Modal parameter identification method, modal parameter identification device, and program

Abstract

To rapidly perform a time region simulation of "a structure in air" or "air with a structure attached thereto".SOLUTION: A method for identifying a modal parameter includes: a first process of causing a computer (10) to calculate a frequency response of a structure when the structure is in air or calculate a frequency response of the air when the structure is attached to the air; a second process of causing the computer (10) to identify a complex eigenvalue, with the inverse Fourier transform of the frequency response as a reference; and a third process of causing the computer (10) to identify a complex unique mode of a vibration point of the structure or a complex unique mode of a vibration point of the air, with the frequency response as a reference.SELECTED DRAWING: Figure 3

Description

Technical Field

[0001] The present disclosure relates to a method for identifying modal parameters, an apparatus for identifying modal parameters, and a program.

Background Art

[0002] As a method for obtaining the dynamic characteristics in a physical model of a structure, the following techniques can be mentioned. For example, Non-Patent Document 1 describes a technique for identifying complex eigenvalues in a general viscous damping system model by using, as a reference, the impulse response of a structure obtained by a single-input multi-output (SIMO) method. Further, Non-Patent Document 2 describes a technique for identifying complex eigenvalues and complex eigenmodes in a general viscous damping system model by using, as a reference, the frequency response of a structure obtained by a multi-input multi-output (MIMO) method.

Prior Art Documents

Non-Patent Documents

[0003]

Non-Patent Document 1

Non-Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0004] However, in the technique described in Non-Patent Document 1, since it is a single-point excitation multi-point reference method, it is difficult to accurately identify complex eigenmodes. In the technique described in Non-Patent Document 2, since it is a multi-point excitation multi-point reference method, the identification accuracy of complex eigenmodes is higher than that when the technique described in Non-Patent Document 1 is used. However, it is difficult to accurately identify complex eigenvalues, and since complex eigenvalues and complex eigenmodes are identified simultaneously, it is difficult to apply to large-scale structures.

Means for Solving the Problem

[0005] A method for identifying modal parameters according to an aspect of the present disclosure is a modal parameter identification method in which a computer identifies modal parameters in a physical model of a structure when the structure exists in air or in a physical model of air when the structure is attached. The method includes: a first process in which the computer calculates a frequency response of the structure when the structure exists in the air or a frequency response of the air when the structure is attached; a second process in which the computer identifies complex eigenvalues using the inverse Fourier transform of the frequency response as a reference; and a third process in which the computer identifies a complex eigenmode of an excitation point in the structure or a complex eigenmode of an excitation point in the air using the frequency response as a reference.

Brief Description of the Drawings

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Embodiments for Carrying Out the Invention

[0007] Hereinafter, a method for identifying modal parameters according to an embodiment of the present disclosure will be described with reference to the drawings. In each figure, the dimensions and scales of each part are appropriately different from the actual ones. In addition, since the embodiments described below are preferred specific examples, various technically preferable limitations are imposed, but the scope of the present invention is not limited to these embodiments unless otherwise specified in the following description.

[0008] First, when performing a time-domain simulation of a structure that can be assumed to be linear, the "mode synthesis method" that expresses the displacement of the structure model as a superposition of eigenmodes is known as the analytical method with the highest cost performance. For a structure model placed in vacuum, a method for calculating the modal parameters of the structure, that is, the real eigenvalues and real eigenmodes, with high accuracy has already been established. Eigenvalue analysis using the Finite Element Method (FEM) is known as the most powerful method for this purpose.

[0009] On the other hand, it has to be said that it is extremely difficult to calculate the high-precision modal parameters of a large-scale structural model placed in the air, specifically in an indoor space of a certain size or larger, an anechoic chamber, or outdoors. The reason for this is that when identifying the eigenmodes of a structural model placed in the air using the finite element method while considering the coupling between the air and the structure, as the model size increases or the analysis frequency increases, the scale of the calculation becomes extremely large, and as a result, the calculation cost becomes unrealistically high. Although the Fast Multipole Boundary Element Method (FMBEM) is known as a numerical analysis method with high cost performance for acoustic-structure coupling problems, what is obtained by this method is the frequency response, not the eigenmode. In short, no method has been proposed so far to accurately calculate the eigenmodes of large-scale "structures placed in the air" at a realistic calculation cost.

[0010] FIG. 12 is a diagram showing the results of calculating the frequency response in a vacuum and the frequency response in the air for the soundboard of a certain musical instrument as an example of a structure. As shown by this example, depending on the structure, there may be a non-negligible difference between the frequency response in a vacuum and the frequency response in the air. The main reasons for such a difference are that in the air, in addition to the natural vibration frequency being lowered due to the mass effect of the air compared to in a vacuum, the energy of the vibration is consumed for acoustic radiation, resulting in increased attenuation. In FIG. 12, the frequency response of the structure in a vacuum is the response calculated as a superposition of the eigenmodes obtained as a result of the finite element eigenvalue analysis of the structure. The frequency response in the air is the response calculated by performing acoustic-structure coupling analysis using the fast multipole boundary element method assuming that the structure is placed in an anechoic chamber while using the results of the finite element eigenvalue analysis of the structure in a vacuum described above.

[0011] Now, many methods have been proposed so far for experimentally identifying the natural modes of a structure, including the methods described in Non-Patent Document 1 or Non-Patent Document 2, and products have also been commercialized as experimental mode identification software. However, since it is inherently difficult to obtain a large amount of high-quality frequency responses in experiments, conventional methods developed for experimental mode identification can only identify at most several to several tens of natural modes, and inevitably cannot handle large-scale models.

[0012] FIG. 1 is a conceptual diagram showing an input and a response to air associated with a structure placed in air.

[0013] In the present embodiment, first, the coupled system of air and the structure is specifically denoted as a linear coupled system Lc, and the linear coupled system Lc is expressed by a general viscous damping system model. The theoretical basis for being able to express the coupled system composed of the main body and air, that is, the acoustic-structure coupled system, by a general viscous damping system model is that the acoustic-structure coupled motion equation by the finite element method when the structural displacement and the air velocity potential are regarded as "variables depending on time and space" can be formally written by a real symmetric mass matrix, damping matrix, and stiffness matrix. The form of the motion equation composed of these three real symmetric matrices is mathematically the same as the form of the motion equation by the finite element method of a model of a structure having general viscous damping (not proportional viscous damping), that is, a general viscous damping system model. Note that the advantage of expressing the acoustic-structure coupled system by a general viscous damping system model is that the natural modes of this model have generalized orthogonality. At this time, a high-speed time-domain simulation using the mode superposition method becomes possible.

[0014] The impulse response in the general viscous damping system model is shown as the following formula (1).

Equation

Equation

[0015] In Equation (1) or Equation (2), j is the imaginary unit, * is the complex conjugate, r is the mode order, i is the index of the excitation point, and l is the index of the response point. λ r is the complex eigenvalue, and λ r = -σ r + jω dr is expressed as such. σ r is the mode damping ratio, and ω dr is the damped natural angular frequency.

[0016] R ril is the mode residue and is expressed by the following equation (3).

Equation

[0017] When expressing the linear interconnected system Lc with the general viscous damping system model, the important point lies in how accurately the modal parameters of the general viscous damping system model can be determined. Therefore, in this embodiment, secondly, taking the "frequency response of the linear interconnected system calculated by the multi-point excitation multi-point reference (MIMO) method using the high-speed multi-pole boundary element method" as a reference, the complex eigenvalue and the complex eigenmode, which are the modal parameters, are identified so as to fit the general viscous damping system model.

[0018] Figure 2 is a block diagram of a computer 10 that executes the modal parameter identification method according to this embodiment. The modal parameter identification method according to this embodiment is realized by the cooperation of a computer and software. The computer 10 includes a control device 11 and a storage device 12.

[0019] The control device 11 is composed of one or more processing circuits such as a CPU (Central Processing Unit), and comprehensively controls each element of the computer 10. In addition to the CPU, the control device 11 may be composed of circuits such as a DSP (Digital Signal Processor) or an ASIC (Application Specific Integrated Circuit).

[0020] The storage device 12 is one or more memories composed of a known recording medium such as a magnetic recording medium or a semiconductor recording medium, and stores programs executed by the control device 11 and various data used by the control device 11. Note that the storage device 12 may be configured by a combination of multiple types of recording media. Also, a portable recording medium detachable from the computer 10 or an external recording medium (for example, online storage) that the computer 10 can communicate with via a communication network may be used as the storage device 12.

[0021] Figure 3 is a block diagram illustrating the functional configuration of the control device 11. By executing the program stored in the storage device 12, the control device 11 functions as a plurality of elements (processing control unit 110, preprocessing unit 111, calculation unit 112, first identification unit 115, second identification unit 116, and third identification unit 117) for identifying modal parameters. Note that a configuration may be adopted in which a part of the functions in the control device 11 is borne by another device, for example, a server device connected via a network.

[0022] Next, the procedure for identifying modal parameters in the computer 10 will be described. FIG. 4 is a flowchart illustrating a procedure for identifying modal parameters.

[0023] First, the processing control unit 110 in the computer 10 causes the preprocessing unit 111 to execute the processing from step S11 to step S14 below to prepare for identifying the modal parameters of the general viscous damping system model representing the linear coupling system Lc. Specifically, the preprocessing unit 111 creates a three-dimensional finite element model of the structure in consideration of the three-dimensional orthotropic properties of the elastic coefficient and the hysteresis damping coefficient of the material constituting the structure, and calculates the mass matrix, damping matrix, and stiffness matrix of the three-dimensional finite element model (step S11). The preprocessing unit 111 performs a non-linear static analysis on the three-dimensional finite element model in consideration of the contact non-linearity and geometric non-linearity associated with manufacturing processes such as adhesion and bolt tightening, and corrects the stiffness matrix calculated in step S11 (step S12). Note that step S12 may be skipped for simplicity of processing.

[0024] The preprocessing unit 111 uses the mass matrix and stiffness matrix calculated in step S11 or corrected in step S12 as inputs to calculate the actual eigenvalues and actual eigenmodes of the three-dimensional finite element model when the three-dimensional finite element model exists in a vacuum, that is, when there is no air, by eigenvalue analysis (step S13). The preprocessing unit 111 uses the damping matrix calculated in step S11 and the actual eigenmode calculated in step S13 as inputs to calculate the mode damping matrix when the three-dimensional finite element model of the structure exists in a vacuum (step S14).

[0025] Next, the processing control unit 110 causes the calculation unit 112, the first identification unit 115, the second identification unit 116, and the third identification unit 117 to execute the following processing to identify the modal parameters (complex eigenvalues and complex eigenmodes) of the general viscous damping system model (step S15).

[0026] FIG. 5 is a flowchart exemplifying in detail the procedure of step S15 in FIG. 4. The calculation unit 112 analyzes the three-dimensional model of the linear coupling system Lc, and calculates the frequency response of the linear coupling system Lc using, for example, the Fast Multipole Boundary Element Method or the finite element method (step S151). The frequency response calculated by this analysis is the response of the displacement of the response point l to the force at the excitation point i in the linear coupling system Lc.

[0027] Here, let the total number of excitation points i be m and the total number of response points l be n. When there are a plurality of excitation directions, such as the x direction, the y direction, and the z direction, at a certain excitation position, each is distinguished as one excitation point. The same applies to the response point l. The set of response points l is assumed to include the set of excitation points i. m and n are integers satisfying n≧m≧2.

[0028] The first identification unit 115 uses the inverse fast Fourier transform of the calculated frequency response as a reference to identify the complex eigenvalue λ r (=-σ r +jω dr ) of the linear coupling system by, for example, ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) (step S152). Note that, when identifying the complex eigenvalue, for example, the self-impulse response at the above m points is referred to. Also, the Prony method may be used for identifying the complex eigenvalue, but the identification accuracy tends to be inferior compared to ESPRIT.

[0029] The second identification unit 116 identifies the complex eigenmode at the excitation point i of the linear connection system Lc using a non-linear optimization method with the calculated frequency response as a reference (step S153). Examples of non-linear optimization methods include the quasi-Newton method with a line search method using the BFGS algorithm (Broyden Fletcher Goldfarb Shanno algorithm), or the modified Gauss-Newton method with a trust region method (also called the Levenberg-Marquardt method). For large-scale problems, the former method is more powerful. Specifically, the real part and the imaginary part of the complex eigenmode at the excitation point i are x ri and y ri as represented in the first term on the right side of Equation (5) described later. Note that when identifying the complex eigenmode at the excitation point i, for example, the self and mutual frequency responses at m·(m + 1) / 2 points are referred to.

[0030] The third identification unit 117 identifies the complex eigenmode at the response point l other than the excitation point i in the linear connection system Lc using a linear optimization method with the frequency response as a reference (step S154). Examples of linear optimization methods include the QR decomposition method or the singular value decomposition method. Specifically, the real part and the imaginary part of the complex eigenmode at the response point l are x rl and y rl as represented in the first term on the right side of Equation (5) described later. Note that when identifying the complex eigenmode at the response point l, for example, the mutual frequency responses at m·(n - m) points are referred to.

[0031] Note that when the scale of the linear connection system Lc is not so large, or when the number of points for which the eigenmodes are desired to be output is not so large, since the computational cost of the frequency response analysis in step S151 does not increase so much, n = m may be set. In this case, step S154 is skipped.

[0032] The modal parameters (complex eigenvalues and complex eigenmodes) of the general viscous damping system model are identified by steps S151 to S154.

[0033] The identification will be described with reference to the following equations (4) and (5). [Number] [Number]

[0034] Identification means that when the left side in Equation (5) is expressed as the residual obtained by subtracting the "frequency response of the reference" in the second term on the right side from the "frequency response recombined using the model" in the first term on the right side, as shown on the right side of Equation (4), the values (real part, imaginary part) that minimize the sum of the squares of the residuals are obtained.

[0035] Next, it will be described how much the modal parameters identified in the general viscous damping system model in this embodiment approach the reference.

[0036] Figures 6 to 8 are diagrams showing the frequency responses (○ marks) by mode synthesis with respect to the frequency responses (solid lines) used as references at three different points (point 1 to 3). In Figures 6 to 8, the characteristics of the phase and amplitude with respect to the frequency are shown in the left column, and the characteristics of the real part and imaginary part with respect to the frequency are shown in the right column, respectively. As shown in Figures 6 to 8, it can be seen that the frequency responses by mode synthesis are almost the same as the frequency responses used as references, indicating that the identification is established with high accuracy.

[0037] Figures 9 to 11 are diagrams showing the impulse responses (○ marks) by mode synthesis with respect to the impulse responses (solid lines) as the IFFT of the frequency responses used as references at the above three points (point 1 to 3). As shown in Figures 9 to 11, it can be seen that the impulse responses by mode synthesis are almost the same as the impulse responses used as references, indicating that the identification is established with high accuracy.

[0038] In the embodiment, the modal parameters in the physical model of the "structure when present in the air" were identified, but the modal parameters in the physical model of the "air when accompanied by the structure" can be identified in the same manner. In the former case, the difference is only that the "frequency response analysis of the structure in air" in step S151 is performed, while in the latter case, the "frequency response analysis of the air when accompanied by the structure" is performed. However, the frequency response to be calculated in the former case is the "Fourier transform of the structural displacement" / "Fourier transform of the excitation force applied to the structure", whereas the frequency response to be calculated in the latter case is the "Fourier transform of the air pressure" / "Fourier transform of the air flow rate".

[0039] According to the method for identifying modal parameters according to this embodiment, since the identification of complex eigenvalues and the identification of complex eigenmodes are executed separately, it becomes easy to apply to the physical model of a "large-scale structure present in the air" or the physical model of "air accompanied by a large-scale structure" with a large number of excitation points and response points. For this reason, it becomes possible to efficiently predict by simulation the dynamic characteristics of a "large-scale structure placed in the air" or "air accompanied by a large-scale structure", which was difficult with conventional methods.

[0040] Thus, according to this embodiment, for products where the characteristics of vibration and sound determine their value, or products where the coupling between the structure and air determines their performance, before prototyping the product, the dynamic characteristics can be predicted by simulation using the physical model, and the causal relationship between cause and effect is clarified, so that the development efficiency of the product can be greatly improved. As an example of the above product, an acoustic musical instrument can be cited. When manufacturing the main body (such as a soundboard, tube body, etc.) of such an acoustic musical instrument, by changing the design of the physical model of the main body and synthesizing a musical sound signal using the changed physical model, the musical sound of the instrument before prototyping can be heard by simulation. Therefore, for example, a new musical instrument can be efficiently developed.

[0041] <Modification Example> The embodiments illustrated above can be variously modified. Specific modification modes applicable to the embodiments are illustrated below. Two or more modes arbitrarily selected from the following illustrations may be combined within a non - conflicting range.

[0042] The function of the computer 10 for synthesizing the sound signal is realized, as described above, by the cooperation of one or more processors constituting the control device 11 and the program stored in the storage device 12. This program can be provided in a form stored in a computer - readable recording medium and installed in the computer. The recording medium is, for example, a non - transitory recording medium, and an optical recording medium (optical disk) such as a CD - ROM is a preferred example, but any known form of recording medium such as a semiconductor recording medium or a magnetic recording medium is also included. Note that the non - transitory recording medium includes any recording medium excluding a transitory, propagating signal and does not exclude a volatile recording medium. Also, in a configuration where the distribution device distributes the program via a communication network, the storage device 12 that stores the program in the distribution device corresponds to the aforementioned non - transitory recording medium.

[0043] <Supplementary Note> From the above description, for example, the preferred embodiments of the present invention can be understood as follows. For the sake of easy understanding of each embodiment, the reference numerals in the drawings are appended in parentheses for convenience below, but the present invention is not intended to be limited to the illustrated embodiments.

[0044] A musical sound synthesis method according to one aspect (Aspect 1) of the present disclosure is a modal parameter identification method in which a computer (10) identifies modal parameters in a physical model of a "structure when present in air" or a physical model of "air when accompanied by a structure", the computer (10) calculating the frequency response of the structure when present in air or the frequency response of the air when accompanied by the structure in a first process, the computer (10) identifying complex eigenvalues using the inverse Fourier transform of the frequency response as a reference in a second process, and the computer (10) identifying the complex eigenmodes of the excitation points in the structure or the complex eigenmodes of the excitation points in the air using the frequency response as a reference in a third process. According to this Aspect 1, the identification of complex eigenvalues and the identification of complex eigenmodes are not performed simultaneously but separately, so it becomes easy to apply to a physical model of a large-scale structure present in air or a physical model of air accompanied by a large-scale structure with a large number of excitation points and response points.

[0045] In a specific example of Aspect 1 (Aspect 2), after the third process, the computer (10) includes a fourth process of identifying the complex eigenmodes of response points different from the excitation points in the structure or the complex eigenmodes of response points different from the excitation points in the air using the frequency response as a reference. According to this Aspect 2, by increasing the number of response points excluding the excitation points, it becomes possible to apply to a larger-scale physical model.

[0046] Also, the method for identifying modal parameters according to Embodiment 1 can be understood as a program according to Embodiment 3. That is, the program according to Embodiment 3 causes the computer (10) to identify modal parameters in a physical model of "a structure when present in air" or a physical model of "air when accompanied by a structure", and includes a calculation unit (112) that causes the computer (10) to calculate a frequency response of "a structure when present in air" or a frequency response of "air when accompanied by a structure", a first identification unit (115) that identifies complex eigenvalues using the inverse Fourier transform of the frequency response as a reference, and a second identification unit (116) that identifies complex eigenmodes of the excitation point in the structure or complex eigenmodes of the excitation point in the air using the frequency response as a reference, and functions as these units.

[0047] Also, the method for identifying modal parameters according to Embodiment 1 can be understood as an apparatus for identifying modal parameters according to Embodiment 4. That is, the apparatus for identifying modal parameters according to Embodiment 4 is an apparatus for identifying modal parameters in a physical model of "a structure when present in air" or a physical model of "air when accompanied by a structure", and includes a calculation unit (112) that calculates a frequency response of "a structure when present in air" or a frequency response of "air when accompanied by a structure", a first identification unit (115) that identifies complex eigenvalues using the inverse Fourier transform of the frequency response as a reference, and a second identification unit (116) that identifies complex eigenmodes of the excitation point in the structure or complex eigenmodes of the excitation point in the air using the frequency response as a reference.

Explanation of Signs

[0048] 10…computer, 11…control device, 12…storage device, 13…performance information output device, 14…sound playback device, 110…processing control unit, 111…preprocessing unit, 112…calculation unit, 115…first identification unit, 116…second identification unit, 117…third identification unit, Lc…linear connection system.

Claims

1. A modal parameter identification method for a computer to identify modal parameters in a physical model of a structure when present in air or a physical model of air when accompanied by the structure, comprising: a first process in which the computer calculates a frequency response of the structure when present in the air or a frequency response of the air when accompanied by the structure; a second process in which the computer identifies complex eigenvalues using the inverse Fourier transform of the frequency response as a reference; a third process in which the computer identifies a complex eigenmode of a excitation point in the structure or a complex eigenmode of a excitation point in the air using the frequency response as a reference; A method for identifying modal parameters in a physical model including the above.

2. After the third process, a fourth process in which the computer identifies a complex eigenmode of a response point different from the excitation point in the structure or a complex eigenmode of a response point different from the excitation point in the air using the frequency response as a reference; The method for identifying modal parameters in a physical model according to Claim 1 including the above.

3. A program for causing a computer to identify modal parameters in a physical model of a structure when present in air or a physical model of air when accompanied by the structure, the program causing the computer to function as: in the computer, a calculation unit that calculates a frequency response of the structure when present in the air or a frequency response of the air when accompanied by the structure; a first identification unit that identifies complex eigenvalues using the inverse Fourier transform of the frequency response as a reference; and a second identification unit that identifies a complex eigenmode of a excitation point in the structure or a complex eigenmode of a excitation point in the air using the frequency response as a reference. A program.

4. A modal parameter identification device for identifying modal parameters in a physical model of a structure when present in air or a physical model of air when accompanied by the structure, comprising: a calculation unit that calculates a frequency response of the structure when present in the air or a frequency response of the air when accompanied by the structure; a first identification unit that identifies complex eigenvalues using the inverse Fourier transform of the frequency response as a reference; A second identification unit that identifies a complex eigenmode of the excitation point in the structure or a complex eigenmode of the excitation point in the air, using the frequency response as a reference; An apparatus for identifying modal parameters including the above.

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