FEM-SEA hybrid calculation method for full-frequency-domain NVH simulation analysis

Abstract

The invention discloses an FEM-SEA hybrid calculation method and device for full-frequency-domain NVH simulation analysis and a storage medium, and belongs to the field of computer aided design. The method comprises the following steps: calculating the modal density n (f) of a to-be-analyzed structure in a target frequency band; the frequency domain type (low frequency, intermediate frequency or high frequency) is automatically judged based on the value of a modal density criterion n (f) delta f; and according to a judgment result, a finite element method module, a statistical energy analysis method module or an FEM-SEA hybrid analysis module is automatically selected and called for simulation calculation. Wherein the FEM-SEA hybrid analysis is based on the direct mixing field reciprocity theorem, and accurate coupling between the deterministic subsystem and the statistical subsystem is realized by constructing an overall dynamic stiffness matrix Dtot, calculating an energy conversion coefficient and solving an energy balance equation. According to the method, full-frequency-domain automatic analysis of NVH simulation from low frequency to high frequency is achieved, dependence of method selection on artificial experience is avoided, and the precision and efficiency of medium-frequency band analysis are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of computer aided engineering (CAE) and simulation technology, in particular to a simulation analysis method for noise, vibration and harshness (NVH), and more particularly to a hybrid finite element method (FEM) and statistical energy analysis method (SEA) calculation method suitable for full frequency domain NVH simulation analysis. BACKGROUND

[0002] Noise and vibration problems are key challenges in the design of complex systems such as spacecraft, aerospace structures, automobiles, etc., directly affecting the reliability, safety and passenger comfort of the structure. Accurate prediction of the response of the structure in a vibration-acoustic coupling environment during the product design phase is crucial for optimizing design and reducing test costs.

[0003] Currently, the mainstream NVH simulation methods include finite element method (FEM), boundary element method (BEM) and statistical energy analysis method (SEA). FEM is suitable for low-frequency vibration analysis, which has high accuracy, but when the analysis frequency is raised to medium-high frequency, the number of grids required to accurately capture short-wavelength deformation will increase exponentially, resulting in unaffordable computational cost, and the results are sensitive to structural parameter uncertainty. SEA is suitable for high-frequency vibration analysis, which treats the system as a statistical population composed of multiple interconnected subsystems, tracks the flow and dissipation of energy, has high computational efficiency, and can handle uncertainty. However, in the medium-low frequency range, the number of subsystem modes is insufficient, the statistical assumption fails, leading to increased prediction error, and local detail response cannot be obtained.

[0004] To solve the problem of medium frequency, the existing technology proposes a FEM-SEA hybrid method, i.e. dividing the system into deterministic FEM regions and random SEA regions for coupled analysis. However, the existing hybrid method has obvious deficiencies: first, for a given analysis problem, how to scientifically divide the FEM and SEA regions, and how to choose pure FEM, pure SEA or hybrid method, highly depends on the personal experience of engineers, lacks objective and automatic judgment criteria, resulting in low standardization of analysis process and poor repeatability of results. Secondly, in the coupling modeling of FEM subsystems and SEA subsystems, how to accurately describe the bidirectional energy flow between them (i.e. the energy radiation of deterministic subsystems to statistical field, and the random excitation of statistical field to deterministic subsystems), the existing coupling model is often simplified or has low computational efficiency, affecting the accuracy and reliability of medium frequency analysis.

[0005] Therefore, there is an urgent need for an NVH simulation analysis method that can automatically and intelligently cover the full frequency domain, and has high accuracy and efficiency in the medium frequency range. SUMMARY

[0006] 1. Technical problems to be solved: The present application aims to overcome the deficiencies of the prior art, and provides an FEM-SEA hybrid calculation method for full-frequency-domain NVH simulation analysis. The method can automatically select the optimal analysis method according to the dynamic characteristics of the structure, and realize efficient and high-precision simulation of the medium frequency band by using a set of accurate coupling theory.

[0007] 2. Technical solutions: To solve the above problems, the present application adopts the following technical solutions.

[0008] In a first aspect, the present application provides an FEM-SEA hybrid calculation method for full-frequency-domain NVH simulation analysis, comprising the following steps: Step S1: obtaining a simulation model of a structure to be analyzed, and calculating the modal density n(f) of the structure in a target frequency range; Step S2: automatically determining the frequency domain type to which the target frequency range belongs based on the modal density criterion; the modal density criterion is: calculating the value of n(f)Δf, where Δf is the analysis bandwidth in the target frequency range; if n(f)Δf is less than a first preset threshold, it is determined to be a low frequency domain; if n(f)Δf is between the first preset threshold and a second preset threshold, it is determined to be a medium frequency domain; if n(f)Δf is greater than the second preset threshold, it is determined to be a high frequency domain; Step S3: automatically calling the corresponding analysis module for NVH simulation calculation according to the determination result of the frequency domain type: If it is determined to be a low frequency domain, a finite element method module is called for calculation; If it is determined to be a high frequency domain, a statistical energy analysis module is called for calculation; If it is determined to be a medium frequency domain, an FEM-SEA hybrid analysis module is called for calculation.

[0009] Preferably, the calculation of the modal density n(f) in step S1 comprises the following sub-steps: S11: solving all natural frequencies f of the structure in the [0, f max ] frequency range by using the finite element method; i where f max is the upper limit of the target frequency range; S12: counting the cumulative modal number N(f) from 0 to the frequency f; S13: calculating the modal density n(f) = [N(f2)-N(f1)] / (f2-f1), where f1 and f2 are the end points of the frequency interval.

[0010] Preferably, the calculation of the FEM-SEA hybrid analysis module in step S3 comprises the following sub-steps: S31: dividing the structure into at least one FEM deterministic subsystem and at least one SEA statistical subsystem; S32: constructing a whole dynamic stiffness matrix D containing the FEM subsystem stiffness and the SEA subsystem direct field stiffness based on the reciprocity theorem of direct and diffuse field tot ; S33: calculating the energy transfer coefficient h between the diffuse field of the SEA subsystem and the FEM subsystem tot,m , and the energy transfer coefficient h between the SEA subsystems n,m ; S34: assembling an energy balance matrix equation and solving the steady-state energy E of each SEA subsystem m ; S35: calculating the node displacement response S of the FEM subsystem according to the formula qq , wherein is an external excitation force, is the diffuse field force of the mth SEA subsystem.

[0011] Preferably, the calculation formula of the energy transfer coefficient h tot,m is: , wherein is the direct field dynamic stiffness matrix of the mth SEA subsystem, and Im(·) represents the imaginary part operation.

[0012] Preferably, the calculation formula of the energy transfer coefficient h n,m is: , wherein is the direct field dynamic stiffness matrix of the n th SEA subsystem.

[0013] Preferably, in the step S34, the energy balance matrix equation is: , , wherein M m = ωn m η m is a modal superposition factor, ω is a circular frequency, n m is the modal density of the mth subsystem, η m is its internal loss factor, is the input power of the mth subsystem under external excitation.

[0014] Preferably, in the step S35, the diffuse field force F of the SEA subsystem is calculated according to the formula: .​​

[0015] In a second aspect, the application provides an electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, the processor implementing the steps of the method of any one of claims 1 to 7 when executing the computer program.

[0016] In a third aspect, the application provides a computer-readable storage medium having stored thereon a computer program, the computer program implementing the steps of the method of any one of claims 1 to 7 when executed by a processor.

[0017] 3. Beneficial effects Compared with the prior art, the technical scheme provided by the application has the following beneficial effects: (1) Full-frequency-domain automatic adaptation: By introducing an objective judgment criterion based on modal density n(f)Δf, the application realizes automatic and intelligent identification of the frequency domain (low frequency, medium frequency, high frequency) to which the analysis problem belongs, and seamlessly calls the optimal simulation method (pure FEM, pure SEA or FEM-SEA hybrid) accordingly, avoiding the uncertainty and inefficiency of relying on manual experience for method selection and model division.

[0018] (2) Significant improvement in medium-frequency analysis accuracy and efficiency: In the hybrid analysis core, the application is based on the "straight mixing field reciprocity theorem", and by constructing the overall dynamic stiffness matrix D tot , and accurately deriving the energy conversion coefficients h tot,m and h n,m , a set of rigorous coupled system energy balance equations is established. This scheme has clear physical meaning and rigorous mathematical expression, and can accurately represent the bidirectional energy flow between the FEM subsystem and the SEA subsystem, and between the SEA subsystems, thus taking into account the local accuracy of FEM and the statistical efficiency of SEA in the medium frequency band, and obtaining more reliable analysis results than existing hybrid methods.

[0019] (3) Strong engineering practicability: The application encapsulates the complex hybrid theory into an automated process, forming a complete software architecture including the underlying calculation support, discipline algorithms, solution control and coupling layer. Users only need to provide the model and excitation, and the system can automatically complete the full-frequency-domain NVH analysis, reducing the use threshold and improving the efficiency of design iteration.

[0020] It should be noted that the structures not introduced by the application do not involve the design points and improvement directions of the application, and are the same as or can be realized by using the prior art, and are not described here. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 A schematic diagram of an electric vehicle powertrain NVH simulation workflow.

[0022] Figure 2 The system architecture diagram of the FEM-SEA hybrid computing model for full frequency domain NVH simulation analysis described in the embodiment of the application.

[0023] Figure 3 The flowchart of the FEM-SEA hybrid computing method for full frequency domain NVH simulation analysis described in the embodiment of the application. DETAILED DESCRIPTION

[0024] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are some of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the application.

[0025] The application provides an automatic full frequency domain NVH simulation solution. Figure 2 The system architecture of the solution is shown, which includes a FEM-SEA coupling layer, a solving flow control layer, a subject algorithm layer and a bottom layer from top to bottom.

[0026] The bottom layer is a computing infrastructure, which provides an MPI parallel computing framework, data storage management and solvers of various equation groups (linear equation groups, generalized eigenvalue equations).

[0027] The subject algorithm layer encapsulates basic algorithms of NVH simulation, including various finite element unit algorithms (such as solid, shell, beam units), material constitutive models, boundary condition application algorithms (such as fixed support, simple support) and load definition algorithms (such as force, pressure).

[0028] The solving flow control layer is a core scheduler. It calls the subject algorithm layer module according to the analysis task (such as modal, frequency response analysis) defined by the user, automatically assembles the overall mass matrix M, stiffness matrix K and damping matrix C of the system, forms the equation group to be solved (for example, [K-ω 2 M+iωC]{q}={f}) after applying boundary conditions, and calls the bottom layer solver for calculation.

[0029] The FEM-SEA coupling layer is the core of the hybrid method. It is specially responsible for performing the FEM-SEA hybrid analysis of step S3 in claim 1, and its internal process strictly follows the steps described in claims 3-7: 1) constructing the overall dynamic stiffness matrix D tot of the coupled system; 2) calculating the input power and energy conversion coefficient h n,m ; h tot,m; 3) Assemble and solve energy balance equations to obtain the steady-state energy E of each SEA subsystem m ; 4) Calculate reverberation field forces and finally solve the response S of the FEM subsystem qq .

[0030] Figure 3 The total flow of applying the method of the present application to a specific physical problem for full frequency domain NVH simulation analysis is shown.

[0031] Firstly, the system reads in the finite element mesh model of the structure to be analyzed and the analysis control parameters (such as the target frequency range f max , analysis bandwidth Δf).

[0032] Subsequently, the automatic frequency domain determination stage is entered (corresponding to steps S1 and S2 of claim 1). The system automatically calls the FEM module to perform modal analysis, solve the natural frequencies of the structure within [0, f max ], and then calculate the modal density function n(f) of the structure. Then, based on the value of the modal density criterion n(f)Δf, an automatic logical judgment is made: if n(f)Δf is less than a first preset threshold (for example, 0.2), it is determined to be a low frequency domain; if n(f)Δf is between the first preset threshold (for example, 0.2) and a second preset threshold (for example, 5), it is determined to be a medium frequency domain; if n(f)Δf is greater than the second preset threshold (for example, 5), it is determined to be a high frequency domain. The determination process is fully automated.

[0033] According to the determination result, the system automatically selects and executes the corresponding analysis path: 1) Low frequency path: call the pure FEM solver to perform deterministic frequency response analysis and output the node displacement, stress and other responses.

[0034] 2) High frequency path: call the pure SEA solver, automatically divide the statistical subsystem, establish and solve the statistical energy balance equation, and output the average energy distribution of each subsystem.

[0035] 3) Medium frequency path (core of the present application): call the FEM-SEA hybrid analysis module. First, divide the FEM subsystem (focus on local details) and the SEA subsystem (modal intensive area). Then perform the FEM-SEA coupling layer process: construct D tot , calculate h tot,m and h n,m , solve the energy balance equation to obtain E m , and finally calculate the displacement response spectrum S qq of the FEM subsystem. This response contains the comprehensive effect of external excitation and SEA reverberation field feedback.

[0036] Finally, the analysis results of all paths enter the unified post-processing stage, output the key indicators such as vibration level, sound pressure level, transfer function, etc., and can generate visual results and reports.

[0037] Embodiment: High-frequency NVH performance analysis of automobile door panel Taking a specific engineering analysis scene as an example, the implementation process of the method of the application is further illustrated.

[0038] Step 1: Model import and preprocessing The user imports the finite element grid model of the door panel of a certain vehicle model, and sets the analysis target as predicting the vibration response of the door panel under loudspeaker excitation in the frequency range of 200Hz to 2000Hz. The analysis bandwidth Δf is set to 20Hz.

[0039] Step 2: Automatic frequency domain determination The system automatically performs modal analysis to calculate the natural frequencies of the door panel in [0, 2000Hz]. Assuming that the modal density n(1000) ≈ 0.8 modes / Hz is obtained near the center frequency 1000Hz. According to the modal density criterion, the determination index is calculated: n(f)Δf=0.8*20=16. Since 16 is greater than the second preset threshold (for example, 5), the system automatically determines that this analysis problem belongs to the high-frequency domain.

[0040] Step 3: Automatic selection and execution of analysis method (high-frequency path) According to the determination result, the system automatically enters the high-frequency analysis path.

[0041] 1. Subsystem automatic division: The system automatically divides the door panel into SEA statistical subsystems such as door outer panel (subsystem 1), door inner panel (subsystem 2), window frame area (subsystem 3), etc. according to the geometric and modal characteristics.

[0042] 2. SEA parameter calculation and equation solving: The system automatically calculates the modal density n m , internal loss factor η m , and coupling loss factor η nm of each subsystem. The loudspeaker excitation spectrum is converted to input power . The statistical energy balance equation (i.e. matrix equation) of all SEA subsystems as claimed in claim 6 is established, and the average vibration energy E m of each subsystem is solved.

[0043] 3. Result output: Map the subsystem energy E m back to the geometric model, and output the vibration velocity level cloud diagram of each area of the door panel.

[0044] (Alternative path description: medium-frequency mixed analysis) If the result of step 2 is the intermediate frequency domain (for example, n(f) Delta f = 3, between 0.2 and 5), the system automatically enters the FEM-SEA hybrid analysis path. Under this path, key detail areas such as window locks are divided into FEM subsystems, while large-area plates are divided into SEA subsystems. The system will perform the complete process of the aforementioned FEM-SEA coupling layer, and finally output the deterministic frequency response curve of the FEM subsystem and the statistical energy of the SEA subsystem, taking into account both local and global characteristics in one analysis.

[0045] Step 4: Unified post-processing The system generates a complete analysis report containing vibration spectrum curves, cloud maps, and key data comparisons.

[0046] The present application adopts two core technologies of "modal density automatic criterion" and "precise coupling solution based on direct mixing field reciprocity theorem", and constructs an intelligent and efficient full-frequency domain NVH automatic simulation platform, which significantly improves the engineering application efficiency and reliability of high-frequency NVH analysis.

[0047] The above description is only a preferred embodiment of the present application, but the protection scope of the present application is not limited thereto. Any skilled person in the art can make equivalent replacements or changes to the technical solutions and inventive concepts of the present application within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A hybrid FEM-SEA calculation method for full-frequency domain NVH simulation analysis, characterized in that, Includes the following steps: Step S1: Obtain the simulation model of the structure to be analyzed and calculate the modal density n(f) of the structure in the target frequency range; Step S2: Based on the modal density criterion, automatically determine the frequency domain type to which the target frequency range belongs; the modal density criterion is: calculate the value of n(f)Δf, where Δf is the analysis bandwidth within the target frequency range; if n(f)Δf is less than a first preset threshold, it is determined to be in the low frequency domain; if n(f)Δf is between the first preset threshold and the second preset threshold, it is determined to be in the mid frequency domain; if n(f)Δf is greater than the second preset threshold, it is determined to be in the high frequency domain. Step S3: Based on the determination result of the frequency domain type, automatically call the corresponding analysis module to perform NVH simulation calculations: If the frequency domain is determined to be low, the finite element method module is invoked for calculation. If it is determined to be in the high-frequency domain, the statistical energy analysis module is invoked for calculation; If the frequency domain is determined to be mid-frequency, the FEM-SEA hybrid analysis module is invoked for calculation.

2. The FEM-SEA hybrid calculation method for full-frequency domain NVH simulation analysis according to claim 1, characterized in that, The calculation of modal density n(f) in step S1 includes the following sub-steps: S11: Solve the structure in [0, f] using the finite element method. max All natural frequencies f within the frequency range i , where f max This represents the upper limit of the target frequency range; S12: Count the cumulative number of modes N(f) from 0 to frequency f; S13: Calculate the modal density n(f)=[N(f2)-N(f1)] / (f2-f1), where f1 and f2 are the endpoints of the frequency interval.

3. The FEM-SEA hybrid calculation method for full-frequency domain NVH simulation analysis according to claim 1, characterized in that, Step S3 involves calling the FEM-SEA hybrid analysis module for calculations, including the following sub-steps: S31: Divide the structure into at least one FEM deterministic subsystem and at least one SEA statistical subsystem; S32: Based on the direct mixing field reciprocity theorem, construct the overall dynamic stiffness matrix D, which includes the stiffness of the FEM subsystem and the direct field stiffness of the SEA subsystem. tot ; S33: Calculate the energy conversion coefficient h between the reverberation field of the SEA subsystem and the FEM subsystem. tot,m And the energy conversion coefficient h between SEA subsystems n,m ; S34: Assemble the energy balance matrix equations and solve for the steady-state energy E of each SEA subsystem. m ; S35: According to the formula Calculate the nodal displacement response S of the FEM subsystem qq ,in As an external incentive, Let be the reverberation field force of the m-th SEA subsystem.

4. The FEM-SEA hybrid calculation method for full-frequency domain NVH simulation analysis according to claim 3, characterized in that, In step S33, the energy conversion coefficient h tot,m The calculation formula is: ,in, Let be the direct field dynamic stiffness matrix of the m-th SEA subsystem, and Im(·) denotes the operation of taking the imaginary part.

5. The FEM-SEA hybrid calculation method for full-frequency domain NVH simulation analysis according to claim 3, characterized in that, In step S33, the energy conversion coefficient h n,m The calculation formula is: ,in, Let be the direct field dynamic stiffness matrix of the nth SEA subsystem.

6. The FEM-SEA hybrid calculation method for full-frequency domain NVH simulation analysis according to claim 3, characterized in that, In step S34, the energy balance matrix equation is: ， Among them, M m =ωn m η m ω is the modal superposition factor, ω is the angular frequency, and n is the modal superposition factor. m Let η be the modal density of the m-th subsystem. m Its internal loss factor, Let be the input power of the m-th subsystem under external excitation.

7. The FEM-SEA hybrid calculation method for full-frequency domain NVH simulation analysis according to claim 3, characterized in that, In step S35, the reverberation field force of the SEA subsystem Calculated according to the reciprocity theorem of direct mixing fields using the following formula: 。 8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 7.

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