0068] Specifically, in the design of commercial vehicle cab acoustic packages, the SFE-FE-SEA model uses two-dimensional smooth domain parameterization technology to rapidly solve multi-objective optimization problems. Using the thickness of the sound insulation layer and the porosity of the porous material as design variables, the objective function can be defined as the frequency band integral of the sound transmission loss (TL):

[0069] (9)

[0070] Using gradient smoothing techniques, the continuity of acoustic impedance at the acoustic envelope's boundaries is enhanced, accurately simulating the transmission and reflection behavior of sound waves in multilayered media. The optimized model achieves a prediction error of less than 10% in the 200Hz to 800Hz frequency range, providing a reliable numerical tool for lightweight acoustic envelope design.

[0071] Specifically, the accuracy of the hybrid FE-SEA model relies on the accurate modeling of the connection correction factors between subsystems. SFE quantifies the non-deterministic characteristics of energy transfer in the connection area by constructing a hybrid connection dynamic stiffness matrix based on the reciprocity principle. The correction factor can be defined as:

[0072] (10)

[0073] in, is the coupling impedance matrix after SFE correction, is the reference impedance, and Re( ) represents the real part of the matrix. SFE supports parametric modeling of complex connections (such as bolted connections and adhesive joints), providing a universal solution for broadband noise control in industrial structures.

[0074] Specifically, an embodiment of the present invention also provides a process for building a hybrid FE-SEA model, including: 1. dividing the FE subsystem and the SEA subsystem; 2. establishing the FE subsystem based on the node information of the finite element model; 3. establishing the SEA subsystem based on the boundary node information of the FE subsystem; 4. connecting the FE and FE subsystems, the FE and SEA subsystems, and the SEA and SEA subsystems to ensure that energy is transferred between the subsystems.

[0075] Specifically, a hybrid FE-SEA calculation model based on wave coupling theory was created using the commercial software VAONE, such as Figure 2As shown in Figure 1, the model consists of three main parts: a double-curvature shell at the top, a cylindrical shell in the middle, and two single-curvature shells at the bottom. These parts are connected by beams to form a complex structural system, in which the double-curvature shell and the cylindrical shell contain acoustic cavities, as shown in Figure 1. Figure 3 shown.

[0076] Specifically, during the model analysis, the top double-curved shell was simulated using the FE subsystem due to its complex geometry and dynamic characteristics. The FE subsystem accurately captures the dynamic response of the structure and is suitable for deterministic structural analysis. The central cylindrical shell and the two single-curved shells at the bottom were modeled using the SEA subsystem, taking into account their acoustic properties and vibration behavior. The SEA subsystem uses plate elements (SEA-plates) to simulate the propagation and radiation of sound waves within the structure. The beams connecting these subsystems are modeled using beam elements (SEA-beams) to ensure efficient transfer of vibrational and acoustic energy between the subsystems. During model construction, precise parameter settings for each subsystem, including material properties, geometric dimensions, and boundary conditions, are required to ensure model accuracy and reliability. Furthermore, to simulate inter-structural coupling, manual SEA point junctions are used to simulate the connections between subsystems. This connection method more accurately simulates the interaction and energy transfer between different subsystems. The entire model construction process requires detailed configuration of the connections between the various subsystems to ensure model integrity and analysis accuracy. This hybrid modeling approach enables more precise prediction and analysis of a structure's vibration and acoustic performance, providing a powerful numerical tool for structural design and noise control. This method is particularly well-suited for analyzing mid- and high-frequency problems, effectively addressing the mechanical environment prediction issues in this band, offering broad potential for engineering applications.

[0077] Specifically, embodiments of the present invention also provide a method for constructing a smooth domain based on a statistical energy model. The core goal of constructing a two-dimensional smooth domain is to improve the continuity and computational accuracy of physical field simulations by optimizing the node distribution and boundary geometry of discrete grids. The method system mainly covers node smoothing, edge smoothing technology, and the combined application of the two. The specific technical route is as follows:

[0078] 1. Node smoothing technology eliminates grid distortion by adjusting the spatial distribution of discrete nodes. Among them, the Laplace smoothing algorithm is the most classic node optimization method. For any internal node in a two-dimensional grid, , whose new position is determined by the geometric center of the neighborhood nodes:

[0079] (11)

[0080] in, is the number of adjacent nodes; in order to prevent the boundary nodes from causing geometric distortion due to excessive movement, a relaxation factor is introduced ∈[0,1] constrains its displacement:

[0081] (12)

[0082] in, The value is usually between 0.3–0.5 to balance the smoothing effect and geometric fidelity. represents the boundary displacement, represents the original displacement, Represents the displacement of the smooth domain; for complex geometric domains, an optimization-based node smoothing method is further adopted to minimize the mesh distortion as the objective function and define the triangle element quality index :

[0083] (13)

[0084] in, is the unit area, is the side length. The global optimization objective function is:

[0085] (14)

[0086] in, is the boundary constraint weight, 、 They represent the boundary nodes of the smooth domain respectively; the Quasi-Newton Method (BFGS) is used to iteratively solve and update the node coordinates as follows:

[0087] (15)

[0088] in, is the Hessian matrix, is the adaptive step size factor to ensure convergence efficiency.

[0089] Specifically, edge smoothing technology focuses on optimizing boundary geometry and cell connectivity. For a convex quadrilateral region formed by adjacent triangles △ABC and △ACD, edge swapping optimization improves cell quality by replacing the common edge AC with BD. The swapping conditions must meet the following:

[0090] (16)

[0091] in, For the curve boundary, the cubic B-spline curve fitting technology is used to separate the discrete nodes Mapping to a smooth curve:

[0092] (17)

[0093] in, is the cubic B-spline basis function, control point Solved by least squares method and introducing smooth regularization term Suppress curvature mutations.

[0094] Specifically, an embodiment of the present invention also provides a three-dimensional smooth domain construction method for solving the continuity problems of complex geometric topology and accurate modeling of energy transfer paths. Its technical system integrates the polyhedron element method, boundary representation method (B-Rep) and node interpolation method, aiming to improve the accuracy of medium and high frequency acoustic vibration coupling analysis through mathematical optimization and physical field reconstruction.

[0095] Specifically, the smooth edge finite element method of polyhedral elements realizes the continuity of local fields by constructing subdomains based on the element boundaries. , whose smooth subdomain is composed of edge endpoints , adjacent face centers and body center Common definition.

[0096] Specifically, the boundary representation method (B-Rep) achieves high-fidelity construction of complex entities through hierarchical modeling of geometric topology. Its process first starts from a discrete point set Starting from, a topological adjacency matrix is ​​established to define the connection relationship between points. Then, the minimum spanning tree algorithm is used to generate closed edge rings to meet the ring integral condition , ensuring global consistency of edge direction. The edge loop is further projected into the local coordinate system to generate non-uniform rational B-spline (NURBS) surface patches, which are finally stitched together to form a closed shell and define the solid space. In order to improve the smoothness of the surface, the moving least squares (MLS) method is used to perform parameter fitting on discrete points:

[0097] (18)

[0098] in, is the MLS basis function, For the control point, by minimizing the energy functional Balance fitting accuracy and curvature continuity.

[0099] Specifically, the node interpolation method realizes the continuous reconstruction of the internal field of the element through natural coordinate mapping. , any point inside Natural coordinates of Satisfy linear constraints:

[0100] (19)

[0101] Specifically, when investigating the vibration response and acoustic radiation of double-curvature shells, cylindrical shells, and single-curvature shells created using FE models, element sizing is crucial. To ensure computational accuracy, the element size in all directions must be appropriately set, typically not exceeding 1 / 6 of the wavelength of the relevant vibration mode. For each model, the analysis frequency is assumed to be within the mid-frequency range of 50 to 500 Hz, and the element side length is uniformly set to 0.1 m. The element size is divided into a number of elements and nodes, the specific number of which depends on the complexity of the model and the required accuracy. For the double-curvature shell, the material elastic modulus is assumed to be 210 GPa, the shear modulus is 84 GPa, the bulk density is 23.5 kN / m³, the Poisson's ratio is 0.3, and the loss factor is 0.03. If the same material properties are used for the central cylindrical shell and the two single-curvature shells at the bottom, their parameters are consistent with those of the double-curvature shell. If different materials are used, the parameters need to be adjusted based on the actual situation. The material properties are shown in Table 1.

[0102] Table 1 Material properties

[0103]

[0104] Specifically, in the model, the beams connecting the double-curvature shell to the cylindrical shell, and between the cylindrical shell and the single-curvature shell, may have material properties that differ from those of the shell material. For example, if the beam is made of steel, its elastic modulus may be 206 GPa, its bulk density may be 78.5 kN / m³, its Poisson's ratio may be 0.3, and its loss factor may be 0.02. The cross-sectional dimensions and moment of inertia of the beam must be determined based on the actual design. The acoustic cavity may be filled with air or another medium, and parameters such as its density, speed of sound, and viscosity will affect the calculated sound radiation. For example, if the cavity is filled with air, the density of air is approximately 1.225 kg / m³, and the speed of sound is approximately 343 m / s (at room temperature and pressure).

[0105] Specifically, during model construction, boundary conditions and load application must be considered. For example, displacement boundary conditions may be applied to the fixed ends of the shell, while external excitations such as wind loads or traffic loads need to be applied as forces at the corresponding locations on the model. By setting these detailed model parameters and defining boundary conditions, you can ensure that the FE-SEA model accurately simulates the vibration and sound radiation characteristics of your model, providing a scientific basis for subsequent structural optimization and noise control.

[0106] Specifically, the embodiment of the present invention further provides a smooth domain model correction method. First, based on the generalized Langevin equation and dissipative structure theory, a non-equilibrium dynamic equation of energy flow in the smooth domain is constructed:

[0107] (20)

[0108] Among them, the energy flow density tensor Satisfies Onsager reciprocal relation, dissipative term Constrained by the Coleman-NOl entropy inequality. By introducing the connection coefficient in differential geometry Establish a covariant derivative operator on the energy manifold:

[0109] (twenty one)

[0110] in, Expressed as a gradient operator, Denotes partial derivatives. This operator fully characterizes the curvature effect and torsion coupling characteristics of energy transfer in a smooth domain. Using the Helinger-Reissner mixed variational principle, a modified functional that includes the inertia-dissipation-wave three-field coupling is constructed:

[0111] (twenty two)

[0112] Specifically, by proving that the modified functional in Sobolev space The existence of weak solutions in the equation is verified, and the Lax-Milgram well-posedness criterion of parameter correction is established to ensure the mathematical convergence of the correction process.

[0113] Specifically, based on the Kolmogorov probability axiom system, the stochastic differential equation of energy flow in the smooth domain is constructed:

[0114] (twenty three)

[0115] Among them, the diffusion coefficient tensor The Hörmander condition is satisfied.

[0116] By constructing the Karhunen-Loève basis function expansion in the Hilbert-Schmidt operator space, a generalized polynomial chaotic agent model is established:

[0117] (twenty four)

[0118] in, is a set of multiple indicators, is the Hermite orthogonal polynomial basis, The energy matrix is ​​represented by . The joint probability density function of the correction parameters is solved using the sparse grid collocation method to verify the model robustness within the 95% confidence region.

[0119] Specifically, the embodiment of the present invention also provides a model verification of the smooth domain correction method. The reference algorithm integrates the finite element-based energy flow analysis and Monte Carlo test, and then compares it with the calculation results of the commercial software VAONE. The finite element method is a method currently widely used in the field of dynamic analysis. Through in-depth development of analysis data sets or formulas, it can achieve accurate analysis of the energy flow of sub-item systems. At the same time, Monte Carlo simulation is used to introduce parameter perturbations, and then describe the impact of uncertainty factors on medium and high frequency responses. Given that the finite element method does not adopt a large number of assumptions, the analysis results obtained by the energy flow analysis-Monte Carlo simulation method can be used as a reference for research and improvement of the SEA method and the medium-frequency mechanical environment prediction method.

[0120] Specifically, the embodiment of the present invention also provides a model simulation analysis with a grid density unit number of 2000. Figure 4 The energy evolution of Plate 1 with a mesh density of 2000 elements is shown. At low frequencies (16-50 Hz), all solutions have low energy values, indicating low energy dissipation. Around 50 Hz and 100 Hz, the energy value of the solution with 6000 elements increases significantly, resulting in greater energy dissipation and a stronger vibration response. At higher frequencies, the energy values ​​converge, but the 6000-element solution still has slightly higher values ​​at certain points, indicating relatively high energy dissipation. Figure 5 The figure shows how the coupling loss factor from plate 1 to plate 2 varies with frequency, for a mesh density of 2000 elements. At low frequencies, the scheme with 2000 elements exhibits the highest coupling loss factor and the lowest energy transfer efficiency. As frequency increases, the coupling loss factors of each scheme decrease, while energy transfer efficiency improves. The scheme with 6000 elements exhibits the lowest coupling loss factor, the highest energy transfer efficiency, and the lowest energy loss, resulting in the best performance. Figure 6 The frequency variation of the vibration velocity of Plate 1 is shown for a mesh density of 2000 elements. At low frequencies, the vibration velocities and vibration response intensities of all schemes are similar. Around 50 Hz and 100 Hz, the vibration velocity of the scheme with 6000 elements increases significantly, reaching a peak before gradually decreasing, indicating that its vibration response intensity is the highest. It then weakens with increasing frequency. At higher frequencies, the vibration velocities tend to be consistent, but the 6000 element scheme still has slightly higher velocities at certain points, indicating that its vibration response intensity is still relatively strong.

[0121] Specifically, the embodiment of the present invention also provides a model simulation analysis with a grid density of 4000 units. Figure 7The energy evolution of Plate 1 is shown for a mesh density of 4000 elements. At low frequencies (16-50 Hz), all solutions exhibit low energy values, indicating minimal energy dissipation. Around 50 Hz and 100 Hz, the energy value for the solution with 6000 elements increases significantly, resulting in greater energy dissipation and a more intense vibration response. At higher frequencies, the energy values ​​converge, but the 6000-element solution still exhibits slightly higher values ​​at certain points, indicating relatively high energy dissipation. Figure 8 The frequency-dependent coupling loss factor from plate 1 to plate 2 is shown for a mesh density of 4000 elements. At low frequencies, the 4000-element solution exhibits the highest coupling loss factor and the lowest energy transfer efficiency. As frequency increases, the coupling loss factors of each solution decrease, while energy transfer efficiency improves. The 6000-element solution exhibits the lowest coupling loss factor, the highest energy transfer efficiency, and the lowest energy loss, resulting in the best performance. Figure 9 The frequency variation of the vibration velocity of Plate 1 is shown for a mesh density of 4000 elements. At low frequencies, the vibration velocities of all schemes are similar, and the vibration response strength is similar. Around 50Hz and 100Hz, the vibration velocity of the scheme with 6000 elements increases significantly, reaching a peak before gradually decreasing, indicating that its vibration response strength is the highest, then weakening with increasing frequency. At higher frequencies, the vibration velocities tend to be consistent, but the scheme with 6000 elements still has slightly higher velocities at certain points, indicating that its vibration response strength is still relatively strong.

[0122] Specifically, the embodiment of the present invention also provides a model simulation analysis with a grid density of 4000 units. Figure 10 The energy evolution of Plate 1 is shown for a mesh density of 6000 elements. At low frequencies (16-50 Hz), all schemes exhibit low energy values, indicating minimal energy dissipation. Around 50 Hz and 100 Hz, the energy value for the 6000-element scheme increases significantly, resulting in greater energy dissipation and a more intense vibration response. At higher frequencies, the energy values ​​converge, but the 6000-element scheme still exhibits slightly higher values ​​at certain points, indicating relatively high energy dissipation. Figure 11 The frequency-dependent coupling loss factor from plate 1 to plate 2 is shown for a mesh density of 6000 elements. At low frequencies, the scheme with 2000 elements exhibits the highest coupling loss factor and the lowest energy transfer efficiency. As frequency increases, the coupling loss factors of each scheme decrease, while energy transfer efficiency improves. The scheme with 6000 elements exhibits the lowest coupling loss factor, the highest energy transfer efficiency, and the lowest energy loss, resulting in the best performance. Figure 12The frequency variation of the vibration velocity of Plate 1 for a mesh density of 6000 elements is shown. At low frequencies, the vibration velocities of all schemes are similar, and the vibration response strength is similar. Around 50Hz and 100Hz, the vibration velocity of the scheme with 6000 elements increases significantly, reaching a peak before gradually decreasing, indicating that its vibration response strength is the highest, and then weakens with increasing frequency. At higher frequencies, the vibration velocities tend to be consistent, but the scheme with 6000 elements still has slightly higher velocities at certain points, indicating that its vibration response strength is still relatively strong.

[0123] The implementation of each embodiment of the present invention is based on programmed processing performed by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of each embodiment of the present invention are encapsulated into various modules. Based on this reality, and in addition to the aforementioned embodiments, an embodiment of the present invention provides a system for constructing and correcting a smooth domain based on a hybrid statistical energy model. This system is used to implement a method for constructing and correcting a smooth domain based on a hybrid statistical energy model described in the aforementioned method embodiments.

[0124] The system includes: a subsystem establishment module, which is used to establish a finite element subsystem based on the node information of the finite element model, and to establish a statistical energy analysis subsystem based on the boundary node information of the finite element subsystem; a hybrid statistical energy model construction module, which is used to build a hybrid statistical energy model based on the finite element subsystem and the statistical energy analysis subsystem; a smooth domain construction and correction module, which is used to construct a smooth domain based on the hybrid statistical energy model and to perform corrections using node smoothing and edge smoothing techniques.

[0125] An embodiment of the present invention provides a smooth domain construction and correction system based on a hybrid statistical energy model. To address the problem that traditional methods are insufficient in modeling complex wave propagation paths, the system adopts several modules to adjust the spatial distribution of discrete nodes, eliminate grid distortion, optimize the geometric shape of the boundary and the unit connection relationship, and correct the constructed smooth domain. This solves the problem that traditional methods are insufficient in modeling complex wave propagation paths, and suppresses the false high-frequency resonance phenomenon caused by discretization in the finite element model.

[0126] Based on the same inventive concept as the aforementioned embodiment, an embodiment of the present invention further provides an electronic device, including a memory and a processor, wherein the memory is used to store computer-executable instructions, and the processor is used to execute computer-executable instructions to implement a smooth domain construction and correction method based on a hybrid statistical energy model as proposed in the aforementioned embodiment.

[0127] The present invention also provides a computer-readable storage medium having a computer program stored thereon. When executed by a processor, the program overcomes the false high-frequency resonance phenomenon caused by discretization in the finite element model, optimizes the geometric shape of the boundary and the connection relationship between the units, is suitable for the analysis of medium and high frequency problems, and can effectively solve the problem of mechanical environment prediction in the medium frequency band.

[0128] The storage medium can be any non-volatile storage device such as a hard disk, solid-state drive, flash drive, optical disk, etc., which is used to store computer program code and necessary data files. The stored computer program includes: a subsystem establishment module, a hybrid statistical energy model building module, and a smooth domain construction and correction module.

[0129] Embodiments of the present invention further provide a computer program product comprising instructions that, when executed on a computer, fully or partially performs the smooth domain construction and correction method based on the hybrid statistical energy model proposed in the above embodiment. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device.

[0130] Finally, it should be noted that the above specific embodiments are merely representative examples of the present invention. Obviously, the present invention is not limited to the above specific embodiments and is susceptible to numerous variations. Any simple modifications, equivalent variations, and modifications to the above specific embodiments based on the technical essence of the present invention shall be deemed to fall within the scope of protection of the present invention.

Claims

1. A smooth domain construction and correction method based on a hybrid statistical energy model, characterized in that: include: A finite element subsystem is established based on the node information of the finite element model, and a statistical energy analysis subsystem is established based on the boundary node information of the finite element subsystem; Build a hybrid statistical energy model based on the finite element subsystem and statistical energy analysis subsystem; A smooth domain is constructed based on a hybrid statistical energy model, and node smoothing and edge smoothing techniques are used for correction.

2. The method for constructing and correcting a smooth domain based on a hybrid statistical energy model according to claim 1, characterized in that: Based on the finite element subsystem and statistical energy analysis subsystem, a hybrid statistical energy model is built, including: The finite element subsystem is used to model the geometry and dynamic characteristics, and the statistical energy analysis subsystem is used to model the acoustic characteristics and vibration behavior.

3. The method for constructing and correcting a smooth domain based on a hybrid statistical energy model according to claim 1, characterized in that: Correction is performed using node smoothing and edge smoothing techniques, including: Node smoothing technology is used to adjust the spatial distribution of discrete nodes and eliminate grid distortion; Edge smoothing technology is used to optimize the boundary geometry and unit connectivity, and a smooth regularization term is introduced to suppress curvature mutations.

4. The method for constructing and correcting a smooth domain based on a hybrid statistical energy model according to claim 1, characterized in that: The method further comprises: Based on the generalized Langevin equation and dissipative structure theory, the non-equilibrium dynamic equation of energy flow in smooth domain is constructed. Based on the Kolmogorov axiom system, the stochastic differential equation of energy flow in smooth domain is constructed. Based on the constructed non-equilibrium dynamics equation and stochastic differential equation, a joint probability density function including correction parameters is obtained.

5. The method for constructing and correcting a smooth domain based on a hybrid statistical energy model according to claim 1, characterized in that: The method further comprises: The beam element model is used to model the beam connecting the finite element subsystem and the statistical energy analysis subsystem.

6. The method for constructing and correcting a smooth domain based on a hybrid statistical energy model according to claim 1, characterized in that: The method further includes: the unit size in each direction of the finite element model does not exceed 1 / 6 of the wavelength of the relevant vibration mode.

7. A smooth domain construction and correction system based on a hybrid statistical energy model, characterized in that: include: A subsystem establishment module is used to establish a finite element subsystem based on the node information of the finite element model, and to establish a statistical energy analysis subsystem based on the boundary node information of the finite element subsystem; Hybrid statistical energy model building module, used to build a hybrid statistical energy model based on the finite element subsystem and the statistical energy analysis subsystem; The smooth domain construction and correction module is used to construct a smooth domain based on a hybrid statistical energy model and to correct it using node smoothing and edge smoothing techniques.

8. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the smooth domain construction and correction method based on the hybrid statistical energy model according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for constructing and correcting a smooth domain based on a hybrid statistical energy model according to any one of claims 1 to 6 are implemented.

10. A computer program product comprising instructions, characterized in that When the method is run on a computer, the computer is enabled to execute the steps of the smooth domain construction and correction method based on the hybrid statistical energy model according to any one of claims 1 to 6.

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